Journal of Bodywork and Movement Therapies Volume 14 2010

398 J. Saratsiotis, E. Myriokefalitakis Schwann cell proliferation and apoptosis are induced the course of time to right wrist and finger extension leading to localised demyelination and remyelination at the weakness. The complaint originally started insidiously injury site as well as axonal sprouting (Pham and Gupta, 4 months previously with pain in the lateral aspect of the 2009). Interestingly, these changes occur in the absence of upper forearm (closer to the elbow). During that period the both morphological and electrophysiological evidence of patient was otherwise in good health. The pain was rated as axonal damage (Pham and Gupta, 2009; McKinnon, 2002). 5 out of 10 on an 11-point Numeric Rating Scale-Pain Intensity (NRS-PI) where 0 represents ‘‘no pain’’ and 10 Depending on the nerve involved, the symptoms of nerve represents ‘‘worst possible pain.’’ The pain did not radiate entrapment syndromes generally involve pain, sensory and into the forearm but was localised approximately 6e7 cm motor changes. Most entrapment syndromes involve mixed distal to the elbow crease (lateral aspect). The patient did sensory and motor nerves and consequently present with all not report any hypesthesia, but did indicate an inability to the aforementioned symptoms. However, there are some extend digits 2 through 5, as well as noticing a weakness in exceptions such as the posterior interosseous nerve (PIN) wrist extension. No other symptoms were reported. The which is a pure motor branch of the radial nerve. The PIN is an patient had been diagnosed with right lateral epicondyl- exception for another reason as well. While most entrap- opathy early-on in his symptomatology (prior to motor ments occur usually due to an osseoligamentous tunnel nar- weakness presentation). Electromyography and nerve rowing, in the case of a PIN entrapment, the compression conduction velocity (NCV) testing revealed no particular occurs within the musculo-tendinous radial tunnel. Specifi- findings (Figures 1 and 2), except for a mild sensory loss and cally, in up to 69.4% of the cases, the nerve is compressed by possible C8 radiculopathy on the right. MRI imaging indi- the fibrous arcade of Frohse (Ritts et al., 1987; Ferdinand cated mild degenerative changes and a disc bulge at the et al., 2006). The arcade is absent in fetuses and is thought to C6/C7 vertebral level. X-ray imaging of the right elbow was develop from repetitive rotational (supinationepronation) unremarkable. Previous treatment included physiotherapy movements of the forearm (overuse) (Links et al., 2009). (TENS, ultrasound, massage to lateral forearm, stretching Anatomic studies have revealed a variable rate of occurrence exercises to extensor muscle group) which according to the which ranges between 30% and 80% of the population patient had produced very little benefit. (Spinner, 1968; Clavert et al., 2009). Compression of the posterior interosseous nerve within the radial tunnel yields Upon observation no swelling was evident in the fore- two different clinical pictures that are believed to reflect arm, however, a finger drop was observed in the right hand. two distinct clinical entities: posterior interosseous nerve Active and passive ranges of motion of the cervical spine, syndrome and radial tunnel syndrome (Ferdinand et al., elbow, wrist, and fingers were performed and were pain- 2006). Posterior interosseous nerve syndrome is character- free and symmetrical except for a notable weakness of the ized by motor deficits in the distribution of the posterior metacarpalphalangeal joints (MCP) on the right side. interosseous nerve. Consequently, it is important for the Specifically, active and resisted extension of the right wrist practitioner to understand the etiology and symptomatology was graded as 4/5 with a slight radial deviation of the wrist. in order to create an effective treatment protocol. Resisted finger extension was graded as 3/5 for fingers 3e5, while the index finger was graded 2/5 (all at the meta- Treatment of a PIN syndrome consists of either conser- carpalphalangeal e MCP-joints). Elbow flexion was within vative or surgical management. Initially, wrist and/or normal limits and tested 5/5 in both flexion and extension. elbow splints may be used, physical therapy, use of NSAIDs, Resisted supinationepronation caused discomfort in the or a corticosteroid injection in order to reduce local latter. Orthopaedic testing of the cervical spine (compres- inflammation and swelling around the nerve (Hyde and sion, distraction, Jackson’s test) were unremarkable except Gengenbach, 2007). Therapy should continue for approxi- for mild pain during Jackson’s compression test on the mately 3e6 months with regular re-assessment of signs and right. Bilateral sensation was tested and the result was symptoms. If there is no response to therapy, evidence of bilateral and symmetrical, while reflexes were graded 2þ denervation, or persistent paralysis, surgical decompres- bilaterally for the upper extremity. Palpation revealed sion should be considered (Stanley, 2006). Muscle Duration Height Phase Comment_ _ Physical therapy involves the use of cryotherapy, ultra- sound, TENS, and strengthening exercises for weakened Deltoid (R) WNL WNL WNL Small involvement musculature. However, recent literature has advocated the Biceps WNL WNL effectiveness of deep soft tissue mobilization techniques Brachii (R) WNL WNL WNL Small involvement (myofascial release, Active Release Techniqueâ, Graston Extensor WNL WNL Techniqueâ) in conjunction with neural gliding (‘‘flossing’’) Digitorum (R) WNL WNL WNL Involvement in order to achieve optimal results (Hyde and Gengenbach, Abductor WNL WNL 2007; Agrios and Crawford, 1999; Buchberger et al., 1996; Pollicis Brevis (R) WNL Small involvement Coppieters et al., 2004). 1st dorsal Interosseus (R) WNL Small involvement A case is presented to illustrate the treatment of Abductor posterior interosseous nerve syndrome using Active Release Digiti min. (R) WNL Small involvement Techniques Soft Tissue Management and Peripheral Nerve Release Systemsâ. Figure 1 EMG results of patient indicating weakness in extensor digitorum on the right. Case study A 62 year old office worker presented with right lateral forearm pain (4 month duration) that had progressed over

Diagnosis and treatment of PIN syndrome 399 Motor Nerve Conduction Study involve the lateral 1 square (Loh et al., 2004; Tubbs et al., 2006). The leash of Henry, the tendinous medial edge of Site Latency (ms) Amplitude Area Distance NCV _ the extensor carpi radialis brevis, the arcade of Frohse, Median (R) 4.44 7.42mV 19.4mVms 205mm 51m/s and the distal tendinous edge of the supinator or bands - 8.46 7.92mV 20.0mVms 147mm 0m/s within the two heads of supinator make the involvement of lateral 2 and 3 squares most likely (Loh et al., 2004; Tubbs Ulnar (R) 3.26 5.88mV 18.9mVms 125mm 60m/s et al., 2006). As seen from Figure 3, the patient’s symptoms - 5.34 7.67mV 24.5mVms 180mm 49m/s localised in the lateral squares 2 and 3. This area, which measured 6e7 cm from the elbow crease, is below the Sensory Nerve Conduction Study proposed superficial landmark for the leash of Henry (approximately 5 cm from lateral epicondyle), which would Site Latency (ms) Amplitude Area Distance NCV__ indicate an entrapment by most likely the ECRB, the Ulnar (R) 2.90 8.90uV 5.34uVms 152mm 52m/s supinator, or the arcade of Frohse. Median (R) 3.26 10.7uV 2.80uVms 168mm 51m/s At this point, a diagnosis of posterior interosseous nerve syndrome was made, ruling out the possibility of lateral Radial (R) 1.34 27.6uV 11.8uVms 80mm 59m/s epicondylopathy, radiculopathy, or radial tunnel syndrome. Figure 2 Nerve conduction velocity (sensry and motor) of Methodology and results the upper extremity indicating neuropathy (hypoaesthesic) and possible C8 radiculopathy. The patient was treated using Active Release Techniquesâ applied to the extensor carpi radialis brevis, supinator, and tender areas of nodular consistency within the supinator, Arcade of Frohse. The treatment of these structures while tissue tension was identified in both the extensor corresponds to protocols 30, 32, 33 from the manual of the carpi radialis longus and supinator on the right, as within Active Release Techniques Soft Tissue Management the extensor carpi ulnaris. Palpation over the anterior Systemâ of the Upper Extremity. The intended purpose of radiohumeral joint and lateral epicondyle did not cause any this treatment was to decrease tissue tension as well as to pain or tenderness. normalize tissue function. Following soft tissue therapy, nerve traction techniques were performed to the posterior The Rule of Nine test was then performed where a large interosseous nerve, once again according to protocol 8 from squared box was drawn over the anterior aspect of the right the Active Release Techniquesâ Soft Tissue Management proximal forearm. The sides of the square were determined System for Nerve Entrapments (Figure 4). by the width of the elbow crease with a fully extended elbow and a fully supinated forearm and the square was The purpose of nerve gliding/traction is to maximize the further divided into nine smaller equal squares giving three movement of the nerve in relation to the anatomic struc- columns and three rows (Loh et al., 2004). It has been tures adjacent to it, in this case the supinator muscle and suggested that the PIN travels through the lateral column, the Arcade of Frohse. After nine visits (with 1 day between the median nerve travels through the middle column, while visits) the patient reported lateral upper forearm pain the medial column is traversed by neither (Loh et al., rated as 1 out 10 on the 11-point NRS-PI scale. Motor defi- 2004). The areas of pain have been identified in Figure 3. cits observed with wrist and finger extension resolved and resisted muscle testing was graded 5/5 bilaterally for wrist According to Loh et al., the presence of the fibrous bands connecting brachialis and brachioradialis overlying the PIN at the level of the radial head is most likely to Figure 3 Rule of Nine test and areas of pain upon palpation Figure 4 Neural gliding using the Active Release Techniquesâ of patient’s right upper lateral forearm. Soft Tissue Management System for Nerve Entrapments of the posterior interosseous nerve: at this point in the technique, the nerve is lengthened proximal to the contact site and shortened distal to the contact site.

400 J. Saratsiotis, E. Myriokefalitakis extension and finger extension of digits 2e5. The patient tendinous arch, the arcade of Frohse. Formed by the upper was given strengthening exercises for wrist and finger free border of the superficial head of the supinator, the extension and asked to return in 1 months time for re- arcade of Frohse is a semicircular fibrous arch that remains assessment. During re-assessment the patient reported no fibrous medially and is found in 30e80% of anatomical pain in his forearm and noted full strength in his right wrist specimens (Spinner, 1968; Clavert et al., 2009). Just before and hand. At 6 months following treatment the same results the arcade of Frohse, a number of arterial branches (leash were observed. of Henry) that arise from the recurrent radial artery cross over the PIN (Moore and Dalley, 1999; Sellards and Kue- Discussion brich, 2005). Within the radial tunnel, the PIN rests on the deep head of the supinator. The posterior interosseous nerve is a branch of the radial nerve. The radial nerve is the main continuation of the After emerging from the tunnel beneath the supinator, posterior chord (C6eC8, and occasionally T1) of the the PIN lies posteriorly to the interosseous membrane of brachial plexus (Moore and Dalley, 1999; Sellards and Kue- the forearm and innervates the extensor digiti minimi, brich, 2005). The radial nerve enters the arm posterior to extensor carpi ulnaris, medially the extensor digitorum the brachial artery, medial to the humerus, and anterior to communis, and laterally the extensor indicis proprius, the long head of the triceps (Moore and Dalley, 1999). At extensor pollicis longus and brevis, and abductor pollicis mid arm, the radial nerve descends behind the humerus, longus (Ferdinand et al., 2006; Moore and Dalley, 1999; deep to the long head of the triceps, and then spirals Sellards and Kuebrich, 2005). around the humerus in between the medial and lateral heads of the triceps in the spiral groove. Approximately Entrapment of the PIN can occur right at the division of 10 cm above the lateral humeral epicondyle, the nerve the radial nerve into motor and sensory branches, within pierces the lateral intermuscular septum and enters the the radial tunnel, or after the nerve bifurcates into medial anterior compartment of the arm (Moore and Dalley, 1999; and lateral branches (Ferdinand et al., 2006; Moore and Sellards and Kuebrich, 2005). Here, it immediately enters Dalley, 1999). Consequently, depending on where the the deep, muscular groove bordered medially by the biceps entrapment is, the presenting signs and symptoms will and laterally by the brachioradialis, the extensor carpi slightly vary (depending on which muscles have lost inner- radialis longus (ECRL), and the extensor carpi radialis brevis vation). With respect to the radial tunnel, entrapment can (ECRB). The nerve then courses immediately in front of the occur due to compression from fibrous bands attached to radiocapitellar joint capsule, where it divides into the the radiocapitellar joint, the radial recurrent vessels motor PIN and the sensory superficial radial nerve (see (branches of Henry), the tendinous origin of the extensor Figure 5). carpi radialis brevis, the tendinous origin of the supinator (arcade of Frohse), and fibrous thickenings within and at Branches innervating the brachioradialis and ECRL come the distal margin of the supinator (Clavert et al., 2009; off before the bifurcation while the ECRB is innervated by Moore and Dalley, 1999; Sellards and Kuebrich, 2005; Kon- either the radial nerve or the PIN (Moore and Dalley, 1999). jengbam and Elangbam, 2004). The PIN enters the radial tunnel underneath a musculo- Compression of the posterior interosseous nerve (PIN) Figure 5 The radial nerve courses immediately in front of within the radial tunnel yields two different clinical the radiocapitellar joint capsule, where it divides into the deep pictures that are believed to reflect two distinct clinical motor (PIN) and the sensory superficial radial nerve. entities: PIN syndrome and radial tunnel syndrome (Ferdi- [Reproduced with kind permission by Elsevier from Spinner, M., nand et al., 2006). Both are considered entrapments of the 1968. J. Bone Joint Surg. Br. 50, 809e812]. PIN, however, the latter involves pain along the radial aspect of the proximal forearm (mimics lateral epi- condylitis) and is characterized by the absence of neuro- logical findings (motor deficit) (Ferdinand et al., 2006; Lister et al., 1979). Electrodiagnostic examination findings fail to demonstrate any abnormality of the PIN, and are not useful in confirming the diagnosis for radial tunnel syndrome, which is generally made on the basis of a phys- ical examination (Ferdinand et al., 2006). One theory suggests that the PIN, while mainly a motor nerve, carries sensory afferent fibres from the wrist as well as group IIA afferent fibres from the muscles along its distribution (Ritts et al., 1987; Lister et al., 1979). It is possible that only afferent fibres are affected with radial tunnel syndrome, whereas only the motor fibres are affected with PIN syndrome (Ritts et al., 1987). Some authors believe radial tunnel syndrome may represent an early posterior interosseous nerve syndrome (Ritts et al., 1987). In the case presented, this might potentially explain the unremarkable results from the electrodiagnostic testing which was performed on the patient early-on in his symptomatology. Most likely, the condition had started as a radial tunnel syndrome that

Diagnosis and treatment of PIN syndrome 401 progressed to a PIN syndrome due to repetitive compression neuropathies (neural tension test). Similarly, rehabilitation of the nerve. The repetitive overuse (supinationeprona- techniques used to stretch the nerves and restore neural tion) of the patient’s right forearm potentially promoted gliding are frequently successful in relieving patient symp- histological changes to the radial tunnel structures, toms (Hyde and Gengenbach, 2007; Coppieters et al., 2004). particularly the supinator and arcade of Frohse, with Consequently, Active Release Techniques Peripheral Nerve progressive development of a local fibrous zone (Clavert Release Systemsâ was used on the posterior interosseous et al., 2009). nerve in order to increase gliding motion of the nerve. The Active Release Technique Soft Tissue Management Overall improvement in symptomatology was observed System (ARTâ) has proven to be clinically promising in in this patient with restoration of motor deficits and treating conditions related to overuse (Spina, 2007; Leahy, decrease in pain. The patient was also given strengthening 1995). Within the rehabilitation arena, cumulative trauma exercises in order to re-educate and strengthen soft tissue disorders are often treated with ARTâ. These types of structures affected by compression of the PIN. disorders follow the law of repetitive motion developed by P. Michael Leahy, D.C.: Conclusion IZNF=AR Posterior interosseous nerve syndrome is an entrapment neuropathy that is not common in the upper extremity, where, I Z insult to tissues, N Z number of repetitions, however it can be debilitating due to symptoms of pain and F Z tension of each repetition as percentage of maximum motor deficiency in the wrist and hand. This condition muscle strength, A Z amplitude of each repetition, and should not be confused with radial tunnel syndrome which R Z relaxation time between repetitions (Leahy, 1995). It is involves compression of the same nerve. Chronically obvious from the above equation, that if the number of repetitive movement patterns lead to constriction of the repetitions ‘‘N’’ is increased, such as in a case of cumula- nerve due to the development of local fibrosis within the tive trauma, the insult to the tissues also increases. soft tissues surrounding the nerve which also affects nerve According to Leahy, this soft tissue insult will reduce traction and mobility. Frequently, according to literature, circulation in the area of concern ultimately leading to conservative treatment of such conditions involves very tissue hypoxia (Leahy, 1995). Related research has indi- little manual therapy. In the case presented, a conservative cated that as the partial pressure of oxygen (PO2) begins to treatment protocol that included deep soft tissue mobili- decrease, due to hypoxic conditions, fibroblasts are stim- zation techniques (ARTâ) as well as neural gliding (‘‘floss- ulated by such conditions and start to proliferate at the site ing’’) techniques was introduced with positive results even of injury (Falanga et al., 2002). This results in abnormally 1 and 6 months following treatment. Histological studies high amounts of collagen deposition causing excessive support the decision to use such treatment methods while fibrosis (scar tissue formation). Studies have suggested that the results of this study confirm the need to introduce new deep tissue mobilization techniques induce a controlled effective conservative techniques prior to considering amount of microtrauma in an area composed of excessive nerve decompression surgery. Further research into the scar tissue, which in turn appears to stimulate connective pathophysiology of nerve entrapments will have immediate tissue remodelling through resorption of excessive fibrosis, impact on the management of neuropathies and likely along with inducing repair and regeneration of collagen result in emphasizing conservative management and reha- secondary to fibroblast recruitment (Melham et al., 1998; bilitation rather than surgical intervention particularly in Gehlsen et al., 1999). A preliminary report on the use of cases not involving denervation or paralysis. ARTâ for a variety of upper extremity overuse syndromes found a 71% efficacy rate (Schiottz-Christensen et al., References 1999). Agrios, P., Crawford, J.W., 1999. Double crush syndrome of the Furthermore, localised fibrosis around a nerve leads to upper extremity. J. Sports Chiropr. Rehab. 13 (3), 111e114. compression of the nerve and consequent compression- induced neuronal swelling, even 1 week after compression is Buchberger, D.J., Rizzoto, H., McAdam, B.J., 1996. Median nerve applied (Chien et al., 2003). The swelling occurs proximal to entrapment resulting in unilateral action tremor of the hand. J. the constriction site and studies show it might be the result of Sports Chiropr. Rehab. 10 (4), 176e180. either abnormal cytoplasmic axonal transport or ischemic conditions (McKinnon, 2002; Chien et al., 2003). Histopath- Chien, A.J., Jamadar, D.A., Jacobson, J.A., Hayes, C.W., Louis, D.S., ologic studies have indicated the swelling is associated with 2003. Sonography and MR imaging of posterior interosseous nerve perineural and epineural fibrosis rather than nerve fibre syndrome with surgical correlation. AJR 181, 219e221. pathology (McKinnon, 2002; Chien et al., 2003). Once the nerve is released in these situations, axonal diameter Clavert, P., Lutz, J.C., Adam, P., Wolfram-Gabel, R., Apr 2009. equalizes a few days later (Chien et al., 2003). The rapid Frohse’s arcade is not the exclusive compression site of the radial recovery of motor deficiency following treatment in the case nerve in its tunnel. Orthop. Traumatol. Surg. Res. 95 (2), 114e118. presented would indicate chronic nerve compression due to fibrosis rather than axonal nerve injury. Coppieters, M., Bartholomeeusen, K., Stappaerts, K., Nov 2004. Incor- porating nerve-gliding techniques in the conservative treatment of Furthermore, this fibrosis would prevent the nerve fibres cubital tunnel syndrome. J. Manip. Physiol. Ther. 27 (9), 560e568. themselves from going through a full range of movement, without traction, and decreased gliding. Clinical tests that Falanga, V., Zhou, L., Yufit, T., Apr 2002. Low oxygen tension put a stretch on the nerve will provoke patient symptoms stimulates collagen synthesis and COL1A1 transcription through and have been used to diagnose specific compression the action of TGF-beta1. J. Cell. Physiol. 191 (1), 42e50. Ferdinand, B.D., Rosenberg, Z.S., Schweitzer, M.E., Stuchin, S.A., Jazrawi, L.M., Lenzo, S.R., Jul 2006. MR imaging features of

402 J. Saratsiotis, E. Myriokefalitakis radial tunnel syndrome: initial experience. Radiology 240 (1), successfully treated with a new non-invasive augmented soft 161e168. tissue mobilization technique (ASTM): a case report. Med. Sci. Gehlsen, G.M., Ganion, L.R., Helfst, R., April 1999. Fibroblast Sports Exerc. 30 (6), 801e804. responses to variation in soft tissue mobilization pressure. Med. Moore, K.L., Dalley, A.F. (Eds.), 1999. Clinical Oriented Anatomy, Sci. Sports Exerc. 31 (4), 531e535. fourth ed. Lippincott Williams and Wilkins, Baltimore. Hyde, T.E., Gengenbach, M.S., 2007. Conservative Management Pham, K., Gupta, R., Feb 2009. Understanding the mechanisms of of Sports Injuries. Jones and Bartlett Publishing, Sudbury, entrapment neuropathies. Review article. Neurosurg. Focus 26 MA. (2), E7. Konjengbam, M., Elangbam, J., Jan 2004. Radial nerve in the radial Ritts, G.D., Wood, M.B., Lindscheid, R.L., 1987. Radial tunnel tunnel: anatomic sites of entrapment neuropathy. Clin. Anat. 17 syndrome. A ten-year surgical experience. Clin. Orthop. 219, (1), 21e25. 201e205. Leahy, P.M., 1995. Improved treatments for carpal tunnel and Schiottz-Christensen, B., Mooney, V., Azxad, S., Selstad, D., related syndromes. Chiropr. Sports Med. 9, 6e9. Gulick, J., Bracker, M., 1999. The role of Active Release Manual Links, A.C., Graunke, K.S., Wahl, C., Green, J.R., Matsen, F.A., Therapy for Upper Extremity Overuse Syndromes e a prelimi- JaneFeb 2009. Pronation can increase the pressure on the nary report. J. Occup. Rehab. 9 (3), 201e211. posterior interosseous nerve under the arcade of Frohse: Sellards, R., Kuebrich, C., 2005 Mar. The elbow: diagnosis and a possible mechanism of palsy after two-incision repair for treatment of common injuries. Prim. Care 32 (1), 1e16. distal biceps rupturedclinical experience and a cadaveric Spina, A.A., 2007 Mar. External coxa saltans (snapping hip) treated investigation. J. Shoulder Elbow Surg. 18 (1), 64e68. with active release techniques(R): a case report. J. Can. Lister, G.D., Belsole, R.B., Kleinert, H.E., Jan 1979. The radial Chiropr. Assoc. 51 (1), 23e29. tunnel syndrome. J. Hand Surg. Am. 4 (1), 52e59. Spinner, M., 1968. The arcade of Frohse and its relationship to Loh, Y.C., Lam, W.L., Stanley, J.K., Soames, R.W., June 2004. posterior interosseous nerve paralysis. J. Bone Joint Surg. Br. A new clinical test for radial tunnel syndrome e the-rule-of- 50, 809e812. Nine test: a cadaveric study. J. Orhtop. Surg. 12 (1), 83e86. Stanley, J., ApreJun 2006. Radial tunnel syndrome: a surgeon’s McKinnon, S.E., May 2002. Pathophysiology of nerve compression. perspective. J. Hand Ther. 19 (2), 180e184. Hand Clin. 18 (2), 231e241. Tubbs, R.S., Salter, E.G., Wellons, J.C., Blount, J.P., Oakes, W.J., Melham, T.J., Sevier, T.L., Malnofski, M.J., Wilson, J.K., May 2006. Superficial surgical landmarks for identifying the Helfst Jr., R.H., June 1998. Chronic ankle pain and fibrosis posterior interosseous nerve. J. Neurosurg. 104 (5), 796e799.

Journal of Bodywork & Movement Therapies (2010) 14, 403e410 available at www.sciencedirect.com journal homepage: www.elsevier.com/jbmt PREVENTION & REHABILITATION: EDITORIAL PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN Chains, trains and contractile fields Matt Wallden, MSc Ost Med, DO, ND, Associate Editor In the film, Planes, Trains and Automobiles, the underlying within the presenting ecological niche that single-celled, theme is that two men are trying to get home in time for photosynthesising organisms found themselves in. a major social celebration. The story is focused around the challenges these men face as the route from a to b became Early animal forms, such as sponges, anemones and increasingly convoluted and indirect. jellyfish all showed very primitive circumferential move- ment patterns. These movement patterns have been In animal locomotion, this same theme of getting from described as the “radial chain” musculature (Beach, 1989, a to b in the most efficient way is often a key aspect of Personal Communication) or “radial contractile field” organismal evolutionary fitness. (Beach, 2008; Wallden, 2008). However, there may be some cases in which a more Later animal forms, such as flat worms and round worms convoluted, indirect route may be of survival benefit; for also exhibit this circumferential movement pattern, but do example, if you were to track a course of musculature so sequentially across body segments. around the body in a spiral fashion (Beach, 2007; Wallden, 2008; Myers, 2001), the longer your route from a to b, the It was not until the evolution of vertebrates in the form more muscle fibres can be utilised, and therefore the more of fish that effective longitudinal contraction down the power can be generated. This is why when power genera- body wall could take place (Kardong, 2002; Wallden, 2008). tion occurs in sports, such as when hitting, throwing, kicking or punching, it typically involves a rotary twist of Subsequent development merely elaborated on the the body; to access this fast twitch spiral musculature established fish-based body plan (Erwin et al., 1997); this coursing from the lower limb through and around the trunk, was the premise of Gracovetsky’s (1988) Spinal Engine and back out via a different limb to its extremity. theory, the concept that the spine is what drives the legs forward; the limbs simply amplifying spinal motion in Of course, the more powerful a movement, the less steady-state gait. efficient it generally is; this applies as much to the human body as it does to planes trains and automobiles. If a Ferrari Recent times competes with smart car, the Ferrari may win, but in the long run, the Smart car will go further on the same amount Various thinkers from the exercise and rehabilitation fields of fuel. Equally, there is little sense in a creature retaining have made attempts to understand these developments in fuel if it is to be some other creatures dinner as a result. the musculoskeletal function of organisms; among them Organismal biological design still seems to have the edge on early pioneers including Raymond A. Dart’s Double Helix synthetic counterparts; especially in terms of versatility. Mechanism of the Spine, Phillip Beach’s Muscle Chains (1989), which evolved into a concept now called Contrac- Going even further back, prior to human evolution, may tile Fields (2007/2008), Andry Vleeming’s and Diane Lee’s provide even deeper insight; for this, it is necessary to look Slings (Vleeming et al., 1997) and Thomas Myer’s Anatomy back into deep time. Trains (2001). Deep time In short, these people e and many others alongside e were all doing “joined-up-thinking” in the field of human Early life on Earth exhibited poor or limited motility; locomotor anatomy. nevertheless, such motility was sufficient to satisfy survival In the last issue of this Journal, the co-editor of this E-mail address: [email protected] section of JBMT, Warrick McNeill PT, included a paper on the importance of the deep longitudinal sling in hamstring strain (Panayi, 2010). This sling, described by van Wing- erden et al. (1996), Vleeming et al. (1997) and Gracovetsky 1360-8592/$ - see front matter ª 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbmt.2010.07.001

PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN 404 M. Wallden (1997) is key in both stabilization of the lumbopelvic body; especially if this occurs under load or velocity, such complex and, Gracovetsky argues, in utilising ground as in a sporting event, creates significant computational reaction force to de-rotate the spine in gait. stress onto the nervous system, to adapt to a situation that it isn’t reflexively equipped for. Further research, such as Hungerford et al.’s (2003) paper suggest that this sling may also become facilitated as Perhaps a clinical realisation arising from this is that not a result of sacroiliac joint (SIJ) pain; the deeper, intrinsic or only are ergonomics key, but also paying attention to other “inner unit” musculature being somewhat inhibited or causes of creep on the ligamentous system, such as the delayed in response in SIJ pain patients e when compared hypnotic effect of computer and TV screens, the sedative with controls e and the biceps femoris firing ahead of these effects of alcohol consumption or of chronic sleep depri- muscles in a feed-forward mechanism. vation; potentially switching the body off from its own mechanoreceptive feedback, may offer greater under- This may have a logical cross-over to the issues discussed standing in preventing low back injury. in the paper in this section, by Hashemirad et al. (2010), on the flexor-relaxation phenomenon. They describe how Muscle, fascia and force transmission a lumbar spine which has undergone creep due to prolonged flexion (for just 7 min or more) will create a statistically A second paper appearing in this edition’s Rehabilitation significant delayed flexor-relaxation phenomenon. and Prevention section is titled “Muscle fascia and force transmission” by Peter Purslow, (2010a) PhD. This paper For those unfamiliar with this response, the typical explains in great detail how the inner fascial components of clinical response being observed is a switch from the muscle; the endomysium, which surrounds the myofi- a “muscular” trunk strategy (erector spinae) to a “liga- bril, and the perimysium, which surrounds the muscle fibre mentous” trunk strategy (transversus abdominis pulls on bundles, form a network to create fascial continuity the thoracolumbar fascia and whole posterior ligamentous between different contractile units; even if one unit is system of the spine tightens) at around 45 degrees of trunk fatigued, damaged, being repaired or, indeed, is simply flexion or around 90% of lumbar flexion. This reflex is growing. stimulated by mechanoreceptors in the posterior ligamen- tous system of the spine inhibiting the lumbar erectors. A muscle can be imagined to behave a little like a bridge, connecting one piece of land (bone) to another An implication of Hashemirad et al.’s findings, is that the piece of land (bone) while traversing some kind of ditch or normal stretch does not activate the flexor-relaxation of gap (joint). In this way the bridge (muscle) would be built of the lumbar erectors at the usual time; this means that the hundreds of units e perhaps bricks e (sarcomeres) placed hamstrings, the transversus abdominis (and it’s tensioning both end to end (in series) and alongside each other (in of the deep layer of the thoracolumbar fascia) which nor- parallel). These bricks (sarcomeres) are designed to both mally become dominant at this point in the movement, are withhold and to generate great forces. In the structure of delayed in their action. the bridge, this is a relatively static role, but in the struc- ture of the muscle, this is a far more complex dynamic The upshot is decreased intra-abdominal pressure (due interplay between resting tone, and various contractile to delayed TrA contraction), decreased force closure at the states (concentric, eccentric, isometric and so on). sacroiliac joints (due to TrA not activating the nut-cracker phenomenon of force closure at the SIJ), decreased If one or more bricks were to become damaged, or be extensor moment action of the diamond-shaped middle knocked out of the structure of the bridge, its integrity and layer of the thoracolumbar fascia, extended lumbar erector ability to both withstand and to generate force would be contraction in a position of increased flexion and therefore significantly impaired. However, in both muscles and in greater risk of posterior annular loading and potential bridges this happens regularly, and reconstruction and injury. maintenance is an ongoing feature of such a functional load-bearing structure. In short, from one simple act of flexing the lumbar spine for a little too long, the ability of the body to effectively In order to be able to safely repair the bridge while it transfer loads during lifting or squatting, via a posterior can still allow loads to be taken, some kind of extrinsic myofascial chain incorporating the hamstrings, sacrotu- scaffolding needs to be in place; probably across the whole berous ligaments, thoracolumbar fascia, posterior liga- bridge (the epimysium), and it is likely that a more focused mentous system, lumbar erectors and transversus brace (perimysium) will need to be placed under the abdominis, is compromised. This means that the SIJ’s and section of bridge that is to be repaired; while, specifically, the discs become more vulnerable to injury; and the the bricks (sarcomeres) in contact with the actual brick to ramifications may be greater than that. be repaired (damaged sarcomere) may need a very specific, localised brace to hold them, while the stone mason is The later that the hamstrings become dominant in this doing his work. This allows replacement of the damaged movement pattern, for example, the greater the leverage brick (sarcomere) and effective force transmission between on their proximal insertion due to the angle of trunk incli- the adjacent bricks (sarcomeres) so that the bridge nation. Might this influence their risk for becoming (muscle) doesn’t lose much, if any functional capacity. This strained? If the loading on the hamstring changes its real- is critical to maintain motility of the system of which the time orientation based on the body’s long-established muscle (bridge) is a part (Fig. 1). reflex mechanisms, could this have ramifications further down the deep longitudinal sling e as far as the arch of the As Purslow goes on to discuss, there is more to these foot and its role in absorption, storage and recoil of ground systems than just biomechanics. He illustrates, for example reaction forces? At this point the answers are unclear, but what is known is that a change in the spatiotemporal relationships of the

Chains, trains and contractile fields 405 Figure 1 Muscle, fascia and force transmission. The 3 key components of the fascia which envelops a muscle; the endomysium, PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN perimysium and epimysium, can be seen a little like the struts that may support a brick bridge that is under repair. Since muscle tissue is constantly under conditions of growth, damage and repair, there must be mechanisms in place to allow continued function of the muscle when required. The endomysium and perimysium appear to allow for this, and for intra-muscular force transmission, while the epimysium may be more involved in intermuscular force transmission. that additional crosslinks may form through advanced gly- without significant compromise to performance or to cation end products (AGEs); typical of the changes in repair. connective tissues in those with blood sugar dysregulation, from smoking and from aging. Connective tissue function is Interestingly, Hunter (2005) presented prospective not just, then, about how the body is used biomechanically, research on English Premiership soccer players which but what it is exposed to biochemically. demonstrated that those players with greater measurable stiffness in their hamstrings at the beginning of the season Purslow’s work is also relevant to the concept of slings were the least likely to suffer a hamstring strain during that discussed by Panayi (2010) in JBMT issue 14(1), by Myers season. Muscle stiffness is known to be generated by the (1997a, b) many times in this Journal and in his book series elastic components, which act like springs in between Anatomy Trains, as well as by Beach (2007, 2008). each sarcomere (Sarhmann, 2002). Therefore, the more sarcomeres (bricks) in parallel, the more series elastic These slings are, important in providing a whole-body components, the greater the stiffness, and the more possible appreciation of dysfunctional states, helping us to track pathways for force transmission e as well as for running back to where a problem may have arisen from and, repairs during play and across the season in general. indeed, as McNeill (2010) and Chaitow (2010) have dis- cussed, to predict where a future problem may arise. As to whether these forces can pass out of the con- tracting muscle and into the surrounding fascia (epimy- What Purslow’s work seems to indicate is that sium), Purslow is uncertain, but explains that it would seem contractile forces passing through the sarcomeres and entirely feasible and that there is certainly evidence of direct into the myotendinous junction are route-1 for force a hydraulic amplifier mechanism occurring between agonist generation, but that if a given line of sarcomeres has muscles within a compartment. a damaged unit in series (or “brick” in the line), then this doesn’t stop every other sarcomere in that series from Purslow (2010b, Personal Communication) states: working; but simply allows contractile forces to be trans- “Whether epimysium in some muscles at least can also act mitted laterally across to a parallel series of sarcomeres in the same way to hydraulically stiffen the muscle so that (line of bricks) allowing continued function of the muscle, Text box 1. Evidence for hydraulic amplification between agonists in muscle compartments “.compartmentalisation increases the efficiency of muscle contraction. The contraction of one muscle within the group pressurises the compartment (from 15 mmHg in normal contractions up to approx. 80 mmHg in tetanic condi- tions), and even a small elevation in pressure raises the contractile efficiency of all members in the muscle group. Cutting the fascia releases 50% of this normal pressure generation and decreases contractile force for a given extension by 16% (Garfin et al., 1981). The interactions of the contractile proteins actin and myosin in muscle are known to be sensitive to high pressures, but very large pressures (10 MPa, or 100 atm) are required, and the effect of these are to reduce the active tension generated (Knight et al., 1993). Perhaps the more useful explanation of the effect observed at such low pressures is the lateral constraint effect proposed by Aspden (1990), which argues that the reduction in lateral expansion that pres- surisation of neighbouring muscles may cause increases the effective muscle stiffness in active contraction, thus leading to increased force production for a given length of contraction.”

406 M. Wallden it produces more force for a given length change is, as far Adolescents from two schools in the Rift Valley Province as I know, not known, but in some muscles with heavy were also compared: one group (4) who have never worn sheets of tendon-like epimysium it certainly looks shoes; and another group (5) who have been habitually shod a possibility.” most of their lives. PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN Load transfer Subject Condition RFS MFS FFS Research conducted by Vleeming et al. (1997) supports this Habitually shod Barefoot 83 17 0 notion of the capacity of the epimysium to transfer load adults, USA Shod 100 0 0 across compartments into adjoining muscle groups. Recently shod Barefoot 90 91 Research conducted both on the transfer of load adults, Kenya Shod 29 18 54 between the gluteus maximus and the contralateral lat- issimus dorsi via the thoracolumbar fascia, and on the Habitually barefoot Barefoot 25 0 75 peroneus longus through to the tendon of biceps femoris, adults, USA Shod 50 13 37 showed that a percentage (approximately 18%) of forces applied to the cadaveric myofascial system were, indeed, Barefoot adolescents, Barefoot 12 22 66 transferred across muscle groups. The most likely expla- Kenya (never) Shod ee e nation for this (as had been hypothesized by authors such as Myers, Beach and others) is the direct fascial attachments; Shod adolescents, Kenya Barefoot 62 19 19 but specifically of the epimysium (as opposed to contribu- Shod 97 3 0 tions from the endomysium or perimysium). RFS Z Rearfoot strike. The limitations of these studies are clear, inasmuch as MFS Z Midfoot strike. the subjects were not living, had been prepared as FFS Z Forefoot strike. cadavers (factors which will both significantly alter tissue What these results seem to clearly demonstrate is that, properties) and were assessed on a dissection table (ie not while humans are able to rearfoot, midfoot or forefoot in a functional load-bearing or sports-specific position), and strike, it would appear that the primary discriminating using extrinsic application of force rather than intrinsic factor in this behaviour, is more to do with whether they myogenic contractile forces. are shod, rather than their genetic or biomechanical heri- tage (Figure 2). Nevertheless, such research allows the bodyworker and At this early stage in the research, it would seem that movement therapist the possibility of making associations the working conclusion is that the natural state for running between the apparent “functional anatomy” and what they appears to be a forefoot strike, while adorning the foot see clinically. with a running shoe seems to be the primary causative factor in rearfoot strike behaviour. Time to rewrite the biomechanics books? Clinical implications One such example is the biomechanics of gait. For the last 10 years or so, the running community has Assuming further ongoing research seems to support this notion, what may be the clinical implications for such an been in debate about whether running with a heel strike is understanding? functional or not. Many running coaches have suspected that the natural state is to strike the ground with the Firstly, of course, the biomechanics books may have to forefoot since a higher proportion of elite distance runners be re-written with respect to running gait. Interestingly, of forefoot strike, than those in the lower echelons of the course, most such texts have been written since people sport. Yet, despite this, heel striking runners still started wearing running shoes in 1970s and beyond; and outnumber the forefoot strikers by some significant margin therefore have used data from shod groups. (Downey, 2009). Secondly, other findings, both within this research from This is why the research from Lieberman et al. (2010) Lieberman and from other groups suggest that barefoot published earlier this year met with so much interest from running and shod running differ with respect to lower limb the world’s media and, in particular with the biomechanics joint angles, muscle activation firing patterns, leg stiffness, and podiatry communities. joint torques, and so on (DeWit et al., 2000; Divert et al., 2005; Kerrigan et al., 2010). What Lieberman et al. (2010) did, for the first time, was to assess groups of habitually unshod runners, versus Weaker epidemiological studies suggest the possibility that habitually shod runners, from different cultures, these factors may reduce injury profiles (Warburton, 2001). comparing their running style both barefoot and in running shoes. While research from the strength and conditioning field suggests that increasing leg stiffness; something that Adults were sampled from three groups of individuals happens naturally when running barefoot, is a key way to who run a minimum of 20 km per week: (1) habitually shod increase top flight running speed (Peak Performance, athletes from the USA; (2) athletes from the Rift Valley 2009). Province of Kenya (famed for endurance running), most of whom grew up barefoot but now wear cushioned shoes when running; and (3) US runners who grew up shod but now habitually run barefoot or in minimal footwear.

Chains, trains and contractile fields 407 PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN Figure 2 Rearfoot Strike and Forefoot Strike (adapted from reaction force against the heel, in tandem with the Lieberman et al., 2010). When running in supportive trainers, descending load of the bodyweight through the talocrural the majority of runners will strike the ground with their heel. joint, will result in a very strong eccentric load through This changes the gait cycle, the cadence, the biomechanics this lower portion of the sling (which is when a muscle is and the loading profile. When running barefoot, the majority of strongest); effectively controlling both plantar flexion of runners will strike the ground with their forefoot. Since cush- the ankle and pronation of the medial longitudinal arch. ioned shoes are a recent phenomenon, it is likely that the But, if the natural state of running is to plantarflex the barefoot condition is more akin to the “natural condition” and foot and to forefoot strike, then this system suddenly to the way human biomechanics have evolved to function. becomes very inefficient; not serving to control prona- tion, nor to translate forces up the sling to provide force Back to the fusion closure to the load-bearing sacroiliac joint. In forefoot strike, the deep longitudinal sling’s appears to be prac- If we are to place this research regarding the natural tically nullified. biomechanical state into the context of “joined-up- anatomy”, or the fusion of musculature hitherto regarded Since this forefoot strike appears to be the natural state; as “separate” entities, it may be possible to identify a dual and this in tandem with the prevailing theory of human speed system: one for low-speed gait (walking) and one for evolutionary nutrition, for the last 2 million years, it seems supra-walking pace gait (running, to include jogging, and relied heavily on the persistence hunt where the prey is sprinting). literally run to exhaustion (Lieberman et al., 2010; Lie- benberg, 2006), it would seem that effective load transfer The reason for this is that there is a potential problem through the myofascial net would be key in allowing our with the deep longitudinal system, as described by van ancestors to optimally exploit their ecological niche. Wingerden (2006), Vleeming (1997), Panayi (2010), in the context of this new research on the forefoot strike; it can So what is the answer? Perhaps there is another means of only really work if you heel strike. explaining the efficiency of natural state human running gait. The stability of a moving object increases as its Though it wasn’t explicitly discussed by Panayi (2010), velocity increases. Similar to a cyclist moving at a very slow the lower portion of the deep longitudinal sling, namely speed, versus at high speeds, gait may also be recognized the tibialis anterior and the peroneus longus, which form for the fact that there is greater transverse plane motion; a connective tissue stirrup around the arch of the foot, to translated into greater pronation stresses during walking, control pronation of the medial longitudinal arch, will than there is during sprinting. Indeed, the efficacy with work very well if the foot is dorsiflexed before heel which the human body can create sagittal plane or forward strike, as it means that the leverage of the ground momentum is key in its ability to get from a to b quickly and without energy “leakage” into the frontal or transverse planes. Hence it would be reasonable to assume that the later- ally placed (and therefore counter-pronation) musculature of the deep longitudinal system (peroneus longus, tibialis anterior and biceps femoris into sacrotuberous ligament), may be more important at slower, walking velocities, but that it may become usurped in a higher velocity activities such as running, but another sling mechanism. Myers’ superficial back line or “train” has been described in earlier editions of JBMT (Myers, 1997a, b) and in his book “The Anatomy Trains”, Myers depicts this myo- fascial sling as running from the deep toe flexors (active eccentrically in forefoot strike) and plantar fascia and, direct through the connective tissues into the Achilles tendon and into the triceps surae. The ankle being plantarflexed before heel strike means that as the forefoot strikes the ground, the triceps surae will be eccentrically loaded (where they are at their strongest) and, interestingly, it is eccentric loading that is missing from the gait cycle if someone rearfoot strikes. Could there be a correlation between a lack of forefoot striking and Achilles tendinopathy, after all, since the work of Alfredson (1998), one of the primary methodologies for treating tendinopathic injury has been to prescribe an eccentric loading protocol. Following the anatomy up, the two heads of the gastrocnemius run medially to their super-incumbent hamstrings, the semimembranosus/tendinosus and the two heads of biceps femoris; sweeping around laterally to insert on the condyles of the femur.

408 M. Wallden PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN 12 12 11 11 13 10 11 10 9 10 9 8 8 7 7 6 5 6 4 5 3 2 1 Myers Superficial Back Line. Myer’s description of the superficial back line runs from 1) the deep toe flexors into, 2) theplantar fascia to, 3) the junctional fascia between the plantar fascia and Achilles tendon. 4) is the triceps surae and 5) is where the two head of the gastrocnemius wrap around the tendons of 6) the medial and lateral hamstring groups. The hamstrings course up and are continuous and are continuousboth with each other and with 7) the sacrotuberous ligament, which spans from 8) the ischial tuberosity up to 9) the sacroiliac joint, where it blends with 10) the deep fibres of the multifidus and the erector group _ finally running all the way up to 11) epicraneus and 12) the frontalis muscle. The functional relevance of this is that if there is a strong Vleeming et al. (1997) in their description of the deep contraction of the triceps surae complex, as would be longitudinal sling. expected during landing with a forefoot strike, this will create a sudden sharp pull on the hamstring tendons; akin to A possible parallel field of investigation a tendon-jerk reflex. This will stimulate a strong and bilateral contraction of both hamstring groups (in contrast to just the In the field of podiatry, there is an emerging concept laterally placed biceps femoris of the deep longitudinal around a similar dual mechanism focused around the foot sling), which will transfer loads into the sacrotuberous liga- mechanics; termed biaxial propulsion- see Textbox 2 below ment and across the load-bearing sacroiliac joint. (Curran, 2010a). It has been reported by Vleeming et al. (1997), as though In summary, the high and low gear axis really only works it is only the tendon of the biceps femoris which blends with during the propulsive phase, so it may be that during (and therefore transfers load into) the sacrotuberous liga- a forefoot strike, the autosupport of the foot may gain high ment, yet to quote Gray’s Anatomy 37th edition (1989), the gear (a functionally pronated forefoot) and appropriate biceps femoris has two proximal attachments: a long head, calcaneocuboid stability as a result. If this were correct, attached to . the ischial tuberosity by a tendon common then with the toe-heel-toe loading of forefoot stike to it and the semitendonosis, which blends with the lower runners, it would seem to imply that the high gear mech- part of the sacrotuberous ligament. anism may be engaged to provide stability “in both direc- tions” both receiving load and expressing load. The same This edition of Gray’s goes on to say of the proximal may be said of the windlass mechanism; that it may both semimembarnosus that its fibres are partly interwoven store up energy on toe strike and recoil energy on toe-off. It with the biceps femoris and semitendinosus, so it would seem quite logical to deduce that all three muscles may contribute something to the force closure described by

Chains, trains and contractile fields 409 Text box 2. Biaxial Propulsion and Calcaneocuboid locking PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN During the late 1970s, the Danish anatomist Finn Bojsen-Møller described the interrelationship of the loading mech- anism of the calcaneocuboid joint that is secondary to the timely tightening of the plantar fascia. Reliant on weight flow through to the first web space, the overall effect of this complex, yet essential mechanism produced stability of the rearfoot and midfoot via compression of the calcaneocuboid joint prior to heel lift. During his investigations, Bojsen-Møller also examined the metatarsal parabola (2 > 1 > 3 > 4 > 5 or 2 > 1 Z 3 > 4 > 5), which revealed an anterior protrusion of the 2nd metatarsal; a seemingly consistent feature associated with the normal foot. In effect, two different axes of propulsion at the MTP joints were observed to exist. One passing transversely through the heads of the first and second metatarsal (transverse or high gear axis) and the other passing obliquely through the second through to the fifth metatarsal heads as the (oblique or low gear axis). Further investigation of these propulsive axes revealed a number of functional advantages, and in particular the transverse axis. By evaluating the distance between each axis from a central point of the ankle joint, the distance to the perpendicular bisection of the transverse axis was documented as being greater (approximately 15e20%) when compared to the same distance to the perpendicular bisection of the oblique axis. Therefore, during high gear (transverse axis) propulsion in which weight flow is directed medially, the forefoot was observed to be functionally pronated (partly through the action of the peroneus longus). It is hypothesized that the position of the forefoot brings the dorsal border of the calcaneus and calcaneal process of the cuboid together. This in turn, provides an osseous block to further motion creating stability and is referred to as the “closed-packed position.” The greater distance from Bojsen-Møller’s central point of the ankle joint to the perpendicular bisection of the transverse axis was assumed to produce a taut attitude of the plantar fascia. This provides further compression of the cuboid on the calcaneus that results in the crucial stability required for propulsion. Conversely, during lateral weight flow (oblique axis or low gear propulsion), it was hypothesized that because of the inverted position of the foot, the calcaneocuboid joint failed to obtain the closed-packed position as previously described. This is thought to be coupled with an insufficient tightening of the plantar fascia due to the shortened distance associated with oblique axis pro- pulsion. As a result, it can be assumed that the lateral aspect of the forefoot would absorb the majority of the forces. is worth noting that biaxial propulsion is just one of the Beach, P., 2008. The contractile field e a new model of human many autosupport mechanisms of the foot, and is depen- movement e part 3. Journal of Bodywork and Movement dant on timely motions and activation of other mecha- Therapies 12, 158e165. nisms. For example, if someone had a limited first MTP joint then it is likely to disrupt weight flow and failure of Beach, P., 2007. The contractile field e a new model of human appropriate support - and of course this will happen movement. Journal of Bodywork and Movement Therapies 11, whether barefoot or shod if the biomechanical dysfunction 308e317. is already present (Curran 2010b). Nevertheless, barefoot gait poses no restriction on MTP range of motion; so Chaitow, L., 2010. Clinical prediction rules. Journal of Bodywork decreases likelihood of compromise to this mechanism. and Movement Therapies 14 (3), 7e8. Perhaps some of these mechanisms go some way to explain why unshod gait is typically more biomechanically efficient. Curran, S., 2010a. Sagittal plane facilitation of motion theory and associated pathologies. In: Albert, S.F., Curran, S.A. (Eds.), Conclusion Lower Extremity Biomechanics: Theory and Practice. Volume 1. BiPedMed Press, Denver, USA. The body is majestically complex e even in its biomechanical make-up alone. If I were a mechanic working, as fascinating as Curran, S., 2010b. Biaxial propulsion and calcaneo-cuboid locking it may be, with planes, trains and automobiles, I think I would mechanism. Personal communication. look over my shoulder with some envy at the biomechanics who worked with chains, trains and contractile fields. Divert, C., et al., 2005. Stiffness adaptations in shod running. Journal of Applied Biomechanics 21 (4), 311e321. References DeWit, B., et al., 2000. Biomechanical anlaysis of the stance phase Alfredson, H., Pietila¨, T., Jonsson, P., Lorentzon, R, 1998. Heavy during barefoot and shod running. Journal of Biomechanics 33 load eccentric calf muscle training for the treatment of chronic (3), 269e278. Achilles tendinosis. The American Journal of Sports Medicine 26 (3), 360e366. Downey, G., 2009. Lose your shoes. Is barefoot better? http:// neuroanthropology.net/2009/07/26/lose-your-shoes-is- Aspden, R.M., 1990. Constraining the lateral dimensions of uni- barefoot-better/ (accessed 30.06.10). axially loaded materials increases the calculated strength and stiffness-application to muscle and bone. J. Mater. Sci. Mater. Erwin, D., Valentine, J., Jablonski, D., 1997. The origin of animal Med 1, 100e104. body plans. American Scientist 85, 126e137. Beach, P., 1989. Development of muscle chains theory. Personal Garfin, S.R., Tipton, C.M., Mubarak, S.J., Woo, S.L.Y., communication. Hargens, A.R., Akeson, W.H., 1981. Role of fascia in mainte- nance of muscle tension and pressure. Journal of Applied Physiology 51, 317e320. Gracovetsky, S., 1988. The Spinal Engine. Springer, Vienna. Gracovetsky, S., 1997. Linking the spinal engine with the legs: a theory of human gait. In: Vleeming, A., Mooney, V., Dorman, T., Snijders, C., Stoeckart, R. (Eds.), Movement, Stability and Low Back Pain e The Essential Role of the Pelvis. Churchill Livingstone, New York, pp. 243e252. Hashemirad, F., Talebian, S., Olyaei, G., Hatef, B., 2010. Compensatory behaviour of the postural control system to

PREVENTION & REHABILITATIONdEDITOR: MATT WALLDEN 410 M. Wallden flexion-relaxation phenomena. Journal of Bodywork and Move- Myers, T., 1997a. The ‘anatomy trains’. Journal of Bodywork and ment Therapies 14 (2). Movement Therapies 1 (2), 91e101. Hungerford, B., Gilleard, W., Hodges, P., 2003. Evidence of altered lumbopelvic muscle recruitment in the presence of sacroiliac Myers, T., 1997b. The ‘anatomy trains’: part 2. Journal of Body- joint pain. Spine 28 (14), 1593e1600. work and Movement Therapies 1 (3), 135e145. Hunter, G., 2005. Hamstring strain in professional football. Football Association Medical Society Non- League Conference, Lilleshall, Myers, T., 2001. The Anatomy Trains. Churchill Livingstone. UK, October 2005. Panayi, S., 2010. The need for lumbar-pelvic assessment in reso- Kardong, K., 2002. Vertebrates. McGraw-Hill, New York. Kerrigan, D., Casey, M.D., Jason, F., Geoffrey, S., Keenan, M., lution of chronic hamstring strain. Journal of Bodywork and Dicharry, J., Della, U., CroceWilder, R., 2010. The effect of Movement Therapies 14 (1), 294e298. running shoes on lower extremity joint torques. PM&R 1 (12), Peak Performance, 2009. Training for Sprinting, Speed & Acceleration. 1058e1063. Purslow, P., 2010a. Muscle, fascia and force transmission. Journal Knight, P.J., Fortune, N.S., Geeves, M.A., 1993. Effects of pressure of Bodywork and Movement Therapies 14 (2). on equatorial X-ray fiber diffraction from skeletal muscle fibers. Purslow, P., 2010b. Personal communication. Biophysical Journal 65, 814e822. Sarhmann, S., 2002. Diagnosis and Treatment of Movement Liebenberg, L., 2006. Persistence hunting by modern hunter- Impairment Syndromes. Mosby. gatherers. Current Anthropology 47 (6), 1017e1025. Vleeming, A., Snijders, C., Stoeckart, R., Mens, J., 1997. The role Lieberman, D., Venkadesan, M., Werbel, William A.W., of the sacroiliac joins in coupling between spine, pelvis, legs Daoud, A., D’Andrea, S., Davis, I., Ojiambo Mang’Eni, R., and arms. In: Vleeming et al. (Eds.), Movemen, Stability & Low Pitsiladis, Y., 2010. Foot strike patterns and collision forces in Back Pain. Churchill Livingstone, 53–71. habitually barefoot versus shod runners. Nature 463, Wallden, M., 2008. Rehabilitation and Movement Re-education 531ee536. Approaches. Naturopathic Physical Medicine. Elsevier. McNeill, W., 2010. Journal of Bodywork and Movement Therapies 13 Warburton, M., 2001. Barefoot running. Sportscience 5 (3). sportsci.org. (3), 272e275. van Wingerden, J.P., Vleeming, A., Stoeckart, R., Raissadad, K., Snijders, C.J., 1996. Force transfer between biceps femoris and peroneus muscle; a proposal for a longitudinal spring mecha- nism in the leg.

Journal of Bodywork & Movement Therapies (2010) 14, 411e417 available at www.sciencedirect.com journal homepage: www.elsevier.com/jbmt PREVENTION & REHABILITATIONdFASCIA PHYSIOLOGY FASCIA PHYSIOLOGY Muscle fascia and force transmission Peter P. Purslow, PhD Department of Food Science, University of Guelph, Guelph, Ontario N1G 2W1, Canada Received 13 October 2009; received in revised form 3 January 2010; accepted 7 January 2010 KEYWORDS Summary This paper reviews the major intramuscular extracellular matrix (IM-ECM) struc- Muscle; tures (endomysium, perimysium and epimysium) and their possible mechanical contributions Connective tissue; to muscle functions. The endomysium appears to provide an efficient mechanism for transmis- Extracellular matrix; sion of contractile forces from adjacent muscle fibres within fascicles. This coordinates forces Mechanical function; and deformations within the fascicle, protects damaged areas of fibres against over-extension, Myofascial force and provides a mechanism whereby myofibrils can be interrupted to add new sarcomeres transmission; during muscle growth without loss of contractile functionality of the whole column. Good Endomysium; experimental evidence shows that perimysium and epimysium are capable in some circum- Perimysium; stances to act as pathways for myofascial force transmission. However, an alternative role MMPs; for perimysium is reviewed, which involves the definition of slip planes between muscle fasci- ECM turnover cles which can slide past each other to allow large shear displacements due to shape changes in the whole muscle during contraction. As IM-ECM is continually remodelled so as to be me- chanically adapted for its roles in developing and growing muscles, control of the processes governing IM-ECM turnover and repair may be an important avenue to explore in the reduction of fibrosis following muscle injury. ª 2010 Elsevier Ltd. All rights reserved. Introduction pathways by which IM-ECM is remodelled and adapted due to changing functional demands during muscle growth and The soft connective tissues associated with muscle tissue repair, and in response to exercise training or disuse, are have been referred to as the intramuscular extracellular addressed by Kjær and Magnusson (2008). Like most other matrix (IM-ECM), intramuscular connective tissue (IMCT) soft connective tissue structures, the amount and compo- and muscle fasciae (MF). Although these general names can sition of IM-ECM structures are not simply programmed be used interchangeably, the term IM-ECM will be used during embryogenesis and subsequent post-natal matura- here. Substantial reviews of the structure, development, tion processes. The amounts and composition of the various composition and function of IM-ECM exist (Purslow and IM-ECM structures in living tissue represent a dynamic Duance, 1990; Purslow 2002, 2008). The mechanisms and balance between deposition, growth, remodelling and degradation, which is affected by the interplay between E-mail address: [email protected] 1360-8592/$ - see front matter ª 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbmt.2010.01.005

412 P.P. Purslow functional demands on the tissue and the mechanical environment. The cellular mechanisms of mechano- transduction in fibroblasts are reviewed by Chiquet et al. (2009). The purpose of the current review is to highlight information pointing to the crucial roles of IM-ECM in force transmission and accommodation of shape changes in functioning muscle. PREVENTION & REHABILITATION dFASCIA PHYSIOLOGY General structure and biochemical composition of IM-ECM As schematically shown in Fig. 1, each muscle is surrounded Fig. 2 Light micrograph of epimysium from bovine sterno- by epimysium, a connective tissue layer that is continuous mandibularis muscle, showing arrangement of collagen fibres with the tendons that attach the muscles to the bones. In in crossed-plies. The fibres are in two parallel layers lying at some long strap-like muscles the epimysium is composed of þ55 and À55 to the muscle fibre axis. From Purslow (1999), two parallel sets of wavy collagen fibres in a crossed-ply with permission. In epimysium from other muscles the collagen arrangement, embedded in a proteoglycan matrix (see is more aligned with the muscle fibre direction and acts as an Fig. 2). When the muscle is at its resting length, the two exo-tendon or aponeurosis. sets of collagen fibres are arranged at angles of approxi- mately 55 to the long axis of the muscle fibres. In other together the collagen fibre networks in these structures muscles, and especially in pennate muscles, the arrange- (Scott, 1990). Listrat et al. (1999, 2000) show that collagen ment of collagen fibres in the epimysium is parallel to the types I, III, IV, V, VI, XII and XIV are all expressed in muscle long axis of the muscle and forms a dense surface layer that development. Collagen typically represents 1e10% of the functions as a surface tendon. The perimysium is a contin- dry weight of adult skeletal muscle (Bendall, 1967). Fibres uous network of connective tissue which divides the muscle of elastin can be found in the IM-ECM of some muscles, up into fascicles or muscle fibre bundles. Fascicles run principally in the perimysium. However, the amount of along the length of the muscle from tendon to tendon, and elastin is small in most muscles and is typically less than 1% the ends of muscle fibres form highly folded interdigitating of muscle dry weight (Bendall, 1967). joints (the myotendinous junction) with the tendon at this point (Trotter, 1993). The perimysial network merges into Collagen fibres are stabilised by the formation of cova- the epimysium at the surface of the muscle and is lent crosslinks directed by a clear set of post-translational mechanically connected to it. Within each fascicle or modifications which act on the collagen molecules extra- muscle fibre bundle, the endomysium is a continuous cellularly after assembly of the collagen molecules into the network of connective tissue that separates individual quarter-stagger overlapped arrangement characteristic of muscle fibres. fibrils (Bruns and Gross, 1973). The formation of crosslinks is essential for the mechanical strength and stiffness of Each of the epimysium, perimysium, and endomysium collagen fibres (Bailey et al., 1998). During gestation and layers has its own structure and composition, but generally post-natal maturation there are changes in the types and these connective tissue layers are composed of collagen amounts of covalent crosslinks that stabilise the collagen fibres in an amorphous matrix of hydrated proteoglycans molecules within all connective tissues in the body, (PGs) which plays a crucial role in mechanically linking including IM-ECM. There are also non-enzymatic reactions of collagen with glucose and other aldehydes. Formation of Fig. 1 Schematic diagram of IM-ECM structures in a skeletal additional crosslinks through advanced glycation end muscle. Epimysium delineates the surface of the muscle, products (AGEs) is typical of the changes in connective perimysium separates muscle fascicles and endomysium sepa- tissues in diabetes and during ageing and glycation, and is rates individual muscle fibres. Also depicted are the contractile thought to be a significant contributor to changes in the myofibrils within each muscle fibre. (Artwork: Dr. L.-T. Lim). mechanical properties of connective tissues with age (Paul and Bailey, 1996). Advanced glycation end products can be incorporated into the body from dietary sources (e.g. heat processing of some foods creates AGEs) and from tobacco smoke (Avery and Bailey, 2008). In this way, diet and life- style may affect the mechanical properties of IM-ECM via AGE-cross-linking of collagens. IM-ECM changes during muscle development During embryonic development of intramuscular connec- tive tissue, the amounts of the various collagens and PGs

Muscle fascia and force transmission 413 PREVENTION & REHABILITATIONdFASCIA PHYSIOLOGY changes (Velleman et al., 1999; Listrat et al., 1999; Lawson of a network of collagen fibrils and fibres in a proteoglycan and Purslow, 2001). Spatial variations between the endo- matrix. mysium and perimysium within one muscle (Nishimura et al., 1997) and differences in expression of both collagen The thickness of the endomysium as a whole varies with type I and PG components such as laminin between muscles muscle length, becoming thicker at short muscle lengths (Lawson and Purslow, 2001) are both determined early in and thinner as the muscle is extended (see Trotter and prenatal development. In bovine muscles, type I collagen Purslow, 1992). Transmission electron micrography of intact expression is always higher than type III expression at all endomysium in situ confirms that all of the collagen fibres stages of gestation and post-natally (Listrat et al., 1999). in the network layer lie in the plane of the layer (Trotter Thus some differences in the composition of intramuscular and Purslow, 1992). The only location where this does not connective tissue appear to be pre-programmed in hold true is in the junction zones between the perimysium embryogenesis. However, there are some variations in the and the endomysium of muscle cells that lie in the surface amounts of collagens as muscle development progresses. In of the fascicle. bovine psoas and triceps muscles the total collagen concentration and amounts of collagen type I is maximum Swatland (1975) concluded that the reticular layer was at the point in gestation when the expression of myosin a single structure shared between adjacent muscle cells, within muscle fibres changes from the embryonic to the and that this endomysial structure forms a continuous adult form (Listrat et al., 1999). After this, the growing network that runs across the whole muscle fascicle. This diameter of the muscle fibres dilutes out the connective interpretation is very strongly borne out by scanning elec- tissue content of the muscle. In contrast, the pectoralis and tron microscopy of endomysial collagen networks prepared quadriceps muscles of the chick show steady increases in by NaOH-extraction of muscle to remove all cell compo- collagen type I content and laminin content through nents, PGs, plasmalemma, and basement membrane gestation and post-natally (Lawson and Purslow, 2001). structures (Trotter and Purslow, 1992; Purslow and Trotter, Whether these differences between bovine and chick 1994; Nishimura et al., 1994, 1995; Liu et al., 1995). This muscle growth are due to avian versus mammalian phyla preparation technique was first demonstrated on connec- differences or due to functional differences in the muscles tive tissues generally by Ohtani et al. (1988). Fig. 3 (from studied remains unclear. Purslow and Trotter, 1994) shows such a preparation. The structure of the endomysium appears broadly identical in The amounts and composition of endomysium all SEM preparations from skeletal muscle from different and perimysium vary between functionally muscles and species, and also in cardiac muscle (Purslow, different muscles 2008). In fully developed adult animals, there are large differences The planar network of collagen fibres in the thick in the amounts and composition of IM-ECM between different reticular region of the endomysium is often described as muscles in the body. Histological comparison (see Fig. 4 in a random or quasi-random network of irregularly wavy Purslow, 2005) illustrates that the continuous perimysial fibres. These collagen fibres run at almost every angle to network surrounds or separates fascicles of radically the muscle fibre long axis, but the network is not truly different sizes and shapes in different muscles from the same random. Detailed image analysis of the distribution of fibre animal. This difference also results in different thicknesses of directions with respect to the long axis of adjacent muscle perimysial connective tissue. A comparison of the connective cells reveals that there is a preferred direction in the wide tissue content of 14 bovine muscles shows that the endomy- distribution of collagen fibre orientations, and that this sial collagen content is between 0.47% and 1.2% of dry weight, preferred orientation changes with muscle length (Purslow but the perimysial collagen content in the same muscles and Trotter, 1994). At short muscle lengths, more of the ranges from 0.43% up to 4.6% of dry weight (Purslow, 1999). collagen fibres in the endomysial network are aligned cir- The amount of perimysium in muscles varies far more than the cumferentially, and at long muscle lengths there is a higher amount of endomysium. These variations, especially in the preference for fibres to be aligned longitudinally. The amount and spatial organisation of the perimysium have long reorientation of collagen fibres in this network at short and been taken to show that IM-ECM must play strong roles in the long muscle lengths also involves some stretching out of the normal physiological functioning of each muscle. As reviewed wavy fibres, but at all sarcomere lengths a very large in the following two sections, some possible explanations of proportion of the collagen fibres are still wavy. The these roles are emerging but are far from complete. mechanical consequence of this is that the planar network will be very compliant in tension at all physiologically Structure and functional roles of the relevant muscle lengths, and can easily deform to follow endomysium changing muscle lengths in vivo. Although this behaviour potentially provides overload protection at high deforma- As reviewed by Purslow and Duance (1990), each muscle tions, such protection will only occur at muscle lengths well cell is surrounded by its own plasmalemma and basement above those experienced in normal function. These impli- membrane. Filling the intervening region between the cations are confirmed by detailed modelling of the in-plane basement membranes of two adjacent muscle cells is the tensile properties of the endomysium (Purslow and Trotter, much more substantial reticular layer, which is comprised 1994). Their models of the tensile properties of the endo- mysial network are in agreement with experimental force- length measurements by Podolsky (1964) and Magid and Law (1985) who compared the tensile properties of relaxed single muscle fibres with and without endomysium. The difference that the removal of the endomysium makes to

414 P.P. Purslow PREVENTION & REHABILITATION dFASCIA PHYSIOLOGY Fig. 3 Scanning electron micrographs of the collagen fibre bands internal to the muscle and occasionally have myo- scaffolding in IM-ECM structures in bovine sternomandibularis muscular junctions where two muscle fibres have interdig- muscle as revealed by NaOH-digestion of myofibrils, cytoskel- itating folded joints between them, the most common etal proteins, cell membranes, and proteoglycans. Upper termination is a gentle tapering down to an end. These panel; low-magnification view, showing thicker perimysial tapering fibres have no terminating structure that would sheets surrounding fascicles. Lower panel; high-magnification link them directly to another muscle fibre or to the tendon oblique view, showing endomysial networks. From Purslow and (Trotter, 1993). The fibres are staggered by about one Trotter (1994) with permission. quarter of their length with respect to the adjacent muscle the passive elasticity of single fibres is very small at phys- fibres, so that the tapering end of one fibre terminates with iologically relevant sarcomere lengths, showing that the the endomysial network surrounding it forming a seamless endomysium is extremely compliant in tension along the connection to the endomysium of its neighbours (Purslow muscle fibre direction over normal working muscle lengths and Trotter, 1994). The endomysium is the only structure in vivo. that links muscle fibres together within fascicles. In series- fibred muscles, transmission of tension generated in intra- Many muscles in species from many phyla contain muscle fascicularly terminating fibres to the ends of the fascicles fibres that do not run along the entire length of fascicles, absolutely necessitates transmission of force through the but terminate before reaching the myotendinous junction endomysial network, as this is the only structure continu- (Gans and Gaunt, 1991; Trotter, 1993; Trotter et al., 1995). ously linking the fibres (Trotter et al., 1995). Trotter and Muscle fibres in series-fibred muscles are relatively short Purslow (1992) show that the endomysium is compliant in compared to the length of the fascicle except in humans, tension, so that force transmission is unlikely by this means, which appear to have relatively longer fibres in their series- but they also suggest that force transmission is by shear fibred muscles. through its thickness. The key idea is that the endomysium, while very compliant to tensile forces acting within the Although some intrafascicularly terminating muscle plane of the network, is much more efficient in providing fibres do seem to have attachments to connective tissue a non-compliant linkage by shear through its thickness. A formal derivation from fibre composites theory shows that, for practical purposes, the stiffness of the endomysium in shear through its thickness varies only slightly with the orientation of the collagen fibrils in the plane of the endomysium (Purslow, 2002). Any linkage that transmits forces from intrafascicularly terminating muscle fibres to tendinous attachments must be non-compliant (i.e. high stiffness) in order to be efficient. Especially in isometric muscle contractions, any significant stretching in the length of the fascicle due to stretchy connections would result in a very poor transmission of contractile force. The series- elastic nature of this shear linkage can be represented as an apparent longitudinal stiffness Eapp (Purslow, 2002) given by  . 2 ð1Þ EappZG L T where G is the translaminar shear modulus of the endomy- sium, T is its thickness and L the muscle fibre length. Even if we take a fibre as short as 1 cm in length, L/T is in the order of 2000, so that Eapp is going to be in the order of 4 Â 106 greater than the true translaminar shear modulus of the endomy- sium. In a ‘‘composite’’ consisting of two parallel muscle cells with the endomysium sandwiched between them, the apparent longitudinal stiffness of endomysium as it deforms in shear will still be orders of magnitude higher than the tensile stiffness of the muscle fibres themselves. Due to this high value of Eapp the longitudinal stiffness of the entire assembly is going to be dominated by stretching in the muscle fibres themselves rather than in the linking endomysium. This shear linkage through the thickness of the endomysium provides a force transduction pathway from one muscle cell to its neighbours which is highly efficient. However, the endomysium can deform easily in the plane of the network, due to its low tensile stiffness, and so does not restrict changes in muscle fibre length and diameter as muscles contract and relax.

Muscle fascia and force transmission 415 PREVENTION & REHABILITATIONdFASCIA PHYSIOLOGY Lateral load sharing through the endomysium is an (Fang et al., 1999). The collagen fibres lie in the plane of the important concept that also explains how it is possible for perimysium, do not run through its thickness, and all the muscles to grow and to repair damaged sarcomeres. Lateral collagen fibres in each ‘‘ply’’ are parallel to each other and load sharing and coordination of deformations means that lie at Æ55 to the muscle fibre axis at the resting length of the a fibre can be interrupted for the addition of new sarco- muscle. This angle changes with muscle length, varying from meres necessary for muscle lengthening during growth, around 80 at an extremely short sarcomere length of 1.1 mm without loss of function of an entire contractile column. By to approximately 20 at a long sarcomere length of 3.9 mm the same mechanism, the contractile capacity of the (Purslow, 1989). Mathematical modelling of the tensile weakness of a sarcomere in which damaged myofibrils are properties in the plane of this network using fibrous being broken down and remodelled during muscle repair composites theory (Purslow, 1989), and direct measure- does not lead to tearing of the fibre at this point, as the ments of the tensile strength and stiffness of perimysial endomysial connections between adjacent fibres serve to sheets dissected from muscle (Lewis and Purslow, 1989; keep the strains uniform throughout the tissue. In sub- Purslow, 1999), show that the perimysium is easily deformed maximal contractions not all the motor units in the muscle in tension until the collagen fibres have become aligned along are recruited, so that many non-contracting fibres are the stretching direction and the waviness in the fibres pulled usually adjacent to contracting fibres. Coordination by out straight. This shows that the perimysium can build up shear linkages through the endomysium explains how a high tensile stiffness and carry large loads in tension, but sarcomere lengths in non-contacting fibres keep in register only at very large extensions well beyond the range of with those in adjacent, contracting fibres. This maintains working lengths in living muscle. uniform sarcomere lengths in the muscle. The continuous meshwork of endomysium that connects adjacent muscle The tensile properties of the perimysium are, therefore, fibres together, therefore, forms a connecting matrix that similar is nature to the endomysium. Both are initially coordinates force transmission between fibres in a fascicle easily deformed networks that can follow length and and keeps fibres in uniform register (Purslow, 2008). diameter changes imposed by the muscle fibres and fasci- cles contracting and being lengthened by the action of Functional anatomy of the perimysium antagonistic muscles. It is tempting to extend the analogy between endomysium and perimysium by proposing that Two sizes of fascicles and, therefore, two levels of peri- the perimysium could also act to transmit the forces mysial structure can be distinguished in cross-sections of generated in fascicles to their adjacent neighbours by muscle. Small (primary) fascicles or muscle fibre bundles translaminar shear. Although it can be shown that force are delineated by primary perimysium. Groups of primary transmission by such a mechanism can be invoked in fascicles are then organised into larger, secondary fascicles circumstances of extreme muscle damage or by cutting the by secondary perimysium, which tends to be thicker than tendinous attachments to some fascicles (Huijing, 2009), primary perimysium. In porcine semitendinosus muscle, the there are two considerations that we can raise that thicker secondary perimysium is in the order of 10 mm thick diminish the likelihood of this mechanism being involved in at birth and increases to approach 50 mm in 55 month old living muscle, at least under normal working conditions. pigs (Fang et al., 1999). The thickness of primary perimy- Firstly, considering again that the series-elastic nature of sium in cattle muscles ranges from 54.6 m to 133 mm (Brooks a shear linkage can be represented as an apparent longi- and Savell, 2004). tudinal stiffness Eapp and that Eapp given by Eq. (1) above then even if the perimysium can be up to 50 times thicker Both of these perimysial layers form a fenestrated than endomysium, the (L/T )2 term in this equation could network that extends across the entire cross-section of the be up to 2500 times smaller for the same length of peri- whole muscle. The perimysium does not form a distinct mysium than for the endomysium. If the translaminar shear sheath that surrounds one fascicle, but rather is a shared modulus of the perimysium and endomysium would even be structure lying between two fascicles (Purslow and Trotter, within an order of magnitude of each other, this means that 1994). Nodes form at the junction between perimysial sheets thicker perimysium would have a far smaller Eapp, i.e., it and the fascicles occupy polygonal ‘‘holes’’ in this network, would be far more compliant in shear than the endomy- in a manner similar to muscle fibres occupying polygonal sium. This would represent a rather sloppy and inefficient ‘‘holes’’ in the endomysial network (but at a larger scale). At force transmission pathway. the surface of the muscle the perimysium merges and seamlessly joins with the epimysium (Nishimura et al., 1994). The second consideration revolves around the observa- tion that the amounts and structure of endomysium are The perimysial layer separating two fascicles is primarily relatively constant and only slightly vary between different comprised of crossed-plies of wavy collagen fibres in muscles, whereas the amounts of perimysium, its thickness, a proteoglycan matrix. In a few muscles (e.g. bovine sem- and the size and shape of primary and secondary muscle itendinosus) there are substantial amounts of elastin fibres fascicles vary tremendously. The endomysial structures associated with the collagenous network (Rowe, 1981). The providing tight shear linkages between adjacent muscle collagen fibre bundles are far larger in diameter than the fine fibres are reasonably conservative and do not vary so much fibres and fibrils in the endomysium and have a regular from muscle to muscle. So, if the perimysial network sinusoidal waviness, with all collagen fibre bundles lying functions similarly, why should its amounts and spatial parallel to each other in each ply, and having the same wave arrangement vary so much more? periodicity. In porcine semitendinosus muscle the degree of waviness has been observed to increase with animal age Schmalbruch (1985) cites a model originally proposed by Feneis which proposes that the perimysium provides ‘neutral’ connections between adjacent fascicles. These

PREVENTION & REHABILITATION dFASCIA PHYSIOLOGY 416 P.P. Purslow connections permit fascicles to slide past each other, and et al., 2009). Beta-adrenergic agonists (e.g. clenbuterol, rac- also facilitate shape changes in the muscle during contrac- topamine, cimaterol, salbutamol) mimic this effect and tion. All fan-shaped, fusiform, and especially pennate chronic administration of these growth promoters leads to muscles change shape when contracting, and in order to muscle hypertrophy or amelioration of muscle wasting accommodate this there must be slippage, or sliding, of some (Navegantes et al., 2002). Although some reports associate the elements within the muscle (i.e. shear deformations). For effect of catecholamines on protein metabolism with c-AMP pennate muscles it is easy to formally calculate the shear dependent kinase, Yamaguchi et al. (1997) showed that the strains within the muscles as they contract and the pennation p38 MAPK pathway can be activated by beta-adrenergic angles change. In ultrasonic images of human muscles, receptors in kidney cells. Expression of MMPs 1 and 13 is acti- ‘‘boundaries’’ between fascicles can be seen, and vated by the p38 MAPK pathway in keratinocytes (Johansson measurement of changes in the angle of these during et al., 2000). Recent work in our laboratory (Cha and Purslow, contraction allows shear strains to be predicted. Shear unpublished data) shows that both skeletal muscle fibroblasts strains within working human muscles are substantial and and myoblasts increase MMP expression in the presence of vary considerably between human muscles such as quadri- epinephrine, but with different time-courses and degrees of ceps, vastus lateralis and gastrocnemius (Purslow, 2002). If correlation with expression of AMP-activated protein kinase. the endomysium maintains adjacent muscle fibres in tight shear register, then where can these large and variable shear Cardiac muscle is obviously different from striated muscle strains be accommodated? Simple observations on rigor functionally and structurally, yet there are striking similari- muscle that is manipulated to produce internal shear show ties about the organisation and function of ECM structures that deformations preferentially occur at the boundaries between the two muscle types (Purslow, 2008). A change in between fascicles, and that very little shear displacements the balance between synthesis and degradation of ECM in the occur within a fascicle (Purslow, 1999). If the theory that the myocardium is a characteristic of many types of heart division of muscle into fascicles is to facilitate shear defor- failure, including hypertensive heart failure and infarction/ mations that are necessary for contracting muscle to change ischemia (Berk et al., 2007; Graham et al., 2008). Banfi et al. shape is correct, then it seems to offer an explanation of why (2005) reported increased plasma levels of MMPs 2&9 in the amount and distribution of perimysium changes so very patients with chronic heart failure and also a significant markedly from muscle to muscle. Thin perimysia surrounding correlation between norepinephrine and MMP2 levels. small fascicles in long strap-like muscles may be associated Cardiac fibroblasts are known to react to both mechanical with relatively small shear displacements, whereas thicker stimuli and catecholamines in terms of both proliferation and perimysial sheets and larger primary fascicles may relate to expression (Villareal and Kim, 1997), and cardiomyocytes larger shear displacements. However, comprehensive data from chick embryos are known to react to stimulation of the on the relationship between perimysial thickness, fascicle alpha-adrenergic receptor via noradrenaline by activation of size, and the actual distributions of shear strains in working p38 MAPK (Tsang and Rabkin, 2009). Ongoing studies to muscles need to be collected to test this theory. provide fundamental information about the control of expression of IM-ECM forming cells may have far-reaching Control of turnover of IM-ECM as a possible impact on muscle ageing, injury, and repair. treatment in muscle injury and repair of fibrosis References Muscle growth, turnover, and repair necessitate remodelling Avery, N.C., Bailey, A.J., 2008. Restraining cross-links responsible of IM-ECM, principally under the control of matrix metal- for the mechanical properties of collagen fibers; natural and loproteinases (MMPs) and tissue inhibitors of MMPs (TIMPs). artificial. In: Fratzl, P. (Ed.), Collagen: Structure and MMPs are expressed by muscle cells as well as by fibroblasts in Mechanics. Springer, NY, pp. 81e110 (Chapter 4). the IM-ECM (Balcerzak et al., 2001). Adaptation of muscle, including muscle hypertrophy following exercise training is Bailey, A.J., Paul, R.G., Knott, L., 1998. Mechanisms of maturation known to involve increased expression of a range of MMPs and ageing of collagen. Mechanisms of Ageing and Development (Kjaer, 2004). Expression of MMPs is stimulated by mechanical 106, 1e56. forces, hormones, and growth factors as well as nutritional components. Myoblasts express almost as much MMP and total Balcerzak, D., Querengesser, L., Dixon, W.T., Baracos, V.E., 2001. collagenase activity as fibroblasts in cell culture and tend to Coordinate expression of matrix-degrading proteinases and increase this expression more strongly than fibroblasts when their activators and inhibitors in bovine skeletal muscle. Journal mechanically stimulated by biaxial stretching (Cha and Pur- of Animal Science 79, 94e107. slow, unpublished data). Numerically, muscle cells vastly outnumber fibroblasts within normal muscle tissue. Epineph- Banfi, C., Cavalca, V., Veglia, F., Brioschi, M., Barcella, S., rine (adrenaline) is a general agonist of all types of adrenergic Mussoni, L., Boccotti, L., Tremoli, E., Biglioli, P., Agostoni, P., receptors, and in muscle principally acts to increase glycolysis 2005. Neurohormonal activation is associated with increased via a signalling pathway involving AMP-activated protein levels of plasma matrix metal loproteinase-2 in human heart kinase (Shen and Du, 2005). There is also adrenergic control of failure. European Heart Journal 26, 481e488. protein metabolism in skeletal muscle. Epinephrine acts to increase calpastatin levels, so reducing protein turnover by Bendall, J.R., 1967. The elastin content of various muscles of beef calpains and resulting in net muscle accretion (Navegantes animals. Journal of the. Science of Food & Agriculture 18, 553e558. Berk, B.C., Fujiwara, K., Lehoux, S., 2007. ECM remodelling in hypertensive heart disease. Journal of Clinical Investigation 117, 568e575. Brooks, J.C., Savell, J.W., 2004. Perimysium thickness as an indi- cator of beef tenderness. Meat Science 67, 329e334. Bruns, R.R., Gross, J., 1973. High-resolution analysis of the modi- fied quarter-stagger model of the collagen fibril. Biopolymers 13, 931e994.

Muscle fascia and force transmission 417 PREVENTION & REHABILITATIONdFASCIA PHYSIOLOGY Chiquet, M., Gelman, L., Lutz, R., Maier, S., 2009. From mecha- cell-maceration scanning electron-microscope method. notransduction to extracellular matrix gene expression in Archives Of Histology and Cytology 51, 249e261. fibroblasts. Biochimica Biophysica Acta 1793, 911e920. Paul, R.G., Bailey, A.J., 1996. Glycation of collagen: the basis of its central role in the late complications of ageing and diabetes. Fang, S.H., Nishimura, T., Takahashi, K., 1999. Relationship International Journal of Biochemistry and Cell Biology 28, between development of intramusclular connective tissue and 1297e1310. toughness of pork during growth of pigs. Journal of Animal Podolsky, R.J., 1964. The maximum sarcomere length for contraction Science 77, 120e130. of isolated myofibrils. Journal of Physiology 170, 110e123. Purslow, P.P., 1989. Strain-induced reorientation of an intramus- Gans, C., Gaunt, A.S., 1991. Muscle architecture in relation to cular connective tissue network: implications for passive function. Journal of Biomechanics 24, 53e65. muscle elasticity. Journal of Biomechanics 22, 21e23. Purslow P.P., 1999. The intramuscular connective tissue matrix and Graham, H.K., Horn, M., Trafford, A.W., 2008. Extracellular matrix cell-matrix interactions in relation to meat toughness. profiles in the progression to heart failure. Acta Physiologica Proceedings of the 45th Interantional Congress of Meat Science 194, 3e23. and Technology, Yokohama, Japan, pp. 210e219. Purslow, P.P., 2002. The structure and functional significance of Huijing, P.A., 2009. Epimuscular myofascial force transmission: variations in the connective tissue within muscle. Comparative a historical review and implications for new research. Interna- Biochemistry and Physiology. A Molecular And Integrative tional society of biomechanics Muybridge award lecture, Taipei, Physiology 133, 947e966. 2007. Journal of Biomechanics 42, 9e21. Purslow, P.P., 2005. Intramuscular connective tissue and its role in meat quality. Meat Science 70, 435e447. Johansson, N., Alaho, R., Uitto, V.J., Gre´nman, R., Purslow, P.P., 2008. The extracellular matrix of skeletal and Fusenig, N.E., Lo´pez-Otin, C., Ka¨ha¨ri, V.M., 2000. Expression cardiac muscle. In: Fratzl, P. (Ed.), Collagen: Structure and of collagenase-3 (MMP-13) and collagenase-1 (MMP-1) by Mechanics. Springer, NY, pp. 325e358 (Chapter 12). transformed keratinocytes is dependent on the activity of p38 Purslow, P.P., Duance, V.C., 1990. The structure and function of mitogen-activated protein kinase. Journal of Cell Science 113, intramuscular connective tissue. In: Hukins, D.W.L. (Ed.), 227e235. Connective Tissue Matrix, vol. 2. MacMillan, pp. 127e166. Purslow, P.P., Trotter, J.A., 1994. The morphology and mechanical Kjaer, M., 2004. Role of extracellular matrix in adaptation of properties of endomysium in series-fibred muscles; variations tendon and skeletal muscle to mechanical loading. Physiological with muscle length. Journal of Muscle Research and Cell Motility Reviews 84, 649e698. 15, 299e304. Rowe, R.W.D., 1981. Morphology of perimysial and endomysial Kjær, M., Magnusson, S.P., 2008. Mechanical adaptation and tissue connective tissue in skeletal muscle. Tissue and Cell 13, 681e690. remodeling. In: Fratzl, P. (Ed.), Collagen: Structure and Schmalbruch, H., 1985. Skeletal Muscle. Springer, Berlin. Mechanics. Springer, NY, pp. 249e267 (Chapter 9). Scott, J.E., 1990. Proteoglycan: collagen interactions and subfibrillar structure in collagen fibrils. Implications in the development and Lawson, M.A., Purslow, P.P., 2001. Development of components of ageing of connective tissues. Journal of Anatomy 169, 23e35. the extracellular matrix, basal lamina and sarcomere in chick Shen, Q.W., Du, M., 2005. Role of AMP-activated protein kinase in quadriceps and pectoralis muscles. British Poultry Science 42, the glycolysis of postmortem muscle. Journal of the Science of 315e320. Food and Agriculture 85, 2401e2406. Swatland, H.J., 1975. Morphology and development of connective Lewis, G.J., Purslow, P.P., 1989. The strength and stiffness of tissue in porcine and bovine muscle. Journal of Animal Science perimysial connective-tissue isolated from cooked beef muscle. 41, 78e86. Meat Science 26, 255e269. Trotter, J.A., 1993. Functional morphology of force transmission in skeletal muscle. Acta Anatomica 146, 205e222. Listrat, A., Picard, B., Geay, Y., 1999. Age-related changes and Trotter, J.A., Purslow, P.P., 1992. Functional morphology of the location of type I, III, IV, V and VI collagens during development endomysium in series fibered muscles. Journal of Morphology of four foetal skeletal muscles of double muscles and normal 212, 109e122. bovine muscles. Tissue and Cell 31, 17e27. Trotter, J.A., Richmond, F.J.R., Purslow, P.P., 1995. Functional morphology and motor control of series fibred muscles. In: Listrat, A., Lethias, C., Hocquette, J.F., Renand, G., Menissier, F., Holloszy, J.O. (Ed.), Exercise and Sports Sciences Reviews, vol. Geay, Y., Picard, B., 2000. Age related changes and location of 23. Williams and Watkins, Baltimore, pp. 167e213. types I, III, XII and XIV collagen during development of skeletal Tsang, M.Y.C., Rabkin, E.W., 2009. p38 Mitogen-activated protein muscles from genetically different animals. Histochemical kinase (MAPK) is activated by noradrenaline and serves a car- Journal 32, 349e356. dioprotective role, whereas adrenaline induces p38 MAPK dephosphorylation. Clinical and Experimental Pharmacology Liu, A., Nishimura, T., Takahashi, K., 1995. Structural weakening of and Physiology 36, e12ee19. intramuscular connective tissue during post-mortem ageing of Velleman, S.G., Liu, X.S., Eggen, K.H., Nestor, K.E., 1999. Devel- chicken semitendinosus muscle. Meat Science 39, 135e142. opmental downregulation of proteoglycan synthesis and decorin expression during turkey embryonic skeletal muscle formation. Magid, A., Law, D.J., 1985. Myofibrils bear most of the resting Poultry Science 78, 1619e1626. tension in frog skeletal muscle. Science 230, 1280e1282. Villareal, F.J., Kim, N.N., 1997. Regulation of myocardial extra- cellular matrix components by mechanical and chemical growth Navegantes, L.C.C., Migliorini, R.H., Kettelhut, I.C., 2002. Adren- factors. Cardiovascular Pathology 7, 145e151. ergic control of protein metabolism in skeletal muscle. Current Yamaguchi, J., Nagao, M., Kasziro, Y., Itoh, H., 1997. Activation of Opinion in Clinical Nutrition and Metabolic Care 5, 281e286. p38 mitogen-activated protein kinase by signalling through G protein-coupled receptors. Journal of Biological Chemistry 272, Navegantes, L.C.C., Baviera, A.M., Kettelhut, I.C., 2009. The 27771e27777. inhibitory role of sympathetic nervous system in the Ca2þ- dependent proteolysis of skeletal muscle. Brazilian Journal of Medical and Biological Research 42, 21e28. Nishimura, T., Hattori, A., Takahashi, K., 1994. Ultrastructure of the intramuscular connective tissue in bovine skeletal muscle. Acta Anatomica 151, 250e257. Nishimura, T., Hattori, A., Takahashi, K., 1995. Structural weak- ening of intramuscular connective tissue during post mortem ageing of beef. Journal of Animal Science 76, 528e532. Nishimura, T., Ojima, K., Hattori, A., Takahashi, K., 1997. Devel- opmental expression of extracellular matrix components in intramuscular connective tissue of bovine semitendinosus muscle. Histochemistry and Cell Biology 107, 215e221. Ohtani, O., Ushiki, T., Taguchi, T., Kikuta, A., 1988. Collagen fibrillar networks as skeletal frameworks e a demonstration by

Journal of Bodywork & Movement Therapies (2010) 14, 418e423 available at www.sciencedirect.com PREVENTION & REHABILITATIONdSPINAL PHYSIOLOGY journal homepage: www.elsevier.com/jbmt SPINAL PHYSIOLOGY Compensatory behavior of the postural control system to flexionerelaxation phenomena Fahime Hashemirad a,b,c,*, Saeed Talebian a, Gholam R. Olyaei a, Boshra Hatef c a Physical Therapy Department, Rehabilitation Faculty, Tehran University of Medical Sciences and Health Services, Tehran, Iran b Akhavan Spine Physical Therapy Center, University of Social Welfare and Rehabilitation Sciences, Tehran, Iran c Sports Medicine Research Center, Tehran University, Tehran, Iran Received 4 September 2009; received in revised form 16 February 2010; accepted 15 April 2010 KEYWORDS Summary Laxity of the passive tissues of the spine during prolonged spinal flexion has been Creep; shown to disturb spinal stability. This study investigated the effects of short periods of static Erector spinae muscles; lumbar flexion and short rest periods on the flexionerelaxation angle for the erector spinae Flexionerelaxation; muscles in 36 healthy female college students. The surface electromyographic activity of Lumbar spine the erector spinae muscles was measured in three states before the onset of creep, immedi- ately after 7 min of static lumbar flexion, and after a 10 min rest. The results showed that 7 min of static lumbar flexion will produce relaxation of the erector spinae muscles that occurs at greater absolute lumbar and trunk angles, during the forward bending activity (P < 0.05), while the corresponding relative angles did not change before and after creep. The results also indicate that postural compensations are dominant over the muscular compensations for load sharing in flexionerelaxation phenomena of asymptomatic healthy participants. This further highlights the importance of postural modulation in the control of movement and preservation of skeletal stability. Clinical relevance: Considering spinal posture in the upright condition, and its changes by phenomena such as creep, can reduce postural injuries by instructing subjects to approach a more vertical posture, after periods of bending, to compensate the stretching effects of the tissues and thus regaining the normal muscular activity pattern. ª 2010 Elsevier Ltd. All rights reserved. * Corresponding author. Akhavan Spine Physical Therapy Center, University of Social Welfare and Rehabilitation Sciences, Shahid Jaafar Asadi Manesh Alley, After Monirie Square, Valie Asr Avenue, Tehran, Iran. Tel.: þ98 21 66467000. E-mail address: [email protected] (F. Hashemirad). 1360-8592/$ - see front matter ª 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbmt.2010.04.008

Compensatory behavior of the postural control system 419 PREVENTION & REHABILITATIONdSPINAL PHYSIOLOGY Introduction university of Medical Science and Health Services to participate. All participants were free from chronic and Creep deformation in the various passive tissues of the spine current back problems and after being introduced to the including ligaments, intervertebral discs, and joint capsule is nature of the study, signed consent forms that they were thought to increase the laxity of the intervertebral joints, willing to take part. Previous studies have shown the creep- allowing increased relative motion, which destabilizes their related changes to be different in males and females natural alignment, with the potential for consequent injury (Solomonow et al., 2003a). Thus to neutralize the effect of and associated pain (Jackson et al., 2001; Solomonow et al., gender and its consequent confounding factors, and also 1999; Wiliams et al., 2000). High incidence of low back pain since they were more accessible, only females were (LBP) disorders is associated with occupations requiring studied. sustained and repetitive lumbar flexion (Little and Khalsa, 2005). As the trunk is flexed from a standing position The mean (standard deviation) age, height and weight of toward full lumbar flexion, lumbar extensor muscles exhibit the thirty-six participants were 22.3(3.4) years, 1.6(0.1) m myoelectric silence and this phenomenon is called flex- and 56.7(6.3) kg, respectively. ionerelaxation (FRP) (Floyd and Silver, 1955; Kippers and Parker, 1984; Olson et al., 2004). In the fully flexed Instrumentation posture, the body weight is supported mainly by a passively generated extension moment from spinal ligaments, inter- Surface EMG data were collected using a 4-channel elec- vertebral discs and the passive components of the extensor tromyography device (Medelec, Promiere model). The EMG muscle-tendon units (McGill and Kippers, 1994). If the flexed signals were detected by pregelled AgeAgCl electrode pairs posture is maintained, the passive tissues will deform at applied at the L3-4 level over the left erector spinae a slow rate due to their viscoelastic material properties, and musculature (about 4 cm lateral from midline). Center to this creep deformation of the spinal tissues provides more center electrode distance was 2.5 cm; electrodes were laxity in the passive tissues and reduced resistance to longitudinally oriented along the fibers of the erector spi- forward flexion moment (Shin and Mirka, 2007). The change nae muscles. A reference electrode was taped on the left in the passive tissue stiffness is expected to affect the acti- wrist. To identify the L3 level we first found the sacrum and vation level of back extensor muscles because flexion followed the spinous processes of the lumbar vertebrae up moment generated by upper body weight is supported by co- to L3. L3 is located at the center of the lumbar curvature contribution of both active and passive components. and due to its long transverse processes, provides mechanical advantage for the muscles so the investigation The creep response and recovery behavior of erector of muscular activity at this level is preferred (Bogduk, 1997) spinae is an interesting model to study the modulation of and it is more comparable to other research reports lumbar stability. Solomonow et al. (2003a) showed creep, (Solomonow et al., 2003a). developed during a short static lumbar flexion, elicited significant changes in the muscular activity pattern of the The EMG signals were amplified by 1000 with a frequency flexionerelaxation phenomenon. The effects of creep on band pass of 20e500 Hz, Gain 100 mV/Div., 80 dB signals to the upright posture and considering this in EMG activity of noise ratio and CMRR of 90 dB. Maximum acceptable skin erector spinae have not yet been fully identified. Under- impedance level was set at 5 kU. Sampling rate of recording standing how the trunk and lumbar angles are affected by was 1000 Hz and the data were digitized and stored by a 12-bit the creep phenomenon and how the erector spinae muscles A/D board. activation pattern is influenced by these changes, can be helpful in the assessment of the creep phenomenon and Angular variables were estimated by a digital camera choosing a preventive strategy for low back pain. (JVC-GZ-MG50AS) placed 1 m away from the subject at waist level with a direct view of the subject’s right side in The aims of this study were to investigate how a short the sagittal plane. The camera collected kinematics data at static posture of 7 min affects the absolute and relative the rate of 25 frames per second. The markers used to angles of flexionerelaxation response and how a short rest measure the segment angles were attached to the subjects period of 10 min would moderate those effects. Since as follows: three circular markers were attached to the considering the starting posture while measuring range of right greater trochanter, lateral midline along the iliac motion is of great importance (Vachalathiti et al., 1995), it crest and the lower palpable edge of the rib cage was presumed that using the two measures of “absolute” (Solomonow et al., 2003a). Video and EMG data were and “relative” angles would lead to different results, synchronized by an electrical circuit which triggered them therefore in this study, we have chosen the latter to get at the same time. a better estimate of the effect of creep phenomenon on spinal motion characteristics, while keeping the absolute Protocol value for comparative purposes. The skin was cleaned with alcohol preparation pads before Methods attachment of the EMG electrodes. The electrodes and skin markers were placed as described above, and the signal Subjects was checked prior to test trials to make sure of proper marker detection and lack of EMG signal noises. The Thirty-six healthy female students without a history of back subjects stood just behind a horizontally drawn line on the pain during the last 2 years were recruited from Tehran ground barefoot with their feet pelvis-width apart, their wrists hooked together in the front of their body, and their

PREVENTION & REHABILITATIONdSPINAL PHYSIOLOGY 420 F. Hashemirad et al. knees kept straight and bent forward from the waist level Figure 2 Typical recording of EMG activity during the flex- as far as possible. After introducing the task to the subjects ioneextension task. Raw EMG and the linear envelope data and making sure of the accuracy of the maneuver, subjects were used to estimate EMG-Off and EMG-On points. The performed two trials separated by 30e50 s between them. extension phase used for normalization of the EMG linear Each trial consisted of an approximately 3 s of quiet envelope is also provided. standing followed by 3e5 s full forward flexion. The deep flexion was held for 4 s followed by 3e5 s extension to was defined as the angle between the vertical line crossing upright posture, and then static standing through the end of the ilium marker and the line connecting the greater recording. Finally one of the trials was chosen depending on trochanter and ilium markers while the angle of lumbar signal quality for data analysis (Hashemirad et al., 2009). flexion was defined as the difference between the two previous ones (trunk angle À hip angle) (Solomonow et al., After recording EMG and kinematics data, the subjects sat 2003a) (Figure 3). The angle measurements were done as on the floor with their trunk in full lumbar flexion. A hemi- absolute and relative. The relative angles were calculated cylindrical foam bolster was placed under the thighs to tilt the with respect to the corresponding angles in the erect pelvis posteriorly, and reduce hamstring stretch (Solomonow posture. et al., 2003a) (Figure 1). The subjects stayed in this static flexion position for 7 consecutive minutes, immediately after The dependent variables included absolute and relative which they stood up and performed another set of flex- angles of the trunk and lumbar in full flexion, EMG-On and ioneextension tasks similar to the one performed prior to the EMG-Off, in three conditions of before, immediately after static flexion period. Following that the subjects sat on a chair and 10 min after the creep. to recover for 10 min and then the trial, and recordings of EMG and kinematics were all repeated. Data analysis The recorded EMG signals were full-wave rectified and smoothed with the time constant of 50 ms to yield linear envelops. The EMG values were normalized using the peak EMG magnitude during the task. A threshold level of 5% of this magnitude was used to determine the onset and the end of the flexionerelaxation period. The onset of the flexionerelaxation phenomenon (EMG-Off) was defined as the point at which the magnitude of EMG signal got less than the threshold level and the end point of the phenomenon (EMG-On) during the extension phase was defined as the point at which EMG signals amplitude exceeded the threshold level (Olson et al., 2004) (Figure 2). The video data were analyzed using Ulead video studio software (version 7) to match the frame of the video with the corresponding EMG signals (frames of EMG-Off and EMG- On). Measurement of the angles of interest in each specific frame was done with Auto CAD software (2006). The trunk, hip and lumbar angles were measured by lateral markers. Trunk angle was defined as the angle between the vertical line crossing the ilium marker and the line connecting the rib and ilium markers. The hip angle Figure 1 Schematic representation of a subject during the Figure 3 Schematic representation of a subject performing 7 min of static lumbar flexion. the forward bending task and the measured angles where a, b and g are the trunk, hip and lumbar angles, respectively.

Compensatory behavior of the postural control system 421 Table 1 The effect of creep phenomenon on absolute angles at full flexion, EMG-Off and EMG-On in 21 subjects who exhibited FR before and after creep. Parameters Before creep After creep After 10 min rest P value Conditions I,III Conditions I,III (absolute (condition I) (condition II) (condition III) Conditions I,II angles) X(SD) X(SD) X(SD) Trunk angle 103.3(17.1) 106.4(17.7) 106.1(17.7) <0.001 0.008 0.738 PREVENTION & REHABILITATIONdSPINAL PHYSIOLOGY Full flexion 102.7(16.8) 106.1(17.9) 105.5(18.1) <0.001 0.009 0.577 EMG-off 0.328 0.316 EMG-on 83.9(14.8) 84.7(20.4) 87.1(22.2) 0.752 Lumbar angle 48.6(9.0) 50.5(9.4) 50.1(9.7) 0.009 0.011 0.534 Full flexion 48.6(8.9) 50.4(9.4) 50.03(9.9) 0.015 0.010 0.547 EMG-off 45.6(8.7) 46.2(10.1) 0.528 0.187 0.449 EMG-on 46.8(9.8) Statistical analysis Table 3 shows the results related to the relative angles in three conditions of before, immediately and 10 min after the Analysis of variance with repeated measures design (before creep. To calculate the relative angles, the absolute trunk and vs. after 7 min of deep flexion and 10 min of rest) was used to lumbar angles at the EMG-Off and EMG-On points were evaluate the effect of static flexion on EMG activity pattern compared to the corresponding values in the erect posture of erector spinae muscles. The alpha level was set at 0.05. which yielded no significant difference between the relative angles before and after the creep. In other words according to Results the relative angles, the erector spinae muscles were relaxed at the same angles in the before and after creep conditions. Thirty of the 36 subjects (or 83%) exhibited FRP in their erector spinae muscles before creep. Nine out of 30 subjects According to Tables 1 and 3, there was no significant did not show FRP after the creep. The data from 21 of these difference in EMG-On angles for both absolute and relative subjects who also showed FRP after static lumbar flexion measures. In other words, 7 min of static lumbar flexion had were subjected to statistical analysis. Since the focus of this no significant effect on re-activation of the erector spinae study was on investigating the effect of creep on the flex- muscles in the extension phase. ionerelaxation phenomenon, the data from 15 subjects who did not exhibit this phenomenon were not analyzed here. Discussion Table 1 demonstrates the test results of the absolute Differences seen in the responses of FRP in angle trunk and lumbar angles in full flexion, EMG-On and EMG- measurements as absolute and relative, showed that the Off in three conditions of before, immediately after and changes in the trunk and lumbar angles in the erect posture 10 min after the creep. 7 min of static lumbar flexion offset the creep-related increase in absolute angles of EMG- increased trunk and lumbar angles for 3.4 (from 102.7 to Off so that relative angles did not show significant differ- 106.1) and 1.8 (from 48.6 to 50.4) at the EMG-Off point ence before and after the creep. (P < 0.05). There was no difference between immediately after creep and after the 10 min rest period. After the Solomonow et al. (2003a) in a similar study found the creep, the erector spinae muscles remained active in larger changes in trunk and lumbar angles of the 25 female degrees of flexion and the creep response was not fully participants to be 7.3 and 2.7, respectively at the EMG-off recovered after 10 min of rest. point. Our results follow the same trend with the absolute values of the corresponding angles to be 3.4 and 1.8, Table 2 indicates of the trunk and lumbar angles in the respectively, while in both studies these changes were erect posture in three conditions of before, immediately statistically significant. In contrast, the angular changes at and 10 min after the creep. 7 min of static lumbar flexion the point of EMG-on in our study were not statistically led to 2.6 (from 13.5 to 10.9) and 1.7 (from 4.7 to 3.0) meaningful while Solomonow found them significant in his decrease in the trunk and lumbar angles, respectively study. Based on the results of this study, it seems that EMG- (P < 0.05) and following this period of rest, the approxi- Off angles were more sensitive than EMG-On angles because mation of the angles to the reference vertical did not fully the shorter time of static lumbar flexion only provokes recover. changes in the absolute angles at which the EMG turns off. Table 2 The effect of creep phenomenon on angles at erect posture in 21 subjects who exhibited FR before and after creep. Parameters Before creep After creep After 10 min rest P value Conditions I,III Conditions I,III in erect (condition I) X(SD) (condition II) (condition III) Conditions I,II position X(SD) X(SD) Trunk angle 13.5(7.3) 10.9(7.8) 11.3(6.8) <0.001 0.002 0.714 Lumbar angle 4.7(6.6) 3.0(7.7) 2.1(7.2) 0.001 0.001 0.235

422 F. Hashemirad et al. Table 3 The effect of creep phenomenon on relative angles at full flexion, EMG-Off and EMG-On in 21 subjects who exhibited FR before and after creep. Parameters Before creep After creep After 10 min rest P value Conditions I,III Conditions I,III (Relative angles) (condition I) (condition II) (condition III) Conditions I,II X(SD) X(SD) X(SD) PREVENTION & REHABILITATIONdSPINAL PHYSIOLOGY Trunk angle 116.9(17.1) 117.4(18.7) 117.4(16.7) 0.519 0.680 0.992 Full flexion 116.3(16.9) 117.0(18.9) 116.8(17.1) 0.389 0.733 0.878 EMG-off 0.520 0.768 0.163 EMG-on 97.5(12.9) 95.7(20.7) 98.4(21.1) Lumbar angle 53.4(8.2) 53.5(8.8) 52.2(8.2) 0.867 0.109 0.241 Full flexion 53.4(8.4) 53.4(8.7) 52.1(8.3) 0.962 0.088 0.240 EMG-off 50.4(7.4) 49.2(9.2) 48.9(7.9) 0.277 0.143 0.852 EMG-on It seems that static lumbar flexion for durations for as long influencing spinal stability and injury tolerance which can also as 7 min, will impose alterations in the spinal system which, if show the acuity of the spinal performance as lack of this not compensated by the spinal stabilizing system (such as phenomenon has been associated with LBP. In this study, the changing the erect standing posture as the starting and refer- effect of a short period static flexion posture (being critically ence position) might challenge the stability of the system. important from an ergonomic point of view) has been inves- tigated on the FRP and erector spinae muscles activation Panjabi has divided the spinal stabilizing system into pattern. The results included three major interesting findings: active, passive and neural sub-systems. In the normal state, the three sub-systems work together to provide the needed 1) As per previous studies, ES muscles remained active for mechanical stability (Panjabi, 1992). Since the FRP is the longer periods but, when considering the alterations of the product of interplay between active and passive elements upright standing posture at the starting position, it was of the spine, the unchanged behavior of the phenomenon revealed that short periods of static flexion do not alter the indicates that the alterations in the erect starting position range of motion during which ES muscles are active. of the spine provides enough passive tension in the poste- rior elements for the FRP to occur, and the erector spinae 2) 10 min of rest is not sufficient to offset the biome- muscles to relax at the same relative angles. chanical consequences of 7 min of static flexion posture. It seems that a longer period of rest is needed Considering the effects of static lumbar flexion on erect to offset the effects of creep. posture, an important suggestion can be constructed from the findings of this study: when the lower back is exposed to 3) It seems that not only LBP patients fail to exhibit FRP but static loading due to activities such as manual material there are also subjects without low back problems, in handling, the process of muscle recovery can be substan- which FRP is absent. A follow-up study might show if lack tially improved by modulating the starting erect posture to of FRP is a predictive factor for the incidence of LBP or not. decrease the developed laxity in the passive tissues. Conflict of interest statement The findings of this study confirm the results of previous ones, showing that creep and increased muscular activity that There is no conflict of interest regarding the publication of were developed during the 7 min of flexion, were not fully this paper. recovered by the 10 min rest period (Shin and Mirka, 2007; Solomonow et al., 2003b; Solomonow, 2004). Following Acknowledgements these results, it emerges that the rest duration of 10 min is not capable of allowing full recovery, even if a static lumbar The authors gratefully thank Dr. Mohamad Parnianpour for flexion of less than 10 min is applied to the lumbar spine. his valuable comments on the manuscript and Amir H. Kahlaee for reviewing the manuscript. We also appreciate As elicited in the results of this study, six of the 36 the financial support of rehabilitation faculty of Tehran subjects (or 17%) before creep and nine of the 30 subjects University of Medical Sciences and Health Services which (or 30%) after creep despite being asymptomatic did not made this project possible. exhibit FRP. This heterogeneity in the healthy population might shed light on the predisposing factors and develop- References ment mechanisms of LBP which seems worth studying in prospective studies. Further study on the neurophysiologic Bogduk, N., 1997. Clinical Anatomy of the Lumbar Spine and Sacrum, aspects and reflex mechanisms associated with the creep third ed. Churchill Livingstone, New York, p. 228(Appendix). phenomenon will add to the findings of this study. Floyd, W.F., Silver, P.H.S., 1955. The function of the erectores Summary spinae muscles in certain movements and postures in man. Journal of Physiology (London) 129, 184e203. Trunk and lumbar angles have achieved considerable atten- tion in the assessment of body posture and spinal biome- chanics. FRP has also been introduced as an effective factor

Compensatory behavior of the postural control system 423 PREVENTION & REHABILITATIONdSPINAL PHYSIOLOGY Hashemirad, F., Talebian, S., Hatef, B., Kahlaee, A.H., 2009. The Solomonow, M., 2004. Ligaments: a source of work-related relationship between flexibility and EMG activity pattern of the musculoskeletal disorders. Journal of Electromyography and erector spinae muscles during trunk flexioneextension. Journal Kinesiology 14, 49e60. of Electromyography and Kinesiology 19, 746e753. Solomonow, M., Baratta, R.V., Banks, A., Freudenberger, C., Jackson, M., Solomonow, M., Zhou, B., Baratta, R., Harris, M., Zhou, B.H., 2003a. Flexionerelaxation response to static 2001. Multifidus EMG and tensionerelaxation recovery after lumbar flexion in males and females. Clinical Biomechanics 18, prolonged static lumbar flexion. Spine 26, 715e723. 273e279. Kippers, Y., Parker, A.W., 1984. Posture related to myoelectric Solomonow, M., Baratta, R.V., Zhou, B.H., Burger, E., Zieske, A., silence of erectors spinae during trunk flexion. Spine 9, 740e745. Gedalia, A., 2003b. Muscular dysfunction elicited by creep of lumbar viscoelastic tissue. Journal of Electromyography and Little, J.S., Khalsa, P.S., 2005. Human lumbar spine creep during cyclic Kinesiology 13, 381e396. and static flexion: creep rate, biomechanics, and facet joint capsule strain. Annals of Biomedical Engineering 33 (3), 391e401. Solomonow, M., Zhou, B.H., Baratta, R.V., et al., 1999. Biome- chanics of increased exposure to lumbar injury caused by cyclic McGill, S.M., Kippers, V., 1994. Transfer of loads between lumbar tissues loading: part 1. Loss of reflexive muscular stabilization. Spine during the flexionerelaxation phenomenon. Spine 19, 2190e2196. 24, 2426e2434. Olson, M.W., Li, L., Solomonow, M., 2004. Flexionerelaxation response Vachalathiti, R., Crosbie, J., Smith, R., 1995. Effects of age, to cyclic lumbar flexion. Clinical Biomechanics 19, 769e776. gender and speed on three dimensional lumbar spine kinematics. Australian Journal of Physiotherapy 41, Panjabi, M.M., 1992. The stabilizing system of the spine, part I: 245e252. function, dysfunction, adaptation, and enhancement. Journal of Spinal Disorders 5, 383e389. Wiliams, M., Solomonow, M., Zhou, B., Baratta, R., Harris, M., 2000. Multifidus spasms elicited by prolonged lumbar flexion. Shin, G., Mirka, G., 2007. An in vivo assessment of the low back Spine 25, 2916e2924. response to prolonged flexion: interplay between active and passive tissues. Clinical Biomechanics 22, 965e971.

Journal of Bodywork & Movement Therapies (2010) 14, 424e444 available at www.sciencedirect.com journal homepage: www.elsevier.com/jbmt STRUCTURAL HIERARCHIES Simple geometry in complex organisms Graham Scarr* 60 Edward Street, Stapleford, Nottingham NG9 8FJ, United Kingdom Received 12 August 2008; received in revised form 22 October 2008; accepted 22 November 2008 KEYWORDS Summary Many cultures throughout history have used the regularities of numbers and Crystallography; patterns as a means of describing their environment. The ancient Greeks believed that just five Helix; archetypal forms e the ‘platonic solids’ e were part of natural law, and could describe every- Icosahedron; thing in the universe because they were pure and perfect. The formation of simple geometric Natural law; shapes through the interactions of physical forces, and their development into more complex Platonic solids; biological structures, supports a re-appreciation of these pre-Darwinian laws. The self- Symmetry; assembly of molecular components at the nano-scale, and their organization into the tenseg- Structural hierarchies; rities of complex organisms is explored here. Hierarchies of structure link the nano and micro Tensegrity; realms with the whole organism, and have implications for manual therapies. Tetrahedron ª 2008 Elsevier Ltd. All rights reserved. Introduction during the course of evolution primarily by natural selec- tion for biological function’’ (Denton et al., 2003). Many cultures throughout history have used the regularities A recognition of natural patterns and shapes derived from of numbers and patterns as a means of describing their physical laws seemed to reassert itself in 1917 when d’Arcy environment. The ancient Greeks believed that just five Thompson published his classic ‘On Growth and Form’ archetypal forms e the ‘platonic solids’ e were part of (Thompson, 1961), but in the scientific mainstream this natural law and could describe everything in the universe remained little more than interesting. Using simple geom- because they were pure and perfect (Figure 1) (Fuller, etry to describe a complex organism is likely to generate 1975, sec.820.00). a certain amount of skepticism, as esoteric and occult descriptions seem rather simplistic compared to modern This platonic conception of nature persisted up until the scientific thinking. However, in 1928 Frank Ramsey proved mid nineteenth century when Charles Darwin published his that every complex or random structure necessarily revolutionary ‘Origin of Species’, ‘‘After Darwin the whole contains an orderly substructure. His proof established the lawful scheme was overthrown and organic forms came to fundamentals of a branch of mathematics known as Ramsey be seen as contingent mutable assemblages of matter e theory, which is used to study the conditions under which ‘clever artefact like contrivances’ e put together gradually order must appear, such as in large communication networks and the recognition of patterns in physical * Tel.: þ44 115 9491753. systems. The theory suggests that much of the essential E-mail address: [email protected] structure of mathematics consists of extremely large 1360-8592/$ - see front matter ª 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbmt.2008.11.007

Simple geometry in complex organisms 425 Figure 1 The five platonic solids. numbers (with very complicated calculations) derived from largest area within the minimum boundary, which makes it problems which are deceptively simple (Graham and a ‘minimal-energy’ shape (requiring the least amount of Spencer, 1990; Fuller, 1975, sec.227.00). From the energy to maintain). Circles enclose space, as well as perspective of the human body, Ramsey theory implies that radiate out into it, as can be seen in a drop of oil floating on simple shapes might form part of that underlying water, the growth of fruit mould, and the ripples in a pond. substructure, and an examination of how these could arise However, this efficiency is severely compromised when through the interactions of physical forces is presented. several circles are put next to each other as gaps are left in This supports recent research which reinstates physical between (Figure 2). Other shapes, such as squares and law, and not natural selection, as the major determinant of triangles will both fill the space completely, but the biological complexity in the subcellular realm (Denton proportion of area to boundary is not as good as with the et al., 2003). The development of these shapes into more circle. A square is inherently unstable; while triangles are complex structures, and how they model biology, with very stable, even with flexible joints (Figure 3). Structures implications for manual therapy then follows. that are not triangulated can generate torque and bending moments at their joints, and must be rigidly fixed to Simple geometry prevent them from collapsing. One of the problems that nature seems to solve repeatedly The best compromise between efficient space filling of is that of the most efficient ways of packing objects close the circle and stability of the triangle is the hexagon together. A circle drawn on a piece of paper, i.e. in two (Figure 2). Isolated hexagons are also liable to collapsing, dimensions (2D), demonstrates this. The circle encloses the but when several hexagons are packed together, they support each other as stresses balance at their 3-way Figure 2 The tessellation of different shapes on a flat plane showing the appearance of the hexagon (shaded).

426 G. Scarr Figure 3 Diagram to show that square trusses are inherently unstable at their joints, whereas triangular trusses are rigid. junctions (Figure 4). However, they are only fully stable surface tension, which tries to minimize itself and reduce when triangulated, with sides that form chords of a circle the surface area (Fuller, 1975, sec.825.20; Stewart, 1998, equal to the radius (Figure 4). Hexagons close-pack in an p. 16). Some examples of naturally occurring hexagons are array that can self-generate to produce the same shapes at shown in Figure 7 (Bassnett et al., 1999; Weinbaum et al., different size scales (Figure 5), and even non-uniform 2003; Sanner et al., 2005). shapes approximate to hexagons as they pack together in sheets (Figure 7). All this would seem to make the hexagon the obvious choice for close-packing in two dimensions. In 3D, however, Soap bubbles spontaneously join together with outside a structure which fulfills the same purpose may not be so surfaces that always meet at 120, just like hexagons, readily apparent. The ancient Greeks recognized the whether the bubbles are equal in size or not (Figure 6). This importance of the five regular polyhedra because of their is because soap molecules hold together through their Figure 4 The relationship between hexagons, circles and Figure 5 Hexagonal close-packing and a hierarchy of triangles. hexagons.

Simple geometry in complex organisms 427 Figure 6 (a) Diagram of bubbles joining with an external surface angle of 120, the same as a hexagon; (b) three bubbles form an internal septum (bold lines), also with an angle of 120. intriguing properties (Figure 1) (Fuller, 1975, sec.820.00). closely together, plastic balls have been glued together Their outer faces are made from shapes which are all the (Figure 8). The same arrangements are also shown as same; a sphere circumscribed around each one will touch lattices of steel balls, with coloured magnetic sticks rep- all the corners, while one inscribed within will touch the resenting the inherent ‘minimal-energy’ characteristic of centre of all the faces; and they all have 3, 4 or 5 sides. close-packing (i.e. their centres of mass are at the Joining up the face centres creates the ‘dual’ of that minimum possible distance apart) (Connelly and Back, shape, i.e. the octahedron and cube are duals of each 1998). Adding more spheres to a particular shape creates other; and the dodecahedron and icosahedron similarly; higher-order structures of the same shape, numbered the tetrahedron is unique in that it is a dual of itself. Not according to the [magnetic] connections on their outer a hexagon in sight. yet! edge (Figure 8) (Fuller, 1975, sec.415.55). Just as the circle is the most efficient shape for The tetrahedron (Figure 8) enclosing space in 2D, so its equivalent in 3D is the sphere. Atoms, bubbles, oranges, and planets all approximate to The simplest and most stable arrangement of spheres in 3D spheres. Putting lots of spheres next to each other still is a tetrahedron, because of its triangles (Fuller, 1975, leaves all those wasteful spaces in between, just like the sec.223.87). Methane and ice molecules configure as circles did; but there is a more efficient solution. In order to tetrahedrons; a pile of oranges and grains of sand are rough tease out some of the consequences of packing spheres Figure 7 Some examples of hexagons in natural structures: (a) honeycomb (Wikipedia); (b) close-packing of Polio virus (Fred Murphy & Sylvia Whitfield, Wikipedia); (c) Basalt blocks on the Giants Causeway in Ireland, formed from cooling lava (Matthew Mayer, Wikipedia); (d) stacked layers of carbon atoms in graphite (Benjah-bmm27, Wikipedia); (e) hexagonal close-packing of actin and myosin in a muscle fibril; (f) hexameric complexes of uroplakin covering the epithelial lining of the urinary bladder (redrawn after Sanner et al., 2005); (g) idealized diagram of the sub-cortical cytoskeleton (redrawn after Weinbaum et al., 2003); and (h) cells in the optic lens arranged as hexagons (redrawn after Bassnett et al., 1999).

428 G. Scarr Figure 8 Closest-packing of spheres forms a tetrahedron (1st, 2nd, 3rd and 4th orders). tetrahedrons; and in the early embryo, four cells arrange as The cube (Figure 13) a tetrahedron. Adding more spheres to the tetrahedron produces higher-order structures and the emergence of The addition of a tetrahedron to each of the 8 triangular another shape e the octahedron. faces of the 2nd order cuboctahedron turns it into a cube, or looking at it another way, the cuboctahedron is a cube The octahedron (Figure 9) with the corners cut off. If these were cut away further, it would end up as an octahedron. When four corners of The octahedron appears as an inevitable consequence of a cube are connected diagonally, they enclose a 4th order close-packing. It is naturally found in radiolarian structures tetrahedron (Figure 13b). (Fuller, 1975, sec.203.09), and is the basis of the octet truss used by structural engineers because of its stability. It does The cuboctahedron and cube are not shapes which have 3 equatorial squares at 90 to each other, but their generally appear in biological structures, but they are still stability is maintained because of the triangles at each relevant to the discussion. Table 1 shows a comparison of vertex (Fuller, 1975, sec.420.01). A good approximation of the relative volumes of these shapes when taking each one this truss appears in the bones of birds, probably due its as unity. It can be seen that the volume of the tetrahedron strength and lightness (Thompson, 1961, p. 236). is the only standard where all the others can be expressed as integers; the other comparisons leave awkward fractions The cuboctahedron (Figures 10e12) or irrational numbers which disguises their simple rela- tionships. Man-made structures commonly use cubes with Increasing the tetrahedron to its 4th order (Figures 8 and 10) their 90 angles, but these shapes are relatively rare in the produces the first close-packing of spheres around a central natural world where they are constructed from discrete nucleus, and the emergence of another shape e the cuboc- components, and 60 geometry is more prevalent e an tahedron (which is not a platonic solid) (Fuller, 1975, observation noted by Fuller (1975, sec.410.10). An archi- sec.414.00). This shape is also contained within a 2nd order tect of some renown, he formulated a complete system of octahedron (Figure 11). geometry based on 60, which applied to a wide diversity of the laws formulated in physics and chemistry. Figure 9 (a) Emergence of octahedron (light) within 2nd order tetrahedron (dark). (b) 1st and 2nd order octahedra with construction of octet truss.

Simple geometry in complex organisms 429 Figure 10 Nuclear close-packing starts in the centre of a 4th order tetrahedron to form a cuboctahedron. Figure 11 Nuclear close-packing forms cuboctahedron (a) and octahedron (b).

430 G. Scarr Figure 12 Cuboctahedron (2nd order) and the same with front removed to show nuclear rays. In crystallography, for example, two basic types of close- maximal cubic symmetry (Figure 16) (all these polyhedra packing are described e cubic (Figure 14a) and hexagonal have cubic symmetry) (Read, 1974, p. 83; Sunada, 2008). (Figure 14b) (Read, 1974, p. 21). The different ‘layers’ are described as parallel to the surface of a cube, but as All these shapes naturally occur as inorganic crystals, already shown, the value of this shape as a standard in and there is no suggestion that they can literally be nature is dubious. In ‘cubic’ close-packing, the true layers observed in the human body. This new description, are at 60 to the surface of the cube, and all the energy however, includes them in a unified and comprehensive bonds in these layers are oriented in the same directions approach to understanding natural forms, which are all (Figure 13). (This can be observed in the external angles of influenced by the same energy-efficient ways of packing the hexagon in Figure 13c, which are 60.) In ‘hexagonal’ objects of similar size through the interactions of molecular close-packing, however, every third layer is rotated by 60 forces. around an axis perpendicular to the layer plane, and it doesn’t then produce simple shapes like those already Before getting to more complex structural mechanisms, described. In any case, there are plenty of hexagons in it is necessary to make a brief return to the cuboctahedron, ‘cubic’ close-packing (Figures 13c and 15), and the tetra- where it will be noticed that it is constructed from 12 hedron, octahedron, cuboctahedron and cube are all spheres that create four interlocking hexagons around examples of this (Read, 1974, p. 96). To illustrate this, a central nucleus (Figures 10, 11 and 17a). Pauling (1964) diamond (the hardest natural substance) is constructed described it as a ‘coordination polyhedron’ because its from carbon atoms arranged in a 3D hexagonal lattice; with minimal-energy configuration is the common denominator complete hexagonal rings that form tetrahedral units; of the tetrahedron, octahedron and cube. Fuller (1975, which crystallizes as an octahedron; and uniquely has sec.430.00) considered the links between spheres as energy vectors, and called it the ‘vector equilibrium’. This shape has radial and circumferential vectors which are all the Figure 13 The layers in a cube. (a) 1st corner layer removed (white dotted). (b) 2nd layer removed to show one side of a tetrahedron (white dotted). (c) 3rd layer removed to show a hexagon (white dotted).

Simple geometry in complex organisms 431 Table 1 A comparison of the relative volumes of different Tensegrity shapes with the same edge length, when taking each one as unity. The concepts of tensegrity [tensional integrity] have become increasingly recognized over the last thirty years as Tetrahedron Octahedron Cube Cuboctahedron a useful model for understanding some of the structural properties of living organisms. Their appreciation follows 1 4 6 20 from investigations in the 1940s by Snelson (website) who constructed sculptures with parts that appeared to defy 0.25 1 1.5 5 gravity and float in the air. His structures so impressed the architect Fuller (1975) that he incorporated them into his 0.1666666. 0.666666. 1 3.33333333. developments in building design, and set about exploring the principles underlying their formation. Fuller defined 0.05 0.20 0.30 1 two types of tensegrity structure based on the icosahedron, and termed them geodesic and prestressed. same size. In terms of vectorial dynamics, the outward radial thrust from the nucleus is exactly balanced by the The geodesic dome circumferentially restraining chordal forces (Figures 10 and 11). So, as well as the highest degree of symmetry (cubic), The outstanding feature of all geodesic structures is that we have a coordinating shape (cuboctahedron) and they have a rigid external frame maintaining their shape, a balance of forces (vector equilibrium), the significance of made from multiple struts or trusses arranged in geometric which will be explained later. patterns. These are usually triangles, pentagons or hexa- gons, with triangulated structures being the most stable. It is even possible to pack spheres tighter and at a lower The term ‘geodesic’ actually refers to the shortest path energy level by removing the nucleus. This allows 12 between two points on a surface (equivalent to the spheres to compact differently around a smaller central struts), so strictly speaking this definition should only refer space as 12 interlocking pentagons (Figures 17b and 18a, b). to the triangulated structure. Aside from this, the Joining all the spheres together creates an icosahedron e ‘geodesic’ dome can enclose a greater volume with another platonic solid, but this one is different (Figure 18c). minimal surface area, with less material than any other Adding more spheres to the outside will not create a higher type of structure apart from a sphere. When the diameter order, like in the previous shapes, because the spheres of a sphere doubles, the surface area increases 4-fold and won’t all touch (Figure 18d). A 2nd order icosahedron won’t the volume 8-fold, which makes such structures very close-pack around the basic shape, or a 3rd order around efficient in terms of construction material. The 1st order a 2nd, because they would be unstable (Figure 18e and f), tetrahedron and octahedron are geodesic structures which and can only exist in their own right as a single outer shell. enlarge by adding more spheres to the outside, but they The icosahedron enlarges by subdividing each of its faces then cease to be hollow structures. In contrast the ico- into more triangles, which is why it remains stable sahedron, whose spheres enclose a small central space, (Figure 18g). (The relative volume compared to the tetra- creates an outer geodesic shell which enlarges by adding hedron in Table 1 is 18.51.) more triangular faces within it (Figures 18g and 19). The icosahedron has several attributes that are advantageous In order to understand the full significance of simple for biological structures (Levin, 1995). It is the closest of geometry, we must look at another way that the universe uses to deal with complexity, namely, integration. Figure 14 (a) ‘Cubic’ close-packing in a cube. The orientation of energy bonds in each layer of spheres remains the same (compare Figure 13). (b) ‘Hexagonal’ close-packing shows the third layer of spheres (white dotted) rotated by 60 on the layer below.

432 G. Scarr Figure 15 Hexagonal shape in (a) octahedron; (b) 1st order cuboctahedron; (c,d) 2nd order cuboctahedron; and (e) cube (viewed from edge). all the regular polyhedra to being spherical e making it on a football (actually a spherical truncated icosahedron); efficient in terms of construction material; and it is fully viruses; the silica shells of radiolaria; pollen grains; cla- triangulated e giving it stability. It has 12 vertices, 20 thrins (endocytic vesicles beneath the cell membrane); and triangular faces and 30 edges, with five faces and their the cellular cytoskeletal cortex (Figure 20). edges meeting at each vertex; and demonstrates six 5-fold, ten 3-fold and fifteen 2-fold symmetries. In 1956, Crick and Watson, the discoverers of DNA, pointed out that the only way to build a hollow protein shell Fuller introduced his geodesic domes during the 1950s; out of identical subunits is a shape with cubic symmetry. and because their strength increases as they get bigger, it Since then it has been amply confirmed that the icosahedron has been possible to build some very large structures. Some is the best shape for producing the outer capsid shell of the of these can be seen in the Eden project in Cornwall, and ‘spherical’ viruses, because it is a minimum free-energy protective coverings on radar installations. Some natural structure, and spontaneously assembles through the actions structures are: ‘Buckyballs’ e a form of carbon named after of intermolecular forces (Figure 20b) (Crick and Watson, Fuller e with 60 atoms linked together to form 20 hexagons, 1956; Kushner, 1969; Caspar, 1980; Van Workum and Doug- interspersed with 12 pentagons e the same as the pattern las, 2006). These viruses form larger structures, which get Figure 16 (a) Multi hexagonal lattice of carbon atoms in diamond, shown within the ‘standard’ cube; (b) octagonal diamond crystal; (c) enlarged lattice showing tetrahedral apexes (white, compare with (a)); and (d) tetrahedron viewed from apex (cross).

Simple geometry in complex organisms 433 Figure 17 (a) 12 spheres close-pack around a central nucleus to form a cuboctahedron with 4 interlocking hexagons; and (b) around a central space to form an icosahedron with 12 interlocking pentagons (front 3 spheres have been shaded for clarity). Figure 18 Close-packing around a central space (a,b) forms an icosahedron with hexagonal outline (c). Packing more spheres around the icosahedron (d) forms an unstable dodecahedron (e) or icosahedron (f). An icosahedron enlarges by subdividing its surfaces into more triangles (g).

434 G. Scarr Figure 19 Icosahedron subdivided into 2nd and 3rd order geodesic icosahedra. even closer to a sphere, by using more protein subunits compression and tension operating within different parts of (capsomers) to subdivide their triangular faces (Figure 19). each strut, which means that they must be made of The maximum number of identical subunits which can be a material that can deal with both types of loading. Pre- arranged is 60, and to become larger, some subunits must stressed tensegrities, on the other hand, have these two distort slightly in order to form stable bonds. This ‘quasi- components separated, optimizing the material properties equivalence’ is necessary for preserving the icosahedral of each (Ingber, 2003a). template, with multiples of 60 subunits allowing many more triangular faces, but there are always just 12 vertex Prestressed tensegrity pentagons (it is the 5-fold symmetry which creates the geodesic dome) (Caspar, 1980). (The icosahedron has also The description of biological structures as tensegrities first been found to play an important part in the structure of appeared in the literature in the early 1980s, with inde- many electron-deficient substances, including metals and pendent contributions by Ingber et al. (1981) and Levin alloys Pauling, 1964, 1990; Teo and Zhang, 1991.) (1982). Prestressed tensegrities consist of a set of struts under compression, and an arrangement of cables under Multiple icosahedra can arrange neatly together in isometric tension. The resultant pull of the cables is a thick planar sheet because of their hexagonal outline balanced by the struts, providing structural integrity with (Figures 7b and 18c), making the hexagon the link between the compression elements appearing to float within the space filling in 2D and the icosahedron in 3D. They can stack tension network. A load applied to this type of structure in a column or helix; branch or pack around each other causes a uniform increase in tension around all the edges (incompletely) to create curved surfaces; and form more and distributes compression evenly to the struts, which complex patterns and shapes in 3D (Figure 21). remain distinct from each other and do not touch (Skelton et al., 2001; Masic et al., 2006). Fuller described it as: In contrast, tetrahedral and octahedral based trusses ‘‘.continuous tension and discontinuous compression’’ are not omnidirectional in form and function; they have (Fuller, 1975, sec.700). a smaller volume to surface area ratio; they do not close- pack at all well and their shapes do not self-generate. The geodesic icosahedron can be converted into a pre- Cubes and dodecahedra are also inherently unstable unless stressed tensegrity structure by using six new compression they are triangulated; and as they rarely feature in biology, members to traverse the inside, connecting opposite will not be considered further at this point. However, they vertices and pushing them apart (Figure 22) (Fuller, 1975, are still significant to later discussion. sec.700; Levin, 1982). The edges can then be replaced with cables so that the outside is entirely under tension. (Some Applying pressure to any point of a geodesic dome cau- ses force to be transmitted around the edges, with both Figure 20 Geodesic icosahedrons in (a) Radiolarian (Wikipedia); (b) Adenovirus (Wikipedia); and (c) Pollen grains (Dartmouth College, Wikipedia).

Simple geometry in complex organisms 435 Figure 21 (a) Incomplete icosahedral packing; (b) icosahedral branching; and (c) icosahedral helix. of the edges have disappeared in the transition to pre- entire structure, which will optimize automatically so as to stressed tensegrity because they are now redundant and remain inherently stable. not essential to this new structure.) 3. Integration e a change in any one tension or To summarize the significant aspects of this type of compression element causes the whole shape to alter and design (Van der Veen, 2003): distort, through reciprocal tension, distributing the stresses to all other points of attachment. 1. Stability e achieved through the configuration of the whole network, and not because of the individual compo- 4. Energetically efficient e giving maximum stability for nents. It is also omnidirectional, with the different a given mass of material. In mechanical terms it cannot be elements maintaining their respective properties regardless anything other than in a balanced state of minimal energy of the direction of applied load. throughout (Masic et al., 2006; Skelton et al., 2001). 2. Balance e the tension and compression components Since its discovery, the tensegrity concept has devel- are separated and balanced mechanically throughout the oped in four main areas e sculpture (Snelson); building Figure 22 (a) Geodesic icosahedron; and (b) prestressed tensegrity icosahedron.

436 G. Scarr (Fuller); space research and structural biology. Space and stable structures through changes in the lengths of their research has shown a great deal of interest in tensegrities compression members (Connelly and Back, 1998; Skelton because of their lightness and other unusual structural et al., 2001; Nelson et al., 2005; Ingber, 2006a,b, 2008). properties. Defining their complex mathematics will prob- ably lead to new developments in biological research, with Their non-linear stressestrain curve is considered an physical and computerized modelling becoming valuable essential element in biological materials, where it has been tools for exploring their potential in the future (Connelly related to the differing properties of components in their and Back, 1998; Skelton et al., 2001; Coughlin and Stame- nano and microstructures (Figures 24 and 29) (Gordon, novic, 2003; Masic et al., 2006; Yu et al., 2008). 1978, p. 164; Lakes, 1993; Skelton et al., 2001; Puxkandl et al., 2002; Gao et al., 2003; Gupta et al., 2006); one of The ‘geodesic dome’ has been considered distinct from the smallest of these is the helix. ‘prestressed’ tensegrity for the purpose of description so far e one has all the struts touching, and the other has The helix them all separated; although tension maintains their integrity in both cases, and they are really both prestressed The a-helix is a series of curves which all have the same (Fuller, 1975, sec.703.03). They seem to be poles at radius, drawn out like a long spring (Figures 24e29). Prob- opposite ends of a continuum, although even this distinc- ably the most famous of all is DNA e deoxyribonucleic acid tion is an illusion, and as will be explained. A definition e a double helix of two chains running in opposite direc- which satisfies all researchers has so far remained elusive, tions. The discoverers of DNA rightly predicted that helixes particularly in biology, where distinctions become blurred, would be one of the simplest of shapes to spontaneously and the following examples use a broad and inclusive assemble through intermolecular forces (Crick and Watson, approach. 1956; Kushner, 1969; Caspar, 1980; Van Workum and Douglas, 2006). Helical structures are stabilized through The complexity of shape a balance between the attractive (tensional) and resistant (compressional) forces within the molecule, which makes Shape is a direct result of all the forces acting on the them tensegrities. They can also flex without buckling, component structures during development, from a single lengthen without breaking, and are capable of rotation molecule to the complete organism. At a ‘simple’ level, the without deformation (Stecco, 2004, p. 185). All known arrangement of spheres (atoms) is through the spontaneous filamentous viruses are helical (most of the rest are icosa- attraction (tension) of inter-atomic forces. Three spheres hedral) (Figures 20b and 21c). form a triangle and four spheres form a tetrahedron (Figure 8). More spheres can be added to create an octa- In proteins, sequences of amino acids can fold into a- hedron, cuboctahedron or cube (Figures 11 and 13); but helixes and further twist around each other to form double these distinct shapes are generally only stable as fixed or triple coiled-coils (super-coils) (Figure 25), or fold with inorganic crystals. other a-helixes (or b-sheets) to form globular structures. Of the huge number of possible amino acid combinations, In contrast, the molecular dynamics within living organ- protein folding is limited to a set of about 1000 different isms is in continuous flux as conflicting forces attempt to forms because of some basic self-assembly rules, analogous resolve themselves. Eventually they can settle into to the laws of chemistry or crystallography, which corre- a balanced and stable state of minimal-energy, at least until spond to an energy minimum (Denton et al., 2002). some other force exerts its influence. Prestressed tensegr- ities are a most attractive proposition in living systems, The cytoskeleton because they create an energy ‘sink’ for the interacting force fields (a ‘basin of attraction’ in dynamics termi- Within the cytoplasm, the prestressed cytoskeleton is nology), and make possible an enormous number of flexible a lattice consisting of microtubules e tightly packed helices Figure 23 Prestressed tensegrity models (a) icosahedron; (b) icosahedral chain; and (c) icosahedral thick planar sheet.

Simple geometry in complex organisms 437 Figure 24 Diagram to show hierarchies of different components in the structure of muscle e a-helix of tropomyosin, double coiled-coil of tropomyosin; globular g-actin, combined double helix of f-actin and tropomyosin; double a-helix of myosin molecule, myosin thick filament; hexagonal packing of actin and myosin in a myofibril, self-similar packing of myofibrils into a fibre, a fibre bundle and ultimately muscle. of globular tubulin protein under compression (Figure 26); (Figures 7g and 27) (Liu et al., 1987; Weinbaum et al., 2003; microfilaments e double helices of the protein F-actin Li et al., 2005; Zhu et al., 2007). The erythrocyte, with under tension (Figure 27); and helical protein intermediate a diameter of 8 mm, has a composite membrane which filaments which stabilize and integrate the whole structure, distorts as it flows through smaller capillaries, but allows from cell membrane to the nucleus (Ingber, 2008; Maguire the cell to recover its biconcave shape. The network is et al., 2007; Brangwynne et al., 2006). Experimental organized into w33,000 repeating units, each with a short support for the cytoskeleton as a tensegrity structure now central actin protofilament linked by 6 spectrin filaments seems overwhelming (Ingber, 2008), although some studies under tension, to a lipid-bound suspension complex (Sung have been unable to confirm it (Heidemann et al., 1999; and Vera, 2003; Zhu et al., 2007). About 85% of these units Ingber et al., 2000). appear as hexagons, with w3% pentagons and w8% hepta- gons, which suggests that the hexagonal arrangement is The cellular cortex a preference, and not perfect (Liu et al., 1987). The erythrocyte membrane may be considered as many pre- The cellular cortex is essentially made from triangulated stressed tensegrity actin/spectrin units within a geodesic hexagons of the helical protein spectrin (Figure 25), dome, which is itself a bilayered structure of phospholipid coupled to underlying bundles of the helical protein actin molecules with outer heads under tension separated by Figure 25 Spectrin tetramer e each strand of a- and b-spectrin consists of a series of double and triple coiled-coils (super-coils).

438 G. Scarr Figure 26 Microtubule polymer of globular tubulin. hydrophobic tails under compression. It has also been order, and are sensitive to mechanical loading and changes modelled around an icosahedron (Li et al., 2005). Defor- in electro-magnetic fields; which may influence their mation of the membrane network may cause turbining of synthesis and define fibre orientation during morphogenesis the actin protofilaments through the suspension mecha- and tissue remodelling. Even though spider web fibres are nism, thereby facilitating oxygen transfer from one side of secured at their ends to what is effectively a continuous the membrane to the other (Sung and Vera, 2003; Zhu compression component, the whole web has been classed et al., 2007). as a tensegrity on structural engineering grounds (Connelly and Back, 1998). This arrangement of different components at varying size scales is a common feature in biology, where the functions of Fractals each one contribute to a higher collective function within a hierarchy of structures (Figures 24 and 29). The self-similar geometrical structure of collagenous tissues has been demonstrated in the fractal character of Structural hierarchies their polarization properties, with degenerative-dystrophic changes revealed by alterations in these properties (Ho The nano-structures of collagen and spider silk have both et al., 1996; Angelsky et al., 2005). This observation may be been described as prestressed tensegrities (Skelton et al., of value in pre-clinical pathological diagnostics, and 2001) within a hierarchical fibrous structure (Figure 28) a correlation between these findings and tissue palpation (Termonia, 1994; Knight and Vollrath, 2002; Du et al., would be useful research in the future. Fractal analysis is 2006). Collagen, the most abundant structural molecule commonly applied to natural structures, where similar based on the helix, is the main constituent of the extra- shapes and patterns appear at different size scales, linking cellular matrix, fascia, tendons and ligaments. More than hierarchies throughout the body (Mandelbrot, 1983; Skelton twenty different types have been described in different et al., 2001; Jelinek et al., 2006); the branching patterns of tissue specific combinations which are particularly able to blood vessels, the bronchial tree and nerve fibres all display resist tensional stresses. At the nano-scale three helical this property (Zamir, 2001; Palagyia et al., 2006; Phalen procollagen polymers wind around each other to form et al., 1978; Thomas et al., 2005). These characteristic a triple helix of tropocollagen. These molecules then shapes are developmental remnants of non-linear dynamic arrange laterally in a quasi-hexagonal configuration with systems which were sensitive to small changes in the local cross-linking to form collagen microfibrils, and pack environment, created instabilities in growth and caused the sequentially in a hierarchy to form a subfibril, fibril and typical branching pattern which extends from the micro to collagen fibre (Figure 29) (Jager and Fratzl, 2000; Puxkandl the macro scale. They are part of ‘deterministic chaos’ or et al., 2002; Gao et al., 2003; Gupta et al., 2006; Perumal chaos theory (Goldberger et al., 1990). et al., 2008). The matrix Collagens and spider silk are also examples of liquid crystal elastomers e different states, or mesophases of The extracellular matrix, surrounding virtually every cell in matter, that lie between liquids and solid crystals (Ho the body, provides a branching structural framework which et al., 1996; Knight and Vollrath, 2002). They are flexible extends through the fascia to the whole organism. It and malleable, with fibres that show a high degree of orientational order and varying degrees of translational Figure 27 F-actin polymer filament.

Simple geometry in complex organisms 439 Figure 28 A model fibre showing the prestressed tensegrity other cells at some distance. Long-distance transfer of nano-structure with similarities to collagen and spider silk. mechanical forces between different tissues could then attaches to the cellular cytoskeleton through adhesion spatially orchestrate their growth and expansion, allowing molecules in the cell membrane, allowing a transfer of complex multicellular tissue patterns to emerge through mechanical forces between them and changes in the interactions among a hierarchy of different components. cytoskeletal tension (Ingber, 2003a,b,2008). Multiple intracellular signalling pathways are activated as a result Multi-modular hierarchies of form and function can thus which provide multiplexed switching between different be linked, with simplicity evolving into complexity, and the states such as cell growth, differentiation or apoptosis. whole system mechanically functioning as a unit (Stecco, Conversely, local tensional stresses within the cytoskeleton 2004, p. 25; Nelson et al., 2005; Ingber, 2006a, 2008; Parker transfer to the extracellular matrix and produce effects on and Ingber, 2007). As a self-organizing tensegrity construction system, the matrix could repair and replace itself at a local level, by allowing small and incremental changes compatible with the mechanical demands of all its components. Stecco (2004, p. 31) described the fascia as a tensioned network which may coordinate the motor system in a way that the central nervous system is inca- pable of, although this work has yet to be confirmed. Modelling icosahedral tensegrities The icosahedron is particularly useful in modelling the tensegrities of biological structures, because it demon- strates both geodesic and prestressed properties which can be connected to form an infinite variety of shapes (Figures 21, 23 and 31). Even the tension and compression elements can be made from interlinked icosahedra, themselves constructed from smaller icosahedra, repeating further in a self-similar structural hierarchy (Fuller, 1975, sec.740.21; Figure 29 Diagram to show a hierarchy of components in the structure of tendon e a-helix of procollagen, triple coiled-coil of tropocollagen, collagen microfibril, and the self-similar packing arrangement in subfibril, fibril, fibre, fascicle and ultimately tendon.

440 G. Scarr Figure 30 Wheel showing central hub suspended within outer rim; and wheels within wheels model successive joints in the arm. Ingber, 2003a; Levin, 2007). Curved compression elements a corollary which should be added to any definition. Even (Figure 32) differ from straight struts (Figure 22) because the close-packing of atoms (spheres) should be considered their outer convex surfaces are actually under tension and as a ‘tensegrity with invisible struts’ because their centres inner concave surfaces under compression, but like the of mass are held a minimum distance apart (Connelly and struts in a geodesic dome, biological materials deal with Back, 1998). Distinctions of structure and function in both types of loading as a result of their nano and micro biology may essentially be points on a continuum and structures (Gordon, 1978; Lakes, 1993; Puxkandl et al., artefacts of textbook classification. Although ‘geodesic’ 2002; Gao et al., 2003; Gupta et al., 2006; Brangwynne structures appear limited to the cellular size level, ‘pre- et al., 2006). Inferences that this is ultimately due to their stressed’ tensegrities almost certainly dominate beyond tensegrity construction have been made (Skelton et al., this. At the macro scale the fascia, muscles, ligaments and 2001; Levin, 2007; Ingber, 2008). In addition, when spheres capsules provide the tension; while the bones and tissue are added to the outside of an icosahedron they do not bulk of muscles, organs and fluid-filled vessels resist close-pack completely, and an instability develops (Figures compression. 18def and 21a). This apparent ‘flaw’ in the packing arrangement allows another possibility for modelling an Tensegrities within tensegrities infinite variety of shapes, as different parts of the structure branch outwards, and the spaces in between can fill with Levin was the first to describe the higher complexities of smaller icosahedra. the human body in terms of tensegrities, using the analogy of a bicycle wheel, where the compression elements of the It may now be seen that the distinction between central hub and outer rim are held in place by a network ‘geodesic’ and ‘prestressed’ tensegrities is really just of wire spokes in reciprocal tension (Levin, 1997, 2005a; relative to the scale at which they are observed, Connelly and Back, 1998). This type of wheel is a self- contained entity, maintained in perfect balance Figure 31 Right upper extremity modelled as a sequence of throughout, with no bending moments or torque, no interconnecting icosahedral tensegrities with compression fulcrum of action, and no levers (Figure 30). He suggested struts of different lengths. that the scapula may function as the hub of such a wheel, in effect as a sesamoid bone, and transfer its load to the axial skeleton through muscular and fascial attachments (Levin, 1997, 2005a). The sterno-clavicular joint is not really in a position to accept much compressional load, and the transfer of compression across the gleno-humeral joint has been found to be at maximum only when loaded axially at 90 abduc- tion (Gupta and van der Helm, 2004). As compression can only take place normal to the glenoid surface i.e. at 90 (it is essentially a frictionless inclined plane), the joint must rely heavily on ligamentous and muscular tension in all other positions. A humerus hub model would function equally well with the arm in any position. Similarly, the ulna could be a hub within the distal humeral ‘rim’ of muscle attachments, where load bearing across the joint may be significantly tensional, allowing compressional forces to be distributed through a tensioned network, and the hand to lift loads much larger than would otherwise be

Simple geometry in complex organisms 441 Figure 32 A model of the cranial vault as a tensegrity structure (Scarr, 2008). the case (Figure 31). In this respect, zero compression anatomies is in the detail, it seems reasonable to suppose across the femur and meniscii has been observed during that they have some structural properties in common arthroscopy in an extended knee joint under axial loading (Levin, 1982, 2002). Tensegrities are omnidirectional, i.e. in vivo (Levin, 2005b). they are stable irrespective of the direction of loading; and the spine, pelvis and shoulder all demonstrate this property The pelvis is also like a wheel with the iliac crests, (within physiological limits), enabling dancers to tip-toe on anterior spines, pubis and ischia representing the outer rim; one leg, and acrobats to balance on one hand. and the sacrum representing the hub, tied in with strong sacro-iliac, sacro-tuberous and sacro-spinous ligaments. Continuums of structure Similarly, the femoral heads may function as hubs within the ‘spokes’ of the ilio-femoral, pubo-femoral and ischio- Prestressed and geodesic tensegrities may coexist at the femoral ligaments (Levin, 2007). same level within a particular functional unit and have been described in the cranium, where the bony plates of Most joint movements display helicoid motion around the vault substitute for curved prestressed compression a variable fulcrum, and this is demonstrated in the simple struts and do not touch each other; alongside a geodesic tensegrity elbow in Figure 31, a physiological feature not cranial base (Figure 32). Prestressed tension is provided by found in most other models. the dura mater e a tough membrane covering the brain e which regulates bone growth, maintains the separation of Omnidirectionality vault bones at the adjoining sutures, and integrates the whole structure into a single functional unit. It has been According to Wolff’s law, tensional forces remodel the bony suggested that the brain influences the vault to grow contours and alter the positions and orientations of their outwards, through the dura mater, rather than physically attachments, contributing to the complexity of shapes pushing it out (Scarr, 2008). apparent in the skeleton (Kushner, 1940; Kjaer, 2004). As part of a prestressed tensegrity structure, each attachment Balanced mobility would influence all the others, distributing forces throughout the system and avoiding points of potential Balanced and symmetrical tensegrities automatically weakness (Skelton et al., 2001; Masic et al., 2006); in assume the configuration that minimizes their stored contrast to a pure geodesic chain or truss which is vulner- elastic energy, with changes in shape that require very able to buckling (Figure 21c). Such a mechanism would be little control energy; in contrast to classical structures an advantage in long-necked animals such as giraffes and where significant energy is required to work against the old dinosaurs, where the load from the head is distributed equilibrium (Skelton et al., 2001; Masic et al., 2005). Their throughout the neck (Figure 23) (Levin, 1982). The erect high yield strain allows large shape changes to be accom- spine and bipedal weight bearing capability of humans have plished at no loss in stiffness (Masic et al., 2006), traditionally been viewed as a tower of bricks and a distinctive feature in biological structures. The icosahe- compressed disc joints, transferring the body weight down dron has been described as an intermediary in a potential through each segment until it reaches the sacrum, but this oscillating system (Fuller, 1975, sec.460.08) with similari- is a relative rarity amongst vertebrates. Most other species ties to an energy efficient pump (Levin, 2002). If the vector have little or no use for a compressive vertebral column, equilibrium (cuboctahedron) (Figure 11a) is constructed which is frequently portrayed as a horizontal truss and without radial vectors and joined with flexible connectors, cantilever support system (Thompson, 1961, p. 245; Gor- don, 1978, p. 239). As the main difference in vertebrate

442 G. Scarr and is compressed between two opposite triangular faces, extension’ means something different to ‘close-packing of it will contract and rotate symmetrically (due to the spheres’. instability of the square faces) and assume the shape of the slightly smaller icosahedron (each of the square faces now Summary becomes a rhomboid, or essentially, two triangles). Further compression causes the equator to twist and fold, and the The tetrahedron is one of the simplest of shapes in 3D structure transform itself through an octahedron, to because of its close-packing efficiency, minimal-energy the tetrahedron, and back again. The icosahedron is at the configuration and triangular stability. It gives rise to the lowest energy state within the system, and the point octahedron and square in the octet truss, and nuclear close- around which changes in shape occur. Fuller called this packing in the cuboctahedron and cube; all manifesting mechanism the ‘jitterbug’ (Fuller, 1975, sec.460.00). An within each other, and all resulting from ‘60 geometry’. organism utilizing such a system would be able to move The hexagon, and cubic symmetry of these shapes links with the minimum of energy expenditure, and remain them to the polyhedron most suited to fulfill structural stable whilst changing shape. evolution in biology, which is the icosahedron, possibly part of the substructure predicted by Ramsey (Graham and Symmetry and natural laws Spencer, 1990). All these polyhedra undergo a phase tran- sition as they morph into prestressed tensegrity structures, ‘‘The ability. to generate elaborate and beautiful giving endless shape possibilities, but their well-defined forms. comes from a simple but fundamental principle geometries are now obscured. The cuboctahedron links which governs the deep structure of the physical them to the ‘vector equilibrium’ and dynamic ‘jitterbug’, universe: symmetry. .Albert Einstein. argued that where energy efficient transformations of shape become truly fundamental laws of nature must be the same at all significant. Self-assembling helical proteins carry the ten- times and in all places: that is, the laws must be perfectly segrity principle into the nano-structures of the cell and symmetric. Principles of symmetry govern the four extracellular matrix; and through structural hierarchies to forces of nature (gravity, electro-magnetism, and the the whole body. The genes orchestrate a battery of physical strong and weak nuclear forces that act between funda- and chemical processes, but the natural laws of physics still mental particles).’’ (Stewart, 1998, p. 38) provide the construction rules (Stewart, 1998, p. 25; Denton et al., 2003; Harold, 2005; Ingber, 2006b); and shape The ubiquitous nature of symmetry offers a simple expla- becomes determined more by Darwin’s ‘‘natural selection nation for stable crystal lattices and other regular patterns, for biological function’’ (Denton et al., 2003). because of the balance of forces. Instabilities in the dynamics of living systems also generate complex patterns Conclusion and shapes within hierarchies of structure, as self-similar shapes (fractals) scale up through dilation e one of the four ‘‘.ideal geometries.pervade organic form because principal types of symmetry transformation. natural law favours such simplicity as an optimal repre- sentation of forces’’. Stephen Jay Gould (Thompson, ‘‘Instability breaks the overall system symmetry, but it 1961, xi) appears to be a localized fissure that is offset by. a balancing asymmetry elsewhere in the system. Essen- Energy consumption is the key to understanding the struc- tially, the sum of all the asymmetries is symmetrical. tural complexities of living organisms, and as energy-effi- Thus, we have patterns of symmetry that reflect the cient structural mechanisms, tensegrities seem to apply at underlying symmetrical nature of the universe, and every level from the atom to the whole body. The icosa- patterns (and forms) that are generated by instabilities hedron links the simple geometry of the platonic solids to in the system.’’ (Kreigh and Kreigh, 2003) the tensegrities of complex shapes, and lends itself to their modelling. It also becomes a transient in energy efficient That different structures should emerge at different transformations of shape, through the ‘jitterbug’ system levels in complex organisms is typical of evolutionary described by Fuller. selection. Over hundreds of millions of years chance mutations in the genetic code occasionally gave rise to new As a tensioned tensegrity network, the fascia may have characteristics which conferred an advantage to the a coordinating function throughout the body; and as manual organism, whilst existing traits which remained useful were therapies make contact at the whole body level, it provides retained, through natural selection. This bifurcation in a pathway for therapeutic interventions right down to the development creates asymmetries which must be balanced molecular scale. in order to permit new higher-order symmetries (Stewart, 1978, p. 114). Acknowledgements Organization is still part of the self-assembly capacity, but I wish to express my appreciation to Stephen Levin for the resulting form may have a very different appearance information on the icosahedron which initiated this article, from its component substructures (Figures 24 and 29) ‘‘.and and to Nic Woodhead, Chris Stapleton and Andrea Rippe for be arranged into almost any contingent artifactual arrange- the opportunity to discuss some of these concepts with ment we choose’’ (Denton et al., 2003). Correlations with helpful feedback. Also to Rory James for the photographs in ‘60 geometry’ at the macro scale may then be more coin- Figures 9e12 and 15. cidental (Phalen et al., 1978; Thomas et al., 2005); and description such as ‘close-packing of the knee in full

Simple geometry in complex organisms 443 References Ingber, D.E., Heidemann, S.R., Lamoureux, P., Buxbaum, R.E., 2000. Opposing views on tensegrity as a structural framework Angelsky, O.V., Tomka, Y.Y., Ushenko, Y.G., Ushenko, Y.A., 2005. for understanding cell mechanics. Journal of Applied Physiology Investigation of 2D Mueller matrix structure of biological tissues 89, 1663e1678. for pre-clinical diagnostics of their pathological states. Journal of Physics D: Applied Physics 38, 4227e4235. Ingber, D.E., 2003a. Tensegrity I. Cell structure and hierarchical systems biology. Journal of Cell Science 116 (7), 1157e1173. Bassnett, S., Missey, H., Vucemilo, I., 1999. Molecular architecture of the lens fiber cell basal membrane complex. Journal of Cell Ingber, D.E., 2003b. Tensegrity II. How structural networks influ- Science 112, 2155e2165. ence cellular information processing networks. Journal of Cell Science 116, 1397e1408. Brangwynne, C.P., Mackintosh, F.C., Kumar, S., Geisse, N.A., Talbot, J., Mahadevan, L., Parker, K.K., Ingber, D.E., Ingber, D.E., 2006a. Cellular mechanotransduction: putting all the Weitz, D.A., 2006. Microtubules can bear enhanced compressive pieces together again. The FASEB Journal 20 (7), 811e827. loads in living cells because of lateral reinforcement. Journal of Cell Biology 173 (5), 733e741. Ingber, D.E., 2006b. Mechanical control of tissue morphogenesis during embryological development. International Journal of Caspar, D.L.D., 1980. Movement and self-control in protein Developmental Biology 50, 255e266. assemblies. Quasi-equivalence revisited. Biophysical Journal 32 (1), 103e133. Ingber, D.E., 2008 Tensegrity-based mechanosensing from macro to micro. [Review] Progress in biophysics and molecular biology Connelly, R., Back, A., 1998. Mathematics and tensegrity. American 97 (2e3), 163e179. Scientist 86, 142e151. Jager, I., Fratzl, P., 2000. Mineralized collagen fibrils: a mechanical Coughlin, M.F., Stamenovic, D., 2003. A prestressed cable network model with a staggered arrangement of mineral particles. model of the adherent cell cytoskeleton. Biophysical Journal Biophysical Journal 79, 1737e1746. 84 (12), 1328e1336. Jelinek, H.F., Jones, C.L., Warfel, M.D., Lucas, C., Depardieu, C., Crick, F.H.C., Watson, J.D., 1956. Structure of small viruses. Aurel, G., 2006. Understanding fractal analysis? The case of Nature 177 (4506), 473e475. fractal linguistics. Complexus 3, 66e73. Denton, M.J., Marshall, C.J., Legge, M., 2002. The protein folds as Knight, D.P., Vollrath, F., 2002. Biological liquid crystal elastomers. platonic forms: new support for the pre-Darwinian conception Philosophical Transactions of the Royal Society of London B 357, of evolution by natural law. Journal of Theoretical Biology 219, 155e163. 325e342. Kjaer, M., 2004. Role of extracellular matrix in adaptation of Denton, M.J., Dearden, P.K., Sowerby, S.J., 2003. Physical law not tendon and skeletal muscle to mechanical loading. Physiological natural selection as the major determinant of biological complexity Reviews 84, 649e698 [Review]. in the subcellular realm: new support for the pre-Darwinian conception of evolution by natural law. Biosystems 71, 297e303. Kreigh, M., Kreigh, J., 2003. Growth, form and proportion in nature: lessons for human habitation in off planet environ- Du, N., Liu, X.Y., Narayanan, J., Li, L., Lek, Min, Lim, M., Li, D., ments. In: 33rd International Conference on Environmental 2006. Design of superior spider silk: from nanostructure to Systems, Vancouver, Canada. mechanical properties. Biophysical Journal 91 (12), 4528e4535. Kushner, A., 1940. Evaluation of Wolff’s law of bone formation. Fuller, B.B., 1975. Synergetics, Explorations in the Geometry of Journal of Bone and Joint Surgery 22, 589e596. Thinking. Macmillan. Kushner, D.J., 1969. Self-assembly of biological structures. Bacte- Gao, H., Ji, Baohua, Jager, I.L., Arzt, E., Fratz, P., 2003. Materials riological Reviews 33 (2), 302e345. become insensitive to flaws at nanoscale: lessons from nature. Proceedings of the National Academy of Science 100 (10), Lakes, R., 1993. Materials with structural hierarchy. Nature 361, 5597e5600. 511e515. Goldberger, A.L., Rigney, D.R., West, B.J., 1990. Chaos and fractals Levin, S.M., 1982. Continuous tension, discontinuous compression: in human physiology. Scientific American 262 (2), 42e49. a model for biomechanical support of the body. The Bulletin of Structural Integration 8 (1). Gordon, J.E., 1978. Structures, or Why Things don’t Fall Down. Penguin. Levin, S.M., 1995. The importance of soft tissues for structural support of the body. In: Dorman, T. (Ed.), Spine: State of the Art Graham, R.L., Spencer, J.H., 1990. Ramsey theory. Scientific Reviews, vol. 9 (2). Hanley and Belphus, Philadelphia, pp. American (Jul), 80e85. 357e363. Gupta, S., van der Helm, F.C.T., 2004. Load transfer across the Levin, S.M., 1997. Putting the shoulder to the wheel: a new scapula during humeral abduction. Journal of Biomechanics 37 biomechanical model for the shoulder girdle. Journal of (7), 1001e1009. Biomedical Sciences Instrumentation 33, 412e417. Gupta, H.S., Seto, J., Wagermaier, W., Zaslansky, P., Boesecke, P., Levin, S.M., 2002. The tensegrity truss as a model for spine Fratzl, P., 2006. Cooperative deformation of mineral and mechanics: biotensegrity. Journal of Mechanics in Medicine and collagen in bone at the nanoscale. Proceedings of the National Biology 2 (3 and 4), 375e388. Academy of Science 103 (47), 17741e17746. Levin, S.M., 2005a. The scapula is a sesamoid bone. Journal of Harold, F.M., 2005. Molecules into cells: specifying spatial archi- Biomechanics 38 (8), 1733e1734. tecture. Microbiology and Molecular Biology Reviews 69; (4), 544e564 [Review]. Levin, S.M., 2005b. In Vivo Observation of Articular Surface Contact in Knee Joints. Unpublished available at: <www.biotensegrity. Heidemann, S.R., Kaech, S., Buxbaum, R.E., Matus, A., 1999. Direct com>. observations of the mechanical behaviors of the cytoskeleton in living fibroblasts. Journal of Cell Biology 145 (1), 109e122. Levin, S.M., 2007. A suspensory system for the sacrum in pelvic mechanics: biotensegrity. In: Vleeming, A., Mooney, V., Ho, M.W., Haffegee, J., Newton, R., Zhou, Y.M., Bolton, J.S., Stoeckart, R. (Eds.), Movement, Stability and Lumbopelvic Pain. Ross, S., 1996. Organisms as polyphasic liquid crystals. Bio- Churchill Livingstone (Chapter 15). electrochemistry and Bioenergetics 41, 81e91. Li, J., Dao, M., Lim, C.T., Suresh, S., 2005. Spectrin-level modeling Ingber, D.E., Madri, J.A., Jamieson, J.D., 1981. Role of basal of the cytoskeleton and optical tweezers stretching of the lamina in neoplastic disorganization of tissue architecture. erythrocyte. Biophysical Journal 88 (5), 3707e3719. Proceedings of the National Academy of Science 78 (6), 3901e3905. Liu, S.C., Derik, L.H., Palek, J., 1987. Visualization of the eryth- rocyte membrane skeleton. Journal of Cell Biology 104, 527e536.

444 G. Scarr Maguire, P., Kilpatrick, J.I., Kelly, G., Prendergast, P.J., Skelton, R.E., Adhikari, R., Pinaud, J.P., Chan, W., Helton, J.W., Campbell, V.A., O’Connell, B.C., Jarvis, S.P., 2007. Direct 2001. An introduction to the mechanics of tensegrity structures. mechanical measurement of geodesic structures in rat mesen- Proceedings of the 40th IEEE Conference on Decision and Control chymal stem cells. Human Frontier Science Program Journal 5, 4254e4259. 1 (3), 181e191. Snelson, K.. <www.kennethsnelson.net>. Mandelbrot, B., 1983. The Fractal Geometry of Nature. Freeman. Stecco, L., 2004. Fascial Manipulation for Musculoskeletal Pain. Masic, M., Skelton, R.E., Gill, P.E., 2006. Optimization of tensegrity Piccin Nuova Libraria, Padova. structures. International Journal of Solids and Structures 43, Stewart, I., 1998. Life’s Other Secret: The Mathematics of the 4687e4703. Nelson, C.M., Jean, R.P., Tan, J.L., Liu, W.F., Sniadecki, N.J., Living World. Penguin. Spector, A.A., Chen, C.S., 2005. Emergent patterns of growth Sunada, T., 2008. Crystals that nature might miss creating. Notices controlled by multicellular form and mechanics. Proceedings of the National Academy of Science 102 (33), 11594e11599. of the American Mathematical Society 55 (2), 208e215. Parker, K.K., Ingber, D.E., 2007. Extracellular matrix, mechano- Sung, L.A., Vera, C., 2003. Protofilament and hexagon: A three- transduction and structural hierarchies in heart tissue engi- neering. Philosophical Transactions of the Royal Society B: dimensional mechanical model for the junctional complex in Biological Sciences 2114, 1e13. the erythrocyte membrane skeleton. Annals of Biomedical Pauling, L., 1964. The architecture of molecules. Proceedings of Engineering 31 (11), 1314e1326. the National Academy of Science 51, 977e984. Teo, B.K., Zhang, H., 1991. Clusters of clusters: self-organization Pauling, L., 1990. Evidence from electron micrographs that icosa- and self-similarity in the intermediate stages of cluster growth hedral quasicrystals are icosahedral twins of cubic crystals. of AueAg supraclusters. Proceedings of the National Academy Proceedings of the National Academy of Science 87, 7849e7850. of Science 88, 5067e5071. Palagyia, K., Tschirrena, J., Hoffman, E.A., Sonka, M., 2006. Termonia, Y., 1994. Molecular modeling of spider silk elasticity. Quantitative analysis of pulmonary airway tree structures. Macromolecules 27, 7378e7381. Computers in Biology and Medicine 36, 974e996. Thomas, J.B., Antiga, L., Che, S.L., Milner, J.S., Hangan Perumal, S., Antipova, O., Orgel, J.P.R.O., 2008. Collagen fibril Steinman, D.A., Spence, J.D., Rutt, B.K., Steinman, D.A., 2005. architecture, domain organization, and triple-helical confor- Variation in the carotid bifurcation geometry of young versus mation govern its proteolysis. Proceedings of the National older adults. Stroke 36, 2450e2456. Academy of Science 105 (8), 2824e2829. Thompson, d’Arcy W., 1961. In: Bonner, J.T. (Ed.), On Growth and Phalen, R.F., Yeh, H.C., Schum, G.M., Raabe, G., 1978. Application Form. Cambridge University Press. of an idealized model to morphometry of the mammalian Van der Veen, A.C., 2003. Biomechanica: Bewegen, sport en tracheobronchial tree. Anatomical Record 90, 167e176. manuele geneeskunde. Symmetrie en asymmetrie. Sportgericht Puxkandl, R., Zizak, I., Paris, O., Keckes, J., Tesch, W., 57 (5). Bernstorff, S., Purslow, P., Fratzl, P., 2002. Viscoelastic prop- Van Workum, K., Douglas, J.F., 2006. Symmetry, equivalence, and erties of collagen: synchrotron radiation investigations and molecular self-assembly. Physical Review 73 (3 pt 1), 031502. structural model. Philosophical Transactions of the Royal Weinbaum, S., Zhang, X., Han, Y., Vink, H., Cowin, S.C., 2003. Society of London B: Biological Sciences 357, 191e197. Mechanotransduction and flow across the endothelial glyco- Read, H.H., 1974. Rutley’s Elements of Mineralogy, 26th ed. calyx. Proceedings of the National Academy of Science 100 (13), Thomas Murby & Co., London. 7988e7995. Sanner, M.F., Stolz, M., Burkhard, P., Kong, X.P., Min, G., Sun, T.T., Yu, C.H., Haller, K., Ingber, D.E., Nagpal, R., 2008 Morpho: a self- Driamov, S., Aebi, U., Stoffler, D., 2005. Visualizing nature at work deformable modular robot inspired by cellular structure. In: from the nano to the macro scale. NanoBiotechnology 1, 7e21. IEEE/RSJ International Conference on Intelligent Robots and Scarr, G.M., 2008. A model of the cranial vault as a tensegrity Systems, 3571e3578. structure, and its significance to normal and abnormal cranial Zamir, M., 2001. Arterial branching within the confines of fractal L- development. International Journal of Osteopathic Medicine 11 system formalism. The Journal of General Physiology 118 (3), (3), 80e89. 267e276. Zhu, Q., Vera, C., Asaro, R.J., Sche, P., Sung, L.A., 2007. A hybrid model for erythrocyte membrane: a single unit of protein network coupled with lipid bilayer. Biophysical Journal 93, 386e400.