Biomechanics Mechanical Properties of living tissues by Y. C. Fung, 2nd Edition, Springer

12.11 Tendons and Ligaments 535 where L km are constants. The constants L km are subjected to Onsager's princi- ple that L km = L mk , and the non-negative entropy production restriction. Equations (18) and (19) are the desired constitutive equations. 12.10.4 Other Theories An extensive new mathematical development of the multiphasic tissue sub- jected to finite deformation is given by Holmes (1986) and Kwan et al. (1990). Many practical and theoretical problems in physiology and medicine have been studied by the biphasic and triphasic theory, see papers by Holmes, Lai, Mow, and their associates in the list of references. A thorough analysis of the viscoelastic behavior of articular cartilage is given by Mak (1986) on the basis of bi-phasic theory, in which the viscoelasticity of the solid matrix is taken into account, whereas the interstitial fluid is considered as incompressible and inviscid. 12.11 Tendons and Ligaments In the musculoskeletal system, the function of tendons is to transmit forces from muscles to bones in order to move the bones, whereas that of the ligaments it to join bones togther to form joints. A functional unit of a skeletal muscle is bone-tendon-muscle-tendon-another bone. A functional unit of a ligament is bone-ligament-another bone. Tendons and ligaments serve in this capacity by their tensile strength. This strength is derived from collagen. The collagen molecules, fibrils, and fibers have been discussed in Chapter 7. Collagen in blood vessels is discussed in Chapter 8. Theories that aim at deriving the constitutive equations of tendons and ligaments from their microstructures are mentioned in Sec. 7.12. Theories that originate in rational mechanics are discussed in Sect. 7.6. Hence, as far as the representation of mechanical properties by constitutive equations is concerned, tendons and ligaments fall in line with other soft tissues as discussed in Chapter 7. Research on ligaments, tendons, and menisci is advancing vigorously be- cause of its clinical importance. An excellent general reference is the Handbook of Bioengineering, edited by Skalak and Chien (1987), which contains an article by Viidik on the properties of tendons and ligaments. Another general reference is the book Biomechanics of Diarthrodial Joints, edited by Mow, Ratcliffe, and Woo (1990). This book contains an article by Viidik on the structure and function of normal and healing tendons and ligaments, a paper by Frank and Hart on the biology of tendons and ligaments, and a paper by Woo, Weiss, and MacKenna on biomechanics and morphology of the medial collateral and anterior cruciate ligaments. The anterior cruciate ligament and its replacements are discussed further by Butler and Guan, and Markolf, Gorek, Kabo, Shapiro, and Finer- man. Meniscus are discussed by Arnoczky, and Kelly, Fithian, Chern, and Mow. You will see that the biology and clinical problems are made clear by

536 12 Bone and Cartilage biomechanics. See also Basic Orthopaedic Biomechanics, edited by Mow and Hayes (1991). The book Injury and Repair of Musculoskeletal Soft Tissues, edited by Woo and Buckwalter (1988), is a remarkable first exposition of the biology and clinical problems of ligaments and tendons. It is not yet bolstered by bio- mechanics. One could anticipate a deepened and enlarged role of bio- mechanics in future treatment of injury and repair. Concerning the engineering of living tissues, there is a book Tissue Engi- neering, edited by Skalak and Fox (1988), and another book by the same name edited by Woo and Seguchi (1989). But, newer results are coming out fast. Tissue engineering has a lot to do with the reaction of cells to stresses. Some references to cell mechanics are given in Chapter 4, Sec. 4.11. Tissue remodeling in bone, blood vessels, the heart, and other organs is discussed in Fung (1990). The effect of immobilization and exercise on tissue remodeling of tendons and ligaments is discussed in Woo et al. (1982). These references are mostly reviews with comprehensive lists of references. Problems 12.1 Assume that in a piece of bone the collagen fibrils and 'apatite crystals are perfectly bonded parallel to each other. Derive the Young's modulus of the bone in uniaxial tension or compression in a direction parallel to the fibrils. Derive also the Young's modulus in the direction perpendicular to the fibrils, as well as the shear modulus parallel and perpendicular to the fibrils. Express the results in terms of the elastic moduli of the individual components and the ratio of the volumes of the collagen and apatite (see Currey, 1964). 12.2 Relax the perfect bond hypothesis of the previous problem. Introduce some model of bonding between the collagen and apatite to explore the effect of bonding on the mechanical properties of the composite material. 12.3 Use the results of Problems 12.1 and 12.2 to establish a model of an osteon. Then build up a model of a bone by a proper organization of the osteons. What additional experiments should be done to verify whether the model is satisfactory or not? A successful model will then be able to correlate the mechanical prop- erties of the bone with the mass density and structure and composition of the bone, and will be useful in applications to surgery, medicine, nutrition, sports, etc. For some early attempts, which are not quite successful, see Currey (1964), Young (1957), and Knese (1958). 12.4 Consider a long bone of hollow circular cylindrical cross section with inner radius R; and outer radius Ro. Let the bone be subjected to an axial compressive load P. Assume that Eq. (3) of Sec. 12.6 applies. Show that the inner and outer radii will change according to Ro(t) = Ro(O) + koa(1 - e-bt), R;(t) = R;(O) + k;a(1 - e- bt),

Problems 537 where a and b are constants; The constants k; and ko are the values of kll on the inner and outer radii, respec- tively. The limits are Ro( (0) = Ro(O) + koa, R;((0) = Ro(O) - k;a. 12.5 Discuss the preceding problem if the constitutive Eq. (4) of Sec. 12.6 applies. 12.6 A steel plate is attached to a bone by means of screws, thus inducing a compres- sive stress between the plate and the bone. Discuss the remodeling of the bone under the plate if (a) the screws are tightened uniformly so that compressive stress under the plate is uniform, or (b) one screw is given an extra turn or two so that a nonuniform compressive stress results. 12.7 Consider the interaction of the screw threads with the bone in the situations named in Problem 12.6. Discuss the remodeling of the bone around the screws. 12.8 A long bone is subject to a bending moment M. Discuss the remodeling of the bone under bending in the context of Eqs. (1), (2), and (4) of Sec. 12.6. 12.9 Describe the structure of bone, including the blood circulation system therein. Discuss the relevance of blood microcirculation to the healing of a fractured bone. 12.10 Many people have suggested that some tissues are porous media, i.e., they are solids containing some fluids and that the movement of the fluids obeys Darcy's law. Darcy invented the law to describe the movement of water in soil, see Biomechanics: Motion, Flow, Stress, and Growth (Fung, 1990), Chapter 8, Sec. 8.6. In order to obtain some idea as to how such a material may function under an external load, consider the following idealized problem. Let a flat layer of the porous medium be of uniform thickness ho initially, and infinite in extent in the x, z plane, free on one surface (y = ho), and attached to an infinite rigid base on the other surface (y = 0). Let this porous layer be loaded suddenly by a large rigid cylinder, parallel to y, of radius a (a » ho), and with a total of force of W acting in the y direction. Under the load the porous layer will deform and fluid in the pores will move. Assume that the solid matrix material of the porous layer is linearly elastic and obeys Hooke's law. Assume that the fluid movement in the porous medium obeys Darcy's law: K <VI) = --(V<p) - Pig), J1. where <vI) is the macroscopic velocity ofthe fluid, PI is the density ofthe fluid, J1. is the shear viscosity of the fluid, <p) is the macroscopic fluid pressure, g is the gravitational acceleration, 17 is the gradient operator, and K is a constant called the permeability of the porous medium. The cylinder and the base are assumed impermeable. The normal stress acting on the cylinder at the interface with the

538 12 Bone and Cartilage porous layer is equal to the sum of the stress in the matrix material and the fluid pressure. On the free surface of the layer there is nothing to prevent the fluid from moving in or out of the surface. Write down the equations of conservation of mass and momentum. Assuming a » ho, and derive an approximate equation that governs the thickness distri- bution h as a function of location x and time t. If the load W is applied as a step function, determine h(x,t). 12.11 Generalize the investigation proposed in the preceding problem along the fol- lowing lines. (a) The force imposed by the cylinder consists of a normal force W parallel to y and a shear force S parallel to x. (b) The matrix solid behaves like most biological solids with an elastic modulus proportional to the normal stress. See Sec. 7.5, Eq. (3), p. 274. (c) The cylinder is replaced by a sphere. 12.12 Tissues of brain, liver, kidney are rich in capillary blood vessels. If the stress of the tissue is nonuniform, the blood flow in the capillaries is going to be affected. Formulate a theory of the mechanical properties of the tissue affected by the fluid movement. Analyze and compare the following alternatives: (1) A biphasic mixture theory. (2) A Darcy porous medium. (3) A system composed of a viscous fluid in tubular pores in an anisotropic deformable body advocated by H. S. Lew and Y. C. Fung (1970). References Amtmann, E. (1968) The distribution of breaking strength in the human femur shaft. J. Biomech. 1,271-277. Amtmann, E. (1971) Mechanical stress, functional adaptation, and the variation of structure of the human femur diaphysis. Ergebnisse Anat. Entwicklungsgeschichte 44,7-89. Amtmann, E and Schmitt, H. P. (1968) Uber die Verteilung der Corticalisdichte im menschlichen Femurschaft und ihre Bedeutung fur die Bestimung der Knochen- festigkeit. Z. Anat. u. Entwickl.-ges. 127,25-41. Basset, C. A. L. and Pawlick, R. J. (1964) Effect of electrical currents on bone in vivo. Nature 204, 652-653. Becker, R. O. and Murray D. G. (1970) The electrical control system regulating fracture healing in amphibians. Clin. Orthopedics 73,169-198. Bourne, G. H. (ed.) (1972) The Biochemistry and Physiology of Bone, 2nd edition, Vol. 1: Structure. Vol. 2: Physiology and Pathology. Vol. 3: Development and Growth. Academic Press, New York. Bninemark, P.-I., Hansson, B. 0., Breine, u., Lindstrom, J., Hallen, 0., and Ohman, A. (1977) Osseointegrated Implants in the Treatment of the Edentulous Jaw. Almquist and Wiksell, Stockholm, 132 pp. Brannan, E. W., Rockwood, C. A., and Potts, P. (1963) The influence of specific exercises in the prevention of debilitating musculoskeletal disorders. Aerospace M ed. 34, 900-906. Brookes, M. (1971) The Blood Supply of Bone. An Approach to Bone Biology. Butter- worths, London. Carter, D. R. and Hayes, W. C. (1977) The compressive behavior ofbone as a two-phase porous material. J. Bone Joint Surg. 49A, 954-962.

References 539 Carter, D. R., Harris, W. H., Vasu, R., and Caler, W. E. (1981) The mechanical and biological response of cortical bone to in vivo strain histories. In Mechanical Properties of Bone, S. Cowin ed. AMD Vol. 45, American Society of Mechanical Engineering, New York, pp. 81-92. Carter, D. R., Fyhrie, D. P., and Whalen, R. T. (1987) Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy. J. Biomech. 20, 785-794. Carter, D. R. (1987) Mechanical loading history and skeletal biology. J. Biomech. 20, 1095-1109. Carter, D. R., Orr, T. E., Fyhrie, D. P., and Schurman, D. J. (1987) Influences of mechanical stress on prenatal and postnatal skeletal development. Clin. Orthopae- dics 219, 237-250. Carter, D. R. and Wong, M. (1988) Mechanical stresses and endochondralossification in the chondroepiphysis. J. Orthopaedic Res. 6,148-154. Cassidy, J. J. and Davy, D. T. (1985) Mechanical and architectural properties in bovine cancellous bone. Trans. Orthopaedic Res. Soc. 31, 354. Churches, A. E. and Howlett, C. R. (1981) The response of mature cortical bone to controlled time-varying loading. In Mechanical Propoerties of Bone S. Cowin (ed.) AMD Vol. 45. American Society of Mechanical Engineering, New York, pp. 69-80. Cowin, S. C. and Hegedus, D. M. (1976) Bone remodeling. J. Elasticity 6, 313-325, 337-352. Cowin, S. C and Nachlinger, R. R. (1978) Bone remodeling III. J. Elasticity 8,285-295. Cowin, S. C. and Van Buskirk, W. C. (1978) Internal bone remodeling induced by a medullary pin. J. Biomech. 11,269-275. Cowin, S. C. and Van Buskirk, W. C. (1979) Surface remodeling induced by a medullary pin. J. Biomech. 12,269-276. Cowin, S. C. (ed.) (1981) Mechanical Properties of Bone, ASME Publication No. AMD Vol. 45. Cowin, S. C. (1983) The mechanical and stress adaptive properties of bone. Ann. Biomed. Eng. 2, 263-295. Cowin, S. C. (1984) Modeling of the stress adaptation process in bone. Cal. Tissue Int. 36 (Suppl.), S99-S104. Cowin, S. C., Hart, R. T., Balser, J. R., and Kohn, D. H. (1985) Functional adaptation in long bones: Establishing in vivo values for surface remodeling rate coefficients. J. Biomech. 18, 665-684. Cowin, S. C. (1986) Wolff's law of trabecular architecture at remodeling equilibrium. J. Biomech. Eng. 108, 83-88. Cowin, S. C and Van Buskirk, W. C. (1986) Thermodynamic restrictions on the elastic constants of bone. J. Biomech. Eng. 108, 83-88. Cowin, S. c., Van Buskirk, W. c., and Ashman, R. B. (1987) Properties of bone. In Handbook of Bioengineering, R. Skalak and S. Chien (eds.) McGraw-Hill, New York, pp. 2.1-2.27. Cowin, S. C. (1988) Strain assessment by bone cells. In Tissue Engineering, R. Skalak and C. F. Fox (eds.) Alan Liss, New York, pp.181-188. Cowin, S. c., Sadegh, A. M., and Luo, G. M. (1992) An evolutionary Wolff's law for trabecular architecture. J. Biomech. Eng. 114, 129-136. Crowningshield, R. D. and Pope, M. H. (1974) The response of compact bone in tension at various strain rates. Ann. Biomed. Eng. 2, 217-225.

540 12 Bone and Cartilage Culmann, C. (1866 and 1875) Die Graphische Statik. 1st edition, Meyer und Zeller, Zurich. Currey, J. D. (1964) Three analogies to explain the mechanical properties of bone. Biorheology 2, 1-10. Dietrick, J. E., Whedon, G., and Shorr, E. (1948) Effects of immobilization upon various metabolic and physiological functions of normal man. Am. J. Med. 4, 3-36. Dintenfass, L. (1963) Rheology of synovial fluid and its role in joint lubrication. Proc. Int. Congress Rheolog. 4, 489. Dowson, D., Longfield, M., Walker, P., and Wright, V. (1968) An investigation of the friction and lubrication in human joints. Proc. Institution Mech. Eng. (London) 181, Part 3J, 45-54. Dowson, D. and Whoms, T. L. (1968) Effect of surface quality upon the traction characteristics of lubricated cylindrical contacts. Proc. Institution Mech. Eng. (London) 182, Part 1,292-299. Evans, F. G. (1957) Stress and Strain in Bones. Their Relation to Fractures and Osteogenesis. C. C. Thomas, Springerfield, II. Evans, F. G. (1969) The mechanical properties of bone. Artificial Limbs 13, 37-48. Evans, F. G. (1973) Mechanical Properties of Bone. Charles C. Thomas, Springfield, IL. Fein, R. S. (1967) Are synovial joints squeeze film lubricated? Proc. Inst. Mech. Eng. 181, 125-128. Firoozbakhsh, K. and Cowin, S. C. (1980) Devolution of inhomogeneities in bone structure- Predictions of adpative elasticity theory. J. Biomech. Eng. 102, 287- 293. Frost, H. M. (1964) The Laws of Bonre Structure. Charles C. Thomas, Springfield, IL. Fukada, E. and Yasuda, I. (1957) Piezoelectric effect of bone. J. Physical. Soc. Jpn. 12, 1158-1162. Fukada, E. (1968) Mechanical deformation and electrical polarization in biological substances. Biorheology 5, 199-208. Fung, Y. C. (1972) Stress-strain history relations of soft tissues in simple elongation. In Biomechanics: Its Foundations and Objectives. Prentice-Hall, Englewood Cliffs, NJ, pp. 181-208. Fung, Y. C. (1990) Biomechanics: Motion, Flow, Stress, and Growth. Springer-Verlag, New York. Fyhrie, D. P. and Carter, D. R. (1985) A unifying principle relating stress state to trabecular bone morphology. Trans. Orthopaedic Res. Soc. 31, 337. Gjelsvik, A. (1973) Bone remodeling and piezoelectricity. I & II. J. Biomech. 6, 69-77, 187-193. Gliicksmann, A. (1938) Studies on bone mechanics in vitro. I. Influence of pressure on orientation of structure. Anat. Record 72, 97-115. Gliicksmann, A. (1939) II. Role oftension and pressure in chodrogenesis. Anat. Record 73,39-55. Gliicksmann, A. (1942) The role of mechanical stress in bone formation in vitro. J. Anat. 76, 231-239. Ham, A. W. (1969) Histology, 6th edition. Lippincott, Philadelphia. Harrigan, T. and Mann, R. W. (1984) Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci. 19, 761-767. Hayes, W. C. and Snyder, B. (1981) Toward a gnemtitative formulation of Wolff's law

References 541 in trabecular bone. In Mechanical Properties of Bone, S. C. Cowin ed. AMD Vol. 45. American Society of Mechanical Engineers, New York. Hegedus, D. H. and Cowin, S. C. (1976) Bone remodeling II: Small strain adaptive elasticity. J. Elasticity 6,337-352. Hert, J. A., Liskova, M., and Landa, J. (1971) Reaction of bone to mechanical stimuli. Part 1. Continuous and intermittent loading of tibia in rabbit. Folia Morphol. 19, 290-317. Hert, 1., Sklenska, A., and Liskova, M. (1971) Reaction of bone to mechanical stimuli. Part 5. Effect of intermittent stress on the rabbit tibia after resection of the pripheral nerves. Folia Morphol. 19, 378-387. Hoffman, O. (1967) The brittle strength of orthotropic materials. J. Composite Mater. 1,200-207. Holmes, M. H. (1986) Finite deformation of soft tissue: Analysis of a mixture model in uniaxial compression. J. Biomech. Eng. 108, 372-381. Hong, S. Z., Wu, Z. K., and Zu, C. M. (1987) Experiments on human vertebrae cervical. Chin. J. Biomed. Eng. 6, 75-83. Johnson, M. W. and Katz, 1. L. (1987) Electromechanical effects in bone. In Handbook of Bioengineering, R. Skalak and S. Chien (eds.) McGraw-Hill, New York, pp. 3.1-3.11. Jones, H. H., Priest, J. D., Hayes, W. c., Tichemor, C. c., and Nagel, D. A. (1977) Humeral hypertrophy in response to exercise. J. Bone Joint Surg. A 59, 204-208. Justus, R. and Luft, J. H. (1970) A mechanochemical hypothesis for bone remodeling induced by mechanical stress. Calcified Tissue Res. 5, 222-235. Katz, J. L. and Mow, V. C. (1973) Mechanical and structural criteria for orthopaedic implants. Biomat. Med. Dev. Art. Organs 1, 575-638. Kazarian, L. E. and van Gierke, H. E. (1969) Bone loss as a result of immobilization and chelation. Clin. Orthopedics 65, 67-75. Knese, K.-H. (1972) Knochenstruktur als Verbundbau. G. Thieme, Stuttgart. Kummer, B. K. F. (1972) Biomechanics of bone: Mechanical properties, functional structure, and functional adaptation. In Biomechanics: Its Foundations and Objec- tives, Y. C. Fung, N. Perrone, and M. Anliker (eds.) Prentice-Hall, Englewood Cliffs, NJ, pp. 237-271. Kwan, M. K., Lai, W. M., and Mow, V. C. (1984) Fundamentals of fluid transport through cartilage in compression. Ann. Biomedical Eng. 12,537-558. Kwan, M. K., Lai, W. M. and Mow, V. C. (1990) A finite deformation theory for cartilage and other soft hydrated connective tissues. I. Equilibrium results. J. Biomechanics. 23, 145-155. Lai, W. M., Hou, J. S., and Mow, V. C. (1991) A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113,245-258. Lakes, R. S., Katz, J. L., and Sternstein, S. (1979) Viscoelastic properties of wet cortical bone-I. Torsional and biaxial Studies. J. Biomech. 12, 657-678. Lakes, R. S. and Katz, J. L. (1979) Viscoelastic properties of wet cortical bone. II. Relaxation mechanisms. III. A nonlinear constitutive equation. J. Biomech. 12, 679-687, 689-698. Lanyon, L. B. and Baggott, D. G. (1976) Mechanical function as an influence on the structure and form of bone. J. Bone Joint Surg. B 58, 436-443. Lew, H. S. and Fung, Y. C. (1970) Formulation of a statistical equation of motion of

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Author Index Abbot, B. C. 462 Atherton, A. 162 Aberg, A. K. G. 495, 497 Atridge, R. G. C. 315, 317, 319 Abramowitz, M. 314 Axelsson,1. 495, 497 Adkins, J. E. 57,275,307,316,455,463 Ayorinde, O. A. 344, 384 Ahmed, A. M. 543 Azuma. T. 330,333,363,364,384,385 Aidley, D. J. 494, 497 Baer, E. 256, 257, 258, 315, 316, 317, Akeson, W. H. 544 319 Al-Tinawi, A. 384 Alexander, R. M. 314, 393, 394,424 Baez, A. 359, 385, Allen, D. G. 462 Baez,S.359,358,385 Almansi, E. 32, 300 Baggott, D. G. 541 Altman, P. 316 Balazs, E. A. 234-237, 240 Amiel, D. 544 Baldwin, A. L. 385 Amtmann, E. 504, 516, 538 Balser, 1. R. 539 Andersson, G. 22 Banga, G. 314 Anliker, M. 269, 330, 343, 366, 384 Barbee, J. H. 105, 173, 174, 175,215 Anthony, R. L. 316 Barbenel,1. G. 317 Anwar, R. A. 318 Barker, N. 107 Argos, P. 314 Bartlet, D. 159 Basset, A. 499 Armeniades, C. D. 319 Bassett, C. A. L. 369, 518, 538 Armstrong, C. G. 542 Bauer, R. D. 295, 314, 328, 333, 385, 391 Bayliss, W. M. 470, 497 Armstrong, R. C. 65 Beaupre, G. S. 543 Arnoczky,S.P.536 Becker, E. 289,290, 314 Becker, H. 513 Aroesty, J. 215 Becker, P. S. 161 Arridge, R. G. C. 315, 317, 319 Becker, R. O. 369, 518, 538 Ascenzi, A. 513 545 Ashman, R. B. 539 Ashton,F. T. 469, 497 Ashton-Miller,1. A. 22

546 Author Index Belsky, S. A. 315 Branemark,P. 1.158,518,538,543 Benis, A. M. 107 Breine, U. 538 Bennett, V. 140, 158 Brennen, C. 241 Bergel, D. H. 293, 311, 312, 314, 385, Bressan, G. M. 248, 314 Briney, S. R. 544 390,424 Britten, A. 107 Berne, R. M. 428, 431, 461, 462 Brokaw, C. J. 241 Besdo, D. 389 Brookes, M.507,508,509,539 Bessis, M. 158 Brooks, D. E. 105 Beven 1. A. 385 Brutsaert, D. I. 462 Beven, R. D. 385 Bryant, C. A. 106 Biggs, R. 105 Buchtal, F. 277, 280, 314 Bingham, E. C. 103, 104,221,240 Buckwalter, J. A. 536, 544 Biot, M. A. 293, 314 Bugliarello, G. 91, 105 Bird, F. 58,65,513 Bull, B. S. 158 Black, J. 513 Bunch, W. H. 543 Blackshear, P. L. 92, 105, 158 BurakotT, S. J. 153 Blatz, P. J. 275, 276, 314, 315 Burgers, 1. M. 240 Blick, E. F. 162 Burke, D. C. 543 Bo, L. 140, 158 Burnstock, G. 466, 467, 470, 497 Bodner, S. R. 268, 314 Burstein, A. H. 512, 543 Boe, A. 454,455,464 Burton, A. C. 107,116,117,143,158, Bogen, D. 1(.426,457,458,459,462 Bohr, D. F. 385,470,495,497 184,216,326,360,385,390 Boltzmann, L. 46, 65 Busse, R. 301,317,319,330 Bond, T. 111 Bussolari, S. R. 217 Bonfield, W. 513 Butler, D. L. 536 Bonucci, E. 513 Butler, T. M. 382, 498, 536 Bordas, J. 318 Buzard, I(. 316 Borelli, G. A. 2,4,426,457,462 BiiIbring, E. 470, 487, 497 Borg, T. I(. 455, 462 Born, G. V. R. 162 Caler, W. E. 539 Born, M. 239 Cama, F. C. 513 Bornhorst, W. J. 462 Campbell J. H 385 Bornstein, P. 318 Campbell, G. R. 385 Bourne, G. H. 503, 538 Canham, P. B. 116, 117, 121, 158 Bouske\\a, E. 363, 385 Caplan, S. R. 413, 424 Bouzid, A. 162 Carew, T. E. 318 Bowen, T. E., Jr. 453, 463, 464 Carew, T. W. 385 Boyd, C. D. 315 Carlson, F. D. 401, 424 Boyle, R. 2, 4 C~ro, C. G. 194, 195, 197, 198, 215, 217, Braasch, D.l58, 215 Brading, A. F. 497 385 Brady,A. J. 451,453,462 Carter, D. R. 369, 539 Brailsford, J. D 158 Cassidy, J. J. 539 Brankov,G.344,385 Casson,M. 72, 74, 75, 78,102,106 Brannan,E. W.538 Cauchy, A. L. 32, 33, 510 Branton,D. 140, 158 Caulfield, 1. B. 455, 462 Braunwald, E. 465 Chadwick, . 421 Bray, C. 162 Chakrin,L. W.224,229,241

Author Index 547 Chang, P. C. 385 Dai, F. 315, 514 Charm, S. E. 106 Dale, W. C. 257, 258, 315 Cheal, E. J. 542 Daly, C. H. 317 Chen, H. Y. L. 272, 314 Daniels, M. 462 Chen, P. 117, 118, 119, 120, 158 Darcy, H. 537 Chen, Y. D. 424,425 Davidson, C. L. 543 Chern, K. Y. 536 Davies, P. F. 212, 217 Cheung, D. W. 389 Davies, R. E. 498 Cheung, J. B. 386 Davis, B. R. 318 Chew, P. H. 465 Davis, M. J. 388 Chien, S. 67, 69, 84, 106, 116, 136, 145, Davis, S. 228-232, 240 Davy, D. T. 539 153, 158, 159, 162, 184, 196,215, Dawson, C. A. 384 Dawson, S. V. 317 535,543 Deak, S. B. 248, 315 Choe, K. I. 316 Debes,J. 248, 297, 298, 342, 315, 386 Chow, C. Y. 215,216,241 Delfs, E. 241 Chu, B. M. 315 Dellenback, R. J. 106, 159 Chuong, C. J. 357, 386 Demiray, H. J. 344, 386 Churches, A. E. 539 Dempster, W. T. 513 Ciferri, A. 250, 315 Deng, Shanxi 327, 341 Clapeyron, B. P. E. 15 DeRosier, D. J. 425 Clift, A. 233, 240 Descartes, R. 2, 3 Clough, G. 390 Devries, A. 160 Cohen, W. D. 159 Dewey, C. F. 197, 199,203,217 Cohen-Gould, L. 465 DeWitt, M. T. 155, 163 Cokelet, G. R. 67, 68, 69, 71, 121, 159, Diamont, J. 256, 257, 315 Dick, D. A. T. 159 173, 174, 175,215 Dietrick, J. E. 515,540 Collins, R. 295, 315, 386 Dintenfass, L. 96, 97, 106, 121,540 Cooke, R. 416, 424 Dobrin, P. B. 386,497 Copley, A. L. 221 Doi, T. 425 Dong, C. 147, 149, 150, 163 Couette, M. 54 Doring, W. 289, 314 Coutts, R. D. 544 Dorman, F. D. 105 Covell, J. W. 465 Dortmans, L. J. 286, 315 Cowan, M. J. 369,386 Doty, D. 514 Cowan, P. M. 263, 315 Dowson, D. 531, 540, 544 Cowin, S. C. 369, 512, 513, 516, 517, Doyle, J. M. 386 Duffy, J. 426 540 Duhamel, J. M. C. 40 Cox, R. H. 386, 389, 497 Dunn, F. 241, 294, 315 Crapo, J. D. 389 Dyson, E. D. 544 Crimmins, M. 153 East, D. J. 22 Crisp, J. D. C. 316 Edman, K. A. P. 411, 446, 447, 448, 449, Croce, P. A. 216 Crowingshield, R. D. 512, 540 450,451 Edmonds, P. D. 315 Crystal, R. G. 369, 386 Culmann, C. 369 Cunningham, E. 239 Currey, J. D. 513,536, 540 Curry, F. R. E. 217 Curtis, A. S. G. 155,162 Curtiss, C. F. 65

548 Author Index Einstein, A. 240 Frasca, P. 513 Eisenberg, E. 415, 416, 424, 425 Fraser, P. A. 390 Ekstrom, J. 495, 497 Frasher, W. G. 270, 317, 326, 387, 389 Ellis, D. 241, 219, 295 Freeman, G. 317,464 Elzinga, G. 463,464 Freundlich, H. 221 Emery, A. H. 315 Frey-Wyssling, A. 240 Engelhardt, H. 160 Friedman, B. 319 Engelman, T. W. 470, 497 Fronek, 1(. 57,298,315,344, 387,389 Engelson, E. T. 465 Frost, H. M. 515, 540 Erdelyi, A. 380 Fry, D. L. 121, 159, 197, 198,203,217, Eringen, A. C. 57 Erwin, G. 162 387 Euler, L. 2, 4, 32 Fry, W. 1. 315 Evans, E. 112, 113, 114, 115, 132, 134, Fuchs, J. C. A. 391 Fukada,E.369,518,540 135, 136, 137, 139, 140, 142, 144, Fumero, R. 464 150, 159. 163 Fung, Y. C. 12, 13,22,27,47, 57, 59, 65, Evans, F.G. 22,510, 512, 513, 515,540 Evans, 1. H. 317 108,111-122,130,141,146,159, Evans, 1. W. 217 160,170-172,176,178-181,183, 187,188,190-194,206,208,209, Factor, S. M. 465 214-217,225,240,244,246,248, Fahraeus, R. 82, 172, 215 266,269,270,272,282,287,293, Faulkner, J. A. 386 297,298,300-302,305,307,310, Fedorciw, B. 162 311,314-320,328-330,332,335, Fein, R. S. 530, 540 343-347,350-353,357,360,363, Feldman, H. 320, 391 369-376,383,386-390,420,421, Feng,S.S.159 424,434-440,451,452,459, Fenn, W. P.401,404,424 463-465,471-473,475-478,480, Ferenezi, M. A. 424 482-486,488-494,497-499,531, Feughelman, M. 250, 315 533 Fick, A. 2, 5 Fyhrie, D. P. 539, 540 Finerman, G. A. M. 536 Firoozbakhsh, K. 540 Gabelnick, H. L. 240 Fisher, G. M. 386 Gaehtgens, P. 387 Fithian, D. C. 536 Galeski, A. 317 Fitz-Gerald, J. M. 196,215,217 Galileo, G. 1, 2, 3, 22 Flaherty, 1. T. 197,203,217 Gao, Yun Qin 325 Fleming, 248 Garrett, R. R. 263, 315 Flory, P.J. 248,263,315, 316 Garrick, E. 289, 316, 319 Flugge, W. 126, 159 Gathercole, L. J. 257, 315 Folkman, J. 155, 163,387 Gay, W. A. 463 Foppiano, L. 391 Gau,G. S. 197,203,217 Ford, L. E. 424, 462 Geiger, S. R. 461 Forstrom, R. 1. 105 Gerecke, Dr. 316, 318 Fox, C. F. 536, 543 Gerhart, T. N. 542 Gibbs, D. A. 234, 235, 240 Foppl, o. 289, 290, 314 Gibson, T. 317 Giddens, D. 198,217 Frank, J. S. 463 Gilbert, W. 7 Frank, o. 2, 8,21, 328, 387, 535

Author Index 549 Gilliland, E. R. 107 Hammersen, F. 218 Gimbrone, M. A., Jr. 217 Han, H. C. 351, 352, 388 Gizdulich, P. 316, 344 Handa,H.388,389,390 Gjelsvik, A. 540 Handenschild, C. 156, 163 Glagov, S. 163,391 Handley, C. J. 163 Glass, L. 433, 463 Hannappel, J. 498 Glimcher, M. J. 542 Hanson,J.413,425 Glover, F. A. 240 Hansson, B. O. 538 Gliicksmann, A. 515, 540 Harder, I>. R. 384 Goedhard, W. J. A. 317, 388 Hardung, V. 311, 312, 316, 328, 388 Goldman, Y. E. 418, 424 Harkness, M. L. R. 263, 264, 316, Goldsmith, H. L. 83, 85, 86, 87, 88, 90, 388 91, 106, 108, 176, 196,215,216 Harkness, R. I>. 263, 264, 316, Golenhofen, K. 470, 471, 497, 498 Gomez, M. A. 544 388 Goo, Yun Qin 325 Harrigan, T. 541 Goodwin, J. W. 105 Gorden, M. I>.255,316,318 Harris, W. H. 539 Gordon, A. M. 424, 403, 404 Hart, R. T. 535, 539 Gordon, A. R. 498 Hart-Smith, L. J. 316 Gordon, E. F. 217 Gore, R. W. 357, 358, 385, 388 Hartert, H. 96,107 Gorek, J. F. 536 Harvey, E. N. 227, 240 Gosline, J. M. 248, 316 Harvey, W. 2, 3, 7 Gou, P. F. 344, 388 Gow, B. S. 388 Hasegawa, M. 330, 363,364,384,385 Graustein, W. C. 126, 160 Hashimoto, H. 389 Gray, W. R. 249,316,395,396 Hassager, O. 65 Green, A. E. 57,58,65,275,307,316, Haut, R. 294 Hawley, R. H. 426 455,463,514 Hay, E. I>. 318 Green, G. 32, 318 Hayashi, K. 333, 344, 388, 389, 390 Greenfield, J. C. 391 Hayes, W. C. 531, 539 Gregersen, M. I>. 67, 106, 140, 159, 160 Haynes, R. H. 107,172,215 Griffith, P. 240 Healer, J. 513 Groom, A. C. 107 Hearle, J. W. S. 203,250,316 Gross, I>. R. 424 Hefner, L. L. 453, 463, 464 Gross, J. F. 161,215 Hegedus, I>. M. 516, 539 Guan, Y. 536 Heilbrunn, L. V. 227, 240, 241 Guccione, J. M. 433, 463 Hellstrand, P. 495, 498 Gumbel, E. J. 117,160 Helmholtz, H. V. 2, 4, 5 Guth, E. 289, 316 Helmlinger, G. 197,203,218 Guyton, A. C. 470, 498 Herlihy, J. T. 498 Hert, J. A. 516, 517, 541 Hales, S. 8, 9 Hallen, O. 538 Heuningen, R. 465 Ham, A. W. 502, 503, 541 Hamel, G. 32, 300 Heuser, J. E. 248, 318, 416, 424 Hammerle, W. E. 106 Higuchi, H. 418, 424 Hill, A. V. 8,10,399,400,401,402,403, 405,406,411,412,413,419,441, 424,425,445,481,498 Hill, T. L. 414, 415, 416, 424, 425 Histand, M. E. 384 Ho, H. 389

550 Author Index Hochmuth, R. M. 121, 134, 135, 136, Jaffrin, M. Y. 498 137, 139, 143, 144, 150, 160, 181, Jakobs, D. M. 543 182,215 Janicki, J. S. 391 Janssen,1. 3 Hoeber, T. W. 144, 160 Janssen, Z. 3 Hoeltzel, D. A 276, 277, 316 Jay, A. W. C. 184,215 Hoeve, C. A. 1. 248, 316 Jemmott, G. F. 544 Hoffman, B. F. 499 Jennett, W. 158,215 Hoffman, O. 512, 541 Jerrad, W. 360 Holberton, D. V. 160 Jewell, B. R. 426, 464 Holman, M. E. 498 Johannsson, M. 462 Holmes, M. H. 535, 541 Johansson, B. 495, 498 Hong, S. Z. 541 Johnson, E. A. 463,465 Hooke, R. 2,4,30,38,510 Johnson, G. A. 317 Hoppin, F. G. 245, 298 Johnson,M. W.513, 541 Horowitz, A. 455,456, 463 Johnson, P. C. 186,215,359, 388, Hort, W. 463 Hou,1. A. 500, 531, 541 498 Houchin, D. W. 116,117,160 Jonak, R. 318, 319 Howlett, C. R. 539 Jones, A. W. 386, 497 Hsiao, C. C. 386 Jones, D. B. 155, 163 Hsiung, C: C. 218 Jones, H. H. 541 Hu, W. C. 241, 295, 315, 386 Julian, F. 1. 424, 425 Huddart, H. 494, 498 Justus, R. 518, 541 Huisman, R. M. 463 Humphrey, J. D. 306, 311, 317,455,457, Kabo, 1. M. 536 Kage, H. S. 160 459,463 Kaiser, E. 277,280,314 Hunt, S. 494, 498 Kamiya, A. 198, 218 Hunter, P. J. 424,433,463,464 Karlisch, P. 156, 164 Huntsman, L. L. 441, 442, 463, 465 Kastelic, J. 256, 257, 317 Huriyama, H. 498 Kasyanov, V. 344, 388 Hurley, J. V. 163 Katchalsky, A. 143, 160 Huxley, A. F. 413, 414, 415, 424, 425, Katz, J. L. 512,513,514,541 Kay, M. 389 462 Kazarian, L. E. 516, 541 Huxley, H. E. 413, 414, 416, 418, 425, Kedem, D. 160 -Keiper, D. 513 463,464 Keitzer, W. F. 389 Hwang, N. H. C 424 Keller, A. 315 Hyatt, R. E. 317 Kelly, M. A. 536 Kelvin, Lord (W. Thomson). 41, 42, 43, Imholz, B. P. M. 344, 388 Indik, Z. 248 44,45,49,51 Ingber, D. E. 156, 163 Kenedi, R. M. 276, 317 Intaglietta, M. 360, 361, 387, 388 Kenner, T. 328, 388, 391 Ishijima, A. 417, 425 Khouri, R. K. 156, 163 Iwazumi, T. 413,425 Khreningen-Guggenberger, 1. von, 232, JacKenna, D. A. 535 241 Jaeger, R. 159 Kim, D. W. 197,203,218

Author Index 551 Kimura, T. 318 Lamb, H. 2, 148 King,1. R. 118, 160 Lame, G. 15, 38 King, R. G. 237, 238, 241 Lamport, H. 385 Kishino, A. 243, 317,425 Lanczos,D. 280, 317 Klein-Nulend, J. 155, 163 Landa, J. 541 Klibansky, C. 160 Landel, R. I. 275, 320 Klopper, P. J. 543 Lang, S. B. 513 Knese, K. H. 536, 541 Langer, G. A. 463 Knets, I. 388 Langewouters, G. J. 317, 343, 388 Knight, G. W. 543 Langford, G. 159 Knopoff, L. 289, 317 Langsjoen, P. H. 97, 98, 107 Kobayashi, A. S. 384 Lanir, Y. 297, 298, 302, 305, 310, 311, Koch, M. H. J. 318 Kohn, D. H. 539 317,433,455,457,463,464 Kohn, R. R. 315 Lanyon, L. B. 541 Komi, P. V. 22 Lanyon,L.E. 155,163,164 Konishi, J. 542 Konomi, H. 318 Laplace, M. 14 Korecky, B. 464 Larcan, A. 107 Korostoff, E. 513 Korteweg, D. 1. 2, 5, 342 Laszt, L. 328, 389 Koslow, A. R. 199,218 Le Winter, M. M. 317, 464 Kot, P. 186,216 Lee, G. C. 317 Koudsi, B. 163 Lee, J. S. 270, 389 Kral, M. 544 Kreuger,J. W.425,432,464 Lee, M. C. 311, 317, 319,459,464 Krogh, A. 8, 10 Lee, R. M. K. 389 Kron, S. J. 426 Lee, T. J. F. 389 Kronecker, . 32 Leung, D. Y. M. 155, 163 Kuei, S. C. 238, 241, 542, 544 Levesque, M.J. 197,203,218 Kuethe, A. M. 215, 216, 241 Kiimin, K. 172 Levy,M. N.431,438,462 Kummer, B. K. F. 506, 507, 515, 541 Lew,H. S. 181, 183,216,538,542 Kurihara, S. 498 Kuriyama, H. 470, 487, 497 Lewis, D. H. 218 Kurland, G. S. 106 Kwan, M. K. 311, 317, 530, 531, 535, Li, C. H. 513 Lichtman, M. A. 163 541 Liddicoat, R. T. 513 LaChange, P. A. 542 Lighthill, M. 1. 184, 194, 196,216 Lacombe, E. 107 Lindau, L. A. 543 Lagrange, J. L. 32 Lindal, R. G. 390 Lai, W. M. 310, 311,457,500,530,531, Lindholm, U. S. 314 Lindqvist, T. 172, 215 533,535,541 Lindstrom, J. 538 Lai-Fook, S. 293, 317, 384 Lakes, R. S. 513, 514, 540 Linehan,J. H. 384 Lamar,1. K. 241 Lamarck, D. de. 7 Lingard, P. S. 140, 160 Linn, F. C. 525, 530, 542 Lipowsky, R. 161, 163 Lipschitz, H. 542 Lipson, 512 Liskova, M. 541 Litchman, H. M. 426 Litt, M. 224, 229,315 Little, R. 294 Litwak, P. 389

552 Author Index Liu, S. <). 208, 323,324,350,352,370, Martyn, D. A. 441, 443, 444, 463, 464 Mashima, H. 470,497 371,372,373,374,375,376,387, Mason, S. G. 108,176,216 389 Mason, W. P. 289 Llaurado, J. G. 386 Mastrigt, R. van 481, 495, 498 Loeb, L. 389 Mathews, M. B. 163 Lombard, J. H. 389 Longfield, M. 540 Mathieu-Costello, O. 389 Lotz, J. C. 512, 513, 542 Matsuda, M. 384, 389 Lowenstein, L. M. 159 Matsuda, T. 330, 391 Lowther, D. A. 163 Maxwell, J. C. 41, 42. 43,44,45,49,51 Lowy, J. 498 McCown, J. T. 160 Luft, J. H. 518, 541 McCulloch, A. 433, 464, 643 Lugassy, A. A. 513 McCutchen, C. W. 526, 530, 542 Lund, E. 1. 369 Lundberg, J. L. 106 McDonald, D. A. 316, 330, 388, 389 Luo, G. M. 540 McElhaney, J. H. 294, 318, 513 Luse, S. A. 106 McGeachie, J. K. 386 Lutz, R. J. 223, 224, 228, 229, 240 McIntire, L. V. 94, 107 Lux, S. E. 145, 161 McMahon, T. A. 240 McMillan, D. E. 107 ~a,S. P.418,419,426 Meade, K. P. 541 MacConaill, M. A. 530, 542 Mecham, R. P. 248, 318 MacFarlane, R. G. 105 Meiselman, H. J. 121, 159 Mack, P. B. 516, 542 Melnik, L. 159 Mackay, M.J. 389 Melvin, J. W. 320 Madden, J. A. 384 Merati, J. K. 384 Magaribuchi, T. 498 Mercer, R. R. 389 Magnus, W. 380 Merrill, E. W. 66, 68, 69, 70, 240 Majack, R. H. 318 Merrillees, N. C. 498 Mak, A. F. 535, 542 Merz, J. T. 7,16,17,22 Malcolm, L. L. 526, 527, 528, 529, 530, Merz, W. A. 542 Messer, M. 513 542 Messmer, K. 97, 107 Malpighi, M. 3, 8 Meyer,G. H. 369 Maltzahn, W. W. von. 389 Meyers, F. A. 513 Mann, R. W. 541 Meyrick, B. 389 Mansur,J. M. 318 Miller, D. I. 22 Marchesi, S. L. 145, 161 Marchesi, V. T. 145, 161 Miller, E. 1. 254, 318 Margetts, W. G. 107 Mills, C. C. 106 Markin, V. S. 213, 218 Mirandi, J. E. 462 Markolf, K. L. 536 Mirsky, I. 389 Marlow, J. 86, 106 Moens, A. I. 342 Maroudas, A. 530, 542 Marple, R. N. 121, 160,215 Mohandas, N. 143, 160 Marquardt, D. W. 389 Mommaerts, W. F. H. 401, 425, 462 Marsh, B. S. 401, 404, 424 Montevecchi, F. M. 464 Martin, R. B. 542 Martinac, B. 213,218 Montfrans, G. A. 388 Mooney,M.57,275,318 Moore, P. B. 416, 425 Moores, S. U. 498 Morgan, F. R. 276

Author Index 553 Morgan, H. E. 155, 163 Oberhettinger, F. 380 Mori, K. 388 Oda, M. 542 Moritake, K. 333, 388, 389, 390 Odell, G. M. 155, 156, 163 Mow, V. C. 310,311,457,500,513,524, Ogden, E. 384 Ogston, A. G. 220, 221, 234, 241,530, 525,530,531,541,542 Mulvaney, M. 1. 495,498 542 Mulvany, G. 389 Ohman, A. 538 Munn, J. I. 116, 160, 117 Oka, A. 81,82, 107 M uragaki, Y. 318 Okumura, A. 388, 390 Murphy, R. A. 390,495,498 Olmsted, M. 425 Murray, D. G. 518, 538 Olsen, B. R. 255, 316, 318 Onogi, S. 384 Nachemson, A. 22 Op den Kamp, J. A. F. 154, 163 Nachlinger, R. R. 539 Ortgengren, R. 18,22 Nagasawa, S. 388, 390 Osol, G. 389 Nagel, D. A. 541 Oster, G. 163 Nagelsmit, M. 465 Ostwald, . 53 Nair, P.465 Owens, C. 389 Nario, Y. 388, 390 Ozkaya, N. 161 Needham, D. M. 138, 139, 150, 161, 163 Nemat-Nasser, S. 542 Pappenheimer, J. R. 212, 218 Nemetschek, T. 262, 318, 319 Parmley, W. W. 410, 425, 446 Nemetschek-Gansler, H. 318 Parnell, B. L. 116, 117, 160 Nemhauser, I. 159 Pascal, B. 25 Nerem, R. M. 197,203,218,219,390 Pasch, T. 295, 314, 330, 385 Neumann, F. 40 Pasley, P. R. 426 Nevo, E. 433, 464 Patel, D. J. 318, 320, 344, 385, 390, 391, Newton, I. 2, 4, 36 Niedergerke, R. 413, 425 514,544 Nigul, I., and U. 379 Patterson, S. W. 431,464 Niimi, H. 390 Pattitucci, P. 344, 387,424,464,471, Nilsson, E. 411, 446, 447, 448, 449, 450, 472,473,475,488-491,493,494, 451 498 Ninomiya, Y. 318 Patwardham, A. G. 543 Nishimura, I. 318 Pauwels, F. 369, 507, 516, 543 Noble, M. I. 413, 425, 453, 462, 464 Pawlick, R. J. 518, 538 Nolan, A. C. 425 Payne, B. 1. 241 Nollert, M. U. 197,212,218 Peach, M.J. 385 Nolte, H. 163 Peachey, L. D.430,464 Noordergraf, A. 312, 320 Pearson, K. 15, 22 Norris, C. H. 145, 161 Pedley, T. J. 215, 385 North, A. C. T. 315 Pegram, B. L. 385 Nosan, D. 465 Peiper, . 495, 498 Noyes, 294 Pereira, 1. M. 318 Nunn, 138,139, 161 Perl, M. 463 Perrone, N. 269 Oakes, B. W. 163 Phibbs, R. H. 91, 107 Pierce, R. A. 315

554 Author Index Pietrabissa, R. 464 Ridge, M. D. 276, 318, 319 Pinto,J. CJ. 273, 318,432,434,435,437, Riedl, H. 262, 318, 319 Riemann, CJ. F. B. 4 438,439,440,453,454,455,464 Rijnsburger, W. H. 465 Piola, CJ. 299 Riley, D. J. 315 Piper, H. 464 Rivlin, R. S. 57, 58, 65, 275, 319 Pipkin, A. C. 58, 65,149, 161,318,514 Roach, M. R. 326, Plomb, E. P. 361, 388. Robinson, A. J. 389 Podolsky, R. J. 415, 425 Robinson, T. F. 455, 465 Poiseuille, J. 2, 4 Rockwood, C. A. 538 Poisson, S. D. 38 Rodarte, 1. R. 317 Polissar, M. J. 313, 402, 426 Rodbard,S.198,218 Pollack, CJ. H. 413,415,418,425,432, Rogers, T. CJ. 58,65,318,514 Rondinone, J. F. 463, 464 453,464 Rosenquist, T. H. 216, 390 Pollack, S. R. 369 Ross, J., Jr. 465, 451, 452, 465 Ponder, E. 116, 117, 121, 140, 161 Routbart, J. L. 289,319 Ponders, 1. H. 462 Roux, W.369,506,507,543 Pope, M. H. 512, 540 Rowlands, S. 107,215 Potts, P. 538 Rubin, C. T. 164, Powell, M. J. D. 543 Rundgren, A. 263, 264 Prewitt, R. L. 389 Rushmer, R. F. 390 Price,1. M. 471, 472, 473, 475, 488, 489, Rutherford, L. 544 Rydevik, B. 518, 543 490,491,493,494,498 Priest, J. D. 541 Sabbah, H. N. 146, 161 Prosser, C. L. 470, 497 Sachs, F. 154, 164 Prothero, J. 184,216 Sack,H. S.289,319 Purdy, R. E. 385 Sackman, E. 160 Sadegh, A. M. 540 Rachev, A. 385 Saint Venant, B. de 32 Radin, E. L. 241, 530, 531, 542, 543 Sakariassen, K. S. 198,218 Rajagopal, K. R. 315, 317, 320, 514 Sakurada, K. 425 Raju, K. 248, 318 Saltzstein, R. A. 369 Rakussan, K. 464 Salzman, E. W. 107 Ramachandran, CJ. N. 318 Santorio, S. 3 Rand, P. W. 107 Sato, M. 197,218,219, 388, 389, 390 Rand, R. P. 107, 143 Saunders, D. W. 275, 319 Randall, J. T. 315 Sauren, A. A. H. CJ. 315 Rannels, D. E. 155, 164 Schaeder, J. A. 107 Ratcliffe, A. 534, 542 Schenk, R. K. 542 Rawicz, W. 159 Scher, A. M. 461 Reddi, H. 163' Schiling, V. 318 Reedy, M. K.416,426 Schmalzer, E. A. 162 Reid, L. 389 Schmid-Schoenbein, H. 97, 107, 121, Reilly, D. T. 512,543 Remuzzi, A. 217 156, 161 Repin, V. S. 218 Schmid-Schonbein, CJ. W. 57, 121, 150, Rhinelander, F. W. 501, 543, 507 Rhodin,1. A. CJ. 218, 322, 390 151,164,315,387,390,465 Rickaby, D. A. 384

Author Index 555 Schmidt-Nielsen, K. 121, 161 Smail, B. H. 464 Schmitt, H. P. 504, 512, 543 Smaje, L. H. 390 Schneider, D. 311, 319 Smith, K. A. 240 Scholiibbers, J. G. 163 Smith, S. D. 369, 513 Schroter, R. C. 215, 217, 385 Smoluchowski, M. von 227 Schultz, A. B. 18,22,513 Snyder, B. 344, 541 Schultz, S. G. 154, 164 Sobin, P. 244,245,247,365,366,367 Schurman, R. J. 539 Sobin,S. S. 120, 167, 169,216,258,319, Scott-Blair, G. W. 96, 107,240,241 Seaman, G. V. F. 105 361,362,363,387,389,390 Secomb, T. W. 161, 196,216 Sollins, M. R. 425 Sedlin, E. 543 Somlyo, A. P. 385,469,497 Seed, W. A. 215, 385 Somlyo, A. V. 469, 497 Sommer, J. R. 465 Seehar, G. M. 155, 162 Sonneblick, E. H. 410, 425, 446, 465 Segre, G. 216 Spach, M. S. 461 Seguchi, Y. 536, 544 Sparks, H. V. 385, 497 Seifriz, W. 145, 161 Spatz, C. A. 389 Sekraydarian, K. 425 Spencer, A. J. M. 58, 65 Seshadri, V. 216 Sperelakis, N. 461 Sevilla, J. 91, 105 Spilker, R. L. 543 Shabetai, R. 317,464 Spiro, D. 465 Shah,J.S.3l5 Spotnitz, H. M. 465 Shapiro, A. H. 498 Sprague, E. A 219 Shapiro, M. A. 536 Spudich, J. A. 426 Sharma, M. 330, 390 St-Venant 32 Sheinman, 1. 463 Stacy, D. L. 389 Shepherd, J. T. 368, 390 Stainsby, G. 385 Sherwood, T. K. 107 Stanier,1. E. 220, 221, 234, 241, 530, 542 Shettles,241 Stanley, K. K. 314 Shin, H. 107 Starling, E. H. 8, 464, 470, 497 Shoemaker, P. A. 310, 311, 319 Steck, T. L. 145, 161 Shorr, E. 540 Steers, E. 161 Sidrick, N. 319 Stegun, S. 286, 314 Siegman, M. J. 498 Stein, P. D. 146, 161 Siger, A. 401, 424 Stekiel, J. 389 Silberberg, A. 216 Steqart, P. A. 426 Simionescu, M. 219 Sternstein, S. 541 Simionescu, N. 219 Sternstein, S. S. 513, 541 Simmons, R. M. 415, 424, 425, 426, 462 Stewart, D. M. 164 Stewart, P. A. 426 Simon, B. R. 544 Stocki, J. 107 Singer, C. J. 3, 7, 22 Stossel, T. P. 164 Singer, S. J. 145, 161,200,219 Stokes, G. G. 37, 76 Sipkema, P. 463 Stokke, B. T. 162 Skalak, R. 106, 132, 134, 135, 136, 142, Stoltz, J. F. 107 143, 144, 149, 151, 161, 184, 196, Stone, 1. L. 513, 542 216,465,535,536,543 Stoychev, S. 385 Skavgstad, C. 544 Strohman, R. C. 164 Strong, A. B. 199,219 Skibo, L. 215 Sklenska, A. 541

556 Author Index Struik, D. 1. 126, 162 Tremer, H. M.216, 319,390 Strumpf, R. K. 463, 465 Treviranus, G. R. 7 Su, C. 385 Tricomi, F. G. 380 Sugi, H. 416, 426 Triggle. 389 Sugihara-Seki, M. 162 Tristram, G. R. 317 Sugrue, S. 318 Tsang, W. C. 0.116,162 Sung, K. L. P. 147, 149, 151, 153, 164 Tsuchiya, T. 416, 426 Sung, L. A. 145, 149, 153, 162, 164 Tucker, W. K. 318 Sutera, S. P. 121, 160, 183, 184, 185,216, Turner, C. H. 543 Turner, E. 163 217 Tyberg, J. V. 465 Sutton, D. W. 465 Svanes, K. 188,217 Uekermann, V. 387 Swann, D. A. 241, 543 Unsworth, A. 530, 543 Synder, R. W. 300, 319 Urry, D. W. 248, 319, 320 Usami, S. 106, 159 Taber, L. A. 433, 465 Utterback, N. 107 Takamizawa, K. 388, 390 Uvelius, B. 495, 497, 499 Tanaka, T. T. 328, 329, 330, 332, 333, Uyeda, P. 426 335,344,390,498 Vadas, E. B. 108 Taro, G. 417, 426 Vaishnav, R. N. 293, 318, 320, 344, 385, Taylor, C. R. 121, 161 Taylor, G. I. 121,233,241 390,391,514,544 Taylor, M. 106 Valanis, K. C. 275, 320 Taylor, M. G. 388 Van Brocklin, J. D. 295, 320 Tencer, A. F. 543 Van Buskirk, W. C. 539 Ter K. eurs, H. 432, 462, 465 van der Pol, B. 2, 5 Theodorsen, T. 289, 319 van Heuningen, R. 465 Theret, D. 197,219 Vandenburgh, H. H. 154, 164 Thilo-Korner, D. G. S. 219 Vanderby, R. 541 Thoma, R. 91 Vanhoutte, P. M. 368, 390 Thomas, H. W. 107 Vasu, R. 539 Thomson, W. (Lord Kelvin) 45 Vawter, D. 244, 298, 306, 317, 320 Thorson, J. 426 Vayo, M.159 Thurston, G. B. 99, 107, 108 Veltel, D. 163 Tichemor, C. C. 541 Ven, A. A. F., van de 315 Tillack, T. W. 161 Verdugo, P. 465 Todhunter, I. 15,22 Victor, A. C. 462 Togawa, T. 218 Viggers, R. F. 199, 219 Tomioka, Jun 342 Viidik, A. 255, 256, 261-264, 277, 310, Tomita, T. 497 Tong, P. 141, 160,302,303,305, 31l, 319, 320, 535 Villarreal, F. J. 465 319 Vito, R. P. 306, 317 Torino, A. J. 516, 543 Vogt, F. B. 542 Torp, S. 319 Voigt, W. 41, 42, 43, 44, 45, 49,51 Torzilli, P. A. 543 Von Khreningen-Guggenberger, J. 232, T5zeren, A. 150, 162,310,415,416, 241 419,421,426 Treloar, L. R. G. 249, 319

Author Index 557 von Gierke, H. E. 516, 541 Wiederhielm, C. A. 363, 385 von Helmholtz, H. 2, 4, 5 Wieling, W. 388 von Mises. 512 Wiemer, W. 389 Voss, G. 0.105 Wiles, H. C. 160 Vossoughi, J. 352, 391 Williams, P. L. 395, 396, 426 Vost, G. P. 542 Wilmsley, R. 513 Vuust, J. 319, 320 Wilson, T. A. 293, 317, 320 Wineman, A. S. 315, 320, 514 Wack, P. E. 316 Wohlfart, B. 462 Wagner, K. W. 289, 320 Wolf, E. 239 Waldman, L. K. 457, 465 Wolf, S. 494, 499 Walker, P. S. 530, 540, 544 Wolff, H. S. 22 Wallner, A. 425 Wolff, 1. 369, 515, 544 Walmsley, R. 513 Wolinsky, H. 391 Ward, R. S. 389 Wonder, C. C. 516,544 Wardell, J. R., Jr. 227,241 Wong, M. 539 Warrell, D. A. 186,217 Woo, S. L. Y. 310,311,317,514,516, Warrick, H. M. 426 Warrinyar, R. G. 389 520,521,522,523,534,535,544 Warwick, R. 395, 396,426 Woodhead-Galloway, J. 320 Waugh, R. 135, 139, 140, 162 Worthy, P. R. 160 Wayland, H. 186,215,314 Wright, V. 276, 319, 540, 544 Wayne,J. S. 544 Wu, T. Y. 233, 241 Weber, E. H. 21 Wu, Z. K. 541 Weiss, R. 499, 535 Wylie, E. R. 330, 391 Weiss, S. W. 386 Weissenberg, K. 55 Xie, J. P. 351,352,355,363,391 Weisser, P. A. 241, 543 Weizsacker, H. W. 391 Yager, D. 298, 320, 391 Wells, M. K. 384 Yamada, H. 19,22,511,512,544 Wells, R. E. 107, 121, 156, 161 Yanagida, T. 243, 317,425 Wertheim, M. G. 270, 276, 320, 544 Yang, R. F. 391 Werthessen, N. T. 494, 499 Yeh, H. 248 Wesley, R. L. R. 344, 366, 368, 391 Yen, R. T. 108, 170, 171, 172, 188, 190, Wesseling, K. H. 316, 317, 344, 388 West, J. B. 217, 298, 300, 320 191,192,193,194,214,217, Westerhof, N. 312, 320,463 391 Westmann, R. A. 275, 320 Yeung, A. 150, 163 Wetterer, E. 328, 330, 391 Yih, C. S. 239, 241 Whalen, R. T. 539 Yilgor, I. 389 Whalen, W. J. 465 Yin, F. C. P. 306, 311, 459, 460, 463, 465, Whedon, G. 540 476,478,480,499 White, C. F. 240 Yoon, H. S. 513 White, D. C. S. 426 Yoshida, T. 470, 497 White, M. L. 315 Young, J. 6, 8, 22 Whitehouse, W. J. 544 Young,J. T. 320,391,514,544 Whitmore, R. L. 108, 160 Young,J.Z.536,544 Whoms, T. L. 540 Young, T.2,6, 16,38 Yu, Qilian. 351,353,356,391

558 Author Index Zahalak, G. E. 415, 416, 418, 419, 422, Zerna,.57 426 Zhou, J. 353, 391 Zu, C. M. 541 Zarda, P. R. 130 Zupkas,P. F.482,483,484,486,499 Zarins, C. K. 197,219 Zwaal, R. F. A. 154, 155, 164 Zavelier, S. A. 425 Zwart, A. 317 Zeger, S. L. 465 Zweifach, B. W. 111, 121, 188,217, 360, Zeng, Y.J.298,320 Zeng, Y. T. 391 387,388,390,465

Subject Index A-bands, 396,428 Bilayer, 144 Abductin,249 ACH hormone, 518 Bingham plastic, 81,103, 104 Actin, 243 Active myocardium, 445 Biomechanics Active remodeling of tissues, 369-377 , definition of, 1 Adventitia, 322, 323, 325 , history, 2-6 Alignment of cells in flow, 87 , method in, 11-13 Alveolar sheet oflung, 167, 168-172, Biorheology,221 361-363 Aorta, windkessel, 21 Bioviscoelastic fluids, 220-239 Apparent viscosity of blood, 84, 166, 183 , testing methods, 222-238 , in the lung, 168, 170 Bioviscoelastic solids, 242-320 , in a tube, 172 Blood \"Applicable\" deformation, (area , composition of, 66 preserving) 126, 127, 128 , constitutive equation of, 72 Arteries (see Blood vessels) , yield stress of, 68, 69 Arterioles, 357-359 Blood clotting, 93-96 Articular cartilage, 501, 508, 519 Blood flow Articulation, 500 , entry condition of, 99, 175 , laminar, 76-82 Back pain, 17 Balloon, thin-walled, 20 , velocity profile, 80, 88 Bat's wing, 363 Biaxial loading, 295-300 , wall effect, 91-92 Biconcave shape, RBC, 112 , yielding stress effect, 78-82 Blood rheology , effect of, 112 , theory of, 122 , cell alignment, 87 , cell deformation, 84, 85, 90 , constitutive equation, 72-75 , flow rule in plasticity, 74, 75 , myocardial infarction, 97 , radial migration, 91, 92 , rouleaux, 83 559

560 Subject Index Blood rheology (cont.) , torsion tests, 336 , sedimentation, 98 , torsion, 336-343 , thixotropy, 75 , two-dimensional analysis, 321, 326, , thrombosis, 93 , viscoelasticity, 75 349 , yield rule, 74, 75 , uniaxial loading, 326 , yield stress, 69 , vasa vasorum, 325 , veins, 325, 353, 363-369 Blood rouleaux, 83, 84-86 , viscoelasticity, 330-336 Blood vessels, 270, 321-391 , wall bending experiments, 354, 355, , adventitia, 322, 323, 352, 353, 355 356 , arteriole, 357-359 , wall structure, 322-326 , ascending aorta, 355 , wave propagation, 343-345, 366 , biaxial loading, 326 , Young's modulus, 328 , capillary, 360-363 , zero stress state, 349-352 , carotid artery, 334 Blood viscosity , collagen fibers, 324, 325 ,in capillaries, 168-172, 173, 176-182 , collagen/elastin ratio, 325 , coefficients, 73 , composition, 322 , Fahraeus effect, 173, 175 , creep, 333-334 , Fahraeus-Lindqvist effect, 172, 175 , descending aorta, 355 , strain rate invariants, 73 , hysteresis, 334-336 , tubular pinch effect, 175 , intima and adventitia Young's Boltzman model, 46, 47 Bolus flow, 178 modulus, 353, 355 Bone, 500- 519 , intima, 322, 323, 352 , anatomy, 500-503, 506-509 ,meaning of ai' a2 , a4 , 348, 349 , collagen, 503 , media, 322, 352, 353, 355 , as composite material, 503-504 , opening angle, 351 , external remodeling, 516-517 , opening angle, 351, 352 , functional adaptation, 514-519 , pulmonary, 383 , growth, 504, 514-519 , relaxation function, 330-333 , Haversian system, 502 , remodeling, 321, 369-371 , hydroxyapatite, 503 , semilunar valves, 326 , internal remodeling of, 516 , separate layers, 352 , microcirculation, 507-509 , shear modulus, 338, 342 , optimum design, 505 , shear strain energy, 342 , osteointegration, 518 , smooth muscle, 325 , osteon, 502 , strain energy functions, 330, 342, , remodeling of, 514-519 , resorption of, 515-519 344-349 , structure, of, 501-503 , strain energy including shear, 342 , surface remodeling of, 517 , stress relaxation, 330-333 , table of strength (deformation and , stress-strain relation, 327, 328, moduli) for, 511, 512 344-349 , tensorial Wolff's law , structure, 322 , viscoelastic properties, 513 , tangent modulus, 328 , wet vs dry, 510 , thoracic aorta, 353 , Wolff's law, 517 , three-dimensional analysis, 321, Boundary condition of blood flow, 76 Broncho-pulmonary disease, 220 349-357 , tissue growth, 369 , tissue growth, 369-377

Subject Index 561 Calcitonin, 518 , osmotic swelling, 129 Capillary blood vessels, 360-363 , shear experiment, 132-135 ,shear modulus, 135, 142, 143, 144 ,lung, 361-363 ,spectrin, 145 , tunnel-in-gel concept, 361 , tethering experiment, 137 Capillary blood flow, 176-196 , viscoelasticity of, 135 , flow pressure distribution, 179 , viscoplasticity of, 136 ,sheet flow, 168-172 Cell-tube interaction, 176-182 ,tubeflow, 176-181 Cell volume regulation, 154 Cartilage, 519-535 Cervical mucus, 232 , articular, 501, 508 Cervix elasticity, 264 , bronchial, 501 , classification, 519 Channels in cell membrane, 154, 155 ,coefficient offriction, 525-531 Circulation in bone, 507-509 , compression test, 523-525 Clotting factors, 93 ,constitutive equation, 531-535 Coagulation of blood (See Thrombus) , cyclic loading, 523 Coefficient of thermal expansion, 40 , fluid movement in, 523, 524 Coefficient of viscosity, 36 ,indentation test, 519 , low friction, 501, 525-531 Collagen, 251-258 ,lubrication, 525-531 , critical temperature of, 263 , relaxation, 521, 522 , fascicle, 257 ,split line, 519 , fibers, 255 , fibrils, 255 , stress-strain relation, 523 , tension test, 520-523 , in blood vessels, 323-325 , triphasic theory, 531-535 , in bone, 503 , types of, 519 , in cervix, 260 , variable shear, 527 , in ligaments, 259 , viscoelasticity, 520, 525 ,in pregnancy, 263, 265 Casson's equation, 69 , in skin, 260 Casson's plot, blood viscosity, 69, 70, 72 , in stress-strain relationship, 260- Cauchy's formula, 28 Cell adhesion, 151, 153 261 Cell deformation in flow, 90 , in tendon, 259 Cell membrane, 154 , molecules, 252 ,post-partum, 263-265 , area dilatation, 131 , molecular change with tension, 262 , area modulus of, 132, 138, 139, 142 , structure in tissues, 257, 259 ,asymmetry of lipids, 154 ,tropocollagen, 252 , tensile stress, 199-201 Collagen/elastin ratio, 325, 326 ,bending of Complementary energy, 307-310 Complex modulus of elasticity, 49, 224 , bending rigidity of, 125-127 , Kelvin body, 49, 50 , Biochemical transduction, 155 , channels, 154 , Maxwell body, 49 , constitutive equation for, 140-144 Complex shear modulus, 224 , cytoskeleton, 144, 145 , loss modulus, 224 , elasticity, 140-144 , storage modulus, 224 , experiments, 128, 129 Complex representation, 48 , fluid mosaic model of, 145 Cone-plate viscometer, 55 , model of, 144 , molecular structure, 145 Constitutive equation, 23, 24, 35-50 , biological soft tissues, 242-320 , from microstructure, 310

562 Subject Index Constitutive equation (cont.) Elastin, 243-249 , generalized Maxwell, Voigt, Kelvin, , incomplete fixation in aldehyde, 244 62-64 , molecule, 248 ,inversion of, 307-310 , inverse temp transition, 248 , mathematical development, 57 , muscle, 420 Elasticity, 38 , triphasic theory of cartilage, 531 , anisotropic, 38 , biaxial, 295 Continuum definition , entropy source, 249 , classical, 23 , experiments, 296 , our definition, 24 , incremental, 292 , classical copy, 24, 25 , measurements of, 56, 57 , nonlinear, 269 Cornea, 277 , pseudoelasticity, 293 Couette viscometer, 54 , pulmonary blood vessels, 383 Creep, 43 , strain rate effect, 294, 295 , triaxial, 298, 299-302 , in blood vessels, 333 , in heart muscle, 273,440 Endocrine, 518 Creep function, 41, 43, 44, 47, 278 Endothelium, vascular, 196-213 , reduced, 278 , tensorial, 47 , blood shear stress, 198 Cross-bridge theories, 396, 397, 413 ,cell nuclei shape, 201-203 ,evidences in support, 415-418 , fluid content hypothesis, 197, , mathematical development, 418- 199-209 420 , force transmission, in side wall, Cylindrical shell, 15, 16 Cytoskeleton, 144, 145 203-209 , geometry, 197,322 '\\' Kronecker delta, 32 , imbulence effect, 211 b(t), unit impulse function, 44 , mass transport affected by stress, Damping, arteries, 343 Deformability of red cells, 120 154-155,212 Deformation, 29, 31 , minimum energy theorem, 208-209 ,nucleus shape, 201-203 , applicable, 126 , shear stress from blood, 198 , isochoric, 126 , solid content, 210 Deformation gradient, 32, 301 , stress in side wall, 203-209 Dense bodies, 469, 470 , tensile stress in membrane, 199,201, Depolarization waves, 461 Diaphysis, 501 204,207,208 Dilatancy, 221, 222 , tensile stress in, 201, 203-209 Dimensional analysis, 168-172 , tension field theory, 199 Dimension analyzer, 57 , turbulent flow effect, 211 Dirac delta function, 44 Entry flow, 99, 175 Discharge hematocrit, 192 Epinephrine, 487 Displacement vector, 30 Epiphysis, 501 Duhamel-Newman equation, 40 Exponential integral, 285, 286 Dynamic similarity, 171 Extreme-value statistics, 117 EGTA,487 Fascicle, 257, 258 Fasciculi of muscle, 394 Fenn and Marsh equation, 401 Fahraeus effect, 177, 189

Subject Index 563 Fahraeus-Lindqvist effect, 172, 175 , resting tension correction, 452-453 , inversion of, 182 , series element, 446, 447 , stress-strain element, 437 Fibers, 250 , structure of, 427-430 , crystallization of, 250 , syncytium in, 427 , tubules in, 429, 430 Fibrin, 95 , unstimulated, 433-441 Fibrinogen, 95 , whole heart experiments for, 433 Flow in tube, 76 Hematocrit, 67, 175 , at branching point, 187 , Casson fluid, 78-82 ,dynamic, 187 Flow separation, 214 ,in narrow tubes, 189 Fluid, 35, 36 Hemorheology, 221 Hills' equation, 399-405 , non-Newtonian, 40, 220-23 , compared with Fenn and Marsh, 404 ,Stokes, 35 , modified for heart, 449, 451 Fung's modified Hill's equation, , nondimensional, 402, 403 Hill's three-element model, 405, 446 449-452 , isometric-isotonic change over, 409 ,quick release method, 408 Gaussian curvature, 127 , series element, 410, 411 Generalized model of viscoelasticity History of biomechanics, 2-10 Hookean solid, 38 ,Kelvin,64 Hyaluronic acid, 234 , Maxwell, 62 Hydroxyapatite, 502, 503 ,Voigt, 62 Hyperelastic material, 300 Ghost cells, 86 Hysteresis, 41 Green's strain, 32, 60 , in blood vessels, 334 Ground substance, 258 , in soft tissues, 281 Growth plate of bone, 501, 508 Gumbel probability paper, 118 I-bands, 394, 396 Gumbel slope, 117, 118 Incremental elasticity, 292, 293 Interalveolar septa, 167-169 \"-band, 394, 396 Intercalated discs, 427 Hair, 250 Intima, 322, 323 Harmonic oscillation, 48 Invariants, 59, 73 Inversion , complex representation of, 48 ,phase of, 8 , of the Fahraeus-Lindqvist effect, 182 Haversian system, 502 , of the stress-strain relation, 307-310 Heart muscle, 427-465 Inward migration, red cell, 92 ,active, 441-453 Isotropic tensor, 36 ,contractile element of, 446, 447-453 Isotropy, 37 , creep in, 440 Isochoric deformation (volume ,damage in testing of, 431, 432 ,depolarization waves in, 461 preserving), 126 , elastic response of, 436-438 Isotonic solution, 110 , Hill's equation, 399,449 ,modified Hill's equation, 449, 451 Kelvin model, 41, 62 , oscillations of, 438 , parallel element, new method, 453 , parallel element, new theory, 455 , Pinto's method, 453 , relaxation of, 434-436

564 Subject Index Kinematic similarity, 171 , Lame, 39 Kronecker delta, 32 , Young's, 38 Microstructure, 310 Lame constants, 38 Minute rhythm, 471, 472 Laplace, law of, 14-17,339 Mitochondria, muscles, 427, 429 Leak-back, 194 Model of viscoelasticity, 41, 54-56 Length-tension relation, muscle, 404, Modified Hill's equation, 449, 451 Moens-Korteweg equation, 342 442 Mohr's circle, 133 Leukocytes, 174 Modulus, elasticity, 38 , complex, 49 , adhesion, 151 , Lame, 39 , active movement, 151 , Young's, 38 , deformation, 147-150 Mucus, 220, 221, 227-233 Lighthill theory, 194, 195, 196 , cervical, 232 Ligaments, 259, 535 , respiratory tract, 227-231 Ligamentum nuchae, 243 , yield point, 230 Loss shear modulus, 224 Multi-unit smooth muscle, 468 Lubrication layer, 184, 194-196 Muscle Lubrication ofjoints, 525-531 , avoiding end effect, 441 , coefficient of friction, 527, 529 , effect of Ca, 441-445 , compression of tissue, 528 , heart, 427-465 , Malcolm's experiments, 526 , parallel element, new method, 453 , osteoarthritic, 529 , parallel element, new theories, Lung, 306, 361-363 455 M-band, 394, 396 , partial activation, 422 Material , pericardium effect, 459-460 , see \"constitutive equations\" , Hookean, 38 , see \"cross bridge theories\" , Kelvin, 41 , see \"heart\", \"smooth muscle\" , Maxwell, 41 , skeletal, 392-426 , standard linear, 41 , smooth, 466-499 , Voigt, 41 , spindles, 399 Maxwell model, 41, 63, 225 , swelling pressure, 457-459 Media of arterial wall, 322, 323 , test specimens, 431 Medullary cavity, 501, 502 , tone, 399 Meromyosin, 413 , ureteral smooth muscle, 475-487 Mesentery, 271 , use of whole organ for testing, Metaphysis, 501, 502 Methods of biomechanics, II 433 Microcirculation Myocardium (see Heart muscle) , discovery in lung, 3, 8 Myofibrils, muscle, 394, 395 , in bone, 507-509 Myosin, 395, 396, 397 Micropipette experiments, 132, 134-137, Neurons, muscle, 398 152,153 Newtonian fluid, 36 Micropipette measurements, 134-137, Newton's rings, 221, 238 Non-Newtonian fluid, 40-52 139,147,153 No-slip condition, 61 Microrheology, 223 , complex, 49

Subject Index 565 Oka's Casson fluid flow, 81 , geometry of, 109-120 Optimum design of bone, 504, 505 , in capillaries, 111, 172-194 Organogenesis, 155 , in interference microscopy, 113 Osmotic swelling, RBC, 129 , in isotonic solution, 109 Osteoarthritic joint, 236 , internal viscosity of, 121, 122 , largest, 117-120 , cartilage, 529, 530 , life span, 109 , synovial fluid, 236 , 120 day life, 109 Osteon, 502, 503 ,model of, 130, 144, 145 Oswald viscometer, 53 , osmotic swelling of, 129, 130 ,shape of, 110-120 Parameter identification, 347 Pericardium, 306 , in sieves, 140 Periosteum, 501, 502, 508 , sphering of, 113, 115, 116 Phosphocreatine, 401 Pinnate muscle, 394 , stress distribution, 122-128, 130- Plasma expander, 98 137 Plasma-rich layer at wall, 92, 181, 182 Plasma skimming, 175, 181, 188 ,surface area of, 114-120 Platelets, 66, 93, 94, 95 , tank treading of, 156 Pleura, 306 , thickness equation for, 113 Plug flow, 89 ,volume of, 114-120 Poisson's ratio, 38 Red cell membrane (see Cell membrane) Polissar equation, 402 Relative viscosity, 166, 170, 172 Polycarbonate sieves, 140 Relaxation function, 42-45 Preconditioning, 261, 262, 270 , blood vessel, 330-333 Pressure in incompressible material, 302 ,cartilage, 521, 522 Prothrombin, 95 , heart muscle, 434-436 Protoplasm, 220, 222 Pseudo-elasticity, 301 , mesentery, 271, 272 , smooth muscle, 490-492 , in arteries, 330-335 , spectrum, 47 , in veins, 365 , spectrum of arteries, 335 Pseudo strain energy, 301, 342, 375 Pulmonary blood flow, 167-172 ,reduced,278,280 Pulmonary blood vessel elasticity, 383 , tensorial, 47 Pulmonary capillaries, 361-363 Relaxation spectrum, 47 Remodeling of blood vessels, 369-377 Quasi-linear viscoelasticity, 277-292 , limitations, 291 (see Tissue remodeling) , Rivlin, Pipkin theories, 291 Remodeling of tissues and their Red Blood cells properties , deformability of, 109, 110 , zero-stress state, 373 ,deformation and turbulence, 146 , composition and structure, 370- ,deformation in flow of, 120-128, 146 , deformation in tube flow, 176-182 373 , dimensions of, 112-120 , mechanical properties, 374 , unified interpretation, 376 , bone, 518 Resilin, 249 Return period statistics, 118 Rheogoniometer, 221 Rheology, 221 Rheometer, 223 Rheopexy, 221, 222 Rouleaux of red cells, 83-86

566 Subject Index Saliva viscoelasticity, 220 , structure of, 469 Sarcomeres, 396 ,taenia coli, minute rhythm, 471- Sarcosomes, 427 Sedimentation, red cell, 98 475 Semen, 232 , taenia coli, resting, active, 487- Serum, 66 Shear, 29 494 , types of, 466 , simple, 133 , ureter, 475-487 ,pure, 133 , vascular, 359 Shear rate, 67 Soft tissue Shear thickening, 222 , uniaxial loading, 269-277 Shear thinning, 222 , viscoelasticity, 277-292 Sheet flow in lung, 167-172 Spectrin, 145 Sickle cells, 85 Spectrum, relaxation, 47 Silk,250 Spermatozoa swimming, 233 Similarity laws, 170 Sphericity index, RBC, 117 SI units, conversion table, 25 Spinability, 221 Skeletal muscle, 392-426 Spindles, muscle, 399 , contractile element, 406 Split line, cartilage, 519 , crab chela, 393 Spontaneous contraction, 471, 472 , Fenn and Marsh equation, 404 Statistics, extreme value, 117 , functional arrangements, 393 STH hormone, 518 . , Hills' equation, 399 Stokes fluid, 37 , length-tension relation, 404 Stokes formula, 225, 226, 239 , maximum velocity of contraction, Storage shear modulus, 224 Strahler system, 13 403 Strain, 32 , parallel element, 406 , Almansi, 32, 300 , Polissar equation, 402 ,Cauchy, 32 , series element, 406 , Eulerian, 32 , single twitch, 397 ,Green's, 32, 299, 300, 307 , sliding element theory, 397 , Hamel, 32, 300 , structure, 394-397 , infinitesimal, 33, 300 , tetanization of, 399 , Lagrangian, 32, 353 , velocity of contraction, 411 , shear, 29, 33 , wave summation, 398 , St. Venant, 32, 299, 300 Skin, 302 Strain energy function, 269, 291, 300- , constitutive equation of, 302-306 Sliding element theory, 397 302 Smooth muscles, 466-499 , complementary, 308 , actin, 469, 470 ,of blood vessel, 330, 342, 344-349 , bundles of, 467 , of skin, 302 , cell dimensions, 466 , of veins, 365 , dense bodies, 469, 470 ,psuedo, 300, 302-306 , extracellular space between, 468 Strain rate, tensor, 34, 35 , minute rhythm, 471, 472 Stress, 25 , multi-unit, 467 , Cauchy, 301, 307, 337 , myosin filaments, 469, 470 ,Euler, 301 , relaxation function, 490-492 , Kirchoff, 301, 303, 307, 336 , spontaneous contraction, 471, 472 , Lagrangian, 301 ,Piola, 301

Subject Index 567 Stress relaxation (see Relaxation) Thermodynamics of deformation, 265- Stress and growth relationship, 369 (see 269 remodeling) Thermodynamic source of elasticity Stress-strain relation , entropy source, 266 , structural source, 266 , for arteries, 328, 336, 343, 344 , free energy source, 267, 268 , for blood vessels (see above) and, , strain energy, 269 362,365,376 Thixotropy, 221, 222 , for bone, 510, 513, 514, 517 Thrombosis, 93 , for cartilage, 523, 531 Thrombus , for taenia coli, 490, 492 , for ureter, 479, 481 , antithrombotic agents, 96 , for veins, 362, 365 , clotting factors, 93 , inversion, 307-310 , dissolution, 95 Stretch activation of ion channels, , formation, 93 , genesis, 94 154 Thrombus dissolution, 95 Stretch ratio, 29 , antithrombotic agents, 96 Summation convention, 29 Thrombus formation, 93 Surfaces, applicable (area preserving), , human clotting factors, 93 , thrombogenesis, 94 126 , intrinsic, extrinsic, common Syncytium, 427 Synovial fluid, 221, 233, 238 pathways, 95 Tissue growth, 369 , osteoarthritic, 236 Tissue engineering, 14, 155, 156,369 Synovial joint, 525, 531 Tissue remodeling Taenia coli, 471-475, 487-493 , blood vessels, 369-377 , active tension, 474 , mechanical properties, 374 , active/resting tension ratio, 493 , morphological, 370 , cyclic loading, 492 , stress-growth law, 376 , EGTA effect, 489 , structural, 370 , epinephrine effect, 490 , zero-stress state, 373 , frequency effect, 491 Tone, muscle, 399 , Lmax (definition), 474, 475 Tools of biomehanics, 12 , minute rhythm, 471 Trachea, strain energy, 352 , relaxation of, 487 Traction (stress), 26 , relaxation function for, 490 Transduction, strain-biochemical, , relaxation spectrum, 490 , resting, 493, 494 155 , spectrum of relaxation, 490, 492 Tube flow analysis , spontaneous contraction of, 471 , step length change, 473 , Newtonian, 76-78 , step tension change in, 474 , non-Newtonian, 78-82 , strain-rate effect, 491 Tube hematocrit, 192 , stress-strain relation, 492 Tubular pinch effect, 176 , wave form, 471 Tubules, 429 Tunnel-in-gel capillaries, 361 Temperature effect of elasticity, 40 Turbulence, 146 Tendons, 290, 535 Turbulence in blood flow, 146,211 Tensor transformation, 29 Tentanization, 398 Unit-impulse function, 44

568 Subject Index Unit-step function, 43 Viscosity Universal function Q(P), 310 , apparent, 166, 170-175 Ureter, 475-486 , coefficient, 37 , Newtonian, 36 , active tension, 475, 481-483 , non-Newtonian, 40 , creep in, 481 , of air, 37 , cyclic stretching of, 477, 478 , of blood, 67-75,170-175 , relaxation of, 479, 480 , of hemoglobin, 121 , resting tension, 476 , of protoplasm, 226 , stress-strain relation, 479 , of water, 37 , relative, 166 Vascular endothelium (see Endothelium) , temperature effect, 68 Vascular smooth muscle, 359 VDA (video dimension analyzer), 56 Viscous fluid (see Viscosity) Veins (see Blood vessels) Vitamin effect on bone growth, 518 Visceral smooth muscle, 468 Voigt model, 41, 64, 225 Viscoelasticity, 41-52, 277-292, 330- Vorticity tensor, 35 335,365 Wall effect on blood flow, 91 , applications of, 50-52 Waves in arterial wall , BoItzman theory, 46 , generalized tensor equation, 306 , decay rate of, 343 , models, 41, 62-64, 288 , in arteries, 342, 344 , of biosolids, 242-320 Wave summation, muscle twitch, 398 , of blood, 75, 99 Weissenberg effect, 55 , of blood vessels, 330-336 White blood cell, 110 , of cartilage, 523 Windkessel theory, 21 , of cervical mucus, 232 Wolff's law, 515, 517 , of heart muscles, 434-440, 454 , of mucus, 223-226, 227-231 Yield stress , of saliva, 231 , of blood, 69-71 , of smooth muscle, 487-493 , of mucus, 230, 231 , of semen, 233 , of synovial fluid, 233-238 Young's modulus, 38, 353, 363, 365 Viscometers, 53-56 , Couette, 54 Z-bands, 396, 428 , cone-plate, 55 Zero stress state , falling sphere, 56 , oscillating rod, 56 , arteries, 349-351 , Ostwald, 53 , remodeling of, 370, 373, 374 , tuning fork, 56 , veins, 363