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RESEARCH PAPERS

J Biomech Eng. 1984;106(2):97-104. doi:10.1115/1.3138480.

This paper surveys biomechanical models of the nonimpact type, involving the musculo-skeletal system. Models of bones, joints and body segments, including human gait and motion of the whole body are discussed. In particular, stress analysis of bone, calculation of ligament and muscle forces across joints and the kinetics and kinematics of locomotion are discussed. The models are described in terms of the method of formulation, the method of solution and the realism of the results obtained. There is a need for more data on material properties of various body tissues and more experimental research to develop techniques for validating many of the models. Further work on the selection of appropriate objective functions for indeterminate problems is also required.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):105-111. doi:10.1115/1.3138465.

The pulsatile deformations of the large arteries can be viewed as small time-varying deformations superposed on large deformations. This motivates the study of the incremental deformations of the vascular tissue. Unfortunately, because of the variety of possible choices of definitions of stresses and strains, the choice of the characterizing incremental moduli is not unique, which has led to much ambiguity and confusion in the literature. This communication systematically presents some of the options available for characterization of orthotropic incremental deformations of the vascular tissue, and provides explicit formulas for interconversions of incremental elastic moduli for uniaxial tests on strips of incompressible tissue. Relative merits of various choices are discussed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):112-114. doi:10.1115/1.3138466.

Glycerol solution with the viscosity coefficient similar to that of blood is used in evaluating the performance characteristics of prosthetic heart valves in the laboratory. However, physiological saline solution is used as a test fluid in testing tissue heart valves even though the viscosity coefficient does not match that of human blood. It is commonly believed that glycerol is absorbed by the tissue valves and hence the leaflets become stiff, making the test results invalid. However, in our laboratory a comparison of tissue valves exposed to glycerine solution at various times does not indicate any difference in the leaflet opening characteristics. Hence, it is suggested that glycerine solution be used as a test fluid for the evaluation of tissue valves also.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):115-122. doi:10.1115/1.3138467.

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechnaical wave guides which are of interest in the mammalian circulation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):123-130. doi:10.1115/1.3138468.

A comprehensive thermal model of the normal woman’s breast is presented. The model is developed taking into consideration metabolic heat production, tissue perfusion with capillary blood, arterial and venous blood thermal interaction and change of arterial blood temperature with position. A series of computer programs are written using a 3-dimensional finite-element technique to evaluate the surface temperature distribution of the breast. Comparison between the results obtained for the model and those from thermograms of a woman’s breast are in good agreement.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):131-136. doi:10.1115/1.3138469.

Morphometic data of the pulmonary artery in the cat’s right lung are presented. Silicone elastomer casts of cat’s right lung were made, and measured, counted and analyzed. The Strahler system is used to describe the branching pattern of the arterial vascular tree. These data are needed for any quantitative approach to the study of the pulmonary circulation. For all the pulmonary blood vessels of the cat lying between the main pulmonary artery and the capillary beds, there are a total of 10 orders of vessels in the right upper lobe, 9 orders of vessels in the right middle lobe and 11 orders of vessels in the right lower lobe. The ratio of the number of branches in successive orders of vessels or the branching ratio, is 3.58. The corresponding average diameter ratio is 1.72, whereas the average length ratio is 1.81.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):137-143. doi:10.1115/1.3138470.

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):144-150. doi:10.1115/1.3138471.

There are no previously published data on changes in the mechanical behaviors of human tendon from maturation in the second decade to senectitude in the seventh decade or thereafter. In this study, 44 tendons from individuals ranging in age from 16 to 88 yr were subjected to an extensive series of mechanical tests which included preconditioning, extensions at strain rates of 100 percent/s, 1 percent/s, and 0.01 percent/s, and stress relaxation with cyclic and constant extensions. Pairs of extensions at 1 percent/s were run throughout the protocol to evaluate the repeatability of tissue response. It was found that these responses changed little for any single sample within a pair of such tests; however, throughout the protocol, the peak stresses and moduli decreased. Extensions at different rates revealed a definite rate dependency of tendon responses with sample modulus being directly related to extension rate and slightly less hysteresis at 1 percent/s than at 100 percent/s or 0.01 percent/s. The load relaxation in samples subjected to either cyclic or constant extensions was generally best described by a linear function of the logarithm of time. The rate of relaxation with constant extension varied little with extension magnitude. The rate of relaxation in the cyclic tests was greater at 10 Hz than at 0.1 Hz. The results indicate that subject age has no effect on tendon modulus and a very small effect on hysteresis and relaxation. Extensive information on subject history was not available in this study for correlation with mechanical responses so that an age effect may have been masked by other variables, possibly health, diet, disease, or exercise.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):151-158. doi:10.1115/1.3138473.

Swelling of normal bovine articular cartilage equilibrated in NaCl solutions was dimensionally measured in thin strips of tissue. The ion-induced strains show that free swelling of articular cartilage is anisotropic and inhomogeneous. For the molar concentrations used, contraction increased linearly with concentration, defining a “coefficient of chemical contraction” (αc ). Isometrically constrained specimens registered a rise in tensile force followed by stress relaxation. An extension of the biphasic theory incorporating this ion-induced strain is proposed. This theory can describe the equilibrium anisotropic swelling behavior of cartilage and explain the transient force history observed in the isometric experiment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):159-164. doi:10.1115/1.3138474.

A quasilinear viscoelastic model was used to develop relaxation and creep forms for a constitutive law for soft tissues. Combined relaxation and cyclic test data as well as preconditioned and nonpreconditioned creep data were used to demonstrate the approach for normal bovine articular cartilage. Values for mechanical parameters in the analytical models were determined using a generalized least squares method.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):165-173. doi:10.1115/1.3138475.

Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the “biphasic” continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young’s modulus and Poisson’s ratio of the solid matrix.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):174-176. doi:10.1115/1.3138476.

It has been reported previously that collagen fibers will stain either red or green by Masson’s and other trichrome methods depending on whether they have been respectively stressed or relaxed prior to fixation. This was shown in skin [1, 2, 3] tendon [4, 5] bone[6] and films of collagen [7]. If this stain-stress dependence is of a unique quantitative nature, then staining could be used as a tension probe for collagen fibers. Relaxed and stressed collagen bundles of rat tail tendon and rat Achilles tendon have been stained using various staining periods, and results indicate that the change in staining may be associated with denser packing of the fibers in the bundle under stress rather than directly due to the stress itself. Denser packing may reduce the rate of penetration of the counterstain thus causing the staining differences. Since this rate of penetration is dependent on a number of other variables (unrelated to stress), it is concluded that collagen staining is not a reliable tension probe.

Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

J Biomech Eng. 1984;106(2):177-180. doi:10.1115/1.3138477.

Discretized surface strains for human tendon and fascia were photogrammetrically determined with high-speed cinematography and were displayed topographically using three-dimensional computer graphics. Substantial differences were found between estimates of tissue strain measured from grip motion versus discretized strain estimates from highspeed films. The computer-generated contour maps also provide a useful technique for analyzing the nonhomogeneity of tendon and fascial strains during high rate tests.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):181-182. doi:10.1115/1.3138478.

This short note presents the results from experiments performed on an artificial heart valve, in particular, the aortic valve located at the exit of the left ventricle of the heart. The valve was tested in a full-scale elastic model of the arterial system, with a cam-piston unit duplicating the pumping action of the heart. The dependence of the arterial flow distribution on the angular orientation of the valve was investigated and it was found that there was no discernible influence of valve orientation on the arterial flow distribution.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1984;106(2):182-185. doi:10.1115/1.3138479.

Pressure-volume relations of aorta and arteries are considered using a fiber-fluid continuum analysis. A Windkessel model is revised to investigate the effects of the exponential pressure-volume relation of the present study on the cardiovascular system. It is shown that the elastic properties of the fibers in large blood vessels play an important role in the circulation of blood in health and in disease.

Commentary by Dr. Valentin Fuster

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