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RESEARCH PAPERS

J Biomech Eng. 1988;110(1):1-10. doi:10.1115/1.3108400.

A bioartificial pancreas is an implantable device which contains insulin secreting cells (Langerhans islets), separated from the circulating blood by a semi-permeable membrane to avoid rejection. This paper describes the operation of such a device and evaluates the respective contributions of diffusion and ultrafiltration to the glucose and insulin mass transfer. It is shown that the pressure drop along the blood channel produces across the first half of the channel an ultrafiltration flux toward the islet compartment followed in the second half by an equal flux in reverse direction from islets to blood. The mass transfer analysis is carried out for an optimal geometry in which a U-shaped blood channel surrounds closely a very thin islet compartment formed by a folded flat membrane. A complete model of insulin release by this device is developed and is compared with in vitro data obtained with rats islets. Satisfactory kinetics is achieved with a polyacrylonitrile membrane used in hemodialysis. But the model shows that the membrane hydraulic permeability should be increased by a factor of 10 to significantly improve the performance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):11-19. doi:10.1115/1.3108399.

Tendon specimens were repeatedly extended to peak strains of either 2, 3, 4, or 6 percent. During the three 1800 s (30 min.) periods of cyclic extension, the peak loads relaxed with decreases in hysteresis and increases in slack strain. During the two 1800 s wait periods of no extension, the specimens recovered with increases in peak load and hysteresis and decreases in slack strain. However, the recovery during the wait periods was eradicated in the first few subsequent extensions and the relaxation continued as if there were no 1800 s wait periods. Stress-strain responses were well fit with power relations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):20-26. doi:10.1115/1.3108401.

A theoretical analysis of blood flow in the microcirculation of skeletal muscle is provided. The flow in the microvessels of this organ is quasi steady and has a very low Reynolds number. The blood is non-Newtonian and the blood vessels are distensible with viscoelastic properties. A formulation of the problem is provided using a viscoelastic model for the vessel wall which was recently derived from measurements in the rat spinotrapezius muscle (Skalak and Schmid-Schönbein, 1986b). Closed form solutions are derived for several physiologically important cases, such as perfusion at steady state, transient and oscillatory flows. The results show that resting skeletal muscle has, over a wide range of perfusion pressures an almost linear pressure-flow curve. At low flow it exhibits nonlinearities. Vessel distensibility and the non-Newtonian properties of blood both have a strong influence on the shape of the pressure-flow curve. During oscillatory flow the muscle exhibits hysteresis. The theoretical results are in qualitative agreement with experimental observations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):27-36. doi:10.1115/1.3108402.

The following analysis presents an experimental and theoretical study of the passive viscoelastic behavior of human leukocytes. Individual neutrophils in EDTA were observed both during their partial aspiration into a small micropipette and after expulsion from a large micropipette where the cell had been totally aspirated and deformed into a sausage shape. To analyze the data, a passive model of leukocyte rheology has been developed consisting of a cortical shell containing a Maxwell fluid which describes the average properties of the cell cytoplasm. The cortical shell represents a crosslinked actin layer near the surface of the cell and is assumed to be under pre-stressed tension. This model can reproduce the results of experiments using micropipette for both short-time small deformation and slow recovery data after large deformation. In addition, a finite element scheme has been established for the same model which shows close agreement with the analytical solution.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):37-41. doi:10.1115/1.3108403.

Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):42-49. doi:10.1115/1.3108404.

A new finite element has been developed to enforce normal and shear stress continuity at bimaterial interface points in order to alleviate the problem of high stress discontinuity predictions by the conventional displacement finite element method. The proposed element is based on a five node isoparametric quadrilateral element where the fifth node is located at the interface boundary of the element. A series of validation tests have been carried out to assess the correctness of the stress distribution obtained by the new element at interfaces of highly dissimilar materials. The results of the tests are compared to analytical solutions and to results from convergence studies performed by the conventional finite element method (SAP-IV). Overall, the proposed element has been demonstrated to have a very satisfactory degree of reliability, especially in view of the observed inability of the conventional method to yield interpretable interface stress values for most cases analyzed. Finally, the new interface element has been applied to the analysis of an axisymmetric model of the knee tibial implant. The superiority of the proposed element over the conventional one has been demonstrated in this case by a convergence study.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):50-56. doi:10.1115/1.3108405.

When a compressive impact load is applied on the chest, as in automobile crash or bomb explosion, the lung may be injured and show evidences of edema and hemorrhage. Since soft tissues have good strength in compression, why does a compression wave cause edema? Our hypothesis is that tensile and shear stresses are induced in the alveolar wall on rebound from compression, and that the maximum principal stress (tensile) may exceed critical values for increased permeability of the epithelium to small solutes, or even fracture. Furthermore, small airways may collapse and trap gas in alveoli at a critical strain, causing traumatic atelectasis. The collapsed airways reopen at a higher strain after the wave passes, during which the expansion of the trapped gas will induce additional tension in the alveolar wall. To test this hypothesis, we made three new experiments: (1), measuring the effect of transient overstretch of the alveolar membrane on the rate of lung weight increase; (2) determining the critical pressure for reopening collapsed airways of rabbit lung subjected to cyclic compression and expansion; (3) cyclic compression of lung with trachea closed. We found that in isolated rabbit lung overstretching increases the rate of edema fluid formation, that the critical strain for airway reopening is higher than that for closing, and that these critical strains are strain-rate dependent, but independent of the state of the trachea, whether it is open or closed. Furthermore, a theoretical analysis is presented to show that the maximum principal (tensile) stress is of the same order of magnitude as the maximum initial compressive stress at certain localities of the lung. All these support the hypothesis. But the experiments were done at too low a strain rate, and further work is needed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):57-61. doi:10.1115/1.3108406.

A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):62-68. doi:10.1115/1.3108407.

A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness, and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):69-73. doi:10.1115/1.3108408.

An experimental approach for an in vitro investigation of some aspects of dynamic force transmission through the human knee joint is presented. Essentially, the behavior of the joint was analyzed by measuring the responses to low level random excitation of the tibia while the femur was clamped. A global equilibrium position of the joint was attained by exerting static forces on the tibia via three tendinous muscle attachments. The responses to the applied dynamic loads were measured using a multi-channel dynamic measuring system and quantified by means of transfer function analysis techniques. Some preliminary experimental results are presented to illustrate the effects of variation of the direction and the magnitude of the applied dynamic and static loads.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(1):74-81. doi:10.1115/1.3108409.

The extensive series of experiments reported in Lemons et al. [1] show that measureable local tissue temperature fluctuations are observed primarily in the vicinity of the 100–500 μm countercurrent vessels of the microcirculation and thus strongly support the basic hypothesis in the new bioheat equation of Weinbaum and Jiji [2] that these countercurrent microvessels are the principal determinants of local blood-tissue heat transfer. However, the detailed temperature profiles in the vicinity of these vessels indicate that large asymmetries in the local temperature field can result from the significant differences in size between the countercurrent artery and vein. Using the superposition techniques of Baish et al. [9] , the paper first presents a solution to the classic problem of an unequal countercurrent heat exchanger with heat loss to the far field. This solution is then used to generalize the Weinbaum-Jiji bioheat equation and the conductivity tensor that appears in this equation to vessels of unequal size. An asymptotic analysis has also been developed to elucidate the relationship between the near field temperature of the artery-vein pair and the local average tissue temperature. This analysis is used to rigorously prove the closure approximation relating the local arterial-venous temperature difference and the mean tissue temperature gradient which had been derived in [2] using a more heuristic approach.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1988;110(1):82-84. doi:10.1115/1.3108410.

The no-load configuration of a living organ is, in general, not the zero-stress state. The difference can be revealed by cutting up an unloaded organ to such an extent that the stress becomes zero in the tissue everywhere. For the aorta, it is shown that the configuration of the zero-stress state differs considerably from being a cylindrical tube. It is, in fact, an open sector with opening angles varying along the arterial tree. This article presents data on the zero-stress state in the arteries of the rat in normal condition.

Commentary by Dr. Valentin Fuster

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