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RESEARCH PAPERS

J Biomech Eng. 1985;107(2):91-95. doi:10.1115/1.3138541.

The fluid force acting on single human red cells in a high shear flow was analyzed. A two-dimensional elliptical microcapsule as a model of the deformed red cells was adopted to numerically calculate the distributions of the shear forces on both sides of the cell membrane. It is theoretically shown that the cell membrane undergoes an unsteady cyclic loading under the rotational motion around the interior. The mechanism leading to blood cell trauma is examined by repeatedly loading the continuously moving cell membrane.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):96-103. doi:10.1115/1.3138542.

Theoretical and experimental results are presented which demonstrate the mechanical effects of running along a circular turn. The theory is a simple one-parameter model, requiring only the top speed v0 of the runner as an input. The dimensionless parameter (Rg/v0 2 ) , a reciprocal Froude number or dimensionless radius, appears as a natural result of the theory. This radial Froude number allows for the comparison of the theory and experiment for a large number of individuals on the same set of axes. The parameters of speed, foot contact time, ballistic air time, step length, stride length, and stride time are all predicted and measured for 23 different subjects. The agreement between theory and experiment is good. Exact solutions and approximate asymptotic results for the speed-radius relation are presented. Applications are made to the practical problem of the design of indoor and outdoor running tracks for athletic competition.

Topics: Design
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):104-111. doi:10.1115/1.3138530.

Intramedullary rodding of femur fractures, although a safe and rapidly performed procedure, can result in several complications. If the rod fit is too loose, fracture instability, rod migration, and delayed union may result. If the rod fit is too tight, cracking of the femur may occur during rod insertion. These complications were investigated in terms of geometric and mechanical parameters of the bone-implant system. Results showed that rods of the same nominal size from different manufacturers showed more than twofold difference in flexural rigidity and a threefold difference in torsional modulus. These differences appear to be due to differences in cross sectional shape and wall thickness of the rods. Measurements of pushout force and hoop stress in cadaver femora showed a large difference in pushout force with different rods, and significantly lower forces in distal than in proximal femoral fracture components. Pushout force decreased with fracture component length proximally and dropped to zero in distal components less than 170 mm long. An increase in ream diameter in the distal components of just 1 mm was found to decrease the mean pushout force from 740N to 90N. The most significant variable was found to be anterior offset of the starting hole more than 6 mm from the centerline of the medullary canal which resulted in consistent lifting of the anterior cortex during insertion of the rod.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):112-122. doi:10.1115/1.3138531.

The development of a one-dimensional numerical (finite-difference) model of the arterial network surrounding the circle of Willis is described based on the full Navier-Stokes and conservation of mass equations generalized for distensible vessels. The present model assumes an elastic wall defined by a logarithmic pressure-area relation obtained from the literature. The viscous term in the momentum equation is evaluated using the slope of a Karman-Pohlhausen velocity profile at the vessel boundary. The afferent vessels (two carotids and two vertebrals) are forced with a canine physiologic pressure signature corresponding to an aortic site. The network associated with each main efferent artery of the circle is represented by a single vessel containing an appropriate amount of resistance so that the mean flow through the system is distributed in accordance with the weight of brain irrigated by each vessel as determined from a steady flow model of the same network. This resistance is placed a quarter wave-length downstream from the heart to insure proper reflection from the terminations, where the quarter wavelength is determined using the frequency corresponding to the first minimum on an input impedance-frequency diagram obtained at the heart. Computer results are given as time histories of pressure and flow at any model nodal point starting from initial conditions of null flow and constant pressure throughout the model. Variations in these pressure and flow distributions caused by the introduction of pathologic situations into the model illustrate the efficacy of the simulation and of the circle in equalizing and redistributing flows in abnormal situations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):123-130. doi:10.1115/1.3138532.

It is now generally accepted that the intercellular cleft between adjacent endothelial cells is the primary pathway for the transluminal movement of water and small ions in the vasculature. A steady-state theoretical model has been developed to show quantitatively how the geometry of the intercellular cleft between adjacent endothelial cells is related to both the water movement and pressure distribution in the subendothelial space and to examine how the existence of a subendothelial interaction layer affects the hydraulic resistance of the media of vessels of varying wall thickness. The velocity and pressure fields in the media are described using porous matrix theory based on Darcy’s law and a lubrication-type analysis is used to describe the flow in a variable geometry intercellular cleft. These two equations are solved simultaneously to determine the unknown pressure distribution beneath the endothelium and the flow in the arterial media. Application of this model shows that, when the tight junction in the cleft is 26 Å or less, more than half of the total hydraulic resistance of the wall occurs across the endothelial cell monolayer, for a vessel whose wall thickness is less than 0.02 cm. This finding is in good agreement with the experimental findings of Vargas, et al. (1978) for rabbit aorta. Contrary to previous belief, the model shows that the filtration resistance of an arterial wall with intact endothelium does not scale linearly with wall thickness due to the highly nonlinear resistance of the endothelial interaction layer.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):131-139. doi:10.1115/1.3138533.

A new simplified three-dimensional bioheat equation is derived to describe the effect of blood flow on blood-tissue heat transfer. In two recent theoretical and experimental studies [1, 2] the authors have demonstrated that the so-called isotropic blood perfusion term in the existing bioheat equation is negligible because of the microvascular organization, and that the primary mechanism for blood-tissue energy exchange is incomplete countercurrent exchange in the thermally significant microvessels. The new theory to describe this basic mechanism shows that the vascularization of tissue causes it to behave as an anisotropic heat transfer medium. A remarkably simple expression is derived for the tensor conductivity of the tissue as a function of the local vascular geometry and flow velocity in the thermally significant countercurrent vessels. It is also shown that directed as opposed to isotropic blood perfusion between the countercurrent vessels can have a significant influence on heat transfer in regions where the countercurrent vessels are under 70-μm diameter. The new bioheat equation also describes this mechanism.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):140-146. doi:10.1115/1.3138534.

A biomechanical model is presented which represents the upper edge of the posterior knee capsule in the cat as a two-segment, vertically loaded catenary suspension cable from which the capsule sheet is suspended. Data are presented which show that the upper edge of the capsule is organized as a cable, which spans the notch between the femoral condyles. When a point load is applied to the cable, measurement of the cable shape allows for calculation of the cable tension and the downward distributed loads acting on the cable. This method was used to measure the in-vivo cable tension and the distributed downward loading acting on the capsule cable. The results show that the lateral side of the posterior joint capsule sustains a higher loading than the medial side.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):147-157. doi:10.1115/1.3138535.

A comparative study of four different muscle models in a musculoskeletal motion problem is made. The models vary in complexity from the simple input-output model to the more complex model of Hatze [I]. These models are used to solve a minimum time kicking problem using an optimal control algorithm. The results demonstrate the strong influence of the model choice on the various predicted kinematic and kinetic parameters in the problem. The study illustrates some of the advantages and disadvantages involved in trade-offs between model complexity and practicability in musculoskeletal motion studies. The results also illustrate the importance of appropriate detailed parameter estimation studies in the mathematical modeling of the musculoskeletal system.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):158-165. doi:10.1115/1.3138536.

The objectives of this study are twofold. First, to further develop the understanding of the relationship between the observed mechanical response and changes in the crimp pattern in human patellar tendon bone units. This is accomplished through the use of a specially constructed test frame and microscope system that permits observation and measurement of the crimp patterns as a function of load. Second, the results of the experimental study are used to develop a constitutive equation that includes spatial variation in the crimp pattern. The results of both the experimental and analytical study imply that local strain in the proximity of the attachment site is significantly larger than the strain in the central region of the tendon. The experimental and histological results are for specimens taken from four human bone-patellar tendon-bone units.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):166-174. doi:10.1115/1.3138537.

While the tensile failure properties of rat-tail tendon depend on strain rate, the sensitivity to strain rate decreases with age, especially during sexual maturation. The object of this study was to determine the effect of an experimental model of chronic lathyrism on age-dependent changes in the sensitivity of developing tendon strength to strain rate. Tensile failure experiments were conducted at high and low strain rate on tendons excised from test and control animals aged 1 to 6 mo. The tensile “yield” response of tendon was significantly affected by the diet resulting in a reduced tensile strength and failure strain. While the sensitivity of tendon failure to strain rate was slightly elevated by the experimental diet, age-dependent changes compared with controls. Since the diet supplement is thought to inhibit covalent crosslinking of collagen in the developing tendon, other factors are likely responsible for decrease in the sensitivity of tendon strength to strain rate during maturation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):175-182. doi:10.1115/1.3138538.

This paper gives an insight about compression and tension cracks as encountered at a bone-cement interface. Within the context of continuum theory of fracture, an analytical solution is presented for the problem of a bimaterial interface edge crack under uniaxial tension or compression, assuming no tangential slip along the crack faces since cement pedicles penetrate into the cancellous bone several millimeters. Also essential to the solution are cohesive zone effects that account for a strengthening mechanism over the crack faces. The solution provides a methodological framework for quantifying the influence of the cohesive zone on the magnitude of the stress singularity. Mode I crack tip stress intensity factors are calculated at different stages of the loading and unloading phases under uniaxial tension or compression. Finally, an inelastic mechanism is presented that gives theoretical support to explain the formation of interfacial compression cracks, a phenomenon that was not previously appreciated and that arises from the rigid cement being forced into the more compliant cancellous bone.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1985;107(2):183-188. doi:10.1115/1.3138539.

The influences of heterogeneity, anisotropy and geometric irregularity on the unrestrained, linearly elastic torsional response of long bones are assessed. Longitudinal geometric variations contribute insignificantly to the torsional response for typical long bone geometries. Anisotropy, heterogeneity and transverse geometric irregularity significantly influence the torsional response. A procedure is discussed which uses an approximate means to characterize both heterogeneity and anisotropy in predicting the torsional response. The accuracy of circular and elliptical annulus models of the bone cross-sectional geometry are assessed by comparing the stress predictions of these simple models to those of finite element models of the bone geometry.

Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

J Biomech Eng. 1985;107(2):189-191. doi:10.1115/1.3138540.

A technique is established which allows an effective torsional shear modulus to be determined for long bones, while remaining nondestructive to whole bone specimens. Strain gages are bonded to the diaphysis of the bone. Strains are then recorded under pure torsional loads. Theoretical stress predictions are combined with experimental strain recordings to arrive at a modulus value. Shear modulus calculations for four canine radii are reported using theoretical stress predictions from circular, elliptical and finite element models of the transverse bone geometry. The effective shear modulus, obtained from an average of the shear moduli determined at strain gage locations, serves to average the heterogeneous shear modulus distribution over the cross section. The shear modulus obtained is that associated with the “circumferential” direction in transverse planes.

Commentary by Dr. Valentin Fuster

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