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IN MEMORIAM

J Biomech Eng. 1988;110(3):165. doi:10.1115/1.3108425.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J Biomech Eng. 1988;110(3):166-171. doi:10.1115/1.3108426.

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):172-179. doi:10.1115/1.3108427.

Flush mounted hot film anemometer probes were used to measure wall shear stress magnitudes on the inside and outside walls of a rigid model of the human aortic arch. The effects of the presence of an Ionescu-Shiley tri-leaflet bioprosthetic heart valve at the entrance of the aortic arch and the side flows through arteries located in the mid-arch region on wall shear stress magnitudes were determined. It was found that the presence of the tri-leaflet valve leads to an elevation of wall shear stress (relative to the same flow without a valve) over the entire aortic arch region by as much as 50 percent. The valve influence extended to about 180 deg from the entrance to the aorta on the inside wall and even further on the outside wall based on extrapolation of available data. Peak wall shear stress magnitudes measured on the outside wall were in the range of 1.5—4.0 N/m2 (15—40 dynes/cm2 ) over the length of the aortic arch and took on their highest values in the mid-arch region. Inside wall values were of comparable magnitude. It was observed that the presence of the aortic valve and side flow from the top of the aortic arch reduced wall shear stress reversal in the arch region.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):180-184. doi:10.1115/1.3108428.

A time-of-flight MRI velocity measurement technique is evaluated against corresponding LDV measurements in a constriction tube model over a range of physiologic flow conditions. Results from this study show that MR displacement images can: 1) be obtained within both laminar and turbulent jets (maximum stenotic Re≅4,200), 2) measure mean jet velocities up to 172 cm/s, and, 3) detect low forward and reverse stenosis (0≤L/D≤2). Regions between the jet termination point and re-establishment of laminar flow (Re≥1500, ≥1000, and ≥110 downstream of 40, 60, and 80 percent stenosis, respectively) cannot presently be detected by this technique.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):185-189. doi:10.1115/1.3108429.

The nonlinear elastic response of large arteries subjected to finite deformations due to action of biaxial principal stresses, is described by simple constitutive equations. Generalized measures of strain and stress are introduced to account for material nonlinearity. This also ensures the existence of a strain energy density function. The orthotropic elastic response is described via quasi-linear relations between strains and stresses. One nonlinear parameter which defines the measures of strain and stress, and three elastic moduli are assumed to be constants. The lateral strain parameters (equivalent to Poisson’s ratios in infinitesimal deformations) are deformation dependent. This dependence is defined by empirical relations developed via the incompressibility condition, and by the introduction of a fifth material parameter. The resulting constitutive model compares well with biaxial experimental data of canine carotid arteries.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):190-199. doi:10.1115/1.3108430.

Experimental studies have shown that endothelial cells which have been exposed to shear stress maintain a flattened and elongated shape after detachment. Their mechanical properties, which are studied using the micropipette experiments, are influenced by the level as well as the duration of the shear stress. In the present paper, we analyze these mechanical properties with the aid of two mathematical models suggested by the micropipette technique and by the geometry peculiar to these cells in their detached post-exposure state. The two models differ in their treatment of the contact zone between the cell and the micropipette. The main results are expressions for an effective Young’s modulus for the cells, which are used in conjunction with the micropipette data to determine an effective Young’s modulus for bovine endothelial cells, and to discuss the dependence of this modulus upon exposure to shear stress.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):200-207. doi:10.1115/1.3108431.

A three-dimensional constitutive law is proposed for the myocardium. Its formulation is based on a structural approach in which the total strain energy of the tissue is the sum of the strain energies of its constituents: the muscle fibers, the collagen fibers and the fluid matrix which embeds them. The ensuing material law expresses the specific structural and mechanical properties of the tissue, namely, the spatial orientation of the comprising fibers, their waviness in the unstressed state and their stress-strain behavior when stretched. Having assumed specific functional forms for the distribution of the fibers spatial orientation and waviness, the results of biaxial mechanical tests serve for the estimation of the material constants appearing in the constitutive equations. A very good fit is obtained between the measured and the calculated stresses, indicating the suitability of the proposed model for describing the mechanical behavior of the passive myocardium. Moreover, the results provide general conclusions concerning the structural basis for the tissue overall mechanical properties, the main of which is that the collagen matrix, though comprising a relatively small fraction of the whole tissue volume, is the dominant component accounting for its stiffness.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):208-212. doi:10.1115/1.3108432.

Concomitant soft tissue injury resulting from knee instability following cruciate rupture is a serious clinical problem. To study this injury mechanism, the biomechanical properties of the lateral collateral ligament were measured at 0, 4, 8, 12, and 16 weeks post-operatively in rabbits having the anterior and posterior cruciate ligaments sectioned. No significant changes were found in the ligament’s cross-sectional area, tensile mechanical response, or in its hexosamine content. The predominant mode of ligament failure was by bone avulsion at the insertion sites (78 percent) with 86 percent of paired limbs failing in a similar manner.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):213-215. doi:10.1115/1.3108433.

Misalignment between the axes of measurement and the material symmetry axes of bone causes error in anisotropic elastic property measurements. Measurements of Poisson’s ratio were strongly affected by misalignment errors. The mean errors in the measured Young’s moduli were 9.5 and 1.3 percent for cancellous and cortical bone, respectively, at a misalignment angle of 10 degrees. Mean errors of 1.1 and 5.0 percent in the measured shear moduli for cancellous and cortical bone, respectively, were found at a misalignment angle of 10 degrees. Although, cancellous bone tissue was assumed to have orthotropic elastic symmetry, the possibility of the greater symmetry of transverse isotropy was investigated. When the nine orthotropic elastic constants were forced to approximate the five transverse isotropic elastic constants, errors of over 60 percent were introduced. Therefore, it was concluded that cancellous bone is truly orthotropic and not transversely isotropic. A similar but less strong result for cortical bone tissue was obtained.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):216-222. doi:10.1115/1.3108434.

A 3-D nonlinear mathematical model is used to analyze the mechanical response of a lumbar L2–3 motion segment including the posterior elements when subjected to combined sagittal plane loads. The loadings consist of axial compression force, anterior and posterior shear forces, and flexion and extension moments. The facet articulation is modelled as a general moving contact problem and the ligaments as a collection of uniaxial elements. The disk nucleus is considered as an inviscid fluid and the annulus as a composite of collagenous fibers embedded in a matrix of ground substance. The presence of axial compression force reduces the segmental stiffness in flexion whereas a reverse trend is predicted in extension. In the presence of axial compression with and without sagittal shear force, flexion considerably increases the intradiscal pressure while extension reduces it. In other words, under an identical compression force, disk pressure is predicted to be noticeably larger in flexion than in extension. The segmental mechanical response in extension loadings is markedly influenced by the changes in the relative geometry of the articular surfaces at the lower regions. Finally, the deformation of the bony structures plays a significant role in the segmental mechanics under relatively large loads.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):223-229. doi:10.1115/1.3108435.

Dynamic mechanical models of the double limb support phase of human gait were developed for both two-dimensional (sagittal plane) and three-dimensional motion. A “foot” model with a curved plantar surface was also developed such that the model foot motion was kinematically equivalent to that of a walking subject. This foot model was incorporated into the planar model for double limb support. The dynamic formulations were based on Kane’s method and were implemented symbolically using MACSYMA. The development of the formulations for the constrained systems, application of these formulations to the study of normal gait, the sensitivity of the simulation to the frequency content of the input data, the sensitivity of limb displacements to changes in joint moments and the application of a nonlinear feedback controller to correct for perturbations in limb trajectories were investigated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):230-237. doi:10.1115/1.3108436.

This paper presents a dynamical analysis of quadrupedal locomotion, with specific reference to an adult Nubian goat. Measurements of ground reaction forces and limb motion are used to assess variations in intersegmental forces, joint moments, and instantaneous power for three discernible gaits: walking, running, and jumping. In each case, inertial effects of the torso are shown to dominate to the extent that lower-extremity contributions may be considered negligible. Footforces generated by the forelimbs exceed those exerted by the hindlimbs; and, in general, ground reactions increase with speed. The shoulder and hip dominate mechanical energy production during walking, while the knee plays a more significant role in running. In both cases, however, the elbow absorbs energy, and by so doing functions primarily as a damping (control) element. As opposed to either walking or running, jumping requires total horizontal retardation of the body’s center of mass. In this instance, generating the necessary vertical thrust amounts to energy absorption at all joints of the lower extremities.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):238-248. doi:10.1115/1.3108437.

An experimental system for the analysis of knee joint biomechanics is presented. The system provides for the simultaneous recording of ligament forces using buckle transducers and three-dimensional joint motion using an instrumented spatial linkage, as in vitro specimens are subjected to a variety of external loads by a pneumatic loading apparatus with associated force transducers. The system components are described, and results of an evaluation of system errors and accuracy are presented. The experimental setup has been successfully used in the analysis of normal knee ligament mechanics, as well as surgical reconstructions of the anterior cruciate ligament. The system can also be adapted to test other human or animal in vitro joints.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(3):249-253. doi:10.1115/1.3108438.
Abstract
Topics: Cornea
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J Biomech Eng. 1988;110(3):254-256. doi:10.1115/1.3108439.

Presented in this paper is a solution for countercurrent heat exchange between two parallel vessels embedded in an infinite medium with a linear temperature gradient along the axes of the vessels. The velocity profile within the vessel is assumed to be parabolic. This solution describes the temperature field within the vessels, as well as in the tissue, and establishes that the intravessel temperature is not uniform, as is generally assumed to be the case. An explicit expression for the intervessel thermal resistance based on the difference between cup-mixed mean temperatures is derived.

Commentary by Dr. Valentin Fuster

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