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RESEARCH PAPERS

J Biomech Eng. 1988;110(4):259-268. doi:10.1115/1.3108440.

A new prototype model for whole limb heat transfer is proposed wherein the countercurrent heat exchange from the large central arteries and veins in the core of the limb is coupled to microvascular models for the surrounding muscle and the cutaneous tissue layers. The local microvascular temperature field in the muscle tissue is described by the bioheat equation of Weinbaum and Jiji [1]. The new model allows for an arbitrary axial variation of cross-sectional area and blood distribution between the muscle and cutaneous tissue, accounts for the blood flow to and heat loss from the hand and treats the venous return temperature and surface temperature distribution as unknowns that are determined as part of the solution to the overall boundary value problem. Representative solutions are presented for a wide range of environmental conditions for a limb in both the resting state and during exercise.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):269-276. doi:10.1115/1.3108441.

In this paper the conceptual three-dimensional model of the normal woman’s breast presented in Osman and Afify [1], is developed into a detailed quantitative model of the malignant woman’s breast. This model takes into consideration the effect of tumor size and location on the metabolic heat production, blood perfusion rate, and thermal contour plot of the malignant breast for each tumor size, depth, and location. Also the results of this investigation show that a hot spot in the malignant woman’s breast thermal contour plot may not be directly related to an embedded tumor beneath the breast surface.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):277-282. doi:10.1115/1.3108442.

A numerical model of the heat transer normal to an arteriole-venule pair embedded in muscle tissue has been constructed. Anatomical data describing the blood vessel size, spacing, and density have been incorporated into the model. This model computes temperatures along the vessel walls as well as the temperature throughout the tissue which comprises an infinitely long Krogh cylinder around the vessel pair. Tissue temperatures were computed in the steady-state under resting conditions, while transient calculations were made under hyperthermic conditions. Results show that for both large- (1st generation) and medium-sized (5th generation) vessel pairs, the mean tissue temperature within the tissue cylinder is not equal to the mean of the arteriole and venule blood temperatures under both steady-state and transient conditions. The numerical data were reduced so that a comparison could be made with the predictions of a simple two-dimensional superposition of line sources and sinks presented by Baish et al. [1]. This comparison reveals that the superposition model accurately describes the heat transfer effects during hyperthermia, permitting subsequent incorporation of this theory into a realistic three-dimensional model of heat transfer in a whole limb during hyperthermia.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):283-291. doi:10.1115/1.3108443.

Transport of soluble material is analyzed for volume-cycle oscillatory flow in a tapered tube. The equations of motion are solved using a regular perturbation method for small taper angle and order unity amplitude over a range of the Womersley parameter. The transport equation is also solved by a regular perturbation method where uniform end concentrations and no wall flux are assumed. The time-averaged axial transport of solute is calculated for several tapered tubes. There is substantial modification of transport compared to the straight tube case and the results are interpreted with respect to pulmonary gas exchange.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):292-299. doi:10.1115/1.3108444.

A computational model is presented for unsteady flow through a collapsible tube with variable wall stiffness. The one-dimensional flow equations are solved for inlet, outlet and external conditions that vary with time and for a tube with time-dependent, spatially-distributed local properties. In particular, the effects of nonuniformities and local perturbations in stiffness distribution in the tube are studied. By allowing the flow to evolve in time, asymptotically steady flows are calculated. When simulating a quasi-steady reduction in downstream pressure, the model demonstrates critical transitions, the phenomena of wave-speed limitation and the sites of flow limitation. It also exhibits conditions for which viscous flow limitation occurs. Computations of rapid, unsteady changes of the exit pressure illustrate the phenomena occurring at the onset of a cough, and the generation and propagation of elastic jumps.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):300-309. doi:10.1115/1.3108446.

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle “s” shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600–700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):310-319. doi:10.1115/1.3108447.

Flow visualization and pressure measurements were made for physiological conditions in a model derived from a femoral angiorgram of a patient with lesion localization on the inner curvature wall and with vessel taper. Effects of curvature and taper were evaluated separately in other curved, tapered, smooth and straight, tapered, smooth models. Double helical secondary flow patterns were modified by plaque on the inner wall, and flow separations were observed between plaques at higher flow rates and Reynolds numbers. Pressure drop data for the plaque simulation model were similar in trend with Reynolds number as for the smooth model, but flow resistances were 25 to 40 percent higher. Significant pressure drops were measured due to the mild taper which could be estimated from momentum considerations, and smaller increased pressure drops were found due to curvature effects at the higher Dean numbers. Flow resistances for in vivo pulsatile flow simulation were about 10 percent higher than for steady flow for the plaque model, whereas no differences were observed for the smooth model.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):320-325. doi:10.1115/1.3108448.

Spectrum analysis of the Doppler signals was performed 0.5 tube diameters downstream from an axisymmetric constriction with an area reduction of 80 percent in steady flow at a jet Reynolds number of 2840. Both pulsed and continuous wave (CW) Doppler spectra showed significant reverse flow components in the separated flow. The pulsed Doppler spectra exhibited sudden changes when the sample volume crossed the shear layer between the center jet and the separated flow. A power spectrum equation was theoretically derived from continuity of flow to define the Doppler shift frequency for the shear layer velocity. The CW Doppler spectrum showed a minimum spectrum density at a frequency which equalled the shear layer Doppler shift frequency derived from the equation. The pulsed spectra exhibited the sudden changes at the same frequency as well.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):326-333. doi:10.1115/1.3108449.

Wall shear rates at eleven sites within the Penn State Electric Ventricular Assist Device (EVAD) were determined with the pump operating under conditions of 30 and 50 percent systolic duration and a mean flow rate of 5.8 L/min using a flush-mounted hot-film probe. Probe calibrations were performed with the hot-film in two orientations relative to the flow direction: a standard orientation and an orientation in which the hot-film was rotated by 90 deg from the standard orientation. The magnitude and direction of the wall shear stress at each site within the EVAD were estimated from ensemble averaged voltage data recorded for similar standard and rotated film orientations. The results indicate that, during diastole the wall shear stress direction around the pump’s periphery for both operating conditions is predominantly perpendicular to the inflow-outflow plane (in the direction of the pusher plate motion) and reaches a peak value of approximately 350 dynes/cm2 . The highest wall shear stresses were found near the prosthetic aortic valve (inside the EVAD) under the 30 percent systolic duration condition and are estimated to be as high as 2700 dynes/cm2 . Peak shear stress values of 1400 dynes/cm2 were observed in the vicinity of the prosthetic mitral valve under both operating conditions. The results suggested that the valve regions are substantially more hemolytic than other wall regions of the EVAD; the magnitudes of the wall shear stresses are sensitive to operating conditions; and that wall shear in the direction of pusher plate motion can be significant.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):334-343. doi:10.1115/1.3108450.

In a 3:1 scaled model of the human aorta models of the Omniscience, Björk-Shiley Convexo-Concave, Björk-Shiley Monostrut, Medtronic-Hall, Duromedics (Hemex) and the Saint Jude Medical heart valve prostheses are studied in steady flow representing the systolic peak flow phase. Detailed flow visualization experiments show flow separations at all inner ring surfaces as well as at most of the occluders. The resulting stagnation areas increase the risk of thrombus accumulation. Flow separations also stimulate vortex formation and turbulent mixing at the downstream jet boundaries and thus may intensify blood damage by turbulent shear stresses. The different influences of struts and occluder guides on the flow around the occluders are discussed. The effects of the individual valve components on the flow fields are analyzed and correlated with the resulting pressure losses.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):344-348. doi:10.1115/1.3108451.

Compliant vascular grafts were modeled by finite elasticity theory. A linear, biaxial model satisfactorily described the stress-strain behavior in inflation tests, where the sample length was fixed longitudinally and inflated. The model was then used to predict the behavior in a longitudinal test (where the longitudinal stretch was varied while keeping the pressure zero), and in a uniaxial test of a circumferential strip. The model satisfactorily predicted the longitudinal Young’s modulus measured in the longitudinal test. The model was less successful in predicting the circumferential Young’s modulus measured in the uniaxial test, possibly because the state of stress was not purely uniaxial.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):349-351. doi:10.1115/1.3108452.
Abstract
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):352-356. doi:10.1115/1.3108453.

Mechanical properties and collagen structure of excisional wounds left open are compared with wounds closed by clips. In both wound models, collagen fiber diameter increases with time post-wounding and is related to tensile strength. Clipped wounds show a higher ultimate tensile strength and tangent modulus compared with open wounds. In clipped wounds, newly deposited collagen appears as a biaxially oriented network as observed in normal skin. In open wounds a delay in the organization of the collagen network is observed and parallel wavy-shaped ribbons of collagen fibers are deposited. At long term, the high extensibility observed in open wounds may be due to the sliding of ribbons of collagen fibers past each other.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):357-363. doi:10.1115/1.3108454.

Secondary cortical bone is a complicated patchwork of structures which can be viewed as a hierarchy of four different orders. As far as the biomechanical properties of cortical bone are concerned, the lamella is the most important of the four. The relative distribution of longitudinal lamellae (whose fiber bundles and crystallites have a longitudinal course and withstand loading by tension) with respect to transverse lamellae (whose fiber bundles and crystallites have a transverse course and withstand loading by compression) governs the mechanical properties of bone at macroscopic level both in normal and pathological conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):364-373. doi:10.1115/1.3108455.

The in-vitro, three dimensional kinematic characteristics of the human ankle and subtalar joint were investigated in this study. The main goals of this investigation were: 1) To determine the range of motion of the foot-shank complex and the associated range of motion of the ankle and subtalar joints; 2) To determine the kinematic coupling characteristics of the foot-shank complex, and 3) To identify the relationship between movements at the ankle and subtalar joints and the resulting motion produced between the foot and the shank. The tests were conducted on fifteen fresh amputated lower limbs and consisted of incrementally displacing the foot with respect to the shank while the motion of the articulating bones was measured through a three dimensional position data acquisition system. The kinematic analysis was based on the helical axis parameters describing the incremental displacements between any two of the three articulating bones and on a joint coordinate system used to describe the relative position between the bones. From the results of this investigation it was concluded that: 1) The range of motion of the foot-shank complex in any direction (dorsiflexion/plantarflexion, inversion/eversion and internal rotation/external rotation) is larger than that of either the ankle joint or the subtalar joint.; 2) Large kinematic coupling values are present at the foot-shank complex in inversion/eversion and in internal rotation/external rotation. However, only a slight amount of coupling was observed to occur in dorsiflexion/plantarflexion.; 3) Neither the ankle joint nor the subtalar joint are acting as ideal hinge joints with a fixed axis of rotation.; 4) Motion of the foot-shank complex in any direction is the result of rotations at both the ankle and the subtalar joints. However, the contribution of the ankle joint to dorsiflexion/plantarflexion of the foot-shank complex is larger than that of the subtalar joint and the contribution of the subtalar joint to inversion/eversion is larger than that of the ankle joint.; 5) The ankle and the subtalar joints have an approximately equal contribution to internal rotation/external rotation movements of the foot-shank complex.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):374-385. doi:10.1115/1.3108456.

The objective of the present study was to investigate the in-vitro, coupled, three-dimensional load-displacement and flexibility characteristics of the human ankle joint complex consisting of the talocrural and the talocalcaneal joints and to determine the effects that sectioning of the anterior talofibular ligament has on these characteristics. Similar to other anatomical joints such as the knee and the intervertebral joint, the ankle joint complex was found to exhibit highly nonlinear load-displacement characteristics with the angular displacement approaching asymptotic values as the external load was increased. Therefore, a procedure of incremental linearization was used to derive the flexibility characteristics of this structure. According to this procedure, external loads were applied to the calcaneus in small increments and its resulting three dimensional displacements were recorded. The incremental flexibility coefficients were then derived by assuming linear load-displacement relationship for each increment. From the results obtained from fifteen human ankle specimens, it was evident that the ankle joint complex exhibit highly coupled flexibility and load-displacement characteristics. It was further concluded that the ankle joint complex is the most flexible in the neighborhood of the unloaded, neutral position and that all the flexibility coefficients of the structure decrease rapidly toward the extremes of the range of motion. Rupture of the anterior talofibular ligament was found to have a significant effect on the load-displacement and flexibility characteristics of the ankle joint complex. This effect was manifested as a change in the load-displacement characteristics and a large increase in the flexibility coefficients primarily in those corresponding to rotations in the transverse and the coronal plane. The results of the present study can provide the necessary data base for the development of quantitative diagnostic technique for identifying the site and the extent of injury to the collateral ligaments of the ankle.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1988;110(4):386-391. doi:10.1115/1.3108457.

Mechanical energy expenditure during level walking was evaluated and graphed for two unilateral, below-knee amputees over time and a range of adjustments of the flexion-extension alignment angle. The resulting mechanical energy surfaces were then least-squared fitted with an analytical function that was linear in time and quadratic in flexion-extension alignment angle. The least-squares analysis showed that there was a flexion-extension adjustment that minimized the mechanical energy expenditure and that this optimal adjustment was very close to the design point set by certified prosthetists.

Topics: Design , Knee
Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

J Biomech Eng. 1988;110(4):392-395. doi:10.1115/1.3108458.

An automated system is constructed to record the complete course of erythrocyte sedimentation process. In this system a light source and a paired photodetector are employed to monitor the change of light transmittance at the junction of plasma and the sedimenting red blood cell column, thus providing a continuous record of erythrocyte sedimentation as a function of time. Differentiation of this sedimentation—time curve yields a velocity—time curve of erythrocyte sedimentation. Frequently recorded “spikes” on top of the velocity—time curve imply the episodes of very rapid fall of erythrocytes in the sedimentation tube that cannot be explained by the currently accepted theory of erythrocyte sedimentation based mainly on Stokes’ law, and a new mechanism of rouleau coalescing and fracturing is proposed to account for them.

Commentary by Dr. Valentin Fuster

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