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RESEARCH PAPERS

J Biomech Eng. 1989;111(4):263-270. doi:10.1115/1.3168377.

A bioheat transfer model which computes the spatial variations in the arteriole, venule, and muscle temperatures in a human extremity under both resting and hyperthermic conditions is presented. This model uses the two-parameter model first proposed by Baish et al. [2] to account for the heat exchange between tissue and the paired arterioles and venules that comprise the microcirculation. Thermoregulation of the muscle blood flow during hyperthermia is also incorporated into the model. Results show that even when the paired arteriole and venule are assumed to have equal radii, the mean temperature under both steady and transient conditions is not equal to the mean of the arteriole and venule blood temperatures. Tissue temperature profiles during hyperthermia computed with the three-equation model presented in this study are similar in shape and magnitude to those predicted by the traditional one-equation Pennes bioheat transfer model [1] . This is due primarily to the influence of thermoregulatory mechanism in the heated muscle. The unexpected agreement is significant given the inherent relative simplicity of the traditional Pennes model. An “experimental” thermal conductivity is presented to relate the theoretical results to experimental procedures that are widely used to estimate the enhancement of conductivity by perfusion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):271-275. doi:10.1115/1.3168378.

A second order perturbation theory is developed to show the difference between the average artery-vein temperature Tm and the local average tissue temperature θ. This theory demonstrates that the closure approximation in the Weinbaum-Jiji bioheat equation does not require that θ = Tm and that although the difference between these two temperatures is second order the magnitude of the countercurrent convection terms in the Weibaum-Jiji equation can be of order unity. The theory also shows that to second order this new bioheat equation is the same as the simplified set of one-dimensional model equations used in Baish et al. [5] .

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):276-282. doi:10.1115/1.3168379.

A simple technique for measuring thermal conductivity of biomaterials is described. The method is based on depositing a pulse of heat into the material of choice, and fitting the subsequent local temperature decay to that predicted by a theoretical model. This transient method is most suitable in situations where frequent measurements of the thermal conductivity are desired. The method was evaluated by calculating the thermal conductivity of several inert materials. The measured conductivities compared well with published values. The developed technique was also used to examine the applicability of the “apparent conductivity” index to combine both conductive and blood-convective thermal effects in living, blood perfused tissues. Using both simulated and experimental results, it was shown that the changes in the apparent conductivity are highly correlated with changes in blood flow. However, quantitative application of this index must be restricted to conditions that are similar to those which existed at the time the apparent conductivity was measured.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):283-287. doi:10.1115/1.3168380.

This paper describes the production and calibration of a miniature psychrometer treated with a specially developed porous coating. The investigation was conducted to determine localized patterns of rapidly changing temperature and relative humidity in dynamic flowing gas environments (e.g., with particular attention to future applications to the human respiratory system). The technique involved the use of dry miniature thermocouples and wetted miniature thermocouples coated with boron nitride to act as a wicking material. A precision humidity generator was developed for calibrating the psychrometer. It was found that, in most cases, the measured and expected (i.e., theoretically predicted) relative humidity agreed to within 0.5 to 1.0 percent relative humidity. Procedures that would decrease this discrepancy even further were pinpointed, and advantages of using the miniature psychrometer were assessed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):288-297. doi:10.1115/1.3168381.

An instability resembling an avalanche is proposed as the mechanism by which mucus is expelled from the respiratory tract during cough. The cough event was simulated in a model airway. In these experiments, air was forced through a channel whose walls were lined with a non-Newtonian material rheologically similar to tracheal mucus. Frames from high-speed cine photographs showed an unstable event which began as an undulation of the free surface and progressed to a catastrophic clearance of the channel. Measurements of the longitudinal pressure gradient support the hypothesis that the clearance event is initiated when the total stress applied to the mucus analog exceeds its finite yield stress. A continuum model predicts that yielding occurs within the bottom layers of the mucus analog. Calculations based upon estimates of tracheal geometry and air flow show that the clearance event studied here would be expected to occur during a cough but not during normal breathing. Experiments also show that a lubricant introduced between the channel walls and the mucus blanket can reduce the air flow rate required to precipitate the clearance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):298-302. doi:10.1115/1.3168382.

An in vitro comparative study of St. Jude (SJ) and Edwards-Duromedics (DM) Bileaflet valves was performed under steady and physiological pulsatile flow conditions in an axisymmetric chamber using Laser Doppler Anemometry (LDA). LDA measurements were conducted in two different orientations; in the first orientation, the LDA traverse was perpendicular and, in the second orientation, parallel to the tilt axis of the leaflets. The axial velocities were measured in both orientations at two different locations distal to the valves. The velocity profiles at peak systole show the presence of stronger vortex in the sinus region for flow past SJ valve in the first orientation compared to the DM valve. Velocity profile distal to the SJ valve in second orientation was relatively flat where as for the DM valve, a jet-like flow was present. The differences found in the velocity profiles between the two valves can be attributed to the differences in geometry with thicker leaflets, smaller angle of leaflets opening and the presence of the leaflet curvature for the DM valve. The results obtained in this study do not show any fluid dynamic advantages due to the curved leaflet geometry of the DM valve.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):303-310. doi:10.1115/1.3168383.

Flow disturbances in tapered arterial grafts of angles of taper between 0.5 and 1.0 deg were measured in vitro using a pulsed ultrasound Doppler velocimeter. The increase in transition Reynolds numbers with angle of taper and axial distance was determined for steady flow. The instantaneous centerline velocities were measured distal to a 50 percent area stenosis (as a model of a proximal anastomosis), in steady and pulsatile flow, from which the disturbance intensities were calculated. A significant reduction in post-stenotic disturbance intensity was recorded in the tapered grafts, relative to a conventional cylindrical graft. In pulsatile flow with a large backflow component, however, there was an increase in disturbance intensity due to diverging flow during flow reversal. This was observed only in the 1.0 deg tapered graft. These findings indicate that taper is an important consideration in the design of vascular prostheses.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):311-315. doi:10.1115/1.3168384.

The fluid-particle dynamics in a two-dimensonal symmetric branching channel with local occlusions representing a diseased segment of an aortic artery bifurcation has been analyzed. The validated finite element model simulates the trajectories and landing or impact sites of spherical particles for laminar flow in bifurcation channels with generalized wall conditions. Two hypotheses relating critical wall shear stress levels and plaque formation, previously postulated by Kleinstreuer et al. (1988) and Nazemi et al. (1989), have been confirmed. Low shear stress may contribute to the onset of atherosclerotic lesions and areas of critically low and high shear stresses are susceptible to accelerated growth of plaque.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):316-324. doi:10.1115/1.3168385.

Considering steady laminar flow in a two-dimensional symmetric branching channel with local occlusions, a finite element model has been developed to study velocity fields including reverse flow regions, pressure profiles and wall shear stress distributions for different Reynolds numbers, bifurcation angles and lumen reductions. The flow analysis has been extended to include a new submodel for the pseudo-transient formation of plaque at sites and deposition rates defined by the physical characteristics of the flow. Specifically, simulating the onset of atherosclerotic lesions, sinusoidal plaque layers have been placed in areas of critically low wall shear stresses, and simulating the growth of particle depositions, plaque layers have been added in a stepwise fashion in regions of critically high and low shear. Thus two somewhat conflicting hypothetical correlations between critical wall shear stress levels and atheroma have been tested and a solution has been postulated. The validated computer simulation model is a predictive tool for analyzing the effects of local changes in wall curvature due to surgical reconstruction and/or atherosclerotic lesions, and for investigating the design of aortic bifurcations which mitigate plaque formation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):325-335. doi:10.1115/1.3168386.

Examination of changes occurring in the zero-stress state of an organ provides a way to study cellular growth in the organ due to change of physical stresses. The zero-stress state of the aorta is not a tube. It is a sector with an opening angle that varies with the location on the aorta and changes with cellular remodeling. Blood vessel remodeling can be induced by imposing a constriction on the abdominal aorta by a metal clip (aortic banding), which causes an increase of blood pressure, hypertrophy of the aortic wall, and large change of opening angle. The correlation of the opening angle with the blood vessel wall thickness and blood pressure changes in rat’s aorta due to aortic banding is presented in this report. The opening angle changes daily following the aortic banding. Blood pressure rises in vessels of the upper body, but that in the lower body decreases at first and then rises to an asymptotic value. Blood vessel wall thickness increases in rough proportion to blood pressure. Vessel diameter changes also. But the most dramatic is the course of change of the zero-stress state. Typically, the time to reach 50 percent of asymptotic hypertrophy of blood vessel wall thickness is about 3–5 days. The corresponding time for blood pressure is about 7 days. The opening angle of the zero-stress state, however, increases rapidly at first, reaches a peak in about 2 to 4 days, then decreases gradually to a reduced asymptote. The exact values of the time constants depend on the location along the aortic tree. In general, the course of change of residual strain is very different from those of the blood pressure and the blood vessel wall thickness.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):336-341. doi:10.1115/1.3168388.

This paper provides a simple model for predicting the relationship between steadystate heart rate and arterial blood pressure. Two current state-of-the-art models of the cardiovascular system as a pump operating in its circuit are reformulated and combined in order to highlight the role of the duration of the heart cycle. The proposed model establishes that the cardiac cycle lengthens linearly with the inverse of the average blood pressure. Experimental data are reported for sixteen preoperated conscious dogs resting quietly on their sides. Vagal and sympathetic blocks have been produced in four dogs in order to obtain a wide range of sympathetic and parasympathetic tones, namely, to cover the entire range of physiological values of the heart rate. For these dogs a comparison between the experimental values and the theoretical predictions shows a good agreement, the results of the linear regression model being statistically significant at the p = 0.001 level for three dogs and at the p = 0.01 level for the fourth dog.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):342-349. doi:10.1115/1.3168389.

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):350-354. doi:10.1115/1.3168390.

Previous studies of biomechanical properties of femur-anterior cruciate ligament-tibia complex (FATC) utilized a wide variety of testing methodologies, particularly with respect to ligament orientation relative to loading direction. A new device was designed and built to test the anterior-posterior displacement of the intact porcine knee at 30 and 90 deg of flexion, as well as the tensile properties of the FATC at any loading direction and flexion angle. Tensile tests were performed with the knees at 30 and 90 deg of flexion with the loading direction along either the axis of the tibia (tibial axis) or the axis of the anterior cruciate ligament (ligament axis). The results showed that the stiffness, ultimate load and energy absorbed were all significantly increased when the FATC was tested along the ligament axis. This study demonstrates the importance of alignment in the evaluation of the biomechanical characteristics of the femur-ACL-tibia complex.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1989;111(4):355-360. doi:10.1115/1.3168391.

Theoretical predictions of internal bone remodeling around an elliptical hole are studied. The internal remodeling theory due to Cowin and Hegedus is employed. The bone is modeled as an initially homogeneous adaptive elastic plate with an elliptical hole under a superposed steady compressive load. It is shown that there will exist a final inhomogeneous remodeling distribution around the hole that will disappear away from the hole. The remodeling is such that the compressive stress concentration causes the bone structure to evolve to one of greater density and stiffer elastic coefficients. The speed of remodeling around the hole and its variation with respect to distance is investigated and discussed. It is shown that the rate of bone reinforcement in the area of compressive stress concentration is much higher than the rate of bone resorption in the area of existing tensile stress. Special cases of a circular hole and vertical and horizontal slots are studied and discussed.

Commentary by Dr. Valentin Fuster

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Commentary by Dr. Valentin Fuster

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Commentary by Dr. Valentin Fuster

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