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RESEARCH PAPERS

J Biomech Eng. 1993;115(1):1-12. doi:10.1115/1.2895465.

The endothelium lining human arteries is a continuum of endothelial cells. The flowing blood imposes a shear stress on the endothelium. To compute the internal stress in the endothelium, we use two alternative hypotheses: 1) The cell content is fluid-like so that at steady-state it has no shear stress. 2) The cell content is solid-like. Under hypothesis No. 1, the membrane tension in the upper cell membrane grows in the direction opposite to the blood flow at a rate equal to the blood shear stress. At the junction of two neighboring cells the membrane tension in the downstream cell is transmitted partly to the basal lamina, and partly to the upstream cell. The transmission depends on the osmotic or static pressure difference between the cell and blood. If the static pressure difference is zero, the tension in the upper cell membrane will accumulate upstream. At other values of static pressure, the cell membrane tension may increase, decrease, or fluctuate along the vessel depending on the inclination of the side walls of the cells at the junctions. To determine the sidewall inclinations, we propose to use the complementary energy theorem. Under hypothesis No. 2, the cell content can bear shear, which tends to reduce the cell membrane tension; but the cell membrane tension accumulation phenomenon discussed above remains valid. These results are used to analyze the interaction of the cell membrane and cell nucleus; and the effect of turbulences in the flow on causing large fluctuations in cell membrane tension and vertical oscillations of the nuclei. The implication of tensile stress on the permeability of the cell membrane is discussed. We conclude that for the study of mass transport and stress fibers in the endothelial cells, one should consider the interaction of neighboring endothelial cells as a continuum, and shift attention from the shear stress in the blood to the principal stresses in the cells.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):13-22. doi:10.1115/1.2895464.

There is a limited amount of information available on the mechanical and functional response of the nervous system to loading. While deformation of cerebral, spinal, or peripheral nerve tissue can have particularly severe consequences, most research in this area has concentrated on either demonstrating in-vivo functional changes and disclosing the effected anatomical pathways, or describing material deformations of the composite structure. Although such studies have successfully produced repeatable traumas, they have not addressed the mechanisms of these mechanically induced injuries. Therefore, a single cell model is required in order to gain further understanding of this complex phenomena. An isolated squid giant axon was subjected to controlled uniaxial loading and its mechanical and physiological responses were monitored with an instrument specifically designed for these experiments. These results determined that the mechanical properties of the isolated axon are similar to those of other soft tissues, and include features such as a nonlinear load-deflection curve and a hysteresis loop upon unloading. The mechanical response was modeled with the quasi-linear viscoelastic theory (Fung, 1972). The physiological response of the axon to quasi-static loading was a small reversible hyperpolarization; however, as the rate of loading was increased, the axon depolarized and the magnitude and the time needed to recover to the original resting potential increased in a nonlinear fashion. At elongations greater than twenty percent an irreversible injury occurs and the membrane potential does not completely recover to baseline.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):23-28. doi:10.1115/1.2895466.

Mechanical properties of the stress-shielded patellar tendon were studied in the rabbit knee. Stress shielding was accomplished by stretching a stainless-steel wire installed between the patella and tibial tubercle and thus, releasing the tension in the patellar tendon completely. Tensile tests were carried out on the specimens obtained from the patellar tendons which were exposed to the stress shielding for 1 to 6 weeks. The stress shielding changed the mechanical properties of the patellar tendon significantly: it decreased the tangent modulus and tensile strength to 9 percent of the control values after 3 weeks. There was a 131 percent increase in the cross-sectional area and a 15 percent decrease in the tendinous length. Remarkable changes were also observed in the structural properties: for example, the maximum load of the bone-tendon complex decreased to 20 percent of the control value after 3 weeks. Histological studies showed that the stress shielding increased the number of fibroblasts and decreased the longitudinally aligned collagen bundles. These results imply that if no stress is applied to the autograft in the case of augmentative reconstruction of the knee ligament, the graft strength decreases remarkably.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):29-36. doi:10.1115/1.2895467.

Using matrix algebra, a mathematical model is formulated for a particular type of external fixator with wires (system developed by Ilizarov) for the treatment of bone fractures. The mathematical model is used to give a linear estimate of the stiffness under lateral and axial loads in a representative number of practical conditions. Relative displacements of the bone ends at the fracture site are calculated not only in the common case of a gap, but also for various angles of inclined sliding contact; in this case, a realistic load is applied and nonlinear stiffening of the wires under transversal loads is iteratively taken into account.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):37-42. doi:10.1115/1.2895468.

The work shows correct procedures needed in order to gather reliable data from measurement of displacements versus axial load in a laboratory mounting of the Ilizarov external fixator. The mechanism of settling after load cycling is investigated. Detension under load is a major problem of wires. By means of vibration frequency measurements, tests on single wire allow determination of reduction in wire tension due to transverse loading: it is found that, almost independently from the amount of clamp tightening, the tension reaches a lower limit related only to the transverse load and not related to pretension. It is shown that, for higher clamp tightening torques, wire detension must be attributed to permanent plastic deformation of the wires; moreover, it is shown that the unavoidable errors in the spacing of the tensioned wires lead to marked decrease of their stiffness under transverse load.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):43-46. doi:10.1115/1.2895469.

Range of motion (ROM), the displacement between two limits, is one of the most common parameters used to describe joint kinematics. The ROM is a one-dimensional parameter, although the motion at many normal and pathological joints is three-dimensional. Certainly, the ROM yields vital information, but an overall measure of the three-dimensional mobility at a joint may also be useful. The volume of motion (VOM) is such a measure. The translational VOM is the volume defined by all possible ROMs of a point on a rigid body. The rotational VOM, although its interpretation is not as tangible as the translational VOM, is a measure of the three-dimensional rotational mobility of a rigid body. The magnitude of the VOM is proportional to mobility; the VOM is a scaler, which does not contain any directional information. Experimental determination of the VOM is not practical since it would require applying loads in an infinite number of directions. The mathematical derivation given here allows the VOM to be calculated, with the assumption of conservative elasticity, from the resultant displacements of three distinct load vectors of equal magnitude. An example of the VOM is presented in the comparison of the biomechanical stabilizing potential of various spinal fixation devices.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):47-52. doi:10.1115/1.2895470.

A measurement system was designed to investigate longitudinal wave propagation through the lower extremity generated from foot strikes. The principal goal of the design was to eliminate measurement time lag and amplitude reduction, such that the acceleration measured by Skin Mounted Accelerometer—SMA is equal to the actual acceleration of the bone measured by Bone Mounted Accelerometer—BMA. For accurate dynamic measurement, it is important that the gain and phase of the measurement system are as close as possible to a constant and zero, respectively, for the frequency range being covered. An in vitro experiment was carried out to simultaneously measure skin and bone accelerations. The obtained information was used for identification of a linear spring/damper model representing the interface between the BMA and the SMA. The present work showed that the SMA overestimated the BMA by 12 percent in the signals between 15–30 Hz.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):53-62. doi:10.1115/1.2895471.

The calculation of human joint forces and moments during locomotion is usually based on the solution of the “inverse dynamics problem.” A new approach, called the Integrated Kinematic Sensor (IKS) approach, is proposed. It combines measurements of position, linear acceleration and angular velocity, coupled with six degrees of freedom analysis of rigid body motion, for the purpose of deriving high quality link kinematics and joint loads (force and moment) estimates. The IKS approach is tested on an instrumented compound pendulum to simulate the swing of a lower limb segment. The results show a high degree of correlation between the loads estimated by the IKS and those directly measured by the instrumented joint. The approach is illustrated by studying the kinematic and dynamic variables of the human shank segment during normal walking. The results agree with the basic patterns reported in the literature, while adding new information on transients during heel strike and toe off.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):63-71. doi:10.1115/1.2895472.

An adjoint formulation is derived and used to determine the elements in the Jacobian matrix associated with the inverse problem of estimating the blood perfusion and temperature fields during hyperthermia cancer treatments. This method and a previously developed influence coefficient method for obtaining that matrix are comparatively evaluated by solving a set of numerically simulated inverse hyperthermia problems. The adjoint method has the advantage of requiring fewer solutions of the bioheat transfer equation to estimate the Jacobian than does the influence coefficient method when the number of measurement sensors is significantly smaller than the number of unknown parameters. Thus, it could be a preferable method to use in hyperthermia applications where the number of sensors is strictly limited by patient considerations. However, the adjoint method requires that CPU time intensive convolutions be numerically evaluated. Comparisons of the performance of the adjoint formulation and the influence coefficient method show that, first, there is a critical ratio of the number of measurement sensors to the number of unknown parameters at which the CPU time per iteration required to calculate the Jacobian matrix is the same for both methods. The adjoint method is faster than the influence coefficient method only when the value of the ratio is less than that critical value. For the hyperthermia problems investigated in the present study, this only occurs for cases with a very small number of measurement sensors. This presents a potential problem for clinical applications because the fewer measurement sensors used, the less information that can be gathered to correctly solve the inverse problem. Thus, second, when both techniques were utilized to solve several inverse hyperthermia problems it was found that the total CPU time for the adjoint formulation was larger than that for the influence coefficient method for all of the cases which were solved successfully. That is, all inverse solutions which were successful had ratios greater than the critical value. Thus, for practical hyperthermia problems it appears that the influence coefficient method is preferable to the adjoint formulation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):72-81. doi:10.1115/1.2895473.

Constitutive relations for active fiber stress in cardiac muscle are proposed and parameters are found that allow these relations to fit experimental data from the literature, including the tension redeveloped following rapid deactivating length perturbations. Contraction is driven by a length-independent free calcium transient. The number of actin sites available to react with myosin is determined from the total number of actin sites (available and inhibited), free calcium and the length history-dependent association and dissociation rates of two Ca2+ ions and troponin as governed by a first-order, classical kinetics, differential equation. Finally, the relationship between active tension and the number of available actin sites is described by a general cross-bridge model. Bridges attach in a single configuration at a constant rate, the force within each cross-bridge varies linearly with position, and the rate constant of bridge detachment depends both on position and time after onset of contraction. In Part II, these constitutive relations for active stress are incorporated in a continuum mechanics model of the left ventricle that predicted end-systolic transmural strain distributions as observed experimentally.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):82-90. doi:10.1115/1.2895474.

Models of contracting ventricular myocardium were used to study the effects of different assumptions concerning active tension development on the distributions of stress and strain in the equatorial region of the intact left ventricle during systole. Three models of cardiac muscle contraction were incorporated in a cylindrical model for passive left ventricular mechanics developed previously [Guccione et al. ASME Journal of Biomechanical Engineering, Vol. 113, pp. 42-55 (1991)]. Systolic sarcomere length and fiber stresses predicted by a general “deactivation” model of cardiac contraction [Guccione and McCulloch, ASME Journal of Biomechanical Engineering, Vol. 115, pp. 72-81 (1993)] were compared with those computed using two less complex models of active fiber stress: In a time-varying “elastance” model, isometric tension development was computed from a function of peak intracellular calcium concentration, time after contraction onset and sarcomere length; a “Hill” model was formulated by scaling this isometric tension using the force-velocity relation derived from the deactivation model. For the same calcium ion concentration, the sarcomeres in the deactivation model shortened approximately 0.1 μm less throughout the wall at end-systole than those in the other models. Thus, muscle fibers in the intact ventricle are subjected to rapid length changes that cause deactivation during the ejection phase of a normal cardiac cycle. The deactivation model predicted rather uniform transmural profiles of fiber stress and cross-fiber stress distributions that were almost identical to those of the radial component. These three components were indistinguishable from the principal stresses. Transmural strain distributions predicted at end-systole by the deactivation model agreed closely with experimental measurements from the anterior free wall of the canine left ventricle.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):91-96. doi:10.1115/1.2895475.

Dispersion and uptake of gas boli of a range of solubilities was examined in lung airway models; first a straight tube, then a four generation network. Airway liquid lining was simulated with gelatin. The bolus dispersion was determined from the first three moments of the concentration profile measured at two positions downstream. The disruption of the flow by the bifurcations significantly reduces the dispersion of an insoluble gas, compared to that predicted in an equivalent network of parallel straight tubes. Retention of gas in the wall increases with solubility causing increased bolus dispersion and decreased average speed. For highly soluble gases this process dominates and the effect of bifurcations becomes less significant.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):97-103. doi:10.1115/1.2895476.

In vitro pulsatile flow visualization studies were conducted to assess the effects of varying radii of curvature of the right ventricular outflow tract (RVOT) and main pulmonary artery (MPA) on the flow fields in the main, right, and left pulmonary arteries of a one month lamb pulmonary artery model. Three glass flow-through models were studied; one with no curvature, one with the correct anatomic curvature, and one with an overaccentuated curvature on the RVOT and MPA. All other geometric parameters were held constant. Pulsatile flow visualization studies were conducted at nine flow conditions; heart rates of 70, 100, and 140 bpm, and cardiac outputs of 1.5, 2.5 and 3.5 l/min with corresponding mean pulmonary pressures of 10, 20, and 30 mmHg. Changes were observed in the pulmonary flow fields as the curvature of the outflow tract, heart rate and mean pulmonary pressure were varied. An increase in vessel curvature led to an increase in the overall radial nature of the flow field as well as flow separation regions which formed faster, originated further downstream, and occupied more of the vessel area. At higher heart rates, the maximum size of the separation regions decreased, while flow separation regions appeared earlier in the cardiac cycle and grew more quickly. Heart rate also affected the initiation of flow reversal; flow reversal occurred later in the cardiac cycle at lower heart rates. Both heart rate and mean pulmonary pressure influenced the stability of the pulmonary flow field and the appearance of coherent structures. In addition, an increase in mean pulmonary pressure increased the magnitude of reverse flow. These flow visualization observations have directed more quantitative studies such as pulsed Doppler ultrasound and laser Doppler anemometry velocity measurements.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):104-111. doi:10.1115/1.2895456.

Flow behavior in models of end-to-side vascular graft anastomoses was studied under steady and pulsatile flow conditions. Models were constructed to simulate geometries employed in experimental studies on intimal thickening in a canine model. Reynolds numbers, division of flow in the outflow tracts and the pulsatile waveform employed were taken from measurements obtained in the canine model. Flows in the scaled-up, transparent models were visualized with white, neutrally buoyant particles which were photographed under laser illumination and also recorded on video tape under bright incandescent light. Strong, three-dimensional helical patterns which formed in the anastomotic junction were prominent features of the flow fields. Regions of low wall shear, oscillatory wall shear and long particle residence time were identified from the flow visualization experiments. Comparisons with the limited qualitative data available on intimal thickening in vascular graft anastomoses suggest a relation between localization of vascular intimal thickening and those surfaces experiencing low shear and long particle residence time.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):112-118. doi:10.1115/1.2895457.

In order to understand the possible role that hemodynamic factors may play in the pathogenesis of distal anastomotic intimal hyperplasia, we carried out numerical simulations of the flow field within a two-dimensional 45 degree rigid-walled end-to-side model anastomosis. The numerical code was tested and compared with experimental (photochromic dye tracer) studies using steady and near-sinusoidal waveforms, and agreement was generally very good. Using a normal human superficial femoral artery waveform, numerical simulations indicated elevated instantaneous wall shear stress magnitudes at the toe and heel of the graft-host junction and along the host artery bed. These sites also experienced highly variable wall shear stress behavior over the cardiac cycle, as well as elevated spatial gradients of wall shear stress. These observations provide additional evidence that intimal hyperplasia may be correlated to wall shear stresses over the cardiac cycle, high wall shear stress gradients, or a combination of the three. The limitations of the present work (especially in regard to the two-dimensional nature of the flow simulations) are discussed, and results are compared to previous observations about distal anastomotic intimal hyperplasia.

Commentary by Dr. Valentin Fuster

ERRATA

TECHNICAL BRIEFS

J Biomech Eng. 1993;115(1):119-121. doi:10.1115/1.2895458.

An analytical, cylindrical coordinate formula for the thermal resistance around small cylindrical objects has been incorporated into finite difference equations in Cartesian coordinates to improve the accuracy of the numerical simulations of hyperthermia cancer treatments. This is done by introducing a circular finite difference control volume which is centered on the cylindrical object. The temperature distributions calculated from this new formulation and from the formulation obtained from a conventional, rectangular control volume are compared to the predictions from an analytical solution. The results show that for a given Cartesian grid spacing, the new method is superior to the conventional one. This will allow more accurate numerical solutions to be obtained at larger grid spacings when the effect of blood vessels or other cylindrical objects, such as ferromagnetic implants, hot water tubes, etc., are being investigated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):121-122. doi:10.1115/1.2895459.

This paper describes the design and development of a new device which allows the surgeon to locate an internal point following two X-ray views with an image intensifier. Three dimensional coordinates of the target point are directly estimated by means of two ring-and-bead sights and no computer calculations are necessary. After the location of the target point it is possible to choose any track to it by means of the rotation of an arc and the circumferential sliding of the arc. The system reduces radiation doses and it can be used for many purposes such as percutaneous discectomies and chemonucleolysis, biopsies and screw insertion of interlocking nails.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):123-125. doi:10.1115/1.2895461.

Our goal was to evaluate physical factors in the initiation and propagation of dissections in human aortas. Aortic dissection was simulated in 21 open unpressurized human autopsy aortas by infusing dyed isotonic saline into the media at constant flow. Pressure during growth of the fluid filled cavity was monitored and correlated with volume to give pressure-volume curves, from which distensibility, peak pressure, and work data were calculated. Dissections in specimens occurred at a very high nonphysiological mean pressure of 79 ± 29 (SD) kPa (596 ± 214 mmHg). Age and tear depth had no significant effect on medial strength of human aortas but sex, location and atherosclerotic plaque formation did (p < 0.05). The mean pressure value for the female abdominal fibrous/calcified group (92 ± 30 kPa, 691 ± 222 mmHg) differed from that of the male abdominal fibrous/calcified group (69 ± 36 kPa, 508 ± 269 mmHg). We also observed a significant difference between the male thoracic fibrous calcified (80 ± 31 kPa, 601 ± 230 mmHg) and male abdominal fibrous/calcified (68 ± 36 kPa, 508 ± 269 mmHg) groups. Significant differences were observed between the female fatty/normal (75 ± 25 kPa, 562 ± 187 mmHg) and fibrous/calcified (91 ± 23 kPa, 685 ± 176 mmHg) groups of the thoracic aorta and between the male fatty/normal (86 ± 23 kPa, 650 ± 169 mmHg) and fibrous/calcified (68 ± 36 kPa, 508 ± 269 mmHg) groups of the abdominal aorta. Distensibility data showed no trends. It is probable that dissection does not occur spontaneously in the absence of a connective tissue disorder and/or surgical procedure. Atherosclerosis is not responsible for dissection initiation but may alter the propagation of dissection.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(1):125-126. doi:10.1115/1.2895462.

We have investigated the dispersion characteristics of a highly soluble tracer gas in a coiled tube lined with wet gelatine. Our experiments indicate that absorption and desorption of the gas at the wall dominates tracer dispersion along the tube. The results confirm previous experiments in a branching geometry indicating that the influence of secondary flows on dispersion is reduced if the tracer is very soluble in the wall.

Commentary by Dr. Valentin Fuster

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