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TECHNICAL PAPERS

J Biomech Eng. 1999;121(4):361-369. doi:10.1115/1.2798332.

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):370-375. doi:10.1115/1.2798333.

Blood flow dynamics in the human right coronary artery have not been adequately quantified despite the clinical significance of coronary atherosclerosis. In this study, a technique was developed to construct a rigid flow model from a cast of a human right coronary artery. A laser photochromic method was used to characterize the velocity and wall shear stress patterns. The flow conditions include steady flow at Reynolds numbers of 500 and 1000 as well as unsteady flow with Womersley parameter and peak Reynolds number of 1.82 and 750, respectively. Characterization of the three-dimensional geometry of the artery revealed that the largest spatial variation in curvature occurred within the almost branch-free proximal region, with the greatest curvature existing along the acute margin of the heart. In the proximal segment, high shear stresses were observed on the outer wall and lower, but not negative, stresses along the inner wall. Low shear stress on the inner wall may be related to the preferential localization of atherosclerosis in the proximal segment of the right coronary artery. However, it is possible that the large difference between the outer and inner wall shear stresses may also be involved.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):376-385. doi:10.1115/1.2798334.

We incorporated a three-dimensional generalization of the Huxley cross-bridge theory in a finite element model of ventricular mechanics to examine the effect of nonaxial deformations on active stress in myocardium. According to this new theory, which assumes that macroscopic tissue deformations are transmitted to the myofilament lattice, lateral myofilament spacing affects the axial fiber stress. We calculated stresses and deformations at end-systole under the assumption of strictly isometric conditions. Our results suggest that at the end of ejection, nonaxial deformations may significantly reduce active axial fiber stress in the inner half of the wall of the normal left ventricle (18–35 percent at endocardium, depending on location with respect to apex and base). Moreover, this effect is greater in the case of a compliant ischemic region produced by occlusion of the left anterior descending or circumflex coronary artery (26–54 percent at endocardium). On the other hand, stiffening of the remote and ischemic regions (in the case of a two-week-old infarct) lessens the effect of nonaxial deformation on active stress at all locations (9–32 percent endocardial reductions). These calculated effects are sufficiently large to suggest that the influence of nonaxial deformation on active fiber stress may be important, and should be considered in future studies of cardiac mechanics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):386-392. doi:10.1115/1.2798335.

The elements of Quasi-Linear Viscoelastic (QLV) theory have been applied to model the internal shear mechanics of fresh and glutaraldehyde-fixed porcine aortic valve leaflets. A novel function estimation method was used to extract the material functions from experimental shear data obtained at one strain rate, and the model was used to predict the material response at different strain rates. In general, experiments and predictions were in good agreement, the larger discrepancies being in the prediction of peak stresses and hysteresis in cyclic shear. In shear, fixed tissues are stiffer (mean initial shear modulus, 13 kPa versus 427 Pa), take longer to relax to steady state (mean τ2 4,736 s versus 1,764 s) with a slower initial relaxation rate (mean magnitude of Ġ(0), 1 s−1 versus 5 s−1 ), and relax to a lesser extent than fresh tissues (mean percentage stress remaining after relaxation, 60 versus 45 percent). All differences were significant at p = 0.04 or less, except for the initial relaxation slope. We conclude that shear experiments can complement traditional tensile and biaxial experiments toward providing a complete mechanical description of soft biomaterials, particularly when evaluating alternative chemical fixation techniques.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):393-398. doi:10.1115/1.2798336.

The objective of this study was to evaluate two calibration methods for the “Arthroscopically Implantable Force Probe” (AIFP) that are potentially suitable for in vivo use: (1) a direct, experimentally based method performed by applying a tensile load directly to the graft after it is harvested but prior to implantation (the “pre-implantation” technique), and (2) an indirect method that utilizes cadaver-based analytical expressions to transform the AIFP output versus anterior shear load relationship, which may be established in vivo, to resultant graft load (the “post-implantation” technique). The AIFP outputs during anterior shear loading of the knee joint using these two calibration methods were compared directly to graft force measurements using a ligament cutting protocol and a 6 DOF load cell. The mean percent error ((actual – measured)/(actual) * 100) associated with the pre-implantation calibration ranged between 85 and 175 percent, and was dependent on the knee flexion angle tested. The percent error associated with the post-implantation technique was evaluated in two load ranges: loads less than 40 N, and loads greater than 40 N. For graft force values greater than 40 N, the mean percent errors inherent to the post-implantation calibration method ranged between 20 and 29 percent, depending on the knee flexion angle tested. Below 40 N, these errors were substantially greater. Of the two calibration methods evaluated, the post-implantation approach provided a better estimate of the ACL graft force than the pre-implantation technique. However, the errors for the post-implantation approach were still high and suggested that caution should be employed when using implantable force probes for in vivo measurement of ACL graft forces.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):399-405. doi:10.1115/1.2798337.

To provide data for fatigue life prediction and testing of structural components in off-road bicycles, the objective of the research described herein was to quantify the loads input to an off-road bicycle as a result of surface-induced loads. A fully instrumented test bicycle was equipped with dynamometers at the pedals, handlebars, and hubs to measure all in-plane structural loads acting through points of contact between the bicycle and both the rider and the ground. A portable data acquisition system carried by the standing rider allowed, for the first time, this loading information to be collected during extended off-road testing. In all, seven experienced riders rode a downhill trail test section with the test bicycle in both front-suspension and full-suspension configurations. The load histories were used quantitatively to describe the load components through the computation of means, standard deviations, amplitude probability density functions, and power spectral density functions. For the standing position, the coefficients of variation for the load components normal to the ground were greater than 1.2 for handlebar forces and 0.3 and 0.5–0.6 for the pedal and hub forces, respectively. Thus, the relative contribution of the dynamic loading was much greater than the static loading at the handlebars but less so at the pedals and hubs. As indicated by the rainflow count, high amplitude loading was developed approaching 3 and 5 times the weight of the test subjects at the front and rear wheels, respectively. The power spectral densities showed that energy was concentrated in the band 0–50 Hz. Through stress computations and knowledge of material properties, the data can be used analytically to predict the fatigue life of important structural components such as those for steering. The data can also be used to develop a fatigue testing protocol for verifying analytical predictions of fatigue life.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):406-413. doi:10.1115/1.2798338.

This paper presents some results on the modeling and the parameter estimation of the human knee joint. Based on the geometric characteristics of the femur condyle and the tibia plateau, a part of femoro-tibial joint model includes an involute-on-plane submodel. Data recorded by camera type device are used to analyze the kinematic characteristics of the knee joint and to estimate the corresponding submodel parameters. Experimental results are presented and the model is further validated.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):414-422. doi:10.1115/1.2798339.

In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai–Wu, Principal Strain, and von Mises phenomenological criteria—all normalized to minimize effects of interspecimen heterogeneity of strength—to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (± S.D.) percentage errors between measured values and criterion predictions were 7.7 ± 12.6 percent, 19.7 ± 23.2 percent, 22.8 ± 18.9 percent, and 82.4 ± 64.5 percent for the Cellular Solid, Tsai–Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were –5.2 ± 11.8 percent, 14.3 ± 12.5 percent, 6.9 ± 7.6 percent, and 57.7 ± 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1999;121(4):423-431. doi:10.1115/1.2798340.

We developed a noninvasive method to evaluate bone structural integrity. It is based on the measurement of the dynamic characteristics of the bone using sweeping sound excitation in the range of acoustic frequencies. The Quality Factor (a measure of material damping) has been used as an indicator of the tendency of the bone to fracture. Results of animal studies have supported this hypothesis since linear correlations were observed between bone density, quality factor, and impact strength. A vibration excitation in the form of an acoustic sweep signal is applied to a bone to measure the quality factor. Rat bones were tested, obtained from animals with osteoporosis age-dependent (tested in vitro) or ovariectomy-induced (tested in vivo), and compared with bones of healthy (control) rats. The change in damping was, on average, equal or greater to the change in density. Moreover, excellent correlation of the quality factor was obtained with bone fracture energy measured with an impact test. During a vibration cycle, the changing strain results in temperature changes due to the reciprocity of temperature and strain. Nonreversible conduction of heat due to the unequal temperature change results in entropy production that is enhanced due to the stress concentration about the voids associated with bone porosity. Damping is a measure of the production of entropy. Its measure, the quality factor, represents a potentially useful tool for monitoring bone integrity, which is deteriorating in diseases characterized by disruption of the trabecular architecture, such as osteoporosis. A computational model yielded results that are in good correlation with the experimental results.

Commentary by Dr. Valentin Fuster

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