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TECHNICAL PAPERS

J Biomech Eng. 1997;119(3):221-227. doi:10.1115/1.2796083.

We measured the step response of a surrogate human pelvis/impact pendulum system at force levels between 50 and 350 N. We then fit measured response curves with four different single-degree-of-freedom models, each possessing a single mass, and supports of the following types: standard linear solid, Voigt, Maxwell, and spring. We then compared model predictions of impact force during high-energy collisions (pendulum impact velocity ranging from 1.16 to 2.58 m/s) to force traces from actual impacts to the surrogate pelvis. We found that measured peak impact forces, which ranged from 1700 to 5600 N, were best predicted by the mass-spring, Maxwell, and standard linear solid models, each of which had average errors less than 3 percent. Reduced accuracy was observed for the commonly used Voigt model, which exhibited an average error of 10 percent. Considering that the surrogate pelvis system used in this study exhibited nonlinear stiffness and damping similar to that observed in simulated fall impact experiments with human volunteers, our results suggest that these simple models allow impact forces in potentially traumatic falls to be predicted to within reasonable accuracy from the measured response of the body in safe, simulated collisions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):228-231. doi:10.1115/1.2796084.

The presence of a femoral hip stem changes local mechanical signals inside the surrounding bone. In this study we examined the hypothesis that the eventual loss of bone can be estimated from the initial patterns of elastic energy deviation, as determined in FE models of the intact bone and the operated femur. For that purpose two hypothetical relations between elastic energy reduction and resorption were investigated. Their estimates of bone loss were compared to the results of iterative computer simulations. Two kinds of FE model were used, and in each stem stiffness and remodeling threshold (a measure of “biological reactivity”) were varied. Provided that reasonable values of the remodeling threshold are assumed and that the stem is firmly bonded to the bone, we found that the difference between direct estimates and simulation models was 4 percent of bone loss. It is therefore concluded that initial patterns of elastic energy deviation give a reasonable indication of expected bone loss.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):232-236. doi:10.1115/1.2796085.

A system was refined for the determination of the bulk ultrasonic wave propagation velocity in small cortical bone specimens. Longitudinal and shear wave propagations were measured using ceramic, piezoelectric 20 and 5 MHz transducers, respectively. Results of the pulse transmission technique were refined via the measurement of the system delay time. The precision and accuracy of the system were quantified using small specimens of polyoxymethylene, polystyrene-butadiene, and high-density polyethylene. These polymeric materials had known acoustic properties, similarity of propagation velocities to cortical bone, and minimal sample inhomogeneity. Dependence of longitudinal and transverse specimen dimensions upon propagation times was quantified. To confirm the consistency of longitudinal wave propagation in small cortical bone specimens (<1.0 mm), cut-down specimens were prepared from a normal rat femur. Finally, cortical samples were prepared from each of ten normal rat femora, and Young’s moduli (Eii ), shear moduli (Gij ), and Poisson ratios (vij ) were measured. For all specimens (bone, polyoxymethylene, polystyrene-butadiene, and high-density polyethylene), strong linear correlations (R2 > 0.997) were maintained between propagation time and distance throughout the size ranges down to less than 0.4 mm. Results for polyoxymethylene, polystyrene-butadiene, and high-density polyethylene were accurate to within 5 percent of reported literature values. Measurement repeatability (precision) improved with an increase in the wave transmission distance (propagating dimension). No statistically significant effect due to the transverse dimension was detected.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):237-240. doi:10.1115/1.2796086.

While the majority of experimental cervical spine biomechanics research has been conducted using slowly applied forces and/or moments, or dynamically applied forces with contact, little research has been performed to delineate the biomechanics of the human neck under inertial “noncontact” type forces. This study was designed to develop a comprehensive methodology to induce these loads. A minisled pendulum experimental setup was designed to test specimens (such as human cadaver neck) at subfailure or failure levels under different loading modalities including flexion, extension, and lateral bending. The system allows acceleration/deceleration input with varying wave form shapes. The test setup dynamically records the input and output strength information such as forces, accelerations, moments, and angular velocities; it also has the flexibility to obtain the temporal overall and local kinematic data of the cervical spine components at every vertebral level. These data will permit a complete biomechanical structural analysis. In this paper, the feasibility of the methodology is demonstrated by subjecting a human cadaver head-neck complex with intact musculature and skin under inertial flexion and extension whiplash loading at two velocities.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):241-247. doi:10.1115/1.2796087.

The novel concept of swelling-type intramedullary hip implants that attain self-fixation by an expansion-fit mechanism resulting from controlled swelling of the implant (by absorption of body fluids) was examined in detail using a finite element model of the implant-femur system. Some of the potential advantages of this technique over traditional techniques include enhanced fixation, lower relative micromotions, improved bony ingrowth, and elimination of acrylic cement. The finite element model created in this study incorporated: (i) the major aspects of the three-dimensional geometry of the implant and femur, (ii) the anisotropic elastic properties of bone and implant materials and the changes in orientation of the principal axes of anisotropy along the length of the implant-femur system, (iii) a layer of cancellous bone between the implant and cortical bone in the proximal femoral region, and (iv) frictional sliding between the bone and implant. The model was used to study quantitatively the parametric influence of various material design variables on the micromotions and stress fields in the bone-swelling-type implant system. The results of the finite element analyses were used to establish material behavior goals and provide targets for a material development study.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):248-253. doi:10.1115/1.2796088.

To optimize the performance of off-road bicycle suspension systems, a dynamic model of the bicycle/rider system would be useful. This paper takes a major step toward this goal by developing a dynamic system model of the cyclist. To develop the cyclist model, a series of four vibrational tests utilizing random inputs was conducted on seven experienced off-road cyclists. This allowed the transfer functions for the arms and legs to be determined. To reproduce the essential features (i.e., resonance peaks) of the experimental transfer functions, the system model included elements representing the visceral mass along with the arms and legs. Through simulations, the frequency responses of the system model of the rider in each of the four tests were computed. Optimal stiffness and damping parameter values for each subject were determined by minimizing the difference between the experimental and simulation results. Good agreement between experimental and simulation results indicates that modeling the rider as a lumped parameter system with linear springs and dampers is possible.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):254-260. doi:10.1115/1.2796089.

Problems associated with premature failure of total knee replacements (TKR’s) include: wear, creep, and oxidation of ultrahigh-molecular-weight polyethylene (UHM-WPe) as well as adverse tissue reactions to polyethylene wear debris. These problems are associated in part with the mechanical behavior of UHMWPe. In TKR’s, contact stress analyses have been performed on the UHMWPe tibial component; however, most have employed simplified material properties and not accounted for joint kinematics. A nonlinear viscoelastic rolling model was developed for TKR’s to predict the contact stress and rolling friction for varying rolling speed, conformity, applied load, and tibial plateau thickness. Results indicated that the contact stress increased and rolling friction decreased with increasing rolling speed. Effects of conformity, applied load, and tibial plateau thickness were consistent with previous models. At large rolling speeds, predicted peak contact stresses were almost twice their static value, resulting in a compound fatigue problem in UHMWPe components due to normal cyclic loading, moving point of contact, and velocity-dependent stresses.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):261-268. doi:10.1115/1.2796090.

We present a method for solving the governing equations from our anisotropic biphasic theory of tissue-equivalent mechanics (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed finite element method is used for discretization of the spatial derivatives, and the DASPK subroutine (Brown et al., 1994) is used to solve the resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Dembo’s (1994) adaptation of the Uzawa algorithm for viscous flows, provides an efficient and scaleable solution method, with the finite element method discretization being first-order accurate in space. In the cylindrical isometric cell traction assay, the chosen test problem, a cylindrical tissue equivalent is adherent at either end to fixed circular platens. As the cells exert traction on the collagen fibrils, the force required to maintain constant sample length, or load, is measured. However, radial compaction occurs during the course of the assay, so that the cell and network concentrations increase and collagen fibrils become aligned along the axis of the cylinder, leading to cell alignment along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effect is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and hence the measured load.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):269-277. doi:10.1115/1.2796091.

Optimization of cryosurgical procedures on deep tissues such as liver requires an increased understanding of the fundamental mechanisms of ice formation and water transport in tissues during freezing. In order to further investigate and quantify the amount of water transport that occurs during freezing in tissue, this study reports quantitative and dynamic experimental data and theoretical modeling of rat liver freezing under controlled conditions. The rat liver was frozen by one of four methods of cooling: Method 1—ultrarapid “slam cooling” (≥ 1000° C/min) for control samples; Method 2—equilibrium freezing achieved by equilibrating tissue at different subzero temperatures (−4, −6, −8, −10°C); Method 3°-two-step freezing, which involves cooling at 5°C/min. to −4, −6, −8, −10 or −20°C followed immediately by slam cooling; or Method 4—constant and controlled freezing at rates from 5–400°C/min. on a directional cooling stage. After freezing, the tissue was freeze substituted, embedded in resin, sectioned, stained, and imaged under a light microscope fitted with a digitizing system. Image analysis techniques were then used to determine the relative cellular to extracellular volumes of the tissue. The osmotically inactive cell volume was determined to be 0.35 by constructing a Boyle van’t Hoff plot using cellular volumes from Method 2. The dynamic volume of the rat liver cells during cooling was obtained using cellular volumes from Method 3 (two-step freezing at 5°C/min). A nonlinear regression fit of a Krogh cylinder model to the volumetric shrinkage data in Method 3 yielded the biophysical parameters of water transport in rat liver tissue of: Lpg = 3.1 X 10−13 m3 /Ns (1.86 μ/min-atm) and ELP = 290 kJ/mole (69.3 kcal/mole), with chi-squared variance of 0.00124. These parameters were then incorporated into the Krogh cylinder model and used to simulate water transport in rat liver tissue during constant cooling at rates between 5–100°C/min. Reasonable agreement between these simulations and the constant cooling rate freezing experiments in Method 4 were obtained. The model predicts that the water transport ceases at a relatively high subzero temperature (−10°C), such that the amount of intracellular ice forming in the tissue cells rises from almost none (=extensive dehydration and vascular expansion) at ≤5°C/min to over 88 percent of the original cellular water at ≥50°C/min. The theoretical simulations based on these experimental methods may be of use in visualizing and predicting freezing response, and thus can assist in the planning and implementing of cryosurgical protocols.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):278-288. doi:10.1115/1.2796092.

A new model for muscle tissue heat transfer has been developed using Myrhage and Eriksson’s [23] description of a muscle tissue cylinder surrounding secondary (s) vessels as the basic heat transfer unit. This model provides a rational theory for the venous return temperature for the perfusion source term in a modified Pennes bioheat equation, and greatly simplifies the anatomical description of the microvascular architecture required in the Weinbaum-Jiji bioheat equation. An easy-to-use closed-form analytic expression has been derived for the difference between the inlet artery and venous return temperatures using a model for the countercurrent heat exchange in the individual muscle tissue cylinders. The perfusion source term calculated from this model is found to be similar in form to the Pennes’s source term except that there is a correction factor or efficiency coefficient multiplying the Pennes term, which rigorously accounts for the thermal equilibration of the returning vein. This coefficient is a function of the vascular cross-sectional geometry of the muscle tissue cylinder, but independent of the Peclet number in contrast to the recent results in Brinck and Werner [8] . The value of this coefficient varies between 0.6 and 0.7 for most muscle tissues. In part II of this study a theory will be presented for determining the local arterial supply temperature at the inlet to the muscle tissue cylinder.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):289-297. doi:10.1115/1.2796093.

A finite element model, comprising an assemblage of tetrakaidecahedra or truncated octahedra, is used to represent an alveolar duct unit. The dimensions of the elastin and collagen fibre bundles, and the surface tension properties of the air-liquid interfaces, are based on available published data. Changes to the computed static pressure-volume behavior with variation in alveolar dimensions and fibre volume densities are characterized using distensibility indices (K). The air-filled lung distensibility (Ka ) decreased with a reduction in the alveolar airspace length dimensions and increased with a reduction of total fibre volume density. The saline-filled lung distensibility (Ks ) remained constant with alveolar dimensions and increased with decreasing total fibre volume density. The degree of geometric anisotropy between the duct lumen and alveoli was computed over pressure-volume cycles. To preserve broadly isotropic behavior, parenchyma with smaller alveolar airspace length dimensions required higher concentrations of fibres located in the duct and less in the septa in comparison with parenchyma of larger airspace dimensions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):298-308. doi:10.1115/1.2796094.

This paper considers the effects of non-Newtonian lining-fluid viscosity, particularly shear thinning and yield stress, on the reopening of the airways. The airway was simulated by a very thin, circular polyethylene tube, which collapsed into a ribbonlike configuration. The non-Newtonian fluid viscosity was described by the powerlaw and Herschel-Buckley models. The speed of airway opening was determined under various opening pressures. These results were collapsed into dimensionless pressure-velocity relationships, based on an assumed shear rate γ̇ = U/(0.5 H), where U and H are the opening velocity and fluid film thickness, respectively. It was found that yield stress, like surface tension, increases the yield pressure and opening time. However, shear thinning reduces the opening time. An increased film thickness of the non-Newtonian lining fluid generally impedes airway reopening; a higher pressure is needed to initiate the airway reopening and a longer time is required to complete the opening process.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):309-316. doi:10.1115/1.2796095.

In order to clarify the gas transport process in high-frequency oscillation, we measured the axial velocity profile and the axial effective diffusivity in a single asymmetric bifurcating tube, based on the Horsfield airway model, with sinusoidally oscillatory flow. The axial velocity profiles were measured using a laser-Doppler velocimeter, and the effective diffusivities were evaluated using a simple bolus injection method. The axial velocity profile was found to be nonuniform, promoting axial gas dispersion by the spread of the concentration profile and lateral mixing. The geometric asymmetry of the bifurcation was responsible for the difference in gas transport between the main bronchi. The axial gas transport in the left main bronchus was 2.3 times as large as that of the straight tube, whereas the gas transport in the right main bronchus was slightly larger than that of the straight tube. Thus localized variation in gas transport characterized the heterogeneous respiratory function of the lung.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):317-324. doi:10.1115/1.2796096.

High-grade stenosis can produce conditions in which the artery may collapse. A one-dimensional numerical model of a compliant stenosis was developed from the collapsible tube theory of Shapiro. The model extends an earlier model by including the effects of frictional losses and unsteadiness. The model was used to investigate the relative importance of several physical parameters present in the in vivo environment. The results indicated that collapse can occur within the stenosis. Frictional loss was influential in reducing the magnitude of collapse. Large separation losses could prevent collapse outright even with low downstream resistances. However, the degree of stenosis was still the primary parameter governing the onset of collapse. Pulsatile solutions demonstrated conditions that produce cyclic collapse within the stenosis. This study predicts certain physiologic conditions in which collapse of arteries may occur for high-grade stenoses.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):325-332. doi:10.1115/1.2796097.

Pulsatile and steady flow fields in cerebrovascular aneurysm models of various sizes are presented in terms of laser-Doppler velocimetry measurements and flow visualization. The bifurcation angle was 140 deg and volume flow rate ratio between the branches was 3:1. The mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 600, 800, and 280, respectively. It is found that among the tested sizes there exists a middle range of aneurysm sizes, above and below which the forced-vortex inside the aneurysmal model is weaker and lacking, respectively, whereas in the middle range of the tested sizes the forced vortex is stronger and the fluctuation level is higher near the dome. The present results also identify the major fluid dynamic factors of the aneurysmal promotion or rupture for the medium and larger aneurysms, respectively. Furthermore, the maximum fluctuation intensity is found to increase with aneurysm size. The locations of the maximum fluctuation intensity are found to occur in the bifurcation area or at the neck instead of intra-aneurysm.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):333-342. doi:10.1115/1.2796098.

The goal of this study was to determine how vessel compliance (wall motion) and the phase angle between pressure and flow waves (impedance phase angle) affect the wall shear rate distribution in an atherogenic bifurcation geometry under sinusoidal flow conditions. Both rigid and elastic models replicating the human abdominal aortic bifurcation were fabricated and the wall shear rate distribution in the median plane of the bifurcation was determined using the photochromic flow visualization method. In the elastic model, three phase angle conditions were simulated (+12, −17, −61 deg), and the results compared with those obtained in a similar rigid model. The study indicates a very low (magnitude close to zero) and oscillatory wall shear rate zone within 1.5 cm distal to the curvature site on the outer (lateral) wall. In this low shear rate zone, unsteadiness (pulsatility) of the flow greatly reduces the mean (time-averaged) wall shear rate level. Vessel wall motion reduces the wall shear rate amplitude (time-varying component) up to 46 percent depending on the location and phase angle in the model. The mean wall shear rate is less influenced by the wall motion, but is reduced significantly in the low shear region (within 1.5 cm distal to the curvature site on the outer wall), thus rendering the wall shear rate waveform more oscillatory and making the site appear more atherogenic. The effect of the phase angle is most noteworthy on the inner wall close to the flow divider tip where the mean and amplitude of wall shear rate are 31 and 23 percent lower, respectively, at the phase angle of −17 deg than at −61 deg. However, the characteristics of the wall shear rate distribution in the low shear rate zone on the outer wall that are believed to influence localization of atherosclerotic disease, such as the mean wall shear rate level, oscillation in the wall shear rate waveform, and the length of the low and oscillatory wall shear rate zone, are similar for the three phase angles considered. The study also showed a large spatial variation of the phase angle between the wall shear stress waveform and the circumferential stress waveform (hoop stress due to radial artery expansion in response to pressure variations) near the bifurcation (up to 70 deg). The two stresses became more out of phase in the low mean shear rate zone on the outer wall (wall shear stress wave leading hoop stress wave as much as 125 deg at the pressure-flow phase angle of −61 deg) and were significantly influenced by the impedance phase angle.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):343-348. doi:10.1115/1.2796099.

Severe occlusion of graft–artery junctions due to restenosis, e.g., excessive tissue overgrowth and renewed plaque formation, may occur within a few months or years after bypass surgery. Our hypothesis is that nonuniform hemodynamics, represented by large sustained wall shear stress gradients, trigger abnormal biological processes leading to rapid restenosis and hence early graft failure. In turn, this problem may be significantly mitigated by designing graft-artery bypass configurations for which the wall shear stress gradient (WSSG) is approximately zero and hence nearly uniform hemodynamics are achieved. Focusing on the distal end of several femoral artery bypass junctions, a validated finite volume code has been used to compute the transient three-dimensional velocity vector fields and its first and second surface derivatives in order to test the idea. Specifically, it is shown that the Taylor patch, which generates higher patency rates than standard end-to-side anastomoses, exhibits lower WSSG levels than standard configurations, and that further geometric design improvements reduce the WSSG in magnitude and local extent even more.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):349-356. doi:10.1115/1.2796100.

Investigations of valvular regurgitation attempt to specify flow field characteristics and apply them to the proximal isovelocity surface area (PISA) method for quantifying regurgitant flow. Most investigators assume a hemispherical shape to these equivelocity shells proximal to an axisymmetric (circular) orifice. However, in vivo flow fields are viscous and regurgitant openings vary in shape and size. By using centerline profiles and isovelocity surfaces, this investigation describes the flow field proximal to circular and elliptical orifices. Steady, proximal flow fields are obtained with two- and three-dimensional computational fluid dynamic (CFD) simulations. These simulations are verified by in vitro, laser-Doppler velocimetry (LDV) experiments. The data show that a unique, normalized proximal flow field results for each orifice shape independent of orifice flow or size. The distinct differences in flow field characteristics with orifice shape may provide a mechanism for evaluating orifice characteristics and regurgitant flows. Instead of the hemispherical approximation technique, this study attempts to show the potential to define a universal flow evaluation method based on the details of the flowfield according to orifice shape. Preliminary results indicate that Magnetic Resonance (MR) and Color Doppler (CD) may reproduce these flow details and allow such a procedure in vivo.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1997;119(3):357-363. doi:10.1115/1.2796101.

A perspex (plexiglas) tube was locally deformed into an almost bi-lobar interior cross section, representative of the localized throat at the downstream end of a collapsed tube conveying a flow. The axial and transverse (parallel to the long axis of the deformed cross section) components of fluid velocity were measured in a dense rectangular grid of points covering the whole cross section, at 15 axial sites between one diameter upstream of and three diameters downstream of the center of the constriction. The Reynolds number based on undeformed tube diameter and mean velocity was 705. Results are presented both as surfaces showing the variation of each component over the cross section and as velocity vector profiles. The overall changes in velocity in the streamwise direction are presented in terms of the variation of the maximum and minimum of each component with axial position. Flow downstream of the throat consisted of two parallel side-jets with a broad region of reverse flow in between. This pattern persisted until beyond 2.5 diameters downstream, by which point transverse inflow at the top and bottom of the cross section had converted the side jets into a complete annulus of axial velocity surrounding a central deficit. Jet velocities and reverse flow disappeared relatively abruptly before three diameters downstream.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEF

J Biomech Eng. 1997;119(3):364-366. doi:10.1115/1.2796102.

The objective of the current study was to develop an in vitro testing protocol to evaluate semi-rigid pedicle screw devices. A corpectomy model protocol exists to evaluate rigid spinal implants; however, semi-rigid devices are contraindicated for this condition. This paper describes a technique that simulates more closely the conditions a semi-rigid device would see in vivo. Finally, the new testing protocol is used to evaluate the DDS® pedicle screw-cable system. Benefits and shortcomings of the new protocol are discussed.

Commentary by Dr. Valentin Fuster

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