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TECHNICAL PAPERS

J Biomech Eng. 2001;123(5):381-390. doi:10.1115/1.1392310.

A three-dimensional, neuromusculoskeletal model of the body was combined with dynamic optimization theory to simulate normal walking on level ground. The body was modeled as a 23 degree-of-freedom mechanical linkage, actuated by 54 muscles. The dynamic optimization problem was to calculate the muscle excitation histories, muscle forces, and limb motions subject to minimum metabolic energy expenditure per unit distance traveled. Muscle metabolic energy was calculated by summing five terms: the basal or resting heat, activation heat, maintenance heat, shortening heat, and the mechanical work done by all the muscles in the model. The gait cycle was assumed to be symmetric; that is, the muscle excitations for the right and left legs and the initial and terminal states in the model were assumed to be equal. Importantly, a tracking problem was not solved. Rather, only a set of terminal constraints was placed on the states of the model to enforce repeatability of the gait cycle. Quantitative comparisons of the model predictions with patterns of body-segmental displacements, ground-reaction forces, and muscle activations obtained from experiment show that the simulation reproduces the salient features of normal gait. The simulation results suggest that minimum metabolic energy per unit distance traveled is a valid measure of walking performance.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):391-395. doi:10.1115/1.1395572.

The short- and long-term successes of tibial cementless implants depend on the initial fixation stability often provided by posts and screws. In this work, a metallic plate was fixed to a polyurethane block with either two bone screws, two smooth-surfaced posts, or two novel smooth-surfaced posts with adjustable inclinations. For this last case, inclinations of 0, 1.5, and 3 deg were considered following insertion. A load of 1031 N was eccentrically applied on the plate at an angle of ∼14 deg, which resulted in a 1000 N axial compressive force and a 250 N shear force. The response was measured under static and repetitive loading up to 4000 cycles at 1 Hz. The measured results demonstrate subsidence under load, lift-off on the unloaded side, and horizontal translation of the plate specially at the loaded side. Fatigue loading increased the displacements, primarily during the first 100 cycles. Comparison of various fixation systems indicated that the plate with screw fixation was the stiffest with the least subsidence and liftoff. The increase in post inclination from 0 to 3 deg stiffened the plate by diminishing the liftoff. All fixation systems demonstrated deterioration under repetitive loads. In general, the finite element predictions of the experimental fixation systems were in agreement with measurements. The finite element analyses showed that porous coated posts (modeled with nonlinear interface friction with and without coupling) generated slightly less resistance to liftoff than smooth-surfaced posts. In the presence of porous coated posts, Coulomb friction greatly overestimated the rigidity by reducing the liftoff and subsidence to levels even smaller than those predicted for the design with screw fixation. The sequence of combined load application also influenced the predicted response. Finally, the finite element model incorporating measured interface friction and pull-out responses can be used for the analysis of cementless total joint replacement systems during the post-operation period.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):396-402. doi:10.1115/1.1392311.

Implant separation from bone tissue, resulting in the necessity for revision surgery, is a serious drawback of cementless total joint replacement. Unnatural stress distribution around the implant is considered the main reason for the failure. Optimization of the implant properties, especially its geometric parameters, is believed to be the right way to improve reliability of joint prosthetics. An efficient numerical model of the femur–implant system is presented in the paper, including the finite element formulation featuring computation of sensitivity gradients, parametric mesh generator, and a gradient-based optimization scheme. Numerical examples show results of shape optimization of an implant for two sets of design parameters and for the initial stability criterion taken as the optimization goal. The optimum shape appears to be relatively long and proximally porous-coated on about half of its length. The method can be flexibly adjusted to various implant types, stress- and displacement-based optimum criteria, and geometric design parameters.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):403-409. doi:10.1115/1.1392315.

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (μCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):410-417. doi:10.1115/1.1392316.

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension–compression stress–strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102 , pp. 73–84] to incorporate tension–compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122 , pp. 576–586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37 , pp. 1–38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108 , pp. 123–130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension–compression nonlinearity.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):418-424. doi:10.1115/1.1388292.

Based on the Theory of Porous Media (mixture theories extended by the concept of volume fractions), a model describing the mechanical behavior of hydrated soft tissues such as articular cartilage is presented. As usual, the tissue will be modeled as a materially incompressible binary medium of one linear viscoelastic porous solid skeleton saturated by a single viscous pore-fluid. The contribution of this paper is to combine a descriptive representation of the linear viscoelasticity law for the organic solid matrix with an efficient numerical treatment of the strongly coupled solid-fluid problem. Furthermore, deformation-dependent permeability effects are considered. Within the finite element method (FEM), the weak forms of the governing model equations are set up in a system of differential algebraic equations (DAE) in time. Thus, appropriate embedded error-controlled time integration methods can be applied that allow for a reliable and efficient numerical treatment of complex initial boundary-value problems. The applicability and the efficiency of the presented model are demonstrated within canonical, numerical examples, which reveal the influence of the intrinsic dissipation on the general behavior of hydrated soft tissues, exemplarily on articular cartilage.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):425-431. doi:10.1115/1.1394197.

The antero-inferior capsule (AIC) is the primary restraint to antero-inferior glenohumeral dislocation. This study utilizes a biomechanical model to determine the total strain field of the AIC in a subluxed shoulder. Strains were calculated from two capsule states: a nominal strain state set by inflation and a strained state set by subluxation. Marker coordinates on the AIC were reconstructed from stereoradiographs and strain fields calculated. Peak strain on the glenoid side of the AIC was significantly greater than the humeral side and strain fields were highly variable. This study reports an accurate method for measuring planar strains in a three-dimensional membrane.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):432-439. doi:10.1115/1.1389086.

A validated computational head–neck model was used to understand the mechanical relationships between surface padding characteristics and injury risk during impacts near the head vertex. The study demonstrated that injury risk can be decreased by maximizing the energy-dissipating ability of the pad, choosing a pad stiffness that maximizes pad deformation without bottoming out, maximizing pad thickness, and minimizing surface friction. That increasing pad thickness protected the head without increasing neck loads suggests that the increased cervical spine injury incidence previously observed in cadaveric impacts to padded surfaces relative to lubricated rigid surfaces was due to increased surface friction rather than pocketing of the head in the pad.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):440-445. doi:10.1115/1.1388293.

An analytically solvable model that considers the elasticity of the cornea is developed for use in the current and novel corneal refractive surgery procedures. The model assumes that the cornea is a thin spheroid shell with an elastic response to intraocular pressure. The value of the Young’s modulus of the post-operative cornea and its dependence on the geometric parameters of the ablation zone are estimated employing “best-fit” approach to nomograms currently used in corneal refractive surgery. These elasticity parameters are applied for quantitative modeling of different types of refractive surgery for myopia.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):446-454. doi:10.1115/1.1389096.

In tissue, medical, or dental engineering, when blood comes into contact with a new artificial material, the flow may be influenced by surface tension between the blood and the surface of the material. The effect of surface tension on the flow of blood is significant, especially in microscale. The leading edge of the flowing blood is the triple point where the blood, the material surface, and a stationary gas or fluid meet. The movement of the triple point, i.e., the advancing front of the flow, is driven by surface tension, resisted by viscous shear stress, and balanced by the inertial force (−mass×acceleration). In this article, the dynamics is illustrated in detail in the case of blood flowing into a capillary tube by contact. The capillary tube draws the blood into it. It is shown theoretically that initially the flow of blood in the capillary has a large acceleration, followed by a relatively large deceleration over the next short period of time, then the acceleration becomes small and oscillatory. The velocity history appears impulsive at first, then slows down. The history of the length of blood column appears smooth after integration. Existing solutions of the Navier–Stokes equation permit the analysis of simpler cases. Further fluid mechanics development is needed to meet the practical needs of bioengineering. The importance of experimental study of surface tension and contact angle over a biological surface or a man-made material as a future direction of research is pointed out.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):455-463. doi:10.1115/1.1389460.

Endothelial cells in blood vessels are exposed to blood flow and thus fluid shear stress. In arterial bifurcations and stenoses, disturbed flow causes zones of recirculation and stagnation, which are associated with both spatial and temporal gradients of shear stress. Such gradients have been linked to the generation of atherosclerotic plaques. For in-vitro studies of endothelial cell responses, the sudden-expansion flow chamber has been widely used and described. A two-dimensional numerical simulation of the onset phase of flow through the chamber was performed. The wall shear stress action on the bottom plate was computed as a function of time and distance from the sudden expansion. The results showed that depending on the time for the flow to be established, significant temporal gradients occurred close to the second stagnation point of flow. Slowly ramping the flow over 15 s instead of 200 ms reduces the temporal gradients by a factor of 300, while spatial gradients are reduced by 23 percent. Thus, the effects of spatial and temporal gradients can be observed separately. In experiments on endothelial cells, disturbed flow stimulated cell proliferation only when flow onset was sudden. The spatial patterns of proliferation rate match the exposure to temporal gradients. This study provides information on the dynamics of spatial and temporal gradients to which the cells are exposed in a sudden-expansion flow chamber and relates them to changes in the onset phase of flow.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):464-473. doi:10.1115/1.1389461.

The observation of intimal hyperplasia at bypass graft anastomoses has suggested a potential interaction between local hemodynamics and vascular wall response. Wall shear has been particularly implicated because of its known effects upon the endothelium of normal vessels and, thus, was examined as to its possible role in the development of intimal hyperplasia in arterial bypass graft distal anastomoses. Tapered (4–7 mm I.D.) e-PTFE synthetic grafts 6 cm long were placed as bilateral carotid artery bypasses in six adult, mongrel dogs weighing between 25 and 30 kg with distal anastomotic graft-to-artery diameter ratios (DR) of either 1.0 or 1.5. Immediately following implantation, simultaneous axial velocity measurements were made in the toe and artery floor regions in the plane of the anastomosis at radial increments of 0.35 mm, 0.70 mm, and 1.05 mm using a specially designed 20 MHz triple crystal ultrasonic wall shear rate transducer. Mean, peak, and pulse amplitude wall shear rates (WSRs), their absolute values, the spatial and temporal wall shear stress gradients (WSSG), and the oscillatory shear index (OSI) were computed from these velocity measurements. All grafts were harvested after 12 weeks implantation and measurements of the degree of intimal hyperplasia (IH) were made along the toe region and the artery floor of the host artery in 1 mm increments. While some IH occurred along the toe region (8.35±23.1 μm) and was significantly different between DR groups (p<0.003), the greatest amount occurred along the artery floor (81.6±106.5 μm, mean±S.D.) (p<0.001) although no significant differences were found between DR groups. Linear regressions were performed on the paired IH and mean, peak, and pulse amplitude WSR data as well as the absolute mean, peak, and pulse amplitude WSR data from all grafts. The mean and absolute mean WSRs showed a modest correlation with IH (r=−0.406 and −0.370, respectively) with further improvements seen (r=−0.482 and −0.445, respectively) when using an exponential relationship. The overall best correlation was seen against an exponential function of the OSI (r=0.600). Although these correlation coefficients were not high, they were found to be statistically significant as evidenced by the large F-statistic obtained. Finally, it was observed that over 75 percent of the IH occurred at or below a mean WSR value of 100 s−1 while approximately 92 percent of the IH occurred at or below a mean WSR equal to one-half that of the native artery. Therefore, while not being the only factor involved, wall shear (and in particular, oscillatory wall shear) appears to provide a stimulus for the development of anastomotic intimal hyperplasia.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):474-484. doi:10.1115/1.1395573.

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-averaged Reynolds numbers 50≤Rem≤300, corresponding to a range of peak Reynolds numbers 262.5≤Repeak≤1575. The vortex dynamics induced by pulsatile flow in AAAs is characterized by a sequence of five different flow phases in one period of the flow cycle. Hemodynamic disturbance is evaluated for a modified set of indicator functions, which include wall pressure (pw), wall shear stress w), and Wall Shear Stress Gradient (WSSG). At peak flow, the highest shear stress and WSSG levels are obtained downstream of both aneurysms, in a pattern similar to that of steady flow. Maximum values of wall shear stresses and wall shear stress gradients obtained at peak flow are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):485-492. doi:10.1115/1.1392317.

Both theoretical and experimental studies of pleural fluid dynamics and lung buoyancy during steady-state, apneic conditions are presented. The theory shows that steady-state, top-to-bottom pleural-liquid flow creates a pressure distribution that opposes lung buoyancy. These two forces may balance, permitting dynamic lung floating, but when they do not, pleural–pleural contact is required. The animal experiments examine pleural-liquid pressure distributions in response to simulated reduced gravity, achieved by lung inflation with perfluorocarbon liquid as compared to air. The resulting decrease in lung buoyancy modifies the force balance in the pleural fluid, which is reflected in its vertical pressure gradient. The data and model show that the decrease in buoyancy with perfluorocarbon inflation causes the vertical pressure gradient to approach hydrostatic. In the microgravity analogue, the pleural pressures would be toward a more uniform distribution, consistent with ventilation studies during space flight. The pleural liquid turnover predicted by the model is computed and found to be comparable to experimental values from the literature. The model provides the flow field, which can be used to develop a full transport theory for molecular and cellular constituents that are found in pleural fluid.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):493-499. doi:10.1115/1.1388294.

The flow field less than one diameter downstream of the end of a collapsible tube executing self-excited oscillations was examined using a two-component fiber-optic laser-Doppler anemometer. The time-averaged Reynolds number of the flow was 11,000. With the tube oscillating periodically, results obtained during many cycles of oscillation were combined to yield surface plots of the axial component over the cross section at 16 phases of the cycle. By combining measurements obtained with the laser probe in two different orientations, secondary flow vectors over the cross section were likewise constructed for 16 phases. The measurements showed strongly phasic turbulence intensity, with the phase of high intensity coinciding with the time of maximal tube collapse. Reverse flow occurred during much of the cycle, at places in the cross section that agree with our previous observations of laminar and turbulent steady flow through a rigid simulated collapsed tube.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):500-505. doi:10.1115/1.1392318.

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier–Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04–1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat fiux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):506-512. doi:10.1115/1.1394198.

Although synthetic membranes such as gloves, condoms, and instrument sheaths are used in environments with highly time-varying stresses, their effectiveness as barriers to virus transmission is almost always tested under static conditions. In this paper it is shown how a previously developed mathematical model can be used to transform information from static barrier tests into predictions for more realistic use conditions. Using a rate constant measured for herpes adsorption to latex in saline, and an oscillatory trans-membrane pressure representative of coitus, the amount of virus transmitted through a hole (2 μm diameter) in a condom is computed. Just beyond the exit orifice of the pore, transport is dominated by the rapidly dissipating viscous jet of virus suspension, which results in an accumulation of viruses roughly 20 pore radii from the barrier surface during each cycle. Due to virus adsorption to the barrier surfaces, the simulations reveal a gradual decrease in virus flow with increasing number of cycles, and thus a slow divergence from predictions based upon steady-state conditions. Still, over the 500 cycles simulated, steady-state predictions approximate the net number of viruses transmitted to within 25 percent error.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2001;123(5):513-518. doi:10.1115/1.1394199.

When stressed during normal use, synthetic barriers such as gloves and condoms can develop tears that are undetectable by the user. It is of considerable public-health importance to estimate the quantity of virus transmitted through the tear, in the event of viral contamination of the fluid medium. A mathematical model that accounts for virus adsorption to the barrier material was used to compute the quantity of virus transmitted through defects of various geometries. Slits were modeled as cylinders of elliptic cross section, and upper and lower bounds for the transmission rate of HIV and Hepatitis B virus (HBV) were calculated for barrier-use scenarios such as coitus and gripping of surgical instruments. For a 1-μm high slit, HIV transmission was found to be negligible for all likely use scenarios. HIV transmission became potentially significant for a 5-μm slit. Due to its high titer, HBV transmitted at potentially important levels even through the 1-μm slit. The dependence of the transmission rate upon pore aspect ratio was determined and found to be very strong for high-adsorption situations and near-circular pores. Numerical predictions of virus transport through a laser-drilled hole in a condom matched experimental measurements well, even when the tapered nature of the geometry is ignored.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEF

J Biomech Eng. 2001;123(5):519-522. doi:10.1115/1.1388295.

Observations in compression tests of articular cartilage have revealed unequal load increments for compression and release of the same amplitude applied to a disk with an identical previously imposed compression (in equilibrium). The mechanism of this asymmetric transient response is investigated here using a nonlinear fibril-reinforced model. It is found that the asymmetry is predominantly produced by the fibril stiffening with its tensile strain. In addition, allowing the hydraulic permeability to decrease significantly with compressive dilatation of cartilage increases the transient fibril strain, resulting in a stronger asymmetry. Large deformation also enhances the asymmetry as a consequence of stronger fibril stiffening.

Commentary by Dr. Valentin Fuster

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