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### TECHNICAL PAPERS: Bone/Orthopedic

J Biomech Eng. 2005;127(4):557-562. doi:10.1115/1.1933916.

Damage accumulation plays a key role in weakening bones prior to complete fracture and in stimulating bone remodeling. The goal of this study was to characterize the degradation in the mechanical properties of cortical bone following a compressive overload. Longitudinally oriented, low-aspect ratio specimens $(n=24)$ of bovine cortical bone were mechanically tested using an overload-hold-reload protocol. No modulus reductions greater than 5% were observed following overload magnitudes less than 0.73% strain. For each specimen, changes in strength and Poisson’s ratio were greater $(p=0.02)$ than that in modulus by 10.8- and 26.6-fold, respectively, indicating that, for the specimen configuration used in this study, longitudinal elastic modulus is one of the least sensitive properties to a compressive overload. Residual strains were also proportionately greater by 6.4-fold $(p=0.01)$ in the transverse than axial direction. These results suggest that efforts to relate microcrack density and morphology to changes in compressive mechanical properties of cortical bone may benefit from considering alternative parameters to modulus reductions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):563-570. doi:10.1115/1.1934182.

Fatigue cracking in the cement mantle of total hip replacement has been identified as a possible cause of implant loosening. Retrieval studies and in vitro tests have found porosity in the cement may facilitate fatigue cracking of the mantle. The fatigue process has been simulated computationally using a finite element/continuum damage mechanics (FE/CDM) method and used as a preclinical testing tool, but has not considered the effects of porosity. In this study, experimental tensile and four-point bend fatigue tests were performed. The tensile fatigue S-N data were used to drive the computational simulation (FE/CDM) of fatigue in finite element models of the tensile and four-point bend specimens. Porosity was simulated in the finite element models according to the theory of elasticity and using Monte Carlo methods. The computational fatigue simulations generated variability in the fatigue life at any given stress level, due to each model having a unique porosity distribution. The fracture site also varied between specimens. Experimental validation was achieved for four-point bend loading, but only when porosity was included. This demonstrates that the computational simulation of fatigue, driven by uniaxial S-N data can be used to simulate nonuniaxial loadcases. Further simulations of bone cement fatigue should include porosity to better represent the realities of experimental models.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Cell

J Biomech Eng. 2005;127(4):571-579. doi:10.1115/1.1933981.

Current techniques for measuring the bulk shear or elastic $(E)$ modulus of small samples of soft materials are usually limited by materials handling issues. This paper describes a nondestructive testing method based on embedded spherical inclusions. The technique simplifies materials preparation and handling requirements and is capable of continuously monitoring changes in stiffness. Exact closed form derivations of $E$ as functions of the inclusion force-displacement relationship are presented. Analytical and numerical analyses showed that size effects are significant for medium dimensions up to several times those of the inclusion. Application of the method to DNA-crosslinked gels showed good agreement with direct compression tests.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):580-586. doi:10.1115/1.1934222.

Supra-physiological temperatures are increasingly being used to treat many different soft tissue diseases and injuries. To identify improved clinical treatments, however, there is a need for better information on the effect of the mechanics on the thermal damage process as well as the effect of the incurred damage on the subsequent mechanical properties. In this paper, we report the first biaxial data on the stress relaxation behavior of a collagenous tissue before and after thermal damage. Based on a two-dimensional finite strain viscoelastic model, which incorporates an exponential elastic response, it is shown that the thermal damage can significantly decrease the characteristic time for stress relaxation and the stress residual.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):587-593. doi:10.1115/1.1934145.

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano’s theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordæ tendineæ.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):594-600. doi:10.1115/1.1933997.

Endothelial cells possess a mechanical network connecting adhesions on the basal surface, the cytoskeleton, and the nucleus. Transmission of force at adhesions via this pathway can deform the nucleus, ultimately resulting in an alteration of gene expression and other cellular changes (mechanotransduction). Previously, we measured cell adhesion area and apparent nuclear stretch during endothelial cell rounding. Here, we reconstruct the stress map of the nucleus from the observed strains using finite-element modeling. To simulate the disruption of adhesions, we prescribe displacement boundary conditions at the basal surface of the axisymmetric model cell. We consider different scenarios of the cytoskeletal arrangement, and represent the cytoskeleton as either discrete fibers or as an effective homogeneous layer. When the nucleus is in the initial (spread) state, cytoskeletal tension holds the nucleus in an elongated, ellipsoidal configuration. Loss of cytoskeletal tension during cell rounding is represented by reactive forces acting on the nucleus in the model. In our simulations of cell rounding, we found that, for both representations of the cytoskeleton, the loss of cytoskeletal tension contributed more to the observed nuclear deformation than passive properties. Since the simulations make no assumption about the heterogeneity of the nucleus, the stress components both within and on the surface of the nucleus were calculated. The nuclear stress map showed that the nucleus experiences stress on the order of magnitude that can be significant for the function of DNA molecules and chromatin fibers. This study of endothelial cell mechanobiology suggests the possibility that mechanotransduction could result, in part, from nuclear deformation, and may be relevant to angiogenesis, wound healing, and endothelial barrier dysfunction.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Fluids/Heat/Transport

J Biomech Eng. 2004;127(4):601-610. doi:10.1115/1.1933964.

Motivated by biometric applications, we analyze oscillatory flow in a cone-and-plate geometry. The cone is rotated in a simple harmonic way on a stationary plate. Based on assuming that the angle between the cone and plate is small, we describe the flow analytically by a perturbation method in terms of two small parameters, the Womersley number and the Reynolds number, which account for the influences of the local acceleration and centripetal force, respectively. Working equations for the shear stresses induced both by laminar primary and secondary flows on the plate surface are presented.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):611-618. doi:10.1115/1.1934056.

The fluid flow through a stenosed artery and its bypass graft in an anastomosis can substantially influence the outcome of bypass surgery. To help improve our understanding of this and related issues, the steady Navier-Stokes flows are computed in an idealized arterial bypass system with partially occluded host artery. Both the residual flow issued from the stenosis—which is potentially important at an earlier stage after grafting—and the complex flow structure induced by the bypass graft are investigated. Seven geometric models, including symmetric and asymmetric stenoses in the host artery, and two major aspects of the bypass system, namely, the effects of area reduction and stenosis asymmetry, are considered. By analyzing the flow characteristics in these configurations, it is found that (1) substantial area reduction leads to flow recirculation in both upstream and downstream of the stenosis and in the host artery near the toe, while diminishes the recirculation zone in the bypass graft near the bifurcation junction, (2) the asymmetry and position of the stenosis can affect the location and size of these recirculation zones, and (3) the curvature of the bypass graft can modify the fluid flow structure in the entire bypass system.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):619-629. doi:10.1115/1.1934079.

A mechanistic model of the respiratory system is proposed to understand differences in quasistatic pressure-volume $(p-V)$ curves of the inflation process in terms of the alveolar recruitment and the elastic distension of the wall tissues. In the model, a total respiratory system consists of a large number of elements, each of which is a subsystem of a cylindrical chamber fitted with a piston attached to a spring. The alveolar recruitment is simulated by allowing a distribution of the critical pressure at which an element opens; while the wall distension is represented by the piston displacement. Relations are derived between parameters in the error-function $p-V$ model equation and properties of the mechanistic model. The parameters of the model-based $p-V$ equation are determined for clinical data sets of patients with acute respiratory distress syndrome.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):630-636. doi:10.1115/1.1934099.

Flow limitation in liquid-filled lungs is examined in intact rabbit experiments and a theoretical model. Flow limitation (“choked” flow) occurs when the expiratory flow reaches a maximum value and further increases in driving pressure do not increase the flow. In total liquid ventilation this is characterized by the sudden development of excessively negative airway pressures and airway collapse at the choke point. The occurrence of flow limitation limits the efficacy of total liquid ventilation by reducing the minute ventilation. In this paper we investigate the effects of liquid properties on flow limitation in liquid-filled lungs. It is found that the behavior of liquids with similar densities and viscosities can be quite different. The results of the theoretical model, which incorporates alveolar compliance and airway resistance, agrees qualitatively well with the experimental results. Lung compliance and airway resistance are shown to vary with the perfluorocarbon liquid used to fill the lungs. Surfactant is found to modify the interfacial tension between saline and perfluorocarbon, and surfactant activity at the interface of perfluorocarbon and the native aqueous lining of the lungs appears to induce hysteresis in pressure–volume curves for liquid-filled lungs. Ventilation with a liquid that results in low viscous resistance and high elastic recoil can reduce the amount of liquid remaining in the lungs when choke occurs, and, therefore, may be desirable for liquid ventilation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):637-647. doi:10.1115/1.1934122.

Background: Restenosis after stent implantation varies with stent design. Alterations in secondary flow patterns and wall shear stress (WSS) can modulate intimal hyperplasia via their effects on platelet and inflammatory cell transport toward the wall, as well as direct effects on the endothelium. Method of Approach: Detailed flow characteristics were compared by estimating the WSS in the near-strut region of realistic stent designs using three-dimensional computational fluid dynamics (CFD), under pulsatile high and low flow conditions. The stent geometry employed was characterized by three geometric parameters (axial strut pitch, strut amplitude, and radius of curvature), and by the presence or lack of the longitudinal connector. Results: Stagnation regions were localized around stent struts. The regions of low WSS are larger distal to the strut. Under low flow conditions, the percentage restoration of mean axial WSS between struts was lower than that for the high flow by 10–12%. The largest mean transverse shear stresses were 30–50% of the largest mean axial shear stresses. The percentage restoration in WSS in the models without the longitudinal connector was as much as 11% larger than with the connector. The mean axial WSS restoration between the struts was larger for the stent model with larger interstrut spacing. Conclusion: The results indicate that stent design is crucial in determining the fluid mechanical environment in an artery. The sensitivity of flow characteristics to strut configuration could be partially responsible for the dependence of restenosis on stent design. From a fluid dynamics point of view, interstrut spacing should be larger in order to restore the disturbed flow; struts should be oriented to the flow direction in order to reduce the area of flow recirculation. Longitudinal connectors should be used only as necessary, and should be parallel to the axis. These results could guide future stent designs toward reducing restenosis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):648-655. doi:10.1115/1.1934164.

The cavitation inception threshold of mechanical heart valves has been shown to be highly variable. This is in part due to the random distribution of the initial and final conditions that characterize leaflet closure. While numerous hypotheses exist explaining the mechanisms of inception, no consistent scaling laws have been developed to describe this phenomenon due to the complex nature of these dynamic conditions. Thus in order to isolate and assess the impact of these varied conditions and mechanisms on inception, a system of ordinary differential equations is developed to describe each system component and solved numerically to predict the minimum pressure generated during valve closure. In addition, an experiment was conducted in a mock circulatory loop using an optically transparent size 29 bileaflet valve over a range of conditions to calibrate and validate this model under physiological conditions. High-speed video and high-response pressure measurements were obtained simultaneously to characterize the relationship between the valve motion, fluid motion, and negative pressure transients during closure. The simulation model was calibrated using data from a single closure cycle and then compared to other experimental flow conditions and to results found in the literature. The simulation showed good agreement with the closing dynamics and with the minimum pressure trends in the current experiment. Additionally, the simulation suggests that the variability observed experimentally (when using $dP∕dt$ alone as the primary measure of cavitation inception) is predictable. Overall, results from the current form of this lumped parameter model indicate that it is a good engineering assessment tool.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):656-661. doi:10.1115/1.1934021.

In this study, the thermal stress distribution in cryosurgery of kidney was investigated using a multiphysics finite element model developed in ANSYS (V8.1). The thermal portion of the model was verified using experimental data and the mechanics portion of the model (elastic) was verified using classic analytical solutions. Temperature dependent thermal and mechanical properties were used in the model. Moreover, the model accounts for thermal expansion due to both thermal expansion in single phase and volumetric expansion associated with phase change of tissue water to ice. For a clinical cylindrical cryoprobe inserted into the renal cortex from the top–middle renal capsule, it was found that the thermal stress distributions along the radial position are very different at different depths from the top renal capsule. The thermal stress is much higher at both ends than in the middle of the cryoprobe surface. It was found that there might be more tissue next to the top renal capsule than other region undergoing microcrack formation or plastic deformation. Furthermore, it was found that macrocrack formation is more likely to occur in tissue adjacent to the cryoprobe surface (especially on the sharp point tip) and during the thawing phase of cryosurgery. It was further found that the volumetric expansion associated with phase change induced much higher thermal stress than thermal expansion in a single phase and might therefore be the main cause of the frequently observed crack formation shortly after initiation of thawing in cryosurgery. Because the thermal stress adjacent to the cryoprobe is much higher than the yield stress of frozen renal tissue, a plastic stress model is required for better modeling of the thermal stress distribution in cryosurgery of kidney in future. However the computational effort will then be drastically increased due to the strong nonlinear nature of the plastic model and more experimental studies are indispensable for better understanding of the mechanical behavior of frozen tissue in cryosurgery.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):662-671. doi:10.1115/1.1934040.

An aneurysm is a local artery ballooning greater than 50% of its nominal diameter with a risk of sudden rupture. Minimally invasive repair can be achieved by inserting surgically a stent-graft, called an endovascular graft (EVG), which is either straight tubular, curved tubular, or bifurcating. However, post-procedural complications may arise because of elevated stagnant blood pressure in the cavity, i.e., the sac formed by the EVG and the weakened aneurysm wall. In order to investigate the underlying mechanisms leading to elevated sac-pressures and hence to potentially dangerous wall stress levels and aneurysm rupture, a transient 3-D stented abdominal aortic aneurysm model and a coupled fluid-structure interaction solver were employed. Simulation results indicate that, even without the presence of endoleaks (blood flowing into the cavity), elevated sac pressure can occur due to complex fluid-structure interactions between the luminal blood flow, EVG wall, intra-sac stagnant blood, including an intra-luminal thrombus, and the aneurysm wall. Nevertheless, the impact of sac-blood volume changes due to leakage on the sac pressure and aneurysm wall stress was analyzed as well. While blood flow conditions, EVG and aneurysm geometries as well as wall mechanical properties play important roles in both sac pressure and wall stress generation, it is always the maximum wall stress that is one of the most critical parameters in aneurysm rupture prediction. All simulation results are in agreement with experimental data and clinical observations.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Joint/Whole Body

J Biomech Eng. 2004;127(4):672-679. doi:10.1115/1.1979507.

In this paper we examine a method to control the stepping motion of a paralyzed person suspended over a treadmill using a robot attached to the pelvis. A leg swing motion is created by moving the pelvis without contact with the legs. The problem is formulated as an optimal control problem for an underactuated articulated chain. The optimal control problem is converted into a discrete parameter optimization and an efficient gradient-based algorithm is used to solve it. Motion capture data from an unimpaired human subject is compared to the simulation results from the dynamic motion optimization. Our results suggest that it is feasible to drive repetitive stepping on a treadmill by a paralyzed person by assisting in torso movement alone. The optimized, pelvic motion strategies are comparable to “hip-hiking” gait strategies used by people with lower limb prostheses or hemiparesis. The resulting motions can be found at the web site http://www.eng.uci.edu/∼chwang/project/stepper/stepper.html.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):680-691. doi:10.1115/1.1933879.

Background . As opposed to thoracoplasty (a cosmetic surgical intervention used to reduce the rib hump associated with scoliosis), experimental scoliosis has been produced or reversed on animals by rib shortening or lengthening. In a prior work (J. Orthop. Res., 20, pp. 1121–1128), a finite element modeling (FEM) of rib surgeries was developed to study the biomechanics of their correction mechanisms. Our aims in the present study were to investigate the influence of the rib surgery parameters and to identify optimal configurations. Hence, a specific objective of this study was to develop a method to find surgical parameters maximizing the correction by addressing the issue of high computational cost associated with FEM. Method of Approach . Different configurations of rib shortening or lengthening were simulated using a FEM of the complete torso adapted to the geometry of six patients. Each configuration was assessed using objective functions that represent different correction objectives. Their value was evaluated using the rib surgery simulation for sample locations in the design space specified by an experimental design. Dual kriging (interpolation technique) was used to fit the data from the computer experiment. The resulting approximation model was used to locate parameters minimizing the objective function. Results . The overall coverage of the design space and the use of an approximation model ensured that the optimization algorithm had not found a local minimum but a global optimal correction. The interventions generally produced slight immediate modifications with final geometry presenting between 95–120% of the initial deformation in about 50% of the tested cases. But in optimal cases, important loads $(500–2000Nmm)$ were generated on vertebral endplates in the apical region, which could potentially produce the long-term correction of vertebral wedging by modulating growth. Optimal parameters varied among patients and for different correction objectives. Conclusions . Approximation models make it possible to study and find optimal rib surgery parameters while reducing computational cost.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):692-699. doi:10.1115/1.1933949.

Quantification of knee motion under dynamic, in vivo loaded conditions is necessary to understand how knee kinematics influence joint injury, disease, and rehabilitation. Though recent studies have measured three-dimensional knee kinematics by matching geometric bone models to single-plane fluoroscopic images, factors limiting the accuracy of this approach have not been thoroughly investigated. This study used a three-step computational approach to evaluate theoretical accuracy limitations due to the shape matching process alone. First, cortical bone models of the femur, tibia/fibula, and patella were created from CT data. Next, synthetic (i.e., computer generated) fluoroscopic images were created by ray tracing the bone models in known poses. Finally, an automated matching algorithm utilizing edge detection methods was developed to align flat-shaded bone models to the synthetic images. Accuracy of the recovered pose parameters was assessed in terms of measurement bias and precision. Under these ideal conditions where other sources of error were eliminated, tibiofemoral poses were within $2mm$ for sagittal plane translations and $1.5deg$ for all rotations while patellofemoral poses were within $2mm$ and $3deg$. However, statistically significant bias was found in most relative pose parameters. Bias disappeared and precision improved by a factor of two when the synthetic images were regenerated using flat shading (i.e., sharp bone edges) instead of ray tracing (i.e., attenuated bone edges). Analysis of absolute pose parameter errors revealed that the automated matching algorithm systematically pushed the flat-shaded bone models too far into the image plane to match the attenuated edges of the synthetic ray-traced images. These results suggest that biased edge detection is the primary factor limiting the theoretical accuracy of this single-plane shape matching procedure.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Soft Tissue

J Biomech Eng. 2005;127(4):700-708. doi:10.1115/1.1933900.

Background: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. Method of Approach: A one-dimensional (1-D) FOV reduced relaxation function was developed, replacing the QLV “box-spectrum” function with a fractional relaxation function. A direct-fit, global optimization method was used to estimate material parameters from stress relaxation tests on aortic valve tissue. Results: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant $(τ2)$. The mean $(n=5)$ fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. Results summary: mean QLV parameters were $C=0.079$, $τ1=0.004$, $τ2=76$, and mean FOV parameters were $β=0.29$, $τ=0.076$, and $ρ=1.84$. Conclusions: FOV can provide valuable new insights into tissue viscoelastic behavior. Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2005;127(4):709-715. doi:10.1115/1.1933931.

Evaluation and simulation of the multiaxial mechanical behavior of native and engineered soft tissues is becoming more prevalent. In spite of this growing use, testing methods have not been standardized and methodologies vary widely. The strong influence of boundary conditions were recently underscored by Waldman [2002, J. Materials Science: Materials in Medicine13, pp. 933–938] wherein substantially different experimental results were obtained using different sample gripping methods on the same specimens. As it is not possible to experimentally evaluate the effects of different biaxial test boundary conditions on specimen internal stress distributions, we conducted numerical simulations to explore these effects. A nonlinear Fung-elastic constitutive model (Sun, 2003, JBME125, pp. 372–380, which fully incorporated the effects of in-plane shear, was used to simulate soft tissue mechanical behavior. Effects of boundary conditions, including varying the number of suture attachments, different gripping methods, specimen shapes, and material axes orientations were examined. Results demonstrated strong boundary effects with the clamped methods, while suture attachment methods demonstrated minimal boundary effects. Suture-based methods appeared to be best suited for biaxial mechanical tests of biological materials. Moreover, the simulations demonstrated that Saint-Venant’s effects depended significantly on the material axes orientation. While not exhaustive, these comprehensive simulations provide experimentalists with additional insight into the stress–strain fields associated with different biaxial testing boundary conditions, and may be used as a rational basis for the design of biaxial testing experiments.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS: Other

J Biomech Eng. 2005;127(4):716-725. doi:10.1115/1.1934203.

Background: Nowadays, shape memory alloys (SMAs) and in particular Ni–Ti alloys are commonly used in bioengineering applications as they join important qualities as resistance to corrosion, biocompatibility, fatigue resistance, MR compatibility, kink resistance with two unique thermo-mechanical behaviors: the shape memory effect and the pseudoelastic effect. They allow Ni–Ti devices to undergo large mechanically induced deformations and then to recover the original shape by thermal loading or simply by mechanical unloading. Method of approach: A numerical model is developed to catch the most significant SMA macroscopic thermo-mechanical properties and is implemented into a commercial finite element code to simulate the behavior of biomedical devices. Results: The comparison between experimental and numerical response of an intravascular coronary stent allows to verify the model suitability to describe pseudo-elasticity. The numerical study of a spinal vertebrae spacer, where the effects of different geometries and material characteristic temperatures are investigated, allows to verify the model suitability to describe shape memory effect. Conclusion: the results presented show the importance of computational studies in designing and optimizing new biomedical devices.

Commentary by Dr. Valentin Fuster

### ERRATUM

J Biomech Eng. 2005;127(4):726. doi:10.1115/1.1934242.
FREE TO VIEW
Ateshian, G. A., 2004, “ Response to Dr. Robert W. Mann,” J. Biomech. Eng.JBENDY 0148-0731[[XSLOpenURL/10.1115/1.1785815]], 126, p. 539.Macirowski, T., Tepic, S., and Mann, R. W., 1994, “ Cartilage Stresses in the Human Hip Joint,” J. Biomech. Eng.JBENDY 0148-0731, 116, pp. 10–18.
Commentary by Dr. Valentin Fuster