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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2011;133(5):051001-051001-12. doi:10.1115/1.4003782.

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid $k-ε/k-ω$ flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with $y+$ less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with $y+$ less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051002-051002-12. doi:10.1115/1.4002698.

A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the total crimped fiber model. This model is based on the material and microstructural properties of the two main, passive, load-bearing components of the artery wall, elastin, and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a microstructural total crimped fiber model of pulmonary artery tissue mechanics, which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051003-051003-7. doi:10.1115/1.4003437.

In a previous paper, we reported the virtual axis finder, which is a new method for finding the rotational axes of the knee. The virtual axis finder was validated through simulations that were subject to limitations. Hence, the objective of the present study was to perform a mechanical validation with two measurement modalities: 3D video-based motion analysis and marker-based roentgen stereophotogrammetric analysis (RSA). A two rotational axis mechanism was developed, which simulated internal-external (or longitudinal) and flexion-extension (FE) rotations. The actual axes of rotation were known with respect to motion analysis and RSA markers within $±0.0006 deg$ and $±0.036 mm$ and $±0.0001 deg$ and $±0.016 mm$, respectively. The orientation and position root mean squared errors for identifying the longitudinal rotation (LR) and FE axes with video-based motion analysis (0.26 deg, 0.28 m, 0.36 deg, and 0.25 mm, respectively) were smaller than with RSA (1.04 deg, 0.84 mm, 0.82 deg, and 0.32 mm, respectively). The random error or precision in the orientation and position was significantly better ($p=0.01$ and $p=0.02$, respectively) in identifying the LR axis with video-based motion analysis (0.23 deg and 0.24 mm) than with RSA (0.95 deg and 0.76 mm). There was no significant difference in the bias errors between measurement modalities. In comparing the mechanical validations to virtual validations, the virtual validations produced comparable errors to those of the mechanical validation. The only significant difference between the errors of the mechanical and virtual validations was the precision in the position of the LR axis while simulating video-based motion analysis (0.24 mm and 0.78 mm, $p=0.019$). These results indicate that video-based motion analysis with the equipment used in this study is the superior measurement modality for use with the virtual axis finder but both measurement modalities produce satisfactory results. The lack of significant differences between validation techniques suggests that the virtual sensitivity analysis previously performed was appropriately modeled. Thus, the virtual axis finder can be applied with a thorough understanding of its errors in a variety of test conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051004-051004-9. doi:10.1115/1.4003780.

Accurate knowledge of in vivo anterior cruciate ligament (ACL) forces is instrumental for understanding normal ACL function and improving surgical ACL reconstruction techniques. The objective of this study was to estimate the change in ACL forces under in vivo loading conditions using a noninvasive technique. A combination of magnetic resonance and dual fluoroscopic imaging system was used to determine ACL in vivo elongation during controlled weightbearing at discrete flexion angles, and a robotic testing system was utilized to determine the ACL force-elongation data in vitro. The in vivo ACL elongation data were mapped to the in vitro ACL force-elongation curve to estimate the change in in vivo ACL forces in response to full body weightbearing using a weighted mean statistical method. The data demonstrated that by assuming that there was no tension in the ACL under zero weightbearing, the changes in in vivo ACL force caused by full body weightbearing were $131.4±16.8 N$ at 15 deg, $106.7±11.2 N$ at 30 deg, and $34.6±4.5 N$ at 45 deg of flexion. However, when the assumed tension in the ACL under zero weightbearing was over 20 N, the change in the estimated ACL force in response to the full body weightbearing approached an asymptotic value. With an assumed ACL tension of 40 N under zero weightbearing, the full body weight caused an ACL force increase in $202.7±27.6 N$ at 15 deg, $184.9±22.5 N$ at 30 deg, and $98.6±11.7 N$ at 45 deg of flexion. The in vivo ACL forces were dependent on the flexion angle with higher force changes at low flexion angles. Under full body weightbearing, the ACL may experience less than 250 N. These data may provide a valuable insight into the biomechanical behavior of the ACL under in vivo loading conditions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051005-051005-6. doi:10.1115/1.4003869.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051006-051006-9. doi:10.1115/1.4003871.

Osseointegrated transfemoral implants have been introduced as a prosthetic solution for above knee amputees. They have shown great promise, providing an alternative for individuals who could not be accommodated by conventional, socket-based prostheses; however, the occurrence of device failures is of concern. In an effort to improve the strength and longevity of the device, a new design has been proposed. This study investigates the mechanical behavior of the new taper-based assembly in comparison to the current hex-based connection for osseointegrated transfemoral implant systems. This was done to better understand the behavior of components under loading, in order to optimize the assembly specifications and improve the useful life of the system. Digital image correlation was used to measure surface strains on two assemblies during static loading in bending. This provided a means to measure deformation over the entire sample and identify critical locations as the assembly was subjected to a series of loading conditions. It provided a means to determine the effects of tightening specifications and connection geometry on the material response and mechanical behavior of the assemblies. Both osseoinegrated assemblies exhibited improved strength and mechanical performance when tightened to a level beyond the current specified tightening torque of 12 N m. This was shown by decreased strain concentration values and improved distribution of tensile strain. Increased tightening torque provides an improved connection between components regardless of design, leading to increased torque retention, decreased peak tensile strain values, and a more gradual, primarily compressive distribution of strains throughout the assembly.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051007-051007-12. doi:10.1115/1.4003735.

Characterization of the biomaterial flow through porous bone is crucial for the success of the bone augmentation process in vertebroplasty. The biofluid, biomaterial, and local morphological bone characteristics determine the final shape of the filling, which is important both for the post-treatment mechanical loading and the risk of intraoperative extraosseous leakage. We have developed a computational model that describes the flow of biomaterials in porous bone structures by considering the material porosity, the region-dependent intrinsic permeability of the porous structure, the rheological properties of the biomaterial, and the boundary conditions of the filling process. To simulate the process of the substitution of a biofluid (bone marrow) by a biomaterial (bone cement), we developed a hybrid formulation to describe the evolution of the fluid boundary and properties and coupled it to a modified version of Darcy’s law. The apparent rheological properties are derived from a fluid-fluid interface tracking algorithm and a mixed boundary representation. The region- specific intrinsic permeability of the bone is governed by an empirical relationship resulting from a fitting process of experimental data. In a first step, we verified the model by studying the displacement process in spherical domains, where the spreading pattern is known in advance. The mixed boundary model demonstrated, as expected, that the determinants of the spreading pattern are the local intrinsic permeability of the porous matrix and the ratio of the viscosity of the fluids that are contributing to the displacement process. The simulations also illustrate the sensitivity of the mixed boundary representation to anisotropic permeability, which is related to the directional dependent microstructural properties of the porous medium. Furthermore, we compared the nonlinear finite element model to different published experimental studies and found a moderate to good agreement ($R2=0.9895$ for a one-dimensional bone core infiltration test and a 10.94–16.92% relative error for a three-dimensional spreading pattern study, respectively) between computational and experimental results.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051008-051008-12. doi:10.1115/1.4003872.

Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eight-ply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2011;133(5):051009-051009-10. doi:10.1115/1.4003873.

Cerebrovascular disease continues to be responsible for significant morbidity and mortality. There is, therefore, a pressing need to understand better the biomechanics of both intracranial arteries and the extracranial arteries that feed these vessels. We used a validated four-fiber family constitutive relation to model passive biaxial stress-stretch behaviors of basilar and common carotid arteries and we developed a new relation to model their active biaxial responses. These data and constitutive relations allow the first full comparison of circumferential and axial biomechanical behaviors between a muscular (basilar) and an elastic (carotid) artery from the same species. Our active model describes the responses by both types of vessels to four doses of the vasoconstrictor endothelin-1 ($10−10M$, $10−9M$, $10−8M$, and $10−7M$) and predicts levels of smooth muscle cell activation associated with basal tone under specific in vitro testing conditions. These results advance our understanding of the biomechanics of intracranial and extracranial arteries, which is needed to understand better their differential responses to similar perturbations in hemodynamic loading.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2011;133(5):054501-054501-4. doi:10.1115/1.4003665.

Reproduction of the in vivo motions of joints has become possible with improvements in robot technology and in vivo measuring techniques. A motion analysis system has been used to measure the motions of the tibia and femur of the ovine stifle joint during normal gait. These in vivo motions are then reproduced with a parallel robot. To ensure that the motion of the joint is accurately reproduced and that the resulting data are reliable, the testing frame, the data acquisition system, and the effects of limitations of the testing platform need to be considered. Of the latter, the stiffness of the robot and the ability of the control system to process sequential points on the path of motion in a timely fashion for repeatable path accuracy are of particular importance. Use of the system developed will lead to a better understanding of the mechanical environment of joints and ligaments in vivo.

Commentary by Dr. Valentin Fuster