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### Research Papers

J Biomech Eng. 2010;132(11):111001-111001-7. doi:10.1115/1.4002551.

The mechanical properties of tissue engineering scaffolds play a critical role in the success of repairing damaged tissues/organs. Determining the mechanical properties has proven to be a challenging task as these properties are not constant but depend upon time as the scaffold degrades. In this study, the modeling of the time-dependent mechanical properties of a scaffold is performed based on the concept of finite element model updating. This modeling approach contains three steps: (1) development of a finite element model for the effective mechanical properties of the scaffold, (2) parametrizing the finite element model by selecting parameters associated with the scaffold microstructure and/or material properties, which vary with scaffold degradation, and (3) identifying selected parameters as functions of time based on measurements from the tests on the scaffold mechanical properties as they degrade. To validate the developed model, scaffolds were made from the biocompatible polymer polycaprolactone (PCL) mixed with hydroxylapatite (HA) nanoparticles and their mechanical properties were examined in terms of the Young modulus. Based on the bulk degradation exhibited by the PCL/HA scaffold, the molecular weight was selected for model updating. With the identified molecular weight, the finite element model developed was effective for predicting the time-dependent mechanical properties of PCL/HA scaffolds during degradation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111002-111002-8. doi:10.1115/1.4002552.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111003-111003-12. doi:10.1115/1.4002587.

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111004-111004-7. doi:10.1115/1.4002588.

The structural organization of biological tissues and cells often produces anisotropic transport properties. These tissues may also undergo large deformations under normal function, potentially inducing further anisotropy. A general framework for formulating constitutive relations for anisotropic transport properties under finite deformation is lacking in the literature. This study presents an approach based on representation theorems for symmetric tensor-valued functions and provides conditions to enforce positive semidefiniteness of the permeability or diffusivity tensor. Formulations are presented, which describe materials that are orthotropic, transversely isotropic, or isotropic in the reference state, and where large strains induce greater anisotropy. Strain-induced anisotropy of the permeability of a solid-fluid mixture is illustrated for finite torsion of a cylinder subjected to axial permeation. It is shown that, in general, torsion can produce a helical flow pattern, rather than the rectilinear pattern observed when adopting a more specialized, unconditionally isotropic spatial permeability tensor commonly used in biomechanics. The general formulation presented in this study can produce both affine and nonaffine reorientations of the preferred directions of material symmetry with strain, depending on the choice of material functions. This study addresses a need in the biomechanics literature by providing guidelines and formulations for anisotropic strain-dependent transport properties in porous-deformable media undergoing large deformations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111005-111005-8. doi:10.1115/1.4002491.

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111006-111006-8. doi:10.1115/1.4002550.

Spine degeneration is a pathology that will affect 80% of the population. Since the intervertebral disks play an important role in transmitting loads through the spine, the aim of this study was to evaluate the biomechanical impact of disk properties on the load carried by healthy (Thompson grade I) and degenerated (Thompson grades III and IV) disks. A three-dimensional parametric poroelastic finite element model of the L4/L5 motion segment was developed. Grade I, grade II, and grade IV disks were modeled by altering the biomechanical properties of both the annulus and nucleus. Models were validated using published creep experiments, in which a constant compressive axial stress of 0.35 MPa was applied for 4 h. Pore pressure (PP) and effective stress $(SE)$ were analyzed as a function of time following loading application (1 min, 5 min, 45 min, 125 min, and 245 min) and discal region along the midsagittal profile for each disk grade. A design of experiments was further implemented to analyze the influence of six disk parameters (disk height $(H)$, fiber proportion $(%F)$, drained Young's modulus $(Ea,En)$, and initial permeability $(ka,kn)$ of both the annulus and nucleus) on load-sharing for disk grades I and IV. Simulations of grade I, grade III, and grade IV disks agreed well with the available published experimental data. Disk height $(H)$ had a significant influence $(p<0.05)$ on the PP and $SE$ during the entire loading history for both healthy and degenerated disk models. Young’s modulus of the annulus $(Ea)$ significantly affected not only $SE$ in the annular region for both disk grades in the initial creep response but also $SE$ in the nucleus zone for degenerated disks with further creep response. The nucleus and annulus permeabilities had a significant influence on the PP distribution for both disk grades, but this effect occurred at earlier stages of loading for degenerated than for healthy disk models. This is the first study that investigates the biomechanical influence of both geometrical and material disk properties on the load transfer of healthy and degenerated disks. Disk height is a significant parameter for both healthy and degenerated disks during the entire loading. Changes in the annulus stiffness, as well as in the annulus and nucleus permeability, control load-sharing in different ways for healthy and degenerated disks.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111007-111007-11. doi:10.1115/1.4000089.

Full explanation for the pathogenesis of syringomyelia (SM), a neuropathology characterized by the formation of a cystic cavity (syrinx) in the spinal cord (SC), has not yet been provided. It has been hypothesized that abnormal cerebrospinal fluid (CSF) pressure, caused by subarachnoid space (SAS) flow blockage (stenosis), is an underlying cause of syrinx formation and subsequent pain in the patient. However, paucity in detailed in vivo pressure data has made theoretical explanations for the syrinx difficult to reconcile. In order to understand the complex pressure environment, four simplified in vitro models were constructed to have anatomical similarities with post-traumatic SM and Chiari malformation related SM. Experimental geometry and properties were based on in vivo data and incorporated pertinent elements such as a realistic CSF flow waveform, spinal stenosis, syrinx, flexible SC, and flexible spinal column. The presence of a spinal stenosis in the SAS caused peak-to-peak cerebrospinal fluid CSF pressure fluctuations to increase rostral to the stenosis. Pressure with both stenosis and syrinx present was complex. Overall, the interaction of the syrinx and stenosis resulted in a diastolic valve mechanism and rostral tensioning of the SC. In all experiments, the blockage was shown to increase and dissociate SAS pressure, while the axial pressure distribution in the syrinx remained uniform. These results highlight the importance of the properties of the SC and spinal SAS, such as compliance and permeability, and provide data for comparison with computational models. Further research examining the influence of stenosis size and location, and the importance of tissue properties, is warranted.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111008-111008-7. doi:10.1115/1.4002666.

A theoretical model for the remodeling of collagen gels is proposed. The collagen fabric is modeled as a network of collagen fibers, which in turn are composed of collagen fibrils. In the model, the strengthening of collagen fabric is accomplished by fibroblasts, which continuously recruit and attach more collagen fibrils to existing collagen fibers. The fibroblasts also accomplish a reorientation of collagen fibers. Fibroblasts are assumed to reorient collagen fibers toward the direction of maximum material stiffness. The proposed model is applied to experiments in which fibroblasts were inserted into a collagen gel. The model is able to predict the force-strain curves for the experimental collagen gels, and the final distribution of collagen fibers also agrees qualitatively with the experiments.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111009-111009-11. doi:10.1115/1.4002702.

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number $(α)$, and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111010-111010-6. doi:10.1115/1.4002558.

The role of the pelvic floor soft tissues during the second stage of labor, particularly the levator ani muscle, has attracted much interest recently. It has been postulated that the passage of the fetal head through the pelvis may cause excessive stretching of the levator ani muscle, which may lead to pelvic floor dysfunction and pelvic organ prolapse later in life. In order to study the complex biomechanical interactions between the levator ani muscle and the fetal head during the second stage of labor, finite element models have been developed for quantitative analysis of this process. In this study we have simulated vaginal delivery using individual-specific anatomical computer models of the pelvic floor interacting with a fetal head model with minimal restrictions placed upon its motion. Two constitutive relations were considered for the levator ani muscle (of exponential and neo-Hookean forms). For comparison purposes, the exponential relation was chosen to exhibit much greater stiffening at higher strains beyond the range of the experimental data. We demonstrated that increased nonlinearity in the elastic response of the tissues leads to considerably higher (56%) estimated force required for delivery, accompanied by a more homogeneous spatial distribution of maximum principal stretch ratio across the muscle. These results indicate that the form of constitutive relation beyond the presently available experimental data markedly affects the estimated function of the levator ani muscle during vaginal delivery, due to the large strains that occur. Further experimental data at higher strains are necessary in order to more reliably characterize the constitutive behavior required for modeling vaginal childbirth.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):111011-111011-10. doi:10.1115/1.4002563.

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J Biomech Eng. 2010;132(11):114501-114501-5. doi:10.1115/1.4002368.

This paper proposes a method for comparing data from accelerometers, optical based 3D motion capture systems, and force platforms (FPs) in the context of spatial and temporal differences. Testing method is based on the motion laboratory accreditation test (MLAT), which can be used to test FP and camera based motion capture components of a motion analysis laboratory. This study extends MLAT to include accelerometer data. Accelerometers were attached to a device similar to the MLAT rod. The elevation of the rod from the plane of the floor is computed and compared with the force platform vector orientation and the rod orientation obtained by optical motion capture system. Orientation of the test device is achieved by forming nonlinear equation group, which describes the components of the measured accelerations. Solution for this equation group is estimated by using the Gauss–Newton method. This expanded MLAT procedure can be used in the laboratory setting were either FP, camera based motion capture, or any other motion capture system is used along with accelerometer measurements.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):114502-114502-5. doi:10.1115/1.4002536.

In this paper, a novel multiscale hierarchical model based on finite element analysis and neural network computation was developed to link mesoscopic and macroscopic scales to simulate the bone remodeling process. The finite element calculation is performed at the macroscopic level, and trained neural networks are employed as numerical devices for substituting the finite element computation needed for the mesoscale prediction. Based on a set of mesoscale simulations of representative volume elements of bones taken from different bone sites, a neural network is trained to approximate the responses at the meso level and transferred at the macro level.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):114503-114503-4. doi:10.1115/1.4002537.

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as “motor torque.” However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N m to 22.3 N m between both projections at the shoulder, while differences ranged from 0.8 N m to 3.0 N m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.

Topics: Knee
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):114504-114504-5. doi:10.1115/1.4002611.

A comprehensive understanding of the underlying biomechanical processes during handwriting is needed to accurately guide clinical interventions. To date, quantitative measurement of such biomechanical processes has largely excluded measurements of the forces exerted radially on the barrel of the writing utensil (grip forces) and how they vary over time during a handwriting task. An instrumented writing utensil was deployed for a direct measurement of kinematic and temporal information during a writing task, as well as forces exerted on the writing surface and on the barrel of the pen. The writing utensil was used by a cohort of 35 students (19 males), 16 in first grade and 19 in second grade, as they performed the Minnesota Handwriting Assessment (MHA) test. Quantitative grip force variability measures were computed and tested as correlates of handwriting legibility, form, and strokes. Grip force variability was shown to correlate strongly with handwriting quality, in particular for students classified by the MHA as nonproficient writers. More specifically, static grip force patterns were shown to result in poor handwriting quality and in greater variation in handwriting stroke durations. Grip force variability throughout the writing task was shown to be significantly lower for nonproficient writers (t-test, $p<0.01$) while the number of strokes and per-stroke durations were shown to be higher $(p<0.03)$. The results suggest that grip force dynamics play a key role in determining handwriting quality and stroke characteristics. In particular, students with writing difficulties exhibited more static grip force patterns, lower legibility and form scores, as well as increased variation in stroke durations. These findings shed light on the underlying processes of handwriting and grip force modulation and may help to improve intervention planning.

Topics: Force
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):114505-114505-5. doi:10.1115/1.4002538.

The detailed geometry of atherosclerosis-prone vascular segments may influence their susceptibility by mediating local hemodynamics. An appreciation of the role of specific geometric variables is complicated by the considerable correlation among the many parameters that can be used to describe arterial shape and size. Factor analysis is a useful tool for identifying the essential features of such an inter-related data set, as well as for predicting hemodynamic risk in terms of these features and for interpreting the role of specific geometric variables. Here, factor analysis is applied to a set of 14 geometric variables obtained from magnetic resonance images of 50 human carotid bifurcations. Two factors alone were capable of predicting 12 hemodynamic metrics related to shear and near-wall residence time with adjusted squared Pearson’s correlation coefficient as high as 0.54 and $P$-values less than 0.0001. One factor measures cross-sectional expansion at the bifurcation; the other measures the colinearity of the common and internal carotid artery axes at the bifurcation. The factors explain the apparent lack of an effect of branch angle on hemodynamic risk. The relative risk among the 50 bifurcations, based on time-average wall shear stress, could be predicted with a sensitivity and specificity as high as 0.84. The predictability of the hemodynamic metrics and relative risk is only modestly sensitive to assumptions about flow rates and flow partitions in the bifurcation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2010;132(11):114506-114506-7. doi:10.1115/1.4002589.

Constitutive models facilitate investigation into load bearing mechanisms of biological tissues and may aid attempts to engineer tissue replacements. In soft tissue models, a commonly made assumption is that collagen fibers can only bear tensile loads. Previous computational studies have demonstrated that radially aligned fibers stiffen a material in unconfined compression most by limiting lateral expansion while vertically aligned fibers buckle under the compressive loads. In this short communication, we show that in conjunction with swelling, these intuitive statements can be violated at small strains. Under such conditions, a tissue with fibers aligned parallel to the direction of load initially provides the greatest resistance to compression. The results are further put into the context of a Benninghoff architecture for articular cartilage. The predictions of this computational study demonstrate the effects of varying fiber orientations and an initial tare strain on the apparent material parameters obtained from unconfined compression tests of charged tissues.

Commentary by Dr. Valentin Fuster