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Guest Editorial

J Biomech Eng. 2013;135(8):080301-080301-2. doi:10.1115/1.4024756.

It is with much sadness that we mourn the loss of our great friend and colleague, Dr. Robert L. Spilker, Professor of Biomedical Engineering at Rensselaer Polytechnic Institute. Bob died on October 9, 2012, following a four year battle with cancer. Bob lived a strong, actively involved life, with loving family, his wife Janis Spilker and three children, Jana Spilker Dunbar (Bethlehem, CT), Ryan L. Spilker (Boston, MA), Janel Spilker Holcomb (San Diego, CA), as well as their extended family across the United States.

Commentary by Dr. Valentin Fuster

Research Papers

J Biomech Eng. 2013;135(8):081001-081001-14. doi:10.1115/1.4024275.

Rupture risk assessment of abdominal aortic aneurysms (AAA) by means of biomechanical analysis is a viable alternative to the traditional clinical practice of using a critical diameter for recommending elective repair. However, an accurate prediction of biomechanical parameters, such as mechanical stress, strain, and shear stress, is possible if the AAA models and boundary conditions are truly patient specific. In this work, we present a complete fluid-structure interaction (FSI) framework for patient-specific AAA passive mechanics assessment that utilizes individualized inflow and outflow boundary conditions. The purpose of the study is two-fold: (1) to develop a novel semiautomated methodology that derives velocity components from phase-contrast magnetic resonance images (PC-MRI) in the infrarenal aorta and successfully apply it as an inflow boundary condition for a patient-specific fully coupled FSI analysis and (2) to apply a one-way–coupled FSI analysis and test its efficiency compared to transient computational solid stress and fully coupled FSI analyses for the estimation of AAA biomechanical parameters. For a fully coupled FSI simulation, our results indicate that an inlet velocity profile modeled with three patient-specific velocity components and a velocity profile modeled with only the axial velocity component yield nearly identical maximum principal stress (σ1), maximum principal strain (ε1), and wall shear stress (WSS) distributions. An inlet Womersley velocity profile leads to a 5% difference in peak σ1, 3% in peak ε1, and 14% in peak WSS compared to the three-component inlet velocity profile in the fully coupled FSI analysis. The peak wall stress and strain were found to be in phase with the systolic inlet flow rate, therefore indicating the necessity to capture the patient-specific hemodynamics by means of FSI modeling. The proposed one-way–coupled FSI approach showed potential for reasonably accurate biomechanical assessment with less computational effort, leading to differences in peak σ1, ε1, and WSS of 14%, 4%, and 18%, respectively, compared to the axial component inlet velocity profile in the fully coupled FSI analysis. The transient computational solid stress approach yielded significantly higher differences in these parameters and is not recommended for accurate assessment of AAA wall passive mechanics. This work demonstrates the influence of the flow dynamics resulting from patient-specific inflow boundary conditions on AAA biomechanical assessment and describes methods to evaluate it through fully coupled and one-way–coupled fluid-structure interaction analysis.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081002-081002-7. doi:10.1115/1.4024284.

While various factors have been assumed to affect knee joint biomechanics, few data have been reported on the function of the extensor mechanism in deep flexion of the knee. This study analyzed the patellofemoral joint contact kinematics and the ratio of the quadriceps and patellar tendon forces in living subjects when they performed a single leg lunge up to 150 deg of flexion. The data revealed that in the proximal-distal direction, the patellofemoral articular contact points were in the central one-third of the patellar cartilage. Beyond 90 deg of flexion, the contact points moved towards the medial-lateral edges of the patellar surface. At low flexion angles, the patellar tendon and quadriceps force ratio was approximately 1.0 but reduced to about 0.7 after 60 deg of knee flexion, implying that the patella tendon carries lower loads than the quadriceps. These data may be valuable for improvement of contemporary surgical treatments of diseased knees that are aimed to achieve deep knee flexion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081003-081003-7. doi:10.1115/1.4024628.

Axial loading of vertebral bodies has been shown to modulate growth. Longitudinal growth of the vertebral body is impaired by compressive forces while growth is stimulated by distraction. Investigations of torsional loading on the growth plate in the literature are few. The purposes of this study were two-fold: (1) to develop a torque device to apply torsional loads on caudal vertebrae and (2) investigate numerically and in vivo the feasibility of the application of the torque on the growth plate. A controllable torque device was developed and validated in the laboratory. A finite element study was implemented to examine mechanically the deformation of the growth plate and disk. A rat tail model was used with six 5-week-old male Sprague-Dawley rats. Three rats received a static torsional load, and three rats received no torque and served as sham control rats. A histological study was undertaken to investigate possible morphological changes in the growth plate, disk, and caudal bone. The device successfully applied a controlled torsional load to the caudal vertebrae. The limited study using finite element analysis (FEA) and histology demonstrated that applied torque increased lateral disk height and increased disk width. The study also found that the growth plate height increased, and the width decreased as well as a curved displacement of the growth plate. No significant changes were observed from the in vivo study in the bone. The torsional device does apply controlled torque and is well tolerated by the animal. This study with limited samples appears to result in morphological changes in the growth plate and disk. The use of this device to further investigate changes in the disk and growth plate is feasible.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081004-081004-12. doi:10.1115/1.4023629.

Practically all experimental measurements related to the response of nonlinear bodies that are made within a purely mechanical context are concerned with inhomogeneous deformations, though, in many experiments, much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo, one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data-reduction procedure based on tracking a finite number of markers will, for a general inhomogeneous deformation, introduce an error in the determination of the deformation gradient, even in the idealized case, when the positions of the markers are measured with no error. In our study, we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is, in the quantitative description of the induced error due to the data reduction. We derive a rigorous upper bound on the error, and we discuss what factors influence the error bound and the actual error itself. Finally, we illustrate the results by studying a practically interesting model problem. We show that different choices of the tracked markers can lead to substantially different estimates of the deformation gradient and its invariants. It is alarming that even qualitative features of the material under consideration, such as the incompressibility of the body, can be evaluated differently with different choices of the tracked markers. We also demonstrate that the derived error estimate can be used as a tool for choosing the appropriate marker set that leads to the deformation gradient estimate with the least guaranteed error.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081005-081005-8. doi:10.1115/1.4024134.

Stress fractures are frequently observed in physically active populations, and they are believed to be associated with microcrack accumulation. There are not many tools for real-time monitoring of microdamage formation during fatigue of bone, in vivo or in vitro. Acoustic emission (AE) based detection of stress waves resulting from microdamage formation is a promising method to assess the rate and energetics of microdamage formation during fatigue. The current study aims to assess the time history of the occurrence of AE events during fatigue loading of human tibial cortical bone and to determine the associations between AE variables (energy content of waves, number of AE waveforms, etc.), fatigue life, and bone ash content. Fatigue test specimens were prepared from the distal diaphysis of human tibial cortical bone (N = 32, 22 to 52 years old, male and female). The initiation of acoustic emissions was concomitant with the nonlinear increase in sample compliance and the cumulative number of AE events increased asymptotically in the prefailure period. The results demonstrated that AE method was able to predict the onset of failure by 95% of the fatigue life for the majority of the samples. The variation in the number of emissions until failure ranged from 6 to 1861 implying a large variation in crack activity between different samples. The results also revealed that microdamage evolution was a function of the level of tissue mineralization such that more mineralized bone matrix failed with fewer crack events with higher energy whereas less mineralized tissue generated more emissions with lower energy. In conclusion, acoustic emission based surveillance during fatigue of cortical bone demonstrates a large scatter, where some bones fail with substantial crack activity and a minority of samples fail without significant amount of crack formation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081006-081006-9. doi:10.1115/1.4024664.

It is well-documented that the geometrical dimensions, the longitudinal stretch ratio in situ, certain structural mechanical descriptors such as compliance and pressure-diameter moduli, as well as the mass fractions of structural constituents, vary along the length of the descending aorta. The origins of and possible interrelations among these observed variations remain open questions. The central premise of this study is that having considered the variation of the deformed inner diameter, axial stretch ratio, and area compliance along the aorta to be governed by the systemic requirements for flow distribution and reduction of cardiac preload, the zero-stress state geometry and mass fractions of the basic structural constituents of aortic tissue meet a principle of optimal mechanical operation. The principle manifests as a uniform distribution of the circumferential stress in the aortic wall that ensures effective bearing of the physiological load and a favorable mechanical environment for mechanosensitive vascular smooth muscle cells. A mathematical model is proposed and inverse boundary value problems are solved for the equations that follow from finite elasticity, structure-based constitutive modeling within constrained mixture theory, and stress-induced control of aortic homeostasis, mediated by the synthetic activity of vascular smooth muscle cells. Published experimental data are used to illustrate the predictive power of the proposed model. The results obtained are in agreement with published experimental data and support the proposed principle of optimal mechanical operation for the descending aorta.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081007-081007-10. doi:10.1115/1.4024685.

It is known that arteries experience significant axial stretches in vivo. Several authors have shown that the axial force needed to maintain an artery at its in vivo axial stretch does not change with transient cyclical pressurization over normal ranges. However, the axial force phenomenon of arteries has never been explained with microstructural considerations. In this paper we propose a simple biomechanical model to relate the specific axial force phenomenon of arteries to the predicted load-dependent average collagen fiber orientation. It is shown that (a) the model correctly predicts the authors' experimentally measured biaxial behavior of pig renal arteries and (b) the model predictions are in agreement with additional experimental results reported in the literature. Finally, we discuss the implications of the model for collagen fiber orientation and deposition in arteries.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081008-081008-8. doi:10.1115/1.4024577.

Synthesis of legged locomotion through dynamic simulation is useful for exploration of the mechanical and control variables that contribute to efficient gait. Most previous simulations have made use of periodicity constraints, a sensible choice for investigations of steady-state walking or running. Sprinting from rest, however, is aperiodic by nature and this aperiodicity is central to the goal of the movement, as performance is determined in large part by a rapid acceleration phase early in the race. The purpose of this study was to create a novel simulation of aperiodic sprinting using a modified spring-loaded inverted pendulum (SLIP) biped model. The optimal control problem was to find the set of controls that minimized the time for the model to run 20 m, and this problem was solved using a direct multiple shooting algorithm that converts the original continuous time problem into piecewise discrete subproblems. The resulting nonlinear programming problem was solved iteratively using a sequential quadratic programming method. The starting point for the optimizer was an initial guess simulation that was a slow alternating-gait “jogging” simulation developed using proportional-derivative feedback to control trunk attitude, swing leg angle, and leg retraction and extension. The optimized aperiodic sprint simulation solution yielded a substantial improvement in locomotion time over the initial guess (2.79 s versus 6.64 s). Following optimization, the model produced forward impulses at the start of the sprint that were four times greater than those of the initial guess simulation, producing more rapid acceleration. Several gait features demonstrated in the optimized sprint simulation correspond to behaviors of human sprinters: forward trunk lean at the start; straightening of the trunk during acceleration; and a dive at the finish. Optimization resulted in reduced foot contact times (0.065 s versus 0.210 s), but contact times early in the optimized simulation were longer to facilitate acceleration. The present study represents the first simulation of multistep aperiodic sprinting with optimal controls. Although the minimized objective function was simple, the model replicated several complex behaviors such as modulation of the foot contact and executing a forward dive at the finish line. None of these observed behaviors were imposed explicitly by constraints but rather were “discovered” by the optimizer. These methods will be extended by addition of musculotendon actuators and joints in order to gain understanding of the influence of musculoskeletal mechanics on gait speed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081009-081009-8. doi:10.1115/1.4024286.

The mechanical properties of human joints (i.e., impedance) are constantly modulated to precisely govern human interaction with the environment. The estimation of these properties requires the displacement of the joint from its intended motion and a subsequent analysis to determine the relationship between the imposed perturbation and the resultant joint torque. There has been much investigation into the estimation of upper-extremity joint impedance during dynamic activities, yet the estimation of ankle impedance during walking has remained a challenge. This estimation is important for understanding how the mechanical properties of the human ankle are modulated during locomotion, and how those properties can be replicated in artificial prostheses designed to restore natural movement control. Here, we introduce a mechatronic platform designed to address the challenge of estimating the stiffness component of ankle impedance during walking, where stiffness denotes the static component of impedance. The system consists of a single degree of freedom mechatronic platform that is capable of perturbing the ankle during the stance phase of walking and measuring the response torque. Additionally, we estimate the platform's intrinsic inertial impedance using parallel linear filters and present a set of methods for estimating the impedance of the ankle from walking data. The methods were validated by comparing the experimentally determined estimates for the stiffness of a prosthetic foot to those measured from an independent testing machine. The parallel filters accurately estimated the mechatronic platform's inertial impedance, accounting for 96% of the variance, when averaged across channels and trials. Furthermore, our measurement system was found to yield reliable estimates of stiffness, which had an average error of only 5.4% (standard deviation: 0.7%) when measured at three time points within the stance phase of locomotion, and compared to the independently determined stiffness values of the prosthetic foot. The mechatronic system and methods proposed in this study are capable of accurately estimating ankle stiffness during the foot-flat region of stance phase. Future work will focus on the implementation of this validated system in estimating human ankle impedance during the stance phase of walking.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081010-081010-10. doi:10.1115/1.4024578.

Abdominal aortic aneurysm (AAA) is a vascular condition where the use of a biomechanics-based assessment for patient-specific risk assessment is a promising approach for clinical management of the disease. Among various factors that affect such assessment, AAA wall thickness is expected to be an important factor. However, regionally varying patient-specific wall thickness has not been incorporated as a modeling feature in AAA biomechanics. To the best our knowledge, the present work is the first to incorporate patient-specific variable wall thickness without an underlying empirical assumption on its distribution for AAA wall mechanics estimation. In this work, we present a novel method for incorporating regionally varying wall thickness (the “PSNUT” modeling strategy) in AAA finite element modeling and the application of this method to a diameter-matched cohort of 28 AAA geometries to assess differences in wall mechanics originating from the conventional assumption of a uniform wall thickness. For the latter, we used both a literature-derived population average wall thickness (1.5 mm; the “UT” strategy) as well as the spatial average of our patient-specific variable wall thickness (the “PSUT” strategy). For the three different wall thickness modeling strategies, wall mechanics were assessed by four biomechanical parameters: the spatial maxima of the first principal stress, strain, strain-energy density, and displacement. A statistical analysis was performed to address the hypothesis that the use of any uniform wall thickness model resulted in significantly different biomechanical parameters compared to a patient-specific regionally varying wall thickness model. Statistically significant differences were obtained with the UT modeling strategy compared to the PSNUT strategy for the spatial maxima of the first principal stress (p = 0.002), strain (p = 0.0005), and strain-energy density (p = 7.83 e–5) but not for displacement (p = 0.773). Likewise, significant differences were obtained comparing the PSUT modeling strategy with the PSNUT strategy for the spatial maxima of the first principal stress (p = 9.68 e–7), strain (p = 1.03 e–8), strain-energy density (p = 9.94 e–8), and displacement (p = 0.0059). No significant differences were obtained comparing the UT and PSUT strategies for the spatial maxima of the first principal stress (p = 0.285), strain (p = 0.152), strain-energy density (p = 0.222), and displacement (p = 0.0981). This work strongly recommends the use of patient-specific regionally varying wall thickness derived from the segmentation of abdominal computed tomography (CT) scans if the AAA finite element analysis is focused on estimating peak biomechanical parameters, such as stress, strain, and strain-energy density.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):081011-081011-6. doi:10.1115/1.4024287.

The current study was performed to evaluate the accuracy of computational assessment of the influence of the orientation of the patellar tendon on the patellofemoral pressure distribution. Computational models were created to represent eight knees previously tested at 40 deg, 60 deg, and 80 deg of flexion to evaluate the influence of hamstrings loading on the patellofemoral pressure distribution. Hamstrings loading increased the lateral and posterior orientation of the patellar tendon, with the change for each test determined from experimentally measured variations in tibiofemoral alignment. The patellar tendon and the cartilage on the femur and patella were represented with springs. After loading the quadriceps, the total potential energy was minimized to determine the force within the patellar tendon. The forces applied by the quadriceps and patellar tendon produced patellar translation and rotation. The deformation of each cartilage spring was determined from overlap of the cartilage surfaces on the femur and patella and related to force using linear elastic theory. The patella was iteratively adjusted until the extension moment, tilt moment, compression, and lateral force acting on the patella were in equilibrium. For the maximum pressure applied to lateral cartilage and the ratio of the lateral compression to the total compression, paired t-tests were performed at each flexion angle to determine if the output varied significantly (p < 0.05) between the two loading conditions. For both the computational and experimental data, loading the hamstrings significantly increased the lateral force ratio and the maximum lateral pressure at multiple flexion angles. For the computational data, loading the hamstrings increased the average lateral force ratio and maximum lateral pressure by approximately 0.04 and 0.3 MPa, respectively, compared to experimental increases of 0.06 and 0.4 MPa, respectively. The computational modeling technique accurately characterized variations in the patellofemoral pressure distribution caused by altering the orientation of the patellar tendon.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2013;135(8):084501-084501-7. doi:10.1115/1.4024570.

In scaffold-based tissue engineering, sufficient oxygen and nutrient supply into cells within a scaffold is essential to increase cell viability and the proliferation rate. Generally, oxygen and nutrients reach the cells through the media by diffusion in vitro or in vivo, assuming there is no convection flow through a scaffold with small-sized pores. The scaffold diffusion rate depends mainly on the scaffold pore architecture. Thus, understanding the effect of scaffold pore architecture on the diffusion mechanism is necessary to design an efficient scaffold model. This study proposes a computational method to estimate diffusivity using the finite element analysis (FEA). This method can be applied to evaluate and analyze the effective diffusivity of a freeform fabricated 3D scaffold. The diffusion application module of commercial FEA software was used to calculate the spatial oxygen concentration gradient in a scaffold model medium. The effective diffusivities of each scaffold could be calculated from the oxygen concentration data, which revealed that the scaffold pore architecture influences its effective diffusivity. The proposed method has been verified experimentally and can be applied to design pore architectures with efficient diffusion by increasing our understanding of how the diffusion rate within a scaffold is affected by its pore architecture.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):084502-084502-4. doi:10.1115/1.4024665.

The objective of this study is to propose a method for preliminary processing of the experimental data from an inflation-extension test on tubular arterial specimens. The method is based on the condition for existence of a strain energy function (SEF) and can be used to verify whether the data from a certain experiment validate the assumption that the tissue can be considered as an elastic solid. As an illustrative example of the proposed method, experimental data for a porcine renal artery are used and the sources of the error in satisfying the condition of elasticity are analyzed. The results lead to the conclusion that the experimental data for a renal artery validate that the artery exhibits an elastic mechanical response and a constitutive formulation based on the existence of the SEF is justified. A modification of the proposed method for the case of an in-plane biaxial stretching test of mechanically isotropic and orthotropic tissues is considered.

Commentary by Dr. Valentin Fuster

Errata

J Biomech Eng. 2013;135(8):087001-087001-1. doi:10.1115/1.4024826.
FREE TO VIEW

On page 091007-1 to 091007-10, the Acknowledgment section was not implemented. The correct Acknowledgment section is as follows:

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(8):087002-087002-1. doi:10.1115/1.4024827.
FREE TO VIEW

The following author was not included in the original published version of the paper: Renato V. Iozzo.

Commentary by Dr. Valentin Fuster

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