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IN THIS ISSUE

### Research Papers

J Biomech Eng. 2016;138(12):121001-121001-8. doi:10.1115/1.4034830.

In pulmonary hypertension (PH) diagnosis and management, many useful functional markers have been proposed that are unfeasible for clinical implementation. For example, assessing right ventricular (RV) contractile response to a gradual increase in pulmonary arterial (PA) impedance requires simultaneously recording RV pressure and volume, and under different afterload/preload conditions. In addition to clinical applications, many research projects are hampered by limited retrospective clinical data and could greatly benefit from simulations that extrapolate unavailable hemodynamics. The objective of this study was to develop and validate a 0D computational model, along with a numerical implementation protocol, of the RV–PA axis. Model results are qualitatively compared with published clinical data and quantitatively validated against right heart catheterization (RHC) for 115 pediatric PH patients. The RV–PA circuit is represented using a general elastance function for the RV and a three-element Windkessel initial value problem for the PA. The circuit mathematically sits between two reservoirs of constant pressure, which represent the right and left atriums. We compared Pmax, Pmin, mPAP, cardiac output (CO), and stroke volume (SV) between the model and RHC. The model predicted between 96% and 98% of the variability in pressure and 98–99% in volumetric characteristics (CO and SV). However, Bland Altman plots showed the model to have a consistent bias for most pressure and volumetric parameters, and differences between model and RHC to have considerable error. Future studies will address this issue and compare specific waveforms, but these initial results are extremely promising as preliminary proof of concept of the modeling approach.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121002-121002-10. doi:10.1115/1.4034168.
OPEN ACCESS

Our research aims to design low-cost, high-performance, passive prosthetic knees for developing countries. In this study, we determine optimal stiffness, damping, and engagement parameters for a low-cost, passive prosthetic knee that consists of simple mechanical elements and may enable users to walk with the normative kinematics of able-bodied humans. Knee joint power was analyzed to divide gait into energy-based phases and select mechanical components for each phase. The behavior of each component was described with a polynomial function, and the coefficients and polynomial order of each function were optimized to reproduce the knee moments required for normative kinematics of able-bodied humans. Sensitivity of coefficients to prosthesis mass was also investigated. The knee moments required for prosthesis users to walk with able-bodied normative kinematics were accurately reproduced with a mechanical system consisting of a linear spring, two constant-friction dampers, and three clutches ($R2=0.90$ for a typical prosthetic leg). Alterations in upper leg, lower leg, and foot mass had a large influence on optimal coefficients, changing damping coefficients by up to 180%. Critical results are reported through parametric illustrations that can be used by designers of prostheses to select optimal components for a prosthetic knee based on the inertial properties of the amputee and his or her prosthetic leg.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121003-121003-9. doi:10.1115/1.4034031.

We have developed a novel cell stretching device (called Cell Gym) capable of applying physiologically relevant low magnitude strains to tenocytes on a collagen type I coated membrane. We validated our device thoroughly on two levels: (1) substrate strains, (2) cell level strains. Our cell level strain results showed that the applied stretches were transferred to cells accurately (∼90%). Our gene expression data showed that mechanically stimulated tenocytes (4%) expressed a lower level of COL I gene. COX2 gene was increased but did not reach statistical significance. Our device was then tested to see if it could reproduce results from an in vivo study that measured time-dependent changes in collagen synthesis. Our results showed that collagen synthesis peaked at 24 hrs after exercise and then decreased, which matched the results from the in vivo study. Our study demonstrated that it is important to incorporate physiologically relevant low strain magnitudes in in vitro cell mechanical studies and the need to validate the device thoroughly to operate the device at small strains. This device will be used in designing novel tendon tissue engineering scaffolds in the future.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121004-121004-9. doi:10.1115/1.4034652.

Cardiac hemodynamics can be computed from medical imaging data, and results could potentially aid in cardiac diagnosis and treatment optimization. However, simulations are often based on simplified geometries, ignoring features such as papillary muscles and trabeculae due to their complex shape, limitations in image acquisitions, and challenges in computational modeling. This severely hampers the use of computational fluid dynamics in clinical practice. The overall aim of this study was to develop a novel numerical framework that incorporated these geometrical features. The model included the left atrium, ventricle, ascending aorta, and heart valves. The framework used image registration to obtain patient-specific wall motion, automatic remeshing to handle topological changes due to the complex trabeculae motion, and a fast interpolation routine to obtain intermediate meshes during the simulations. Velocity fields and residence time were evaluated, and they indicated that papillary muscles and trabeculae strongly interacted with the blood, which could not be observed in a simplified model. The framework resulted in a model with outstanding geometrical detail, demonstrating the feasibility as well as the importance of a framework that is capable of simulating blood flow in physiologically realistic hearts.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121005-121005-8. doi:10.1115/1.4034507.

The mucociliary clearance in the bronchial tree is the main mechanism by which the lungs clear themselves of deposited particulate matter. In this work, a macroscopic model of the clearance mechanism is proposed. Lubrication theory is applied for thin films with both surface tension effects and a moving wall boundary. The flow field is computed by the use of a finite-volume scheme on an unstructured grid that replicates a bronchial bifurcation. The carina in bronchial bifurcations is of special interest because it is a location of increased deposition of inhaled particles. In this study, the mucus flow is computed for different values of the surface tension. It is found that a minimal surface tension is necessary for efficiently removing the mucus while maintaining the mucus film thickness at physiological levels.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121006-121006-10. doi:10.1115/1.4034707.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121007-121007-8. doi:10.1115/1.4034654.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121008-121008-8. doi:10.1115/1.4034831.

Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121009-121009-13. doi:10.1115/1.4034506.

Standing balanced reach is a fundamental task involved in many activities of daily living that has not been well analyzed quantitatively to assess and characterize the multisegmental nature of the body's movements. We developed a dynamic balanced reach test (BRT) to analyze performance in this activity; in which a standing subject is required to maintain balance while reaching and pointing to a target disk moving across a large projection screen according to a sum-of-sines function. This tracking and balance task is made progressively more difficult by increasing the disk's overall excursion amplitude. Using kinematic and ground reaction force data from 32 young healthy subjects, we investigated how the motions of the tracking finger and whole-body center of mass (CoM) varied in response to the motion of the disk across five overall disk excursion amplitudes. Group representative performance statistics for the cohort revealed a monotonically increasing root mean squared (RMS) tracking error (RMSE) and RMS deviation (RMSD) between whole-body CoM (projected onto the ground plane) and the center of the base of support (BoS) with increasing amplitude (p < 0.03). Tracking and CoM response delays remained constant, however, at 0.5 s and 1.0 s, respectively. We also performed detailed spectral analyses of group-representative response data for each of the five overall excursion amplitudes. We derived empirical and analytical transfer functions between the motion of the disk and that of the tracking finger and CoM, computed tracking and CoM responses to a step input, and RMSE and RMSD as functions of disk frequency. We found that for frequencies less than 1.0 Hz, RMSE generally decreased, while RMSE normalized to disk motion amplitude generally increased. RMSD, on the other hand, decreased monotonically. These findings quantitatively characterize the amplitude- and frequency-dependent nature of young healthy tracking and balance in this task. The BRT is not subject to floor or ceiling effects, overcoming an important deficiency associated with most research and clinical instruments used to assess balance. This makes a comprehensive quantification of young healthy balance performance possible. The results of such analyses could be used in work space design and in fall-prevention instructional materials, for both the home and work place. Young healthy performance represents “exemplar” performance and can also be used as a reference against which to compare the performance of aging and other clinical populations at risk for falling.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):121010-121010-11. doi:10.1115/1.4034709.

When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, “An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis,” Probab. Eng. Mech., 25(2), pp. 183–197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model’s quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70–80% and 50–90% for the AAA and AVF model, respectively.

Commentary by Dr. Valentin Fuster

### Technical Brief

J Biomech Eng. 2016;138(12):124501-124501-9. doi:10.1115/1.4034653.

Synthetic biomechanical test specimens are frequently used for preclinical evaluation of implant performance, often in combination with numerical modeling, such as finite-element (FE) analysis. Commercial and freely available FE packages are widely used with three FE packages in particular gaining popularity: abaqus (Dassault Systèmes, Johnston, RI), ansys (ANSYS, Inc., Canonsburg, PA), and febio (University of Utah, Salt Lake City, UT). To the best of our knowledge, no study has yet made a comparison of these three commonly used solvers. Additionally, despite the femur being the most extensively studied bone in the body, no freely available validated model exists. The primary aim of the study was primarily to conduct a comparison of mesh convergence and strain prediction between the three solvers (abaqus, ansys, and febio) and to provide validated open-source models of a fourth-generation composite femur for use with all the three FE packages. Second, we evaluated the geometric variability around the femoral neck region of the composite femurs. Experimental testing was conducted using fourth-generation Sawbones® composite femurs instrumented with strain gauges at four locations. A generic FE model and four specimen-specific FE models were created from CT scans. The study found that the three solvers produced excellent agreement, with strain predictions being within an average of 3.0% for all the solvers (r2 > 0.99) and 1.4% for the two commercial codes. The average of the root mean squared error against the experimental results was 134.5% (r2 = 0.29) for the generic model and 13.8% (r2 = 0.96) for the specimen-specific models. It was found that composite femurs had variations in cortical thickness around the neck of the femur of up to 48.4%. For the first time, an experimentally validated, finite-element model of the femur is presented for use in three solvers. This model is freely available online along with all the supporting validation data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):124502-124502-5. doi:10.1115/1.4033883.

Rapid flexion and extension of the neck may occur during scenarios associated with traumatic brain injury (TBI), and understanding the mechanical response of the common carotid artery (CCA) to longitudinal stretch may enhance understanding of contributing factors that may influence CCA vasospasm and exacerbate ischemic injury associated with TBI. Immature (4-week-old) porcine CCAs were tested under subcatastrophic (1.5 peak stretch ratio) cyclic loading at 3 Hz for 30 s. Under subcatastrophic cyclic longitudinal extension, the immature porcine CCA displays softening behavior. This softening can be represented by decreasing peak stress and increasing corner stretch values with an increasing number of loading cycles. This investigation is an important first step in the exploration of fatiguelike behavior in arterial tissue that may be subjected to repeated longitudinal loads.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):124503-124503-6. doi:10.1115/1.4034785.
OPEN ACCESS

The stability of the arteries under in vivo pressure and axial tension loads is essential to normal arterial function, and lumen collapse due to buckling can hinder the blood flow. The objective of this study was to develop the lumen buckling equation for nonlinear anisotropic thick-walled arteries to determine the effect of axial tension. The theoretical equation was developed using exponential Fung strain function, and the effects of axial tension and residual stress on the critical buckling pressure were illustrated for porcine coronary arteries. The buckling behavior was also simulated using finite-element analysis. Our results demonstrated that lumen collapse of arteries could occur when the transmural pressure is negative and exceeded a critical value. This value depends upon the axial stretch ratio and material properties of the arterial wall. Axial tensions show a biphasic effect on the critical buckling pressure. The lumen aspect ratio of arteries increases nonlinearly with increasing external pressure beyond the critical value as the lumen collapses. These results enhance our understanding of artery lumen collapse behavior.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2016;138(12):124504-124504-4. doi:10.1115/1.4034786.

Hemolysis (damage to red blood cells) is a long-standing problem in blood contacting devices, and its prediction has been the goal of considerable research. The most popular model relating hemolysis to fluid stresses is the power-law model, which was developed from experiments in pure shear only. In the absence of better data, this model has been extended to more complex flows by replacing the shear stress in the power-law equation with a von Mises-like scalar stress. While the validity of the scalar stress also remains to be confirmed, inconsistencies exist in its application, in particular, two forms that vary by a factor of $2$ have been used. This article will clarify the proper extension of the power law to complex flows in a way that maintains correct results in the limit of pure shear.

Commentary by Dr. Valentin Fuster