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Research Papers

J Biomech Eng. 2013;135(10):101001-101001-6. doi:10.1115/1.4024824.

Native aortic valve cusps are composed of collagen fibers embedded in their layers. Each valve cusp has its own distinctive fiber alignment with varying orientations and sizes of its fiber bundles. However, prior mechanical behavior models have not been able to account for the valve-specific collagen fiber networks (CFN) or for their differences between the cusps. This study investigates the influence of this asymmetry on the hemodynamics by employing two fully coupled fluid-structure interaction (FSI) models, one with asymmetric-mapped CFN from measurements of porcine valve and the other with simplified-symmetric CFN. The FSI models are based on coupled structural and fluid dynamic solvers. The partitioned solver has nonconformal meshes and the flow is modeled by employing the Eulerian approach. The collagen in the CFNs, the surrounding elastin matrix, and the aortic sinus tissues have hyperelastic mechanical behavior. The coaptation is modeled with a master-slave contact algorithm. A full cardiac cycle is simulated by imposing the same physiological blood pressure at the upstream and downstream boundaries for both models. The mapped case showed highly asymmetric valve kinematics and hemodynamics even though there were only small differences between the opening areas and cardiac outputs of the two cases. The regions with a less dense fiber network are more prone to damage since they are subjected to higher principal stress in the tissues and a higher level of flow shear stress. This asymmetric flow leeward of the valve might damage not only the valve itself but also the ascending aorta.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101002-101002-10. doi:10.1115/1.4024629.

Measures of mean cartilage thickness over predefined regions in the femoral plate using magnetic resonance imaging have provided important insights into the characteristics of knee osteoarthritis (OA), however, this quantification method suffers from the limited ability to detect OA-related differences between knees and loses potentially important information regarding spatial variations in cartilage thickness. The objectives of this study were to develop a new method for analyzing patterns of femoral cartilage thickness and to test the following hypotheses: (1) asymptomatic knees have similar thickness patterns, (2) thickness patterns differ with knee OA, and (3) thickness patterns are more sensitive than mean thicknesses to differences between OA conditions. Bi-orthogonal thickness patterns were extracted from thickness maps of segmented magnetic resonance images in the medial, lateral, and trochlea compartments. Fifty asymptomatic knees were used to develop the method and establish reference asymptomatic patterns. Another subgroup of 20 asymptomatic knees and three subgroups of 20 OA knees each with a Kellgren/Lawrence grade (KLG) of 1, 2, and 3, respectively, were selected for hypotheses testing. The thickness patterns were similar between asymptomatic knees (coefficient of multiple determination between 0.8 and 0.9). The thickness pattern alterations, i.e., the differences between the thickness patterns of an individual knee and reference asymptomatic thickness patterns, increased with increasing OA severity (Kendall correlation between 0.23 and 0.47) and KLG 2 and 3 knees had significantly larger thickness pattern alterations than asymptomatic knees in the three compartments. On average, the number of significant differences detected between the four subgroups was 4.5 times greater with thickness pattern alterations than mean thicknesses. The increase was particularly marked in the medial compartment, where the number of significant differences between subgroups was 10 times greater with thickness pattern alterations than mean thickness measurements. Asymptomatic knees had characteristic regional thickness patterns and these patterns were different in medial OA knees. Assessing the thickness patterns, which account for the spatial variations in cartilage thickness and capture both cartilage thinning and swelling, could enhance the capacity to detect OA-related differences between knees.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101003-101003-9. doi:10.1115/1.4025106.

Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101004-101004-6. doi:10.1115/1.4025112.

Flexion relaxation (FR) in the low back occurs when load is transferred from the spine's extensor musculature to its passive structures. This study investigated the influence of added upper body mass on low back kinetics and kinematics at the FR onset. Sixteen participants (eight male, eight female) performed standing full forward spine flexion with 0%, 15%, and 30% of their estimated upper body mass added to their shoulders. Electromyographic data were obtained from the lumbar erector spinae. Ground reaction forces and kinematic data from the lower limbs, pelvis, and spine were recorded. Extensor reaction moments (determined using a bottom-up linked segment model) and flexion angles at the FR onset were documented along with the maximum spine flexion. The angle at the FR onset increased significantly with added mass (p < 0.05). Expressing the FR onset angle as a percent of the full range of trunk flexion motion for that condition negated any differences between the added mass conditions. These findings demonstrate that low back kinetics play a role in mediating FR in the lumbar spine.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101005-101005-10. doi:10.1115/1.4025100.

Despite considerable effort over the last four decades, research has failed to translate into consistently effective treatment options for spinal cord injury (SCI). This is partly attributed to differences between the injury response of humans and rodent models. Some of this difference could be because the cerebrospinal fluid (CSF) layer of the human spine is relatively large, while that of the rodents is extremely thin. We sought to characterize the fluid impulse induced in the CSF by experimental SCIs of moderate and high human-like severity, and to compare this with previous studies in which fluid impulse has been associated with neural tissue injury. We used a new in vivo pig model (n = 6 per injury group, mean age 124.5 days, 20.9 kg) incorporating four miniature pressure transducers that were implanted in pairs in the subarachnoid space, cranial, and caudal to the injury at 30 mm and 100 mm. Tissue sparing was assessed with Eriochrome Cyanine and Neutral Red staining. The median peak pressures near the injury were 522.5 and 868.8 mmHg (range 96.7–1430.0) and far from the injury were 7.6 and 36.3 mmHg (range 3.8–83.7), for the moderate and high injury severities, respectively. Pressure impulse (mmHg.ms), apparent wave speed, and apparent attenuation factor were also evaluated. The data indicates that the fluid pressure wave may be sufficient to affect the severity and extent of primary tissue damage close to the injury site. However, the CSF pressure was close to normal physiologic values at 100 mm from the injury. The high injury severity animals had less tissue sparing than the moderate injury severity animals; this difference was statistically significant only within 1.6 mm of the epicenter. These results indicate that future research seeking to elucidate the mechanical origins of primary tissue damage in SCI should consider the effects of CSF. This pig model provides advantages for basic and preclinical SCI research due to its similarities to human scale, including the existence of a human-like CSF fluid layer.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101006-101006-11. doi:10.1115/1.4025092.

A novel model for the blood system is postulated focusing on the flow rate and pressure distribution inside the arterioles and venules of the pulmonary acinus. Based upon physiological data it is devoid of any ad hoc constants. The model comprises nine generations of arterioles, venules, and capillaries in the acinus, the gas exchange unit of the lung. Blood is assumed incompressible and Newtonian and the blood vessels are assumed inextensible. Unlike previous models of the blood system, the venules and arterioles open up to the capillary network in numerous locations along each generation. The large number of interconnected capillaries is perceived as a porous medium in which the flow is macroscopically unidirectional from arterioles to venules openings. In addition, the large number of capillaries extending from each arteriole and venule allows introduction of a continuum theory and formulation of a novel system of ordinary, nonlinear differential equations which governs the blood flow and pressure fields along the arterioles, venules, and capillaries. The solution of the differential equations is semianalytical and requires the inversion of three diagonal, 9 × 9 matrices only. The results for the total flow rate of blood through the acinus are within the ballpark of physiological observations despite the simplifying assumptions used in our model. The results also manifest that the contribution of the nonlinear convection term of the Navier-Stokes equations has little effect (less than 2%) on the total blood flow entering/leaving the acinus despite the fact that the Reynolds number is not much smaller than unity at the proximal generations. The model makes it possible to examine some pathological cases. Here, centri-acinar and distal emphysema were investigated yielding a reduction in inlet blood flow rate.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101007-101007-11. doi:10.1115/1.4025179.

Intra- and inter-specimen variations in trabecular anisotropy are often ignored in quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra. The material properties are typically estimated solely from local variations in bone mineral density (BMD), and a fixed representation of elastic anisotropy (“generic anisotropy”) is assumed. This study evaluated the effect of incorporating specimen-specific, trabecular anisotropy on QCT-based FE predictions of vertebral stiffness and deformation patterns. Orthotropic material properties estimated from microcomputed tomography data (“specimen-specific anisotropy”), were assigned to a large, columnar region of the L1 centrum (n = 12), and generic-anisotropic material properties were assigned to the remainder of the vertebral body. Results were compared to FE analyses in which generic-anisotropic properties were used throughout. FE analyses were also performed on only the columnar regions. For the columnar regions, the axial stiffnesses obtained from the two categories of material properties were uncorrelated with each other (p = 0.604), and the distributions of minimum principal strain were distinctly different (p ≤ 0.022). In contrast, for the whole vertebral bodies in both axial and flexural loading, the stiffnesses obtained using the two categories of material properties were highly correlated (R2 > 0.82, p < 0.001) with, and were no different (p > 0.359) from, each other. Only moderate variations in strain distributions were observed between the two categories of material properties. The contrasting results for the columns versus vertebrae indicate a large contribution of the peripheral regions of the vertebral body to the mechanical behavior of this bone. In companion analyses on the effect of the degree of anisotropy (DA), the axial stiffnesses of the trabecular column (p < 0.001) and vertebra (p = 0.007) increased with increasing DA. These findings demonstrate the need for accurate modeling of the peripheral regions of the vertebral body in analyses of the mechanical behavior of the vertebra.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101008-101008-8. doi:10.1115/1.4025108.

Ankle and subtalar joint injuries of vehicle front seat occupants are frequently recorded during frontal and offset vehicle crashes. A few injury criteria for foot and ankle were proposed in the past; however, they addressed only certain injury mechanisms or impact loadings. The main goal of this study was to investigate numerically the tolerance of foot and ankle under complex loading which may appear during automotive crashes. A previously developed and preliminarily validated foot and leg finite element (FE) model of a 50th percentile male was employed in this study. The model was further validated against postmortem human subjects (PMHS) data in various loading conditions that generates the bony fractures and ligament failures in ankle and subtalar regions observed in traffic accidents. Then, the foot and leg model were subjected to complex loading simulated as combinations of axial, dorsiflexion, and inversion loadings. An injury surface was fitted through the points corresponding to the parameters recorded at the time of failure in the FE simulations. The compelling injury predictions of the injury surface in two crash simulations may recommend its application for interpreting the test data recorded by anthropometric test devices (ATD) during crash tests. It is believed that the methodology presented in this study may be appropriate for the development of injury criteria under complex loadings corresponding to other body regions as well.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101009-101009-8. doi:10.1115/1.4025109.

An evaluation of wound mechanics is crucial in reflecting the wound healing status. The present study examined the biomechanical properties of healing rat skin wounds in vivo and ex vivo. Thirty male Sprague-Dawley rats, each with a 6 mm full-thickness circular punch biopsied wound at both posterior hind limbs were used. The mechanical stiffness at both the central and margins of the wound was measured repeatedly in five rats over the same wound sites to monitor the longitudinal changes over time of before wounding, and on days 0, 3, 7, 10, 14, and 21 after wounding in vivo by using an optical coherence tomography-based air-jet indentation system. Five rats were euthanized at each time point, and the biomechanical properties of the wound tissues were assessed ex vivo using a tensiometer. At the central wound bed region, the stiffness measured by the air-jet system increased significantly from day 0 (17.2%), peaked at day 7 (208.3%), and then decreased progressively until day 21 (40.2%) as compared with baseline prewounding status. The biomechanical parameters of the skin wound samples measured by the tensiometer showed a marked reduction upon wounding, then increased with time (all p < 0.05). On day 21, the ultimate tensile strength of the skin wound tissue approached 50% of the normal skin; while the stiffness of tissue recovered at a faster rate, reaching 97% of its prewounded state. Our results suggested that it took less time for healing wound tissues to recover their stiffness than their maximal strength in rat skin. The stiffness of wound tissues measured by air-jet could be an indicator for monitoring wound healing and contraction.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101010-101010-8. doi:10.1115/1.4025110.

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semi-infinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101011-101011-7. doi:10.1115/1.4024825.

Passive-dynamic ankle-foot orthosis (PD-AFO) bending stiffness is a key functional characteristic for achieving enhanced gait function. However, current orthosis customization methods inhibit objective premanufacture tuning of the PD-AFO bending stiffness, making optimization of orthosis function challenging. We have developed a novel virtual functional prototyping (VFP) process, which harnesses the strengths of computer aided design (CAD) model parameterization and finite element analysis, to quantitatively tune and predict the functional characteristics of a PD-AFO, which is rapidly manufactured via fused deposition modeling (FDM). The purpose of this study was to assess the VFP process for PD-AFO bending stiffness. A PD-AFO CAD model was customized for a healthy subject and tuned to four bending stiffness values via VFP. Two sets of each tuned model were fabricated via FDM using medical-grade polycarbonate (PC-ISO). Dimensional accuracy of the fabricated orthoses was excellent (average 0.51 ± 0.39 mm). Manufacturing precision ranged from 0.0 to 0.74 Nm/deg (average 0.30 ± 0.36 Nm/deg). Bending stiffness prediction accuracy was within 1 Nm/deg using the manufacturer provided PC-ISO elastic modulus (average 0.48 ± 0.35 Nm/deg). Using an experimentally derived PC-ISO elastic modulus improved the optimized bending stiffness prediction accuracy (average 0.29 ± 0.57 Nm/deg). Robustness of the derived modulus was tested by carrying out the VFP process for a disparate subject, tuning the PD-AFO model to five bending stiffness values. For this disparate subject, bending stiffness prediction accuracy was strong (average 0.20 ± 0.14 Nm/deg). Overall, the VFP process had excellent dimensional accuracy, good manufacturing precision, and strong prediction accuracy with the derived modulus. Implementing VFP as part of our PD-AFO customization and manufacturing framework, which also includes fit customization, provides a novel and powerful method to predictably tune and precisely manufacture orthoses with objectively customized fit and functional characteristics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101012-101012-10. doi:10.1115/1.4025114.

Experimental studies where cells are seeded on micropost arrays in order to quantify their contractile behavior are becoming increasingly common. Interpretation of the data generated by this experimental technique is difficult, due to the complexity of the processes underlying cellular contractility and mechanotransduction. In the current study, a coupled framework that considers strain rate dependent contractility and remodeling of the cytoskeleton is used in tandem with a thermodynamic model of tension dependent focal adhesion formation to investigate the biomechanical response of cells adhered to micropost arrays. Computational investigations of the following experimental studies are presented: cell behavior on different sized arrays with a range of post stiffness; stress fiber and focal adhesion formation in irregularly shaped cells; the response of cells to deformations applied locally to individual posts; and the response of cells to equibiaxial stretching of micropost arrays. The predicted stress fiber and focal adhesion distributions; in addition to the predicted post tractions are quantitatively and qualitatively supported by previously published experimental data. The computational models presented in this study thus provide a framework for the design and interpretation of experimental micropost studies.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):101013-101013-8. doi:10.1115/1.4025102.

Biodegradable cages have received increasing attention for their use in spinal procedures involving interbody fusion to resolve complications associated with the use of nondegradable cages, such as stress shielding and long-term foreign body reaction. However, the relatively weak initial material strength compared to permanent materials and subsequent reduction due to degradation may be problematic. To design a porous biodegradable interbody fusion cage for a preclinical large animal study that can withstand physiological loads while possessing sufficient interconnected porosity for bony bridging and fusion, we developed a multiscale topology optimization technique. Topology optimization at the macroscopic scale provides optimal structural layout that ensures mechanical strength, while optimally designed microstructures, which replace the macroscopic material layout, ensure maximum permeability. Optimally designed cages were fabricated using solid, freeform fabrication of poly(ε-caprolactone) mixed with hydroxyapatite. Compression tests revealed that the yield strength of optimized fusion cages was two times that of typical human lumbar spine loads. Computational analysis further confirmed the mechanical integrity within the human lumbar spine, although the pore structure locally underwent higher stress than yield stress. This optimization technique may be utilized to balance the complex requirements of load-bearing, stress shielding, and interconnected porosity when using biodegradable materials for fusion cages.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2013;135(10):104501-104501-4. doi:10.1115/1.4025180.

Existing experimental data on the Poisson's ratio of nucleus pulposus (NP) tissue is limited. This study aims to determine whether the Poisson's ratio of NP tissue is strain-dependent, strain-rate-dependent, or varies with axial location in the disk. Thirty-two cylindrical plugs of bovine tail NP tissue were subjected to ramp-hold unconfined compression to 20% axial strain in 5% increments, at either 30 μm/s or 0.3 μm/s ramp speeds and the radial displacement determined using biaxial video extensometry. Following radial recoil, the true Poisson's ratio of the solid phase of NP tissue increased linearly with increasing strain and demonstrated strain-rate dependency. The latter finding suggests that the solid matrix undergoes stress relaxation during the test. For small strains, we suggest a Poisson's ratio of 0.125 to be used in biphasic models of the intervertebral disk.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):104502-104502-5. doi:10.1115/1.4025104.

Lower limb amputee gait during stance phase is related to the angular stiffness of the prosthetic foot, which describes the dependence of ankle torque on angular progression of the shank. However, there is little data on angular stiffness of prosthetic feet, and no method to directly measure it has been described. The objective of this study was to derive and evaluate a method to estimate the angular stiffness of prosthetic feet using a simple linear compression test. Linear vertical compression tests were performed on nine configurations of an experimental multicomponent foot (with known component stiffness properties and geometry), which allowed for parametric adjustment of hindfoot and forefoot stiffness properties and geometries. Each configuration was loaded under displacement control at distinct pylon test angles. Angular stiffness was calculated as a function of the pylon angle, normal force, and center of pressure (COP) rate of change with respect to linear displacement. Population root mean square error (RMSE) between the measured and predicted angular stiffness values for each configuration of the multicomponent foot was calculated to be 4.1 N-m/deg, dominated by a bias of the estimated values above the predicted values of 3.8 ± 1.6 N-m/deg. The best-fit line to estimated values was approximately parallel to the prediction, with R2 = 0.95. This method should be accessible for a variety of laboratories to estimate angular stiffness of experimental and commercially available prosthetic feet with minimal equipment.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(10):104503-104503-8. doi:10.1115/1.4024821.

The liver is one of the most frequently injured organs in abdominal trauma. Although motor vehicle collisions are the most common cause of liver injuries, current anthropomorphic test devices are not equipped to predict the risk of sustaining abdominal organ injuries. Consequently, researchers rely on finite element models to assess the potential risk of injury to abdominal organs such as the liver. These models must be validated based on appropriate biomechanical data in order to accurately assess injury risk. This study presents a total of 36 uniaxial unconfined compression tests performed on fresh human liver parenchyma within 48 h of death. Each specimen was tested once to failure at one of four loading rates (0.012, 0.106, 1.036, and 10.708 s−1) in order to investigate the effects of loading rate on the compressive failure properties of human liver parenchyma. The results of this study showed that the response of human liver parenchyma is both nonlinear and rate dependent. Specifically, failure stress significantly increased with increased loading rate, while failure strain significantly decreased with increased loading rate. The failure stress and failure strain for all liver parenchyma specimens ranged from −38.9 kPa to −145.9 kPa and from −0.48 strain to −1.15 strain, respectively. Overall, this study provides novel biomechanical data that can be used in the development of rate dependent material models and the identification of tissue-level tolerance values, which are critical to the validation of finite element models used to assess injury risk.

Commentary by Dr. Valentin Fuster

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