Research Papers

J Biomech Eng. 2013;135(4):041001-041001-6. doi:10.1115/1.4023521.

The use of computational modeling to predict injury mechanisms and severity has recently been investigated, but few models report failure level ligament strains. The hypothesis of the study was that models built off neutral ankle experimental studies would generate the highest ligament strain at failure in the anterior deltoid ligament, comprised of the anterior tibiotalar ligament (ATiTL) and tibionavicular ligament (TiNL). For models built off everted ankle experimental studies the highest strain at failure would be developed in the anterior tibiofibular ligament (ATiFL). An additional objective of the study was to show that in these computational models ligament strain would be lower when modeling a partial versus complete ligament rupture experiment. To simulate a prior cadaver study in which six pairs of cadaver ankles underwent external rotation until gross failure, six specimen-specific models were built based on computed tomography (CT) scans from each specimen. The models were initially positioned with 20 deg dorsiflexion and either everted 20 deg or maintained at neutral to simulate the cadaver experiments. Then each model underwent dynamic external rotation up to the maximum angle at failure in the experiments, at which point the peak strains in the ligaments were calculated. Neutral ankle models predicted the average of highest strain in the ATiTL (29.1 ± 5.3%), correlating with the medial ankle sprains in the neutral cadaver experiments. Everted ankle models predicted the average of highest strain in the ATiFL (31.2 ± 4.3%) correlating with the high ankle sprains documented in everted experiments. Strains predicted for ligaments that suffered gross injuries were significantly higher than the strains in ligaments suffering only a partial tear. The correlation between strain and ligament damage demonstrates the potential for modeling to provide important information for the study of injury mechanisms and for aiding in treatment procedure.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):041002-041002-9. doi:10.1115/1.4023696.

The biomechanics and function of the anterior cruciate ligament (ACL) have been widely studied using both experimental and simulation methods. It is known that a constitutive model of joint tissue is a critical factor in the numerical simulation. Some different ligament constitutive models have been presented to describe the ACL material behavior. However, the effect of the variation in the ligament constitutive model on joint kinematics and biomechanics has still not been studied. In this paper, a three-dimensional finite element model of an intact tibiofemoral joint was reconstructed. Three ACL constitutive models were compared under different joint loads (such as anterior tibial force, varus tibial torque, and valgus tibial torque) to investigate the effect of the change of the ACL constitutive model. The three constitutive models corresponded to an isotropic hyperelasticity model, a transversely isotropic hyperelasticity model with neo-Hookean ground substance description, and a transversely isotropic hyperelastic model with nonlinear ground substance description. Although the material properties of these constitutive equations were fitted on the same uniaxial tension stress-strain curve, the change of the ACL material constitutive model was found to induce altered joint kinematics and biomechanics. The effect of different ACL constitutive equations on joint kinematics depended on both deformation direction and load type. The variation in the ACL constitutive models would influence the joint kinematic results greatly in both the anterior and internal directions under anterior tibial force as well as some other deformations such as the anterior and medial tibial translations under valgus tibial torque, and the medial tibial translation and internal rotation under varus torque. It was revealed that the transversely isotropic hyperelastic model with nonlinear ground substance description (FE model III) was the best representation of the realistic ACL property by a linear regression between the simulated and the experiment deformation results. But the comparison of the predicted and experiment force of ligaments showed that all the three ACL constitutive models represented similar force results. The stress value and distribution of ACL were also altered by the change in the constitutive equation. In brief, although different ACL constitutive models have been fitted using the same uniaxial tension curve and have the similar longitudinal material property, the ACL constitutive equation should still be carefully chosen to investigate joint kinematics and biomechanics due to the different transverse material behavior.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):041003-041003-13. doi:10.1115/1.4023698.

This paper presents a theoretical analysis based on classic mechanical principles of balance of forces in bipedal walking. Theories on the state of balance have been proposed in the area of humanoid robotics and although the laws of classical mechanics are equivalent to both humans and humanoid robots, the resulting motion obtained with these theories is unnatural when compared to normal human gait. Humanoid robots are commonly controlled using the zero moment point (ZMP) with the condition that the ZMP cannot exit the foot-support area. This condition is derived from a physical model in which the biped must always walk under dynamically balanced conditions, making the centre of pressure (CoP) and the ZMP always coincident. On the contrary, humans follow a different strategy characterized by a ‘controlled fall’ at the end of the swing phase. In this paper, we present a thorough theoretical analysis of the state of balance and show that the ZMP can exit the support area, and its location is representative of the imbalance state characterized by the separation between the ZMP and the CoP. Since humans exhibit this behavior, we also present proof-of-concept results of a single subject walking on an instrumented treadmill at different speeds (from slow 0.7 m/s to fast 2.0 m/s walking with increments of 0.1 m/s) with the motion recorded using an optical motion tracking system. In order to evaluate the experimental results of this model, the coefficient of determination (R2) is used to correlate the measured ground reaction forces and the resultant of inertial and gravitational forces (anteroposterior R2 = 0.93, mediolateral R2 = 0.89, and vertical R2 = 0.86) indicating that there is a high correlation between the measurements. The results suggest that the subject exhibits a complete dynamically balanced gait during slow speeds while experiencing a controlled fall (end of swing phase) with faster speeds. This is quantified with the root-mean-square deviation (RMSD) between the CoP and the ZMP, a relationship that grows exponentially, suggesting that the ZMP exits the support area earlier with faster walking speeds (relative to the stride duration). We conclude that the ZMP is a significant concept that can be exploited for the analysis of bipedal balance, but we also challenge the control strategy adopted in humanoid robotics that forces the ZMP to be contained within the support area causing the robot to follow unnatural patterns.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):041004-041004-8. doi:10.1115/1.4023699.

An analytical approach which is popular in micromechanical studies has been extended to the solution for the interference fit problem of the femoral stem in cementless total hip arthroplasty (THA). The multiple inhomogeneity problem of THA in transverse plane, including an elliptical stem, a cortical wall, and a cancellous layer interface, was formulated using the equivalent inclusion method (EIM) to obtain the induced interference elastic fields. Results indicated a maximum interference fit of about 210 μm before bone fracture, predicted based on the Drucker–Prager criterion for a partially reamed section. The cancellous layer had a significant effect on reducing the hoop stresses in the cortical wall; the maximum press fit increased to as high as 480 μm for a 2 mm thick cancellous. The increase of the thickness and the mechanical quality, i.e., stiffness and strength, of the cortical wall also increased the maximum interference fit before fracture significantly. No considerable effect was found for the implant material on the maximum allowable interference fit. It was concluded that while larger interference fits could be adapted for younger patients, care must be taken when dealing with the elderly and those suffering from osteoporosis. A conservative reaming procedure is beneficial for such patients; however, in order to ensure sufficient primary stability without risking bone fracture, a preoperative analysis might be necessary.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):041005-041005-7. doi:10.1115/1.4023700.

While useful models have been proposed to predict the mechanical impact of damage in tendon and other soft tissues, the applicability of these models for describing in vivo injury and age-related degeneration has not been investigated. Therefore, the objective of this study was to develop and validate a simple damage model to predict mechanical alterations in mouse patellar tendons after aging, injury, or healing. To characterize baseline properties, uninjured controls at age 150 days were cyclically loaded across three strain levels and five frequencies. For comparison, damage was induced in mature (120 day-old) mice through either injury or aging. Injured mice were sacrificed at three or six weeks after surgery, while aged mice were sacrificed at either 300 or 570 days old. Changes in mechanical properties (relative to baseline) in the three week post-injury group were assessed and used to develop an empirical damage model based on a simple damage parameter related to the equilibrium stress at a prescribed strain (6%). From the derived model, the viscoelastic properties of the 300 day-old, 570 day-old, and six week post-injury groups were accurately predicted. Across testing conditions, nearly all correlations between predicted and measured parameters were statistically significant and coefficients of determination ranged from R2 = 0.25 to 0.97. Results suggest that the proposed damage model could exploit simple in vivo mechanical measurements to predict how an injured or aged tendon will respond to complex physiological loading regimens.

Topics: Wounds , Tendons , Stress
Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):041006-041006-11. doi:10.1115/1.4023701.

Congenital heart defects arise during the early stages of development, and studies have linked abnormal blood flow and irregular cardiac function to improper cardiac morphogenesis. The embryonic zebrafish offers superb optical access for live imaging of heart development. Here, we build upon previously used techniques to develop a methodology for quantifying cardiac function in the embryonic zebrafish model. Imaging was performed using bright field microscopy at 1500 frames/s at 0.76 μm/pixel. Heart function was manipulated in a wild-type zebrafish at ∼55 h post fertilization (hpf). Blood velocity and luminal diameter were measured at the atrial inlet and atrioventricular junction (AVJ) by analyzing spatiotemporal plots. Control volume analysis was used to estimate the flow rate waveform, retrograde fractions, stroke volume, and cardiac output. The diameter and flow waveforms at the inlet and AVJ are highly repeatable between heart beats. We have developed a methodology for quantifying overall heart function, which can be applied to early stages of zebrafish development.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):041007-041007-6. doi:10.1115/1.4023702.

The ability to quantify the biomechanical integrity of tendons could provide useful information for both clinical diagnostics and for clinical follow-up in tracking functional recovery of the injured tissue. This study develops and characterizes a functional endoscopy approach for intraoperative quantification of tendon tear severity using both ex vivo and in vivo experimental models. We first verified the accuracy of endoscopic strain (i.e., tissue stretch) imaging in an ex vivo tear model by comparing endoscopic measurements against gold standard measurements with research grade optics. We then tested in vivo feasibility by endoscopically quantifying altered tissue strain distributions in a rat supraspinatus model of partial tendon tear. The endoscopic method was able to achieve diagnostically relevant levels of accuracy compared to research grade optics (mean error = 26.2 ± 19.1%), and tissue strain analysis could sensitively discern torn tendon subregions. Applying this approach to free-hand in vivo endoscopic strain measurements, we were similarly able to discern functional changes in partially torn tendons (average maximum principal strains surrounding the lesion: 5.1 ± 2.9% versus intact controls: 1.9 ± 1.4%; p = 0.023). These findings indicate that the functional endoscopic assessment of tendon mechanical integrity is not only possible but could potentially offer intraoperative arthroscopic guidance for management of tendon tears in man.

Commentary by Dr. Valentin Fuster


J Biomech Eng. 2013;135(4):041008-041008-14. doi:10.1115/1.4023982.

Detailed knowledge of knee joint kinematics and dynamic loading is essential for improving the design and outcomes of surgical procedures, tissue engineering applications, prosthetics design, and rehabilitation. The need for dynamic computational models that link kinematics, muscle and ligament forces, and joint contacts has long been recognized but such body-level forward dynamic models do not exist in recent literature. A main barrier in using computational models in the clinic is the validation of the in vivo contact, muscle, and ligament loads. The purpose of this study was to develop a full body, muscle driven dynamic model with subject specific leg geometries and validate it during squat and toe-rise motions. The model predicted loads were compared to in vivo measurements acquired with an instrumented knee implant. Data for this study were provided by the “Grand Challenge Competition to Predict In-Vivo Knee Loads” for the 2012 American Society of Mechanical Engineers Summer Bioengineering Conference. Data included implant and bone geometries, ground reaction forces, EMG, and the instrumented knee implant measurements. The subject specific model was developed in the multibody framework. The knee model included three ligament bundles for the lateral collateral ligament (LCL) and the medial collateral ligament (MCL), and one bundle for the posterior cruciate ligament (PCL). The implanted tibia tray was segmented into 326 hexahedral elements and deformable contacts were defined between the elements and the femoral component. The model also included 45 muscles on each leg. Muscle forces were computed for the muscle driven simulation by a feedback controller that used the error between the current muscle length in the forward simulation and the muscle length recorded during a kinematics driven inverse simulation. The predicted tibia forces and torques, ground reaction forces, electromyography (EMG) patterns, and kinematics were compared to the experimentally measured values to validate the model. Comparisons were done graphically and by calculating the mean average deviation (MAD) and root mean squared deviation (RMSD) for all outcomes. The MAD value for the tibia vertical force was 279 N for the squat motion and 325 N for the toe-rise motion, 45 N and 53 N for left and right foot ground reaction forces during the squat and 94 N and 82 N for toe-rise motion. The maximum MAD value for any of the kinematic outcomes was 7.5 deg for knee flexion-extension during the toe-rise motion.

Commentary by Dr. Valentin Fuster

Technical Briefs

J Biomech Eng. 2013;135(4):044501-044501-5. doi:10.1115/1.4023523.

Moment arms represent a muscle's ability to generate a moment about a joint for a given muscle force. The goal of this study was to develop a method to measure muscle moment arms in vivo over a large range of motion using real-time magnetic resonance (MR) imaging. Rectus femoris muscle-tendon lengths and knee joint angles of healthy subjects (N = 4) were measured during dynamic knee joint flexion and extension in a large-bore magnetic resonance imaging (MRI) scanner. Muscle-tendon moment arms were determined at the knee using the tendon-excursion method by differentiating measured muscle-tendon length with respect to joint angle. Rectus femoris moment arms were averaged across a group of healthy subjects and were found to vary similarly during knee joint flexion (mean: 3.0 (SD 0.5) cm, maximum: 3.5 cm) and extension (mean: 2.8 (SD 0.4) cm, maximum: 3.6 cm). These moment arms compare favorably with previously published dynamic tendon-excursion measurements in cadaveric specimens but were relatively smaller than moment arms from center-of-rotation studies. The method presented here provides a new approach to measure muscle-tendon moment arms in vivo and has the potential to be a powerful resource for characterizing musculoskeletal geometry during dynamic joint motion.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(4):044502-044502-5. doi:10.1115/1.4023983.

Currently, specimen-specific micro finite element (μFE) analysis based micro computed tomography (μCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution μCT images, conventional μFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR μFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR μFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.

Commentary by Dr. Valentin Fuster

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