Integration of Febio as an Instructional Tool in the Undergraduate Biomechanics Curriculum.

Computer simulations play an important role in a range of biomedical engineering applications. Thus, it is important that biomedical engineering students engage with modeling in their undergraduate education and establish an understanding of its practice. In addition, computational tools enhance active learning and complement standard pedagogical approaches to promote student understanding of course content. Herein, we describe the development and implementation of learning modules for computational modeling and simulation (CM&S) within an undergraduate biomechanics course. We developed four CM&S learning modules that targeted predefined course goals and learning outcomes within the febio studio software. For each module, students were guided through CM&S tutorials and tasked to construct and analyze more advanced models to assess learning and competency and evaluate module effectiveness. Results showed that students demonstrated an increased interest in CM&S through module progression and that modules promoted the understanding of course content. In addition, students exhibited increased understanding and competency in finite element model development and simulation software use. Lastly, it was evident that students recognized the importance of coupling theory, experiments, and modeling and understood the importance of CM&S in biomedical engineering and its broad application. Our findings suggest that integrating well-designed CM&S modules into undergraduate biomedical engineering education holds much promise in supporting student learning experiences and introducing students to modern engineering tools relevant to professional development.

FEBio: History and Advances.

The principal goal of the FEBio project is to provide an advanced finite element tool for the biomechanics and biophysics communities that allows researchers to model mechanics, transport, and electrokinetic phenomena for biological systems accurately and efficiently. In addition, because FEBio is geared toward the research community, the code is designed such that new features can be added easily, thus making it an ideal tool for testing novel computational methods. Finally, because the success of a code is determined by its user base, integral goals of the FEBio project have been to offer support and outreach to our community; to provide mechanisms for dissemination of results, models, and data; and to encourage interaction between users. This review presents the history of the FEBio project, from its initial developments through its current funding period. We also present a glimpse into the future of FEBio.

Hyperelastic material models for simulating deformation of silicone ring pessaries.

Pessaries are removable gynecological prosthetic devices that provide mechanical support for temporary or long-term symptom relief of pelvic floor disorders, such as pelvic organ prolapse and stress urinary incontinence. To date, limited mechanical tests have been performed on physical pessary designs to characterize their behaviour under load; however, custom pessary manufacturing is expensive and time consuming. As an alternative, finite element (FE) modeling can provide detailed numerical insight into the response of a pessary design under load but to date has seen limited application, with little data available for pessary silicone materials. This study aimed to identify hyperelastic material models for two silicone materials used in custom pessary cocoon moulded manufacturing towards FE analysis of ring with support (RWS) pessaries. It was hypothesized that hyperelastic material models could be identified to capture the force and deformation response of multiple RWS sizes under different boundary conditions and silicone materials (Shore 60A and 40A). To understand the material characteristics of pessary silicone, uniaxial tension and compression tests were performed then the experimental data was fit with Mooney-Rivlin (MR) material models. To ensure the material models characterize the pessary behaviour, data from mechanical tests representing the RWS pessary folding and modified 3-point bending were compared to FE recreations (FEBio) of the same tests with the MR materials applied to the pessaries. The FE model results demonstrated good agreement in the force-displacement response for the fold and 3-point bending models for different pessary sizes and silicone stiffnesses. This work demonstrates the hyperelastic material models' efficacy and will enable future studies to improve biomechanical analysis of silicone pessary designs.

Influence of Material Parameter Variability on the Predicted Coronary Artery Biomechanical Environment via Uncertainty Quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification.

Central to the clinical adoption of patient-specific modeling strategies is demonstrating that simulation results are reliable and safe. Indeed, simulation frameworks must be robust to uncertainty in model input(s), and levels of confidence should accompany results. In this study, we applied a coupled uncertainty quantification-finite element (FE) framework to understand the impact of uncertainty in vascular material properties on variability in predicted stresses. Univariate probability distributions were fit to material parameters derived from layer-specific mechanical behavior testing of human coronary tissue. Parameters were assumed to be probabilistically independent, allowing for efficient parameter ensemble sampling. In an idealized coronary artery geometry, a forward FE model for each parameter ensemble was created to predict tissue stresses under physiologic loading. An emulator was constructed within the UncertainSCI software using polynomial chaos techniques, and statistics and sensitivities were directly computed. Results demonstrated that material parameter uncertainty propagates to variability in predicted stresses across the vessel wall, with the largest dispersions in stress within the adventitial layer. Variability in stress was most sensitive to uncertainties in the anisotropic component of the strain energy function. Moreover, unary and binary interactions within the adventitial layer were the main contributors to stress variance, and the leading factor in stress variability was uncertainty in the stress-like material parameter that describes the contribution of the embedded fibers to the overall artery stiffness. Results from a patient-specific coronary model confirmed many of these findings. Collectively, these data highlight the impact of material property variation on uncertainty in predicted artery stresses and present a pipeline to explore and characterize forward model uncertainty in computational biomechanics.

The need for speed - Does the force-velocity property significantly alter strain distributions within skeletal muscle?

Skeletal muscles are complex structures with nonlinear constitutive properties. This complexity often requires finite element (FE) modeling to better understand muscle behavior and response to activation, especially the fiber strain distributions that can be difficult to measure in vivo. However, many FE muscle models designed to study fiber strain do not include force-velocity behavior. To investigate force-velocity property impact on strain distributions within skeletal muscle, we modified a muscle constitutive model with active and passive force-length properties to include force-velocity properties. We implemented the new constitutive model as a plugin for the FE software FEBio and applied it to four geometries: 1) a single element, 2) a multiple-element model representing a single fiber, 3) a model of tapering fibers, and 4) a model representing the bicep femoris long head (BFLH) morphology. Maximum fiber velocity and boundary conditions of the finite element models were varied to test their influence on fiber strain distribution. We found that force-velocity properties in the constitutive model behaved as expected for the single element and multi-element conditions. In the tapered fiber models, fiber strain distributions were impacted by changes in maximum fiber velocity; the range of strains increased with maximum fiber velocity, which was most noted in isometric contraction simulations. In the BFLH model, maximum fiber velocity had minimal impact on strain distributions, even in the context of sprinting. Taken together, the combination of muscle model geometry, activation, and displacement parameters play a critical part in determining the magnitude of impact of force-velocity on strain distribution.

Interstitial flow, pressure and residual stress in the aging carotid artery model in FEBio.

Vascular smooth muscle cells (VSMCs) are subject to interstitial flow-induced shear stress, which is a critical parameter in cardiovascular disease progression. Transmural pressure loading and residual stresses alter the hydraulic conductivity of the arterial layers and modulate the interstitial fluid flux through the arterial wall. In this paper, a biphasic multilayer model of a common carotid artery (CCA) with anisotropic fiber-reinforced soft tissue and strain-dependent permeability is developed in FEBio software. After the verification of the numerical predictions, age-related arterial thickening and stiffening effects on arterial deformation and interstitial flow are computed under physiological geometry and physical parameters. We found that circumferential residual stress shifts outward in each layer and its gradient increases up to 6 times with aging. Internally pressurized CCA displays nonlinear deformation. In the aged artery, the circumferential stress becomes greater on the media layer (82-158 kPa) and lower on the intima and adventitia (19-23 kPa and 25-28 kPa, respectively). The radial compression of the intima reduces the total hydraulic conductivity by 48% in the young and 16% in the aged arterial walls. Consequently, the average radial interstitial flux increases with pressure by 14% in the young and 91% in the aged arteries. Accordingly, the flow shear stress experienced by the VSMCs becomes more significant for aged arteries, which may accelerate cardiovascular disease progression compared to young arteries.

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements.

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Comparison of side-cutting maneuvers versus low impact baseball swing on knee ligament loading in adolescent populations.

BACKGROUND: High impact sports are associated with an increased incidence rate for knee ligament injuries, specifically pertaining to the anterior cruciate ligament and medial collateral ligament. What is less clear is (i) the extent to which high impact activities preferentially load the anterior cruciate ligament versus the medial collateral ligament, and (ii) whether both ligaments experience similar stretch ratios during high loading scenarios. Therefore, the goal of this project was to assess how different loading conditions experienced through more at-risk sporting maneuvers influence the relative displacements of the anterior cruciate ligament and medial collateral ligament. The focus of the study was on adolescent patients - a group that has largely been overlooked when studying knee ligament biomechanics. METHODS: Through kinetic knee data obtained through motion capture experimentation, two different loading conditions (high vs low impact) were applied to 22 specimen-specific adolescent finite element knee models to investigate the biomechanical impact various sporting maneuvers place on the knee ligaments. FINDINGS: The high impact side cutting maneuver resulted in 102% and 47% increases in ligament displacement compared to the low impact baseball swing (p < 0.05) for both the anterior cruciate ligament and medial collateral ligament. INTERPRETATION: Quantifying biomechanical risks that sporting activities place on adolescent subjects provides physicians with insight into knee ligament vulnerability. More specifically, knowing the risks that various sports place on ligaments helps guide the selection of sports for at-risk patients (especially those who have undergone knee ligament surgery).

Development of a continuum damage model to predict accumulation of sub-failure damage in tendons.

Many painful and physically debilitating conditions involve sub-failure mechanical damage to seemingly intact connective tissues such as tendons and ligaments. We found that the amount of denatured collagen in rat tail tendon (RTT) fascicles increased over experiments of cyclic loading to a constant load level (creep cyclic fatigue) with fluorescently tagged collagen hybridizing peptides (CHPs) that bind to denatured collagen. To better understand tendon sub-failure damage progression, computational modeling of tendon materials via finite element analysis in FEBio has been conducted. The objective of this project was to develop, implement, and test the ability of a new continuum damage mechanics (CDM) model in FEBio to represent the sub-failure damage behavior seen in our RTT fascicle creep cyclic fatigue experimental data. There appeared to be two distinct mechanisms responsible for the creep cyclic fatigue softening behavior of RTT fascicles over the number of cycles to failure: the preconditioning effect and overall collagen damage. In our finite element (FE) models, the RTT fascicle undamaged elastic constitutive material was composed of a matrix and fibers described by the Coupled Veronda-Westmann and exponential-linear materials. This undamaged elastic material was convolved with a modified CDM model adapted from Balzani et al., in 2012. The novelty of the Balzani damage model is the inclusion of two interrelated mechanisms described as continuous and discontinuous damage. The continuous damage formulation calculates damage accumulation during the loading and reloading of each new cycle, while the discontinuous damage approach accumulates damage from the maximum strain over the loading history to the current time. We modified the Balzani damage model formulations to represent exponential and sigmoidal increases in damage marked by the preconditioning effect and collagen damage in RTT fascicles as functions of continuous and discontinuous damage. The original Balzani damage model was first verified, then the modified CDM model was implemented into FEBio and used to reproduce the sample specific experimental creep cyclic fatigue stress-strain data as well as predict incremental cyclic fatigue. The resulting model will be useful for future experimental and computational studies of damage mechanics to understand tendon pathologies.

A multiphasic model for determination of water and solute transport across the arterial wall: effects of elastic fiber defects.

Transport of solute across the arterial wall is a process driven by both convection and diffusion. In disease, the elastic fibers in the arterial wall are disrupted and lead to altered fluid and mass transport kinetics. A computational mixture model was used to numerically match previously published data of fluid and solute permeation experiments in groups of mouse arteries with genetic (knockout of fibulin-5) or chemical (treatment with elastase) disruption of elastic fibers. A biphasic model of fluid permeation indicated the governing property to be the hydraulic permeability, which was estimated to be 1.52×10-9, 1.01×10-8, and 1.07×10-8 mm4/µN.s for control, knockout, and elastase groups, respectively. A multiphasic model incorporating solute transport was used to estimate effective diffusivities that were dependent on molecular weight, consistent with expected transport behaviors in multiphasic biological tissues. The effective diffusivity for the 4 kDA FITC-dextran solute, but not the 70 or 150 kDa FITC-dextran solutes, was dependent on elastic fiber structure, with increasing values from control to knockout to elastase groups, suggesting that elastic fiber disruption affects transport of lower molecular weight solutes. The model used here sets the groundwork for future work investigating transport through the arterial wall.

Pivot shift and Lachman test simulation-based exploration in juvenile populations for accurately predicting anterior tibial translation.

Advancements in technology and finite element software have made it possible to develop simulation-based exploration of subject-specific tibiofemoral joint kinematics. In this study, the goal was to develop baseline knee models that accurately predict anterior tibial displacement when undergoing a Lachman and pivot shift test. A total of 22 subject-specific adolescent tibiofemoral joint finite element representations were developed using FEBio. The models were subject to loading conditions established in the literature to simulate the two clinical tests. Anterior tibial translations that were measured through clinical, historical controls were used to validate the proposed models. A 95% confidence interval showed that the simulated Lachman and pivot shift tests of the juvenile knee models were not statistically different from the historical controls and were in accordance with the anterior tibial translations that were measured experimentally. Clinically, simulations are important in advancing the field of knee finite element modeling, particularly in pediatric applications where the surgeon must balance restoring full function in a patient who is skeletally immature and where the growth plate is vulnerable. The methodologies created in developing these foundational models can be utilized to build more anatomically complex finite element representations that can both predict ligament stresses in response to dynamic activities and analyze the effects of different insertion sites.

Automated finite element approach to generate anatomical patient-specific biomechanical models of atherosclerotic arteries from virtual histology-intravascular ultrasound.

Despite advancements in early detection and treatment, atherosclerosis remains the leading cause of death across all cardiovascular diseases (CVD). Biomechanical analysis of atherosclerotic lesions has the potential to reveal biomechanically instable or rupture-prone regions. Treatment decisions rarely consider the biomechanics of the stenosed lesion due in-part to difficulties in obtaining this information in a clinical setting. Previous 3D FEA approaches have incompletely incorporated the complex curvature of arterial geometry, material heterogeneity, and use of patient-specific data. To address these limitations and clinical need, herein we present a user-friendly fully automated program to reconstruct and simulate the wall mechanics of patient-specific atherosclerotic coronary arteries. The program enables 3D reconstruction from patient-specific data with heterogenous tissue assignment and complex arterial curvature. Eleven arteries with coronary artery disease (CAD) underwent baseline and 6-month follow-up angiographic and virtual histology-intravascular ultrasound (VH-IVUS) imaging. VH-IVUS images were processed to remove background noise, extract VH plaque material data, and luminal and outer contours. Angiography data was used to orient the artery profiles along the 3D centerlines. The resulting surface mesh is then resampled for uniformity and tetrahedralized to generate the volumetric mesh using TetGen. A mesh convergence study revealed edge lengths between 0.04 mm and 0.2 mm produced constituent volumes that were largely unchanged, hence, to save computational resources, a value of 0.2 mm was used throughout. Materials are assigned and finite element analysis (FEA) is then performed to determine stresses and strains across the artery wall. In a representative artery, the highest average effective stress was in calcium elements with 235 kPa while necrotic elements had the lowest average stress, reaching as low as 0.79 kPa. After applying nodal smoothening, the maximum effective stress across 11 arteries remained below 288 kPa, implying biomechanically stable plaques. Indeed, all atherosclerotic plaques remained unruptured at the 6-month longitudinal follow up diagnosis. These results suggest our automated analysis may facilitate assessment of atherosclerotic plaque stability.

Biomechanical effects of laminectomies in the human lumbar spine: a finite element study.

BACKGROUND CONTEXT: Previous studies have analyzed the effect of laminectomy on intervertebral disc (IVD), facet-joint-forces (FJF), and range of motion (ROM), while only two have specifically reported stresses at the pars interarticularis (PI) with posterior element resection. These studies have been performed utilizing a single subject, questioning their applications to a broader population. PURPOSE: We investigate the effect of graded PI resection in a three-dimensional manner on PI stress to provide surgical guidelines for avoidance of iatrogenic instability following lumbar laminectomy. Additionally, quantified FJF and IVD stresses can provide further insight into the development of adjacent segment disease. STUDY DESIGN: Biomechanical finite element (FE) method investigation of the lumbar spine. METHODS: FE models of the lumbar spine of three subjects were created using the open-source finite element software, FEBio. Single-level laminectomy, two-level laminectomy, and ventral-to-dorsal PI resection simulations were performed with varying degrees of PI resection from 0% to 75% of the native PI. These models were taken through cardinal ROM under standard loading conditions and PI stresses, FJF, IVD stresses, and ROM were analyzed. RESULTS: The three types of laminectomy simulated in this study showed a nonlinear increase in PI stress with increased bone resection. Axial rotation generated the most stress at the PI followed by flexion, extension and lateral bending. At 75% bone resection all three types of laminectomy produced PI stresses that were near the ultimate strength of human cortical bone during axial rotation. FJF decreased with increased bone resection for the three laminectomies simulated. This was most notable in axial rotation followed by extension and lateral bending. IVD stresses varied greatly between the nonsurgical models and likewise the effect of laminectomy on IVD stresses varied between subjects. ROM was mostly unaffected by the laminectomies performed in this study. CONCLUSIONS: Regarding the risk of iatrogenic spondylolisthesis, the combined results are sufficient evidence to suggest surgeons should be particularly cautious when PI resection exceeds 50% bone resection for all laminectomies included in this study. Lastly, the effects seen in FJF and IVD stresses indicate the degree to which the remainder of the spine must experience compensatory biomechanical changes as a result of the surgical intervention.

Contributions of elastic fibers, collagen, and extracellular matrix to the multiaxial mechanics of ligament.

Elastin is a biopolymer known to provide resilience to extensible biologic tissues through elastic recoil of its highly crosslinked molecular network. Recent studies have demonstrated that elastic fibers in ligament provide significant resistance to tensile and especially shear stress. We hypothesized that the biomechanics of elastic fibers in ligament could be described as transversely isotropic with both fiber and matrix components in a multi-material mixture. Similarly, we hypothesized that material coefficients derived using the experimental tensile response could be used to predict the experimental shear response. Experimental data for uniaxial and transverse tensile testing of control tissues, and those enzymatically digested to disrupt elastin, were used as inputs to a material coefficient optimization algorithm. An additive decomposition of the strain energy was used to model the total stress as the sum of contributions from collagen fibers, elastic fibers, elastic matrix, and ground substance matrix. Matrices were modeled as isotropic Veronda-Westmann hyperelastic materials, whereas fiber families were modeled as piecewise exponential-linear hyperelastic materials. Optimizations provided excellent fits to the tensile experimental data for each treatment case and material model. Given the disparity in magnitude of stresses between longitudinal and transverse/shear tests and agreement between models and experiments, the hypothesized transversely isotropic material of elastin symmetry was supported. In addition, the coefficients derived from uniaxial and transverse tensile experiments provided reasonable predictions of the experimental behavior during shear deformation. The magnitudes of coefficients representing stress, nonlinearity, and stiffness supported the experimental evidence that elastic fibers dominate the low strain tensile and shear response of ligament. These findings demonstrate that the additive decomposition modeling strategy can represent each discrete fiber and matrix constituent and their relative contribution to the material response of the tissue. These experimental data and the validated constitutive model provide essential inputs and a framework to refine existing computational models of ligament and tendon mechanics by explicitly representing the mechanical contributions of elastic fibers.

Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry.

Ailments of the bladder are often treated via intravesical delivery-direct application of therapeutic into the bladder through a catheter. This technique is employed hundreds of thousands of times every year, but protocol development has largely been limited to empirical determination. Furthermore, the numerical analyses of intravesical delivery performed to date have been restricted to static geometries and have not accounted for bladder deformation. This study uses a finite element analysis approach with biphasic solute transport to investigate several parameters pertinent to intravesical delivery including solute concentration, solute transport properties and instillation volume. The volume of instillation was found to have a substantial impact on the exposure of solute to the deeper muscle layers of the bladder, which are typically more difficult to reach. Indeed, increasing the instillation volume from 50-100 ml raised the muscle solute exposure as a percentage of overall bladder exposure from 60-70% with higher levels achieved for larger instillation volumes. Similar increases were not seen for changes in solute concentration or solute transport properties. These results indicate the role that instillation volume may play in targeting particular layers of the bladder during an intravesical delivery.

Computer simulation of lumbar flexion shows shear of the facet capsular ligament.

BACKGROUND CONTEXT: The lumbar facet capsular ligament (FCL) is a posterior spinal ligament with a complex structure and kinematic profile. The FCL has a curved geometry, multiple attachment sites, and preferentially aligned collagen fiber bundles on the posterior surface that are innervated with mechanoreceptive nerve endings. Spinal flexion induces three-dimensional (3D) deformations, requiring the FCL to maintain significant tensile and shear loads. Previous works aimed to study 3D facet joint kinematics during flexion, but to our knowledge none have reported localized FCL surface deformations likely created by this complex structure. PURPOSE: The purpose of this study was to elucidate local deformations of both the posterior and anterior surfaces of the lumbar FCL to understand the distribution and magnitude of in-plane and through-plane deformations, including the prevalence of shear. STUDY DESIGN/SETTING: The FCL anterior and posterior surface deformations were quantified through creation of a finite element model simulating facet joint flexion using a realistic geometry, physiological kinematics, and fitted constitutive material. METHODS: Geometry was obtained from the micro-CT data of a healthy L3-L4 facet joint capsule (n=1); kinematics were extracted from sagittal plane fluoroscopic data of healthy volunteers (n=10) performing flexion; and average material properties were determined from planar biaxial extension tests of L4-L5 FCLs (n=6). All analyses were performed with the non-linear finite element solver, FEBio. A grid of equally spaced 3×3 nodes on the posterior surface identified regional differences within the strain fields and was used to create comparisons against previously published experimental data. This study was funded by the National Institutes of Health and the authors have no disclosures. RESULTS: Inhomogeneous in-plane and through-plane shear deformations were prominent through the middle body of the FCL on both surfaces. Anterior surface deformations were more pronounced because of the small width of the joint space, whereas posterior surface deformations were more diffuse because the larger area increased deformability. We speculate these areas of large deformation may provide this proprioceptive system with an excellent measure of spinal motion. CONCLUSIONS: We found that in-plane and through-plane shear deformations are widely present in finite element simulations of a lumbar FCL during flexion. Importantly, we conclude that future studies of the FCL must consider the effects of both shear and tensile deformations.

A general framework for application of prestrain to computational models of biological materials.

It is often important to include prestress in computational models of biological tissues. The prestress can represent residual stresses (stresses that exist after the tissue is excised from the body) or in situ stresses (stresses that exist in vivo, in the absence of loading). A prestressed reference configuration may also be needed when modeling the reference geometry of biological tissues in vivo. This research developed a general framework for representing prestress in finite element models of biological materials. It is assumed that the material is elastic, allowing the prestress to be represented via a prestrain. For prestrain fields that are not compatible with the reference geometry, the computational framework provides an iterative algorithm for updating the prestrain until equilibrium is satisfied. The iterative framework allows for enforcement of two different constraints: elimination of distortion in order to address the incompatibility issue, and enforcing a specified in situ fiber strain field while allowing for distortion. The framework was implemented as a plugin in FEBio (www.febio.org), making it easy to maintain the software and to extend the framework if needed. Several examples illustrate the application and effectiveness of the approach, including the application of in situ strains to ligaments in the Open Knee model (simtk.org/home/openknee). A novel method for recovering the stress-free configuration from the prestrain deformation gradient is also presented. This general purpose theoretical and computational framework for applying prestrain will allow analysts to overcome the challenges in modeling this important aspect of biological tissue mechanics.

Uniaxial and biaxial mechanical properties of porcine linea alba.

Incisional hernia is a severe complication post-laparoscopic/laparotomy surgery that is commonly associated with the linea alba. However, the few studies on the mechanical properties of the linea alba in the literature appear contradictory, possible due to challenges with the physical dimensions of samples and variations in protocol. This study focuses on the tensile mechanical characterisation of the porcine linea alba, as determined by uniaxial and equi-load biaxial testing using image-based strain measurement methods. Results show that the linea alba demonstrated a non-linear elastic, anisotropic behaviour which is often observed in biological soft tissues. The transverse direction (parallel to fibres) was found to be approximately eight times stiffer than the longitudinal (cross-fibre) direction under both uniaxial and equi-load biaxial loading. The equi-load biaxial tensile tests revealed that contraction could occur in the transverse direction despite increasing load, probably due to the anisotropy of the tissue. Optical surface marker tracking and digital image correlation methods were found to greatly improve the accuracy of stretch measurement, resulting in a 75% change in the apparent stiffness compared to using strain derived from machine cross-head displacement. Additionally, a finite element model of the experiments using a combination of an Ogden and fibre exponential power law model for the linea alba was implemented to quantify the effect of clamping and tissue dimensions (which are suboptimal for tensile testing) on the results. The preliminary model results were used to apply a correction factor to the uniaxial experimental data prior to inverse optimisation to derive best fit material parameters for the fibre reinforced Ogden model. Application of the model to the equi-load biaxial case showed some differences compared to the experimental data, suggesting a more complex anisotropic model may be necessary to capture biaxial behaviour. These results provide an improved assessment of the mechanical properties of the porcine linea alba for wound closure and other studies.

Mechanical characterisation of porcine rectus sheath under uniaxial and biaxial tension.

Incisional hernia development is a significant complication after laparoscopic abdominal surgery. Intra-abdominal pressure (IAP) is known to initiate the extrusion of intestines through the abdominal wall, but there is limited data on the mechanics of IAP generation and the structural properties of rectus sheath. This paper presents an explanation of the mechanics of IAP development, a study of the uniaxial and biaxial tensile properties of porcine rectus sheath, and a simple computational investigation of the tissue. Analysis using Laplace׳s law showed a circumferential stress in the abdominal wall of approx. 1.1MPa due to an IAP of 11kPa, commonly seen during coughing. Uniaxial and biaxial tensile tests were conducted on samples of porcine rectus sheath to characterise the stress-stretch responses of the tissue. Under uniaxial tension, fibre direction samples failed on average at a stress of 4.5MPa at a stretch of 1.07 while cross-fibre samples failed at a stress of 1.6MPa under a stretch of 1.29. Under equi-biaxial tension, failure occurred at 1.6MPa with the fibre direction stretching to only 1.02 while the cross-fibre direction stretched to 1.13. Uniaxial and biaxial stress-stretch plots are presented allowing detailed modelling of the tissue either in silico or in a surrogate material. An FeBio computational model of the tissue is presented using a combination of an Ogden and an exponential power law model to represent the matrix and fibres respectively. The structural properties of porcine rectus sheath have been characterised and add to the small set of human data in the literature with which it may be possible to develop methods to reduce the incidence of incisional hernia development.