Image-based Finite Element Models Research Articles

Development of a continuum-based, meshless, finite element modeling approach for representation of trabecular bone indentation

Implant subsidence into the underlying trabecular bone is a common problem in orthopaedic surgeries; however, the ability to pre-operatively predict implant subsidence remains limited. Current state-of-the-art computational models for predicting subsidence have issues addressing this clinical problem, often resulting from the size and complexity of existing subject-specific, image-based finite element (FE) models. The current study aimed to develop a simplified approach to FE modeling of subject-specific trabecular bone indentation resulting from implant penetration.Confined indentation experiments of human trabecular bone with flat- and sharp-tip indenters were simulated using FE analysis. A generalized continuum-level approach using a meshless smoothed particle hydrodynamics (SPH) approach and an isotropic crushable foam (CF) material model was developed for the trabecular bone specimens. Five FE models were generated with CF material parameters calibrated to cadaveric specimens spanning a range of bone mineral densities (BMD). Additionally, an alternative model configuration was developed that included consideration of bone marrow, with bone and marrow material parameters assigned to elements randomly according to bone volume (BV%) measurements of experimental specimens, owing to the non-uniform nature of trabecular bone tissue microstructure.Statistical analysis found significant correlation between the shapes of the numerical and experimental force-displacement curves. FE models accurately captured the bone densification patterns observed experimentally. Inclusion of marrow elements offered improved response prediction of the flat-tip indenter tests.Ultimately, the developed approach demonstrates the ability of a generalizable continuum-level SPH approach to capture bone variability using clinical bone imaging metrics without needing detailed image-based geometries, a significant step towards simplified subject-specific modeling of implant subsidence.

Heterogeneous Mechanical Stress and Interstitial Fluid Flow Predictions Derived from DCE-MRI for Rat U251N Orthotopic Gliomas.

Mechanical stress and fluid flow influence glioma cell phenotype in vitro, but measuring these quantities in vivo continues to be challenging. The purpose of this study was to predict these quantities in vivo, thus providing insight into glioma physiology and potential mechanical biomarkers that may improve glioma detection, diagnosis, and treatment. Image-based finite element models of human U251N orthotopic glioma in athymic rats were developed to predict structural stress and interstitial flow in and around each animal's tumor. In addition to accounting for structural stress caused by tumor growth, our approach has the advantage of capturing fluid pressure-induced structural stress, which was informed by in vivo interstitial fluid pressure (IFP) measurements. Because gliomas and the brain are soft, elevated IFP contributed substantially to tumor structural stress, even inverting this stress from compressive to tensile in the most compliant cases. The combination of tumor growth and elevated IFP resulted in a concentration of structural stress near the tumor boundary where it has the greatest potential to influence cell proliferation and invasion. MRI-derived anatomical geometries and tissue property distributions resulted in heterogeneous interstitial fluid flow with local maxima near cerebrospinal fluid spaces, which may promote tumor invasion and hinder drug delivery. In addition, predicted structural stress and interstitial flow varied markedly between irradiated and radiation-naïve animals. Our modeling suggests that relative to tumors in stiffer tissues, gliomas experience unusual mechanical conditions with potentially important biological (e.g., proliferation and invasion) and clinical consequences (e.g., drug delivery and treatment monitoring).

Image-based finite element modeling of air flow and thermal transport in Al-fiber-sintered porous materials

In this study, the pressure drop and heat transfer in a heat-transfer tube filled with a sintered porous medium comprising Al fibers were investigated using computational fluid dynamics (CFD) simulations. We reconstructed the sintered fibrous porous structure and generated a computational mesh using X-ray computed tomography data, and the simulated pressure drop and heat transfer agreed well with those reported by Enoki et al. [2021]. The differences in both the form coefficient and the permeability between two different samples can be explained from the differences in both the specific solid surface area and the porosity. Further, the CFD simulations indicated that thermal conduction of the Al solid phase enhanced the heat exchange between the air and Al fibers. To examine the effect of solid-phase thermal conduction, we generated a model of a heat-transfer tube having an ideal wire mesh structure, in which we introduced the interfacial thermal conductivity between Al fibers and the inner tube wall as additional factors. We also performed CFD simulations with four different shell-region thicknesses and found that even a very narrow gap of 5 to 10 μm heavily affected the heat-exchange performance because of the low thermal conductivity of the shell region.

Myocardial biomechanical effects of fetal aortic valvuloplasty.

Fetal critical aortic stenosis with evolving hypoplastic left heart syndrome (CAS-eHLHS) can progress to a univentricular (UV) birth malformation. Catheter-based fetal aortic valvuloplasty (FAV) can resolve stenosis and reduce the likelihood of malformation progression. However, we have limited understanding of the biomechanical impact of FAV and subsequent LV responses. Therefore, we performed image-based finite element (FE) modeling of 4 CAS-eHLHS fetal hearts, by performing iterative simulations to match image-based characteristics and then back-computing physiological parameters. We used pre-FAV simulations to conduct virtual FAV (vFAV) and compared pre-FAV and post-FAV simulations. vFAV simulations generally enabled partial restoration of several physiological features toward healthy levels, including increased stroke volume and myocardial strains, reduced aortic valve (AV) and mitral valve regurgitation (MVr) velocities, reduced LV and LA pressures, and reduced peak myofiber stress. FAV often leads to aortic valve regurgitation (AVr). Our simulations showed that AVr could compromise LV and LA depressurization but itcould alsosignificantly increase stroke volume and myocardial deformational stimuli. Post-FAV scans and simulations showed FAV enabled only partial reduction of the AV dissipative coefficient. Furthermore, LV contractility and peripheral vascular resistance could change in response to FAV, preventing decreases in AV velocity and LV pressure, compared with what would be anticipated from stenosis relief. This suggested that case-specific post-FAV modeling is required to fully capture cardiac functionality. Overall, image-based FE modeling could provide mechanistic details of the effects of FAV, but computational prediction of acute outcomes was difficult due to a patient-dependent physiological response to FAV.

A Finite Element Model to Investigate the Stability of Osteochondral Grafts Within a Human Tibiofemoral Joint

Osteochondral grafting has demonstrated positive outcomes for treating articular cartilage defects by replacing the damaged region with a cylindrical graft consisting of bone with a layer of cartilage. However, factors that cause graft subsidence are not well understood. The aim of this study was to develop finite element (FE) models of osteochondral grafts within a tibiofemoral joint, suitable for an investigation of parameters affecting graft stability. Cadaveric femurs were used to experimentally calibrate the bone properties and graft-bone frictional forces for use in corresponding image-based FE models, generated from µCT scan data. Effects of cartilage defects and osteochondral graft repair were measured by examining contact pressure changes using further in vitro tests. Here, six defects were created in the femoral condyles, which were subsequently treated with osteochondral autografts or metal pins. Matching image-based FE models were created, and the contact patches were compared. The bone material properties and graft-bone frictional forces were successfully calibrated from the initial tests with good resulting levels of agreement (CCC = 0.87). The tibiofemoral joint experiment provided a range of cases that were accurately described in the resultant pressure maps and were well represented in the FE models. Cartilage defects and repair quality were experimentally measurable with good agreement in the FE model pressure maps. Model confidence was built through extensive validation and sensitivity testing. It was found that specimen-specific properties were required to accurately represent graft behaviour. The final models produced are suitable for a range of parametric testing to investigate immediate graft stability.

Geometric determinants of the mechanical behavior of image-based finite element models of the intervertebral disc.

The intervertebral disc is an important structure for load transfer through the spine. Its injury and degeneration have been linked to pain and spinal fractures. Disc injury and spine fractures are associated with high stresses; however, these stresses cannot be measured, necessitating the use of finite element (FE) models. These models should include the disc's complex structure, as changes in disc geometry have been linked to altered mechanical behavior. However, image-based models using disc-specific structures have yet to be established. This study describes a multiphasic FE modeling approach for noninvasive estimates of subject-specific intervertebral disc mechanical behavior based on medical imaging. The models (n = 22) were used to study the influence of disc geometry on the predicted global mechanical response (moments and forces), internal local disc stresses, and tractions at the interface between the disc and the bone. Disc geometry was found to have a strong influence on the predicted moments and forces on the disc (R2 = 0.69-0.93), while assumptions regarding the side curvature (bulge) of the disc had only a minor effect. Strong variability in the predicted internal disc stresses and tractions was observed between the models (mean absolute differences of 5.1%-27.7%). Disc height had a systematic influence on the internal disc stresses and tractions at the disc-to-bone interface. The influence of disc geometry on mechanics highlights the importance of disc-specific modeling to estimate disc injury risk, loading on the adjacent vertebral bodies, and the mechanical environment present in disc tissues.

Multiscale morphological analysis of bone microarchitecture around Mg-10Gd implants.

The utilization of biodegradable magnesium (Mg)-based implants for restoration of bone function following trauma represents a transformative approach in orthopaedic application. One such alloy, magnesium-10weight percent gadolinium (Mg-10Gd), has been specifically developed to address the rapid degradation of Mg while enhancing its mechanical properties to promote bone healing. Previous studies have demonstrated that Mg-10Gd exhibits favorable osseointegration; however, it exhibits distinct ultrastructural adaptation in comparison to conventional implants like titanium (Ti). A crucial aspect that remains unexplored is the impact of Mg-10Gd degradation on the bone microarchitecture. To address this, we employed hierarchical three-dimensional imaging using synchrotron radiation in conjunction with image-based finite element modelling. By using the methods outlined, the vascular porosity, lacunar porosity and the lacunar-canaliculi network (LCN) morphology of bone around Mg-10Gd in comparison to Ti in a rat model from 4 weeks to 20 weeks post-implantation was investigated. Our investigation revealed that within our observation period, the degradation of Mg-10Gd implants was associated with significantly lower (p<0.05) lacunar density in the surrounding bone, compared to Ti. Remarkably, the LCN morphology and the fluid flow analysis did not significantly differ for both implant types. In summary, a more pronounced lower lacunae distribution rather than their morphological changes was detected in the surrounding bone upon the degradation of Mg-10Gd implants. This implies potential disparities in bone remodelling rates when compared to Ti implants. Our findings shed light on the intricate relationship between Mg-10Gd degradation and bone microarchitecture, contributing to a deeper understanding of the implications for successful osseointegration.

Tensile failure analysis of laser stake-welded T-joints: X-ray tomography based conformal finite element and fractal theoretical approaches

To promote the application of complex structural materials in large size, the interfacial joint is the key component for sandwich structure to wipe off the sample size limitation and fabricate multi-material structures. However, the laser welding process inevitably induced void defects in the welded joint, influencing the mechanical properties of the whole structure. In this paper, the aluminum alloy laser stake-welded T-joints were fabricated in a laser welding system. The geometric deviations and internal void defects of T-joints were visualized and quantified by micro X-ray computed tomography (μCT). Two image-based finite element models were reconstructed from CT images to discuss the effect of different manufacturing-induced defects on the tensile behaviour of T-joints. The geometric deviations of T-joints make a response for the decrease of strength and the void defects result in the decrease of Young’s modulus of T-joints. The fractal dimension theory, based on the value of void volume and the distance of the void to the interface obtained from CT images, was developed to predict the strength of the T-joint. The results matched well with the experimental results.

Mechanical Biomarkers in Bone Using Image-Based Finite Element Analysis

The purpose of this review is to summarize insights gained by finite element (FE) model-based mechanical biomarkers of bone for in vivo assessment of bone development and adaptation, fracture risk, and fracture healing. Muscle-driven FE models have been used to establish correlations between prenatal strains and morphological development. Postnatal ontogenetic studies have identified potential origins of bone fracture riskand quantified the mechanical environment during stereotypical locomotion and in response to increased loading. FE-based virtual mechanical tests have been used to assess fracture healing with higher fidelity than the current clinical standard; here, virtual torsion test data was a better predictor of torsional rigidity than morphometric measures or radiographic scores. Virtual mechanical biomarkers of strength have also been used to deepen the insights from both preclinical and clinical studies with predictions of strength of union at different stages of healing and reliable predictions of time to healing. Image-based FE models allow for noninvasive measurement of mechanical biomarkers in bone and have emerged as powerful tools for translational research on bone. More work to develop nonirradiating imaging techniques and validate models of bone during particularly dynamic phases (e.g., during growth and the callus region during fracture healing) will allow for continued progress in our understanding of how bone responds along the lifespan.

Study of Image-Based Finite Element Model for Predicting the Biomechanical Properties of Femur Bone: A Review

Study of Image-Based Finite Element Model for Predicting the Biomechanical Properties of Femur Bone: A Review

Myocardial Biomechanics and the Consequent Differentially Expressed Genes of the Left Atrial Ligation Chick Embryonic Model of Hypoplastic Left Heart Syndrome

Left atrial ligation (LAL) of the chick embryonic heart is a model of the hypoplastic left heart syndrome (HLHS) where a purely mechanical intervention without genetic or pharmacological manipulation is employed to initiate cardiac malformation. It is thus a key model for understanding the biomechanical origins of HLHS. However, its myocardial mechanics and subsequent gene expressions are not well-understood. We performed finite element (FE) modeling and single-cell RNA sequencing to address this. 4D high-frequency ultrasound imaging of chick embryonic hearts at HH25 (ED 4.5) were obtained for both LAL and control. Motion tracking was performed to quantify strains. Image-based FE modeling was conducted, using the direction of the smallest strain eigenvector as the orientations of contractions, the Guccione active tension model and a Fung-type transversely isotropic passive stiffness model that was determined via micro-pipette aspiration. Single-cell RNA sequencing of left ventricle (LV) heart tissues was performed for normal and LAL embryos at HH30 (ED 6.5) and differentially expressed genes (DEG) were identified.After LAL, LV thickness increased by 33%, strains in the myofiber direction increased by 42%, while stresses in the myofiber direction decreased by 50%. These were likely related to the reduction in ventricular preload and underloading of the LV due to LAL. RNA-seq data revealed potentially related DEG in myocytes, including mechano-sensing genes (Cadherins, NOTCH1, etc.), myosin contractility genes (MLCK, MLCP, etc.), calcium signaling genes (PI3K, PMCA, etc.), and genes related to fibrosis and fibroelastosis (TGF-β, BMP, etc.). We elucidated the changes to the myocardial biomechanics brought by LAL and the corresponding changes to myocyte gene expressions. These data may be useful in identifying the mechanobiological pathways of HLHS.

Denosumab treatment is associated with decreased cortical porosity and increased bone density and strength at the proximal humerus of ovariectomized cynomolgus monkeys.

Upper extremity fractures, including those at the humerus, are common among women with postmenopausal osteoporosis. Denosumab was shown to reduce humeral fractures in this population; however, no clinical or preclinical studies have quantified the effects of denosumab on humerus bone mineral density or bone microarchitecture changes. This study used micro-computed tomography (μCT) and computed tomography (CT), alongside image-based finite element (FE) models derived from both modalities, to quantify the effects of denosomab (DMAb) and alendronate (ALN) on humeral bone from acutely ovariectomized (OVX) cynomolgus monkeys. Animals were treated with 12 monthly injections of s.c. vehicle (VEH; n=10), s.c. denosumab (DMAb; 25mg/kg, n=9), or i.v. alendronate (ALN; 50μg/kg, n=10). Two more groups received 6months of VEH followed by 6months of DMAb (VEH-DMAb; n=7) or 6months of ALN followed by 6months of DMAb (ALN-DMAb; n=9). After treatment, humeri were harvested and μCT was used to quantify tissue mineral density, trabecular morphology, and cortical porosity at the humeral head. Clinical CT imaging was also used to quantify trabecular and cortical bone mineral density (BMD) at the ultra-proximal, proximal, 1/5 proximal and midshaft of the bone. Finally, μCT-based FE models in compression, and CT-based FE models in compression, torsion, and bending, were developed to estimate differences in strength. Compared to VEH, groups that received DMAb at any time demonstrated lower cortical porosity and/or higher tissue mineral density via μCT; no effects on trabecular morphology were observed. FE estimated strength based on μCT was higher after 12-months DMAb (p=0.020) and ALN-DMAb (p=0.024) vs. VEH; respectively, FE predicted mean (SD) strength was 4649.88 (710.58) N, and 4621.10 (1050.16) N vs. 3309.4 (876.09) N. All antiresorptive treatments were associated with higher cortical BMD via CT at the 1/5 proximal and midshaft of the humerus; however, no differences in CT-based FE predicted strength were observed. Overall, these results help to explain the observed reductions in humeral fracture rate following DMAb treatment in women with postmenopausal osteoporosis.

Morphological, functional, and biomechanical progression of LV remodelling in a porcine model of HFpEF

Heart failure (HF) with preserved ejection fraction (HFpEF) accounts for about half of heart failure cases, but the progression of cardiac biomechanics during pathogenesis is not completely understood. We investigated a published porcine model of HFpEF, generated by progressive constriction of an aortic cuff causing progressive left ventricle (LV) pressure overload, and characterized by hypertrophy, diastolic dysfunction and overt HF with elevated plasma beta natriuretic peptide (BNP). We characterized morphological and functional features and performed image-based finite element modelling over multiple time points, so as to understand how biomechanics evolved with morphological and functional changes during pathogenesis, and to provide data for future growth and remodeling investigations. Results showed that the hypertrophic responses quickly manifested and were effective at preventing an elevation of systolic myocardial stresses, suggesting active compensated remodeling. Consequent to the hypertrophy, diastolic myocardial stresses decreased despite the elevations in diastolic pressures. The left ventricle hypertrophy (LVH) myocardium also exhibited a quick elevation of active tension at the onset of the disease. There was a progressive and significant decrease in myocardial strain, which was more significant in the longitudinal direction. Further, elevated myocardial stiffness and diastolic pressures, which reflected diastolic dysfunction, also manifested, but this was delayed from the onset of the disease. Correlation analysis showed that hypertrophy was closely correlated to systolic pressure, active tension and systolic myocardial stress, suggesting that these factors may play a role in initiating hypertrophy. Myocardial stiffness was weakly correlated to LV pressures and myocardial stresses.

Image-Based Finite Element Modeling Approach for Characterizing In Vivo Mechanical Properties of Human Arteries.

Mechanical properties of the arterial walls could provide meaningful information for the diagnosis, management and treatment of cardiovascular diseases. Classically, various experimental approaches were conducted on dissected arterial tissues to obtain their stress–stretch relationship, which has limited value clinically. Therefore, there is a pressing need to obtain biomechanical behaviors of these vascular tissues in vivo for personalized treatment. This paper reviews the methods to quantify arterial mechanical properties in vivo. Among these methods, we emphasize a novel approach using image-based finite element models to iteratively determine the material properties of the arterial tissues. This approach has been successfully applied to arterial walls in various vascular beds. The mechanical properties obtained from the in vivo approach were compared to those from ex vivo experimental studies to investigate whether any discrepancy in material properties exists for both approaches. Arterial tissue stiffness values from in vivo studies generally were in the same magnitude as those from ex vivo studies, but with lower average values. Some methodological issues, including solution uniqueness and robustness; method validation; and model assumptions and limitations were discussed. Clinical applications of this approach were also addressed to highlight their potential in translation from research tools to cardiovascular disease management.

Automatic 3D image based finite element modelling for metallic foams and accuracy verification of digital volume correlation

3D image-based finite element (FE) modelling provides the feasibility to explore how the subtle structural features inside metallic foams affect their complex deformation and mechanical responses. But the modelling currently includes frequent manual modifications, which makes it a time and labor consuming task. The quality of generated model depends heavily on experienced creator. This paper demonstrates an automatic procedure to extract structure information from 3D images and generate reliable geometric models for meshing. With self-adaptive algorithms that fit local features of grayscale distribution and internal structure, high-fidelity FE models can be established efficiently without interference from subjective judgments. The generated FE models well reproduce the stress-strain relation and inhomogeneous deformation of aluminium foams, compared with experimental results. Using the simulation with a high-fidelity FE model as “ground truth”, the accuracy of digital volume correlation (DVC) in the deformation measurement of complex cellular materials is for the first time evaluated quantitatively and precisely, based on the definition of an equivalent displacement vector bridging the results obtained by FE simulation and by DVC.

High performance multi-platform computing for large-scale image-based finite element modeling of bone

BackgroundImage-based finite element (FE) modeling of bone is a non-invasive method to estimate bone stiffness and strength. High-resolution imaging data as input allows for inclusion of bone microarchitecture but results in large amounts of data unsuitable for traditional FE solvers. Bone-specific mesh-free solvers have been developed over the past 20 years to improve on memory efficiency in simulated bone loading applications. The objective of this study was to provide linear performance benchmarking for a bone-specific, mesh-free solver (FAIM) using µCT and HR-pQCT image data on Mac, Linux, and Windows operating systems using both single- and multi-thread CPU and GPU processing. MethodsThe focus is on the linear gradient-descent solver using standardized uniaxial loading of bone models from µCT, and first- and second-generation HR-pQCT scans of the radius and tibia. Convergence, speedup, memory, and batch performance tests were completed using CPUs and GPUs on three laboratory-based systems with Windows, Linux, and Mac operating systems. ResultsAlthough varying by system and model size, time-per-iteration was as low as 0.03 s when an HR-pQCT-based radius model (6.45 million DOF) was solved with 3 GPUs. Strong scaling was achieved with GPU and CPU parallel processing, with strong parallel efficiencies when models were solved using 3 GPUs or ≤ 10 CPU threads. Errors in force, strain energy density, and Von Mises stress were as low as 0.1% when a convergence tolerance of 10−3 or smaller was used. ConclusionThe results of this study indicate that to maximize computational efficiency and minimize model solution times using FAIM software under the standardized tested conditions using µCT, XCT1 and XCT2 HR-pQCT image data, convergence tolerance set to 10−4, and 10 threads or 2 GPUs are sufficient for efficient solution times. Less strict convergence tolerances will improve solution times but will introduce more error in the outcome measures.

3D finite-element brain modeling of lateral ventricular wall loading to rationalize periventricular white matter hyperintensity locations

Aging-related periventricular white matter hyperintensities (pvWMHs) are a common observation in medical images of the aging brain. The underlying tissue damage is part of the complex pathophysiology associated with age-related microstructural changes and cognitive decline. PvWMH formation is linked to blood–brain barrier dysfunction from cerebral small vessel disease as well as the accumulation of cerebrospinal fluid in periventricular tissue due to progressive denudation of the ventricular wall. In need of a unifying theory for pvWMH etiology, image-based finite-element modeling is used to demonstrate that ventricular expansion from age-related cerebral atrophy and hemodynamic loading leads to maximum mechanical loading of the ventricular wall in the same locations that show pvWMHs. Ventricular inflation, induced via pressurization of the ventricular wall, creates significant ventricular wall stretch and stress on the ependymal cells lining the wall, that are linked to cerebrospinal fluid leaking from the lateral ventricles into periventricular white matter tissue. Eight anatomically accurate 3D brain models of cognitively healthy subjects with a wide range of ventricular shapes are created. For all models, our simulations show that mechanomarkers of mechanical wall loading are consistently highest in pvWMHs locations (p < 0.05). Maximum principal strain, the ependymal cell thinning ratio, and wall curvature are on average 14%, 8%, and 24% higher in pvWMH regions compared to the remaining ventricular wall, respectively. Computational modeling provides a powerful framework to systematically study pvWMH formation and growth with the goal to develop pharmacological interventions in the future.

Deep learning-based X-ray computed tomography image reconstruction and prediction of compression behavior of 3D printed lattice structures

Complex thermal processing during laser powder bed fusion ( L -PBF) inevitably induces heterogenous and anisotropic defects, which can affect the macromechanical response of components. The initial morphological features of L -PBF printed samples can be reconstructed with X-ray micro-computed tomography (μCT) scans and the effects of defects on the mechanical properties of the sample can be predicted using image-based finite element modeling. However, due to balling phenomena, several powder particles adhere to the surface of the lattice structure and the mechanical properties of these particles differ from that of the parent material. The predicted modulus and strength of the direct reconstructed models are much higher than the experimental values because of overestimated particle effect. Therefore, these particles should be removed from the CT images before high-fidelity numerical simulation. This paper proposes a new image segmentation method based on a U-Net convolutional neural network to remove adhered particles on the L -PBF manufactured lattice structure from μCT slices. High-fidelity image-based finite element models were constructed with and without the deep learning-based image preprocessing. The results were compared with those obtained from simulations using an ideal CAD model and experimental results. The proposed deep learning-based preprocessing method enables high-precision reconstruction and efficient finite element simulation prediction of additive manufactured lattice structures.

Non-segmentation image-based finite element modeling (NSIB-FEM) for mechanical characterization and design of composites of fine particles

Image-based finite element modeling (IB-FEM) is a powerful tool for the characterization and design of various composite materials. However, conventional IB-FEM methods suffer from a number of deficiencies. To eliminate these deficiencies, a so-called non-segmentation image-based finite element modeling (NSIB-FEM) approach is proposed in this paper. The major difference between NSIB-FEM and conventional IB-FEM is that a finite element is allowed to contain more than one material phase, and the key step in NSIB-FEM is to determine element effective material properties. Theoretically, any micromechanics model of particulate composites can be applied for the calculation of element effective properties. A number of such micromechanics models, including Voigt’s model, Reuss’ model and Mori-Tanaka method, were tested to study how they affect the accuracy of NSIB-FEM. NSIB-FEM was validated against reported experimental data and compared with predictions by voxel-based finite element modeling. The results show that NSIB-FEM is a promising approach for the characterization of fine-particulate composites, the micromechanics model used to calculate element effective material properties has significant effect on the accuracy of NSIB-FEM. Further effort needs to be devoted to develop a more accurate method for the calculation of element-level effective material properties with the ability to deal with high volume-fraction of inclusion and element-level material anisotropy.

A 3D model of the soleus reveals effects of aponeuroses morphology and material properties on complex muscle fascicle behavior

The soleus is an important plantarflexor muscle with complex fascicle and connective tissue arrangement. In this study we created an image-based finite element model representing the 3D structure of the soleus muscle and its aponeurosis connective tissue, including distinct fascicle architecture of the posterior and anterior compartments. The model was used to simulate passive and active soleus lengthening during ankle motion to predict tissue displacements and fascicle architecture changes. Both the model’s initial architecture and changes incurred during passive lengthening were consistent with prior in vivo data from diffusion tensor imaging. Model predictions of active lengthening were consistent with axial plane muscle displacements that we measured in eight subjects’ lower legs using cine DENSE (Displacement Encoding with Stimulated Echoes) MRI during eccentric dorsiflexion. Regional strains were variable and nonuniform in the model, but average fascicle strains were similar between the compartments for both passive (anterior: 0.18 ± 0.06, posterior: 0.19 ± 0.05) and active (anterior: 0.12 ± 0.05, posterior: 0.13 ± 0.06) lengthening and were two- to three-times greater than muscle belly strain (0.06). We used additional model simulations to investigate the effects of aponeurosis material properties on muscle deformation, by independently varying the longitudinal or transverse stiffness of the posterior or anterior aponeurosis. Results of model variations elucidate how properties of soleus aponeuroses contribute to fascicle architecture changes. Greater longitudinal stiffness of posterior compared to anterior aponeurosis promoted more uniform spatial distribution of muscle tissue deformation. Reduced transverse stiffness in both aponeuroses resulted in larger differences between passive and active soleus lengthening.