Finite element modeling with patient-specific geometry to assess clinical risks of percutaneous pulmonary valve implantation.

BACKGROUND: Percutaneous pulmonary valve implantation (PPVI) is a non-surgical treatment for right ventricular outflow tract (RVOT) dysfunction. During PPVI, a stented valve, delivered via catheter, replaces the dysfunctional pulmonary valve. Stent oversizing allows valve anchoring within the RVOT, but overexpansion can intrude on the surrounding structures. Potentially dangerous outcomes include aortic valve insufficiency (AVI) from aortic root (AR) distortion and myocardial ischemia from coronary artery (CA) compression. Currently, risks are evaluated via balloon angioplasty/sizing before stent deployment. Patient-specific finite element (FE) analysis frameworks can improve pre-procedural risk assessment, but current methods require hundreds of hours of high-performance computation. METHODS: We created a simplified method to simulate the procedure using patient-specific FE models for accurate, efficient pre-procedural PPVI (using balloon expandable valves) risk assessment. The methodology was tested by retrospectively evaluating the clinical outcome of 12 PPVI candidates. RESULTS: Of 12 patients (median age 14.5 years) with dysfunctional RVOT, 7 had native RVOT and 5 had RV-PA conduits. Seven patients had undergone successful RVOT stent/valve placement, three had significant AVI on balloon testing, one had left CA compression, and one had both AVI and left CA compression. A model-calculated change of more than 20% in lumen diameter of the AR or coronary arteries correctly predicted aortic valve sufficiency and/or CA compression in all the patients. CONCLUSION: Agreement between FE results and clinical outcomes is excellent. Additionally, these models run in 2-6 min on a desktop computer, demonstrating potential use of FE analysis for pre-procedural risk assessment of PPVI in a clinically relevant timeframe.

A Graphical Approach to Visualize and Interpret Biochemically Coupled Biomechanical Models.

The last decade has seen the emergence of progressively more complex mechanobiological models, often coupling biochemical and biomechanical components. The complexity of these models makes interpretation difficult, and although computational tools can solve model equations, there is considerable potential value in a simple method to explore the interplay between different model components. Pump and system performance curves, long utilized in centrifugal pump selection and design, inspire the development of a graphical technique to depict visually the performance of biochemically-coupled mechanical models. Our approach is based on a biochemical performance curve (analogous to the classical pump curve) and a biomechanical performance curve (analogous to the system curve). Upon construction of the two curves, their intersection, or lack thereof, describes the coupled model's equilibrium state(s). One can also observe graphically how an applied perturbation shifts one or both curves, and thus how the other component will respond, without rerunning the full model. While the upfront cost of generating the performance curve graphic varies with the efficiency of the model components, the easily interpretable visual depiction of what would otherwise be nonintuitive model behavior is valuable. Herein, we outline how performance curves can be constructed and interpreted for biochemically-coupled biomechanical models and apply the technique to two independent models in the cardiovascular space. The performance curve approach can illustrate and help identify weaknesses in model construction, inform user-applied perturbations and fitting procedures to generate intended behaviors, and improve the efficiency of the model generation and application process.

Atherosclerotic Calcifications Have a Local Effect on the Peel Behavior of Human Aortic Media.

Aortic dissections, characterized by the propagation of a tear through the layers of the vessel wall, are critical, life-threatening events. Aortic calcifications are a common comorbidity in both acute and chronic dissections, yet their impact on dissection mechanics remains unclear. Using micro-computed tomography (CT) imaging, peel testing, and finite element modeling, this study examines the interplay between atherosclerotic calcifications and dissection mechanics. Samples cut from cadaveric human thoracic aortas were micro-CT imaged and subsequently peel-tested to map peel tension curves to the location of aortic calcifications. Empirical mode decomposition separated peel tension curves into high and low-frequency components, with high-frequency effects corresponding to interlamellar bonding mechanics and low-frequency effects to peel tension fluctuations. Finally, we used an idealized finite element model to examine how stiff calcifications affect aortic failure mechanics. Results showed that atherosclerosis influences dissection behavior on multiple length scales. Experimentally, atherosclerotic samples exhibited higher peel tensions and greater variance in the axial direction. The variation was driven by increased amplitudes of low-frequency tension fluctuations in diseased samples, indicating that more catastrophic propagations occur near calcifications. The simulations corroborated this finding, suggesting that the low-frequency changes resulted from the presence of a stiff calcification in the vessel wall. There were also modifications to the high-frequency peel mechanics, a response likely attributable to alterations in the microstructure and interlamellar bonding within the media. Considered collectively, these findings demonstrate that dissection mechanics are modified in aortic media nearby and adjacent to aortic calcifications.

An Approach to Quantify Anisotropic Multiaxial Failure of the Annulus Fibrosus.

Tears in the annulus fibrosus (AF) of the intervertebral disk (IVD) occur due to multiaxial loading on the spine. However, most existing AF failure studies measure uniaxial stress, not the multiaxial stress at failure. Delamination theory, which requires advanced structural knowledge and knowledge about the interactions between the AF fibers and matrix, has historically been used to understand and predict AF failure. Alternatively, a simple method, the Tsai-Hill yield criteria, could describe multiaxial failure of the AF. This yield criteria uses the known tissue fiber orientation and an equation to establish the multiaxial failure stresses that cause failure. This paper presents a method to test the multiaxial failure stress of the AF experimentally and evaluate the potential for the Tsai-Hill model to predict these failure stresses. Porcine AF was cut into a dogbone shape at three distinct angles relative to the primary lamella direction (parallel, transverse, and oblique). Then, each dogbone was pulled to complete rupture. The Cauchy stress in the material's fiber coordinates was calculated. These multiaxial stress parameters were used to optimize the coefficients of the Tsai-Hill yield. The coefficients obtained for the Tsai-Hill model vary by an order of magnitude between the fiber and transverse directions, and these coefficients provide a good description of the AF multiaxial failure stress. These results establish both an experimental approach and the use of the Tsai-Hill model to explain the anisotropic failure behavior of the tissue.

The long head of the biceps tendon undergoes multiaxial deformation during shoulder motion.

The long head biceps tendon (LHBT) is presumed a common source of shoulder joint pain and injury. Despite common LHBT pathologies, diagnosis and preferred treatment remain frequently debated. This Short Communication reports the development of a subject-specific finite element model of the shoulder joint based on one subject's 3D reconstructed anatomy and 3D in vivo kinematics recorded from bone-fixed electromagnetic sensors. The primary purpose of this study was to use the developed finite element model to investigate the LHBT mechanical environment during a typical shoulder motion of arm raising. Furthermore, this study aimed to assess the viability of material models derived from uniaxial tensile tests for accurate simulation of in vivo motion. The findings of our simulations indicate that the LHBT undergoes complex multidimensional deformations. As such, uniaxial material properties reported in the existing body of literature are not sufficient to simulate accurately the in vivo mechanical behavior of the LHBT. Further experimental tests on cadaveric specimens, such as biaxial tension and combinations of tension and torsion, are needed to describe fully the mechanical behavior of the LHBT and investigate its mechanisms of injury.

Cervical facet capsular ligament mechanics: Estimations based on subject-specific anatomy and kinematics.

Background: To understand the facet capsular ligament's (FCL) role in cervical spine mechanics, the interactions between the FCL and other spinal components must be examined. One approach is to develop a subject-specific finite element (FE) model of the lower cervical spine, simulating the motion segments and their components' behaviors under physiological loading conditions. This approach can be particularly attractive when a patient's anatomical and kinematic data are available. Methods: We developed and demonstrated methodology to create 3D subject-specific models of the lower cervical spine, with a focus on facet capsular ligament biomechanics. Displacement-controlled boundary conditions were applied to the vertebrae using kinematics extracted from biplane videoradiography during planar head motions, including axial rotation, lateral bending, and flexion-extension. The FCL geometries were generated by fitting a surface over the estimated ligament-bone attachment regions. The fiber structure and material characteristics of the ligament tissue were extracted from available human cervical FCL data. The method was demonstrated by application to the cervical geometry and kinematics of a healthy 23-year-old female subject. Results: FCL strain within the resulting subject-specific model were subsequently compared to models with generic: (1) geometry, (2) kinematics, and (3) material properties to assess the effect of model specificity. Asymmetry in both the kinematics and the anatomy led to asymmetry in strain fields, highlighting the importance of patient-specific models. We also found that the calculated strain field was largely independent of constitutive model and driven by vertebrae morphology and motion, but the stress field showed more constitutive-equation-dependence, as would be expected given the highly constrained motion of cervical FCLs. Conclusions: The current study provides a methodology to create a subject-specific model of the cervical spine that can be used to investigate various clinical questions by coupling experimental kinematics with multiscale computational models.

A computational bridge between traction force microscopy and tissue contraction.

Arterial wall active mechanics are driven by resident smooth muscle cells, which respond to biological, chemical, and mechanical stimuli and activate their cytoskeletal machinery to generate contractile stresses. The cellular mechanoresponse is sensitive to environmental perturbations, often leading to maladaptation and disease progression. When investigated at the single cell scale, however, these perturbations do not consistently result in phenotypes observed at the tissue scale. Here, a multiscale model is introduced that translates microscale contractility signaling into a macroscale, tissue-level response. The microscale framework incorporates a biochemical signaling network along with characterization of fiber networks that govern the anisotropic mechanics of vascular tissue. By incorporating both biochemical and mechanical components, the model is more flexible and more broadly applicable to physiological and pathological conditions. The model can be applied to both cell and tissue scale systems, allowing for the analysis of in vitro, traction force microscopy and ex vivo, isometric contraction experiments in parallel. When applied to aortic explant rings and isolated smooth muscle cells, the model predicts that active contractility is not a function of stretch at intermediate strain. The model also successfully predicts cell-scale and tissue-scale contractility and matches experimentally observed behaviors, including the hypercontractile phenotype caused by chronic hyperglycemia. The connection of the microscale framework to the macroscale through the multiscale model presents a framework that can translate the wealth of information already collected at the cell scale to tissue scale phenotypes, potentially easing the development of smooth muscle cell-targeting therapeutics.

The non-affine fiber network solver: A multiscale fiber network material model for finite-element analysis.

Multiscale mechanical models in biomaterials research have largely relied on simplifying the microstructure in order to make large-scale simulations tractable. The microscale simplifications often rely on approximations of the constituent distributions and assumptions on the deformation of the constituents. Of particular interest in biomechanics are fiber embedded materials, where simplified fiber distributions and assumed affinity in the fiber deformation greatly influence the mechanical behavior. The consequences of these assumptions are problematic when dealing with microscale mechanical phenomena such as cellular mechanotransduction in growth and remodeling, and fiber-level failure events during tissue failure. In this work, we propose a technique for coupling non-affine network models to finite element solvers, allowing for simulation of discrete microstructural phenomena within macroscopically complex geometries. The developed plugin is readily available as an open-source library for use with the bio-focused finite element software FEBio, and the description of the implementation allows for the adaptation to other finite element solvers.

MRI-based degeneration grades for lumbar facet joints do not correlate with cartilage mechanics.

Background: Lumbar facet joint arthritis is characterized by degeneration of articular cartilage, loss of joint spacing, and increased boney spur formation. These signs of facet joint degeneration have been previously measured using destructive biochemical and mechanical analysis. Nondestructive clinical evaluation of the facet joint has also been performed using MRI scoring, which ranks the health of the facet joint using the Fujiwara scale. However, nondestructive clinical evaluation of facet joint arthritis using standard MRI scoring provides low resolution images which result in high interobserver variability. Therefore, to assess the accuracy of nondestructive MRI analysis with regard to the health of the facet joint, this study determined whether any correlations existed between lumbar facet joint articular cartilage mechanics, facet articular cartilage biochemical signatures, and Fujiwara scores. Materials and Method: To accomplish this aim, human cadaveric lumbar spines were obtained and imaged using T1 MRI, then independently scored by three spine researchers. An osteochondral plug from each of the L2 thru L5 facet joints was obtained and loaded under unconfined compression. Results: The experiments showed no trends between histological images and changes in the Fujiwara score. The mechanical properties of articular cartilage (thickness, Young's modulus, instantaneous modulus, and permeability) also had no correlations with the Fujiwara score. Conclusions: These results show that the current Fujiwara score cannot accurately describe the biomechanics or biochemical composition of facet joint articular cartilage.

A structural bio-chemo-mechanical model for vascular smooth muscle cell traction force microscopy.

Altered vascular smooth muscle cell (VSMC) contractility is both a response to and a driver for impaired arterial function, and the leading experimental technique for quantifying VSMC contraction is traction force microscopy (TFM). TFM involves the complex interaction among several chemical, biological, and mechanical mechanisms, making it difficult to translate TFM results into tissue-scale behavior. Here, a computational model capturing each of the major aspects of the cell traction process is presented. The model incorporates four interacting components: a biochemical signaling network, individual actomyosin fiber bundle contraction, a cytoskeletal network of interconnected fibers, and elastic substrate displacement due to cytoskeletal force. The synthesis of these four components leads to a broad, flexible framework for describing TFM and linking biochemical and biomechanical phenomena on the single-cell level. The model recapitulated available data on VSMCs following biochemical, geometric, and mechanical perturbations. The structural bio-chemo-mechanical model offers a tool to interpret TFM data in new, more mechanistic ways, providing a framework for the evaluation of new biological hypotheses, interpolation of new data, and potential translation from single-cell experiments to multi-scale tissue models.

The Lumbar Facet Capsular Ligament Becomes More Anisotropic and the Fibers Become Stiffer With Intervertebral Disc and Facet Joint Degeneration.

Degeneration of the lumbar spine, and especially how that degeneration may lead to pain, remains poorly understood. In particular, the mechanics of the facet capsular ligament may contribute to low back pain, but the mechanical changes that occur in this ligament with spinal degeneration are unknown. Additionally, the highly nonlinear, heterogeneous, and anisotropic nature of the facet capsular ligament makes understanding mechanical changes more difficult. Clinically, magnetic resonance imaging (MRI)-based signs of degeneration in the facet joint and the intervertebral disc (IVD) correlate. Therefore, this study examined how the nonlinear, heterogeneous mechanics of the facet capsular ligament change with degeneration of the lumbar spine as characterized using MRI. Cadaveric human spines were imaged via MRI, and the L2-L5 facet joints and IVDs were scored using the Fujiwara and Pfirrmann grading systems. Then, the facet capsular ligament was isolated and biaxially loaded. The nonlinear mechanical properties of the ligament were obtained using a nonlinear generalized anisotropic inverse mechanics analysis (nGAIM). Then a Holzapfel-Gasser-Ogden (HGO) model was fit to the stress-strain data obtained from nGAIM. The facet capsular ligament is stiffer and more anisotropic at larger Pfirrmann grades and higher Fujiwara scores than at lower grades and scores. Analysis of ligament heterogeneity showed all tissues are highly heterogeneous, but no distinct spatial patterns of heterogeneity were found. These results show that degeneration of the lumbar spine including the facet capsular ligament appears to be occurring as a whole joint phenomenon and advance our understanding of lumbar spine degeneration.

Hybrid discrete-continuum multiscale model of tissue growth and remodeling.

Tissue growth and remodeling (G&R) is often central to disease etiology and progression, so understanding G&R is essential for understanding disease and developing effective therapies. While the state-of-the-art in this regard is animal and cellular models, recent advances in computational tools offer another avenue to investigate G&R. A major challenge for computational models is bridging from the cellular scale (at which changes are actually occurring) to the macroscopic, geometric-scale (at which physiological consequences arise). Thus, many computational models simplify one scale or another in the name of computational tractability. In this work, we develop a discrete-continuum modeling scheme for analyzing G&R, in which we apply changes directly to the discrete cell and extracellular matrix (ECM) architecture and pass those changes up to a finite-element macroscale geometry. We demonstrate the use of the model in three case-study scenarios: the media of a thick-walled artery, and the media and adventitia of a thick-walled artery, and chronic dissection of an arterial wall. We analyze each case in terms of the new and insightful data that can be gathered from this technique, and we compare our results from this model to several others. STATEMENT OF SIGNIFICANCE: This work is significant in that it provides a framework for combining discrete, microstructural- and cellular-scale models to the growth and remodeling of large tissue structures (such as the aorta). It is a significant advance in that it couples the microscopic remodeling with an existing macroscopic finite element model, making it relatively easy to use for a wide range of conceptual models. It has the potential to improve understanding of many growth and remodeling processes, such as organ formation during development and aneurysm formation, growth, and rupture.

Statistical shape representation of the thoracic aorta: accounting for major branches of the aortic arch.

Statistical shape modeling (SSM) is an emerging tool for risk assessment of thoracic aortic aneurysm. However, the head branches of the aortic arch are often excluded in SSM. We introduced an SSM strategy based on principal component analysis that accounts for aortic branches and applied it to a set of patient scans. Computational fluid dynamics were performed on the reconstructed geometries to identify the extent to which branch model accuracy affects the calculated wall shear stress (WSS) and pressure. Surface-averaged and location-specific values of pressure did not change significantly, but local WSS error was high near branches when inaccurately modeled.

Elucidating the signal for contact guidance contained in aligned fibrils with a microstructural-mechanical model.

Despite its importance in physiological processes and tissue engineering, the mechanism underlying cell contact guidance in an aligned fibrillar network has defied elucidation due to multiple interdependent signals that such a network presents to cells, namely, anisotropy of adhesion, porosity and mechanical behaviour. A microstructural-mechanical model of fibril networks was used to assess the relative magnitudes of these competing signals in networks of varied alignment strength based on idealized cylindrical pseudopods projected into the aligned and orthogonal directions and computing the anisotropy of metrics chosen for adhesion, porosity and mechanical behaviour: cylinder-fibre contact area for adhesion, persistence length of pores for porosity and total force to displace fibres from the cylindrical volume as well as network stiffness experienced upon cylinder retraction for mechanical behaviour. The signals related to mechanical anisotropy are substantially higher than adhesion and porosity anisotropy, especially at stronger network alignments, although their signal to noise (S/N) values are substantially lower. The former finding is consistent with a recent report that fibroblasts can sense fibril alignment via anisotropy of network mechanical resistance, and the model reveals this can be due to either mechanical resistance to pseudopod protrusion or retraction given their signal and S/N values are similar.

In Situ Lumbar Facet Capsular Ligament Strains Due to Joint Pressure and Residual Strain.

The lumbar facet capsular ligament, which surrounds and limits the motion of each facet joint in the lumbar spine, has been recognized as being mechanically significant and has been the subject of multiple mechanical characterization studies in the past. Those studies, however, were performed on isolated tissue samples and thus could not assess the mechanical state of the ligament in vivo, where the constraints of attachment to rigid bone and the force of the joint pressure lead to nonzero strain even when the spine is not loaded. In this work, we quantified these two effects using cadaveric lumbar spines (five spines, 20 total facet joints harvested from L2 to L5). The effect of joint pressure was measured by injecting saline into the joint space and tracking the 3D capsule surface motion via digital image correlation, and the prestrain due to attachment was measured by dissecting a large section of the tissue from the bone and by tracking the motion between the on-bone and free states. We measured joint pressures of roughly 15-40 kPa and local first principal strains of up to 25-50% when 0.3 mL of saline was injected into the joint space; the subsequent increase in pressure and strain were more modest for further increases in injection volume, possibly due to leakage of fluid from the joint. The largest stretches were in the bone-to-bone direction in the portions of the ligament spanning the joint space. When the ligament was released from the vertebrae, it shrank by an average of 4-5%, with local maximum (negative) principal strain values of up to 30%, on average. Based on these measurements and previous tests on isolated lumbar facet capsular ligaments, we conclude that the normal in vivo state of the facet capsular ligament is in tension, and that the collagen in the ligament is likely uncrimped even when the spine is not loaded.

Experimental and Mouse-Specific Computational Models of the Fbln4SMKO Mouse to Identify Potential Biomarkers for Ascending Thoracic Aortic Aneurysm.

PURPOSE: To use computational methods to explore geometric, mechanical, and fluidic biomarkers that could correlate with mouse lifespan in the Fbln4SMKO mouse. Mouse lifespan was used as a surrogate for risk of a severe cardiovascular event in cases of ascending thoracic aortic aneurysm. METHODS: Image-based, mouse-specific fluid-structure-interaction models were developed for Fbln4SMKO mice (n = 10) at ages two and six months. The results of the simulations were used to quantify potential biofluidic biomarkers, complementing the geometrical biomarkers obtained directly from the images. RESULTS: Comparing the different geometrical and biofluidic biomarkers to the mouse lifespan, it was found that mean oscillatory shear index (OSImin) and minimum time-averaged wall shear stress (TAWSSmin) at six months showed the largest correlation with lifespan (r2 = 0.70, 0.56), with both correlations being positive (i.e., mice with high OSImean and high TAWSSmin tended to live longer). When change between two and six months was considered, the change in TAWSSmin showed a much stronger correlation than OSImean (r2 = 0.75 vs. 0.24), and the correlation was negative (i.e., mice with increasing TAWSSmin over this period tended to live less long). CONCLUSION: The results highlight potential biomarkers of ATAA outcomes that can be obtained through noninvasive imaging and computational simulations, and they illustrate the potential synergy between small-animal and computational models.

Characterizing Tissue Remodeling and Mechanical Heterogeneity in Cerebral Aneurysms.

Accurately assessing the complex tissue mechanics of cerebral aneurysms (CAs) is critical for elucidating how CAs grow and whether that growth will lead to rupture. The factors that have been implicated in CA progression - blood flow dynamics, immune infiltration, and extracellular matrix remodeling - all occur heterogeneously throughout the CA. Thus, it stands to reason that the mechanical properties of CAs are also spatially heterogeneous. Here, we present a new method for characterizing the mechanical heterogeneity of human CAs using generalized anisotropic inverse mechanics, which uses biaxial stretching experiments and inverse analyses to determine the local Kelvin moduli and principal alignments within the tissue. Using this approach, we find that there is significant mechanical heterogeneity within a single acquired human CA. These results were confirmed using second harmonic generation imaging of the CA's fiber architecture and a correlation was observed. This approach provides a single-step method for determining the complex heterogeneous mechanics of CAs, which has important implications for future identification of metrics that can improve accuracy in prediction risk of rupture.

Residual stress and osmotic swelling of the periodontal ligament.

Osmotic swelling and residual stress are increasingly recognized as important factors in soft tissue biomechanics. Little attention has been given to residual stress in periodontal ligament (PDL) biomechanics despite its rapid growth and remodeling potential. Those tissues that bear compressive loads, e.g., articular cartilage, intervertebral disk, have received much attention related to their capacities for osmotic swelling. To understand residual stress and osmotic swelling in the PDL, it must be asked (1) to what extent, if any, does the PDL exhibit residual stress and osmotic swelling, and (2) if so, whether residual stress and osmotic swelling are mechanically significant to the PDL's stress/strain behavior under external loading. Here, we incrementally built a series of computer models that were fit to uniaxial loading, osmotic swelling and residual stretch data. The models were validated with in vitro shear tests and in vivo tooth-tipping data. Residual stress and osmotic swelling models were used to analyze tension and compression stress (principal stress) effects in PDL specimens under external loads. Shear-to-failure experiments under osmotic conditions were performed and modeled to determine differences in mechanics and failure of swollen periodontal ligament. Significantly higher failure shear stresses in swollen PDL suggested that osmotic swelling reduced tension and thus had a strengthening effect. The in vivo model's first and third principal stresses were both higher with residual stress and osmotic swelling, but smooth stress gradients prevailed throughout the three-dimensional PDL anatomy. The addition of PDL stresses from residual stress and osmotic swelling represents a unique concept in dental biomechanics.

Through-thickness regional variation in the mechanical characteristics of the lumbar facet capsular ligament.

The human lumbar facet capsule, with the facet capsular ligament (FCL) that forms its primary constituent, is a common source of lower back pain. Prior studies on the FCL were limited to in-plane tissue behavior, but due to the presence of two distinct yet mechanically different regions, a novel out-of-plane study was conducted to further characterize the roles of the collagen and elastin regions. An experimental technique, called stretch-and-bend, was developed to study the tension-compression asymmetry of the FCL due to varying collagen fiber density throughout the thickness of the tissue. Each healthy excised cadaveric FCL sample was tested in four conditions depending on primary collagen fiber alignment and regional loading. Our results indicate that the FCL is stiffest when the collagen fibers (1) are aligned in the direction of loading, (2) are in tension, and (3) are stretched - 16% from its off-the-bone, undeformed state. An optimization routine was used to fit a four-parameter anisotropic, hyperplastic model to the experimental data. The average elastin modulus, E, and the average collagen fiber modulus, ξ, were 13.15 ± 3.59 kPa and 18.68 ± 13.71 MPa (95% CI), respectively.