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

Continuum Growth Mechanics: Reconciling Two Common Frameworks

The objective of this study was to investigate whether the two most common growth mechanics modeling frameworks, the constrained-mixture growth model and the kinematic growth model, could be reconciled mathematically. The purpose of this effort was to provide practical guidelines for potential users of these modeling frameworks. Results showed that the kinematic growth model is mathematically consistent with a special form of the constrained-mixture growth model, where only one generation of a growing solid exists at any given time, overturning its entire solid mass at each instant of growth in order to adopt the reference configuration dictated by the growth deformation. The thermodynamics of the kinematic growth model, along with the specialized constrained-mixture growth model, requires a cellular supply of chemical energy to allow deposition of solid mass under a stressed state. A back-of-the-envelope calculation shows that the amount of chemical energy required to sustain biological growth under these models is negligibly small, when compared to the amount of energy normally consumed daily by the human body. In conclusion, this study successfully reconciled the two most popular growth theories for biological growth and explained the special circumstances under which the constrained-mixture growth model reduces to the kinematic growth model.

Can lateral tenodesis improve the rotational stability of the ACL reconstruction? A finite element analysis

One of the most common knee injuries is the Anterior Cruciate Ligament (ACL) rupture with severe implications on knee stability. The usual treatment is the ACL Reconstruction (ACLR) surgery where the surgeon replaces the torn ligament with a graft in an effort to restore knee kinematics. In case of excessive rotatory instability, Lateral Extra-Articular Tenodesis (LET) can be performed in combination with ACLR. Additionally, LET appears to reduce ACLR graft forces minimizing graft failure chances. However, there are concerns about overconstraining physiological rotation. To gain insight in this controversial topic, we developed an automatic, open-source tool to create a series of Finite Element (FE) models attempting to investigate the interactions of ACLR and LET through simulation. We started by creating a validated model of the healthy knee joint that served as reference for subsequent FE simulations. Then, we created FE models of standalone ACLR and combined ACLR-LET. Each model was assessed by applying a loading profile that resembles the reduction phase of the Pivot-Shift clinical exam. We measured the External Tibia Rotation (ETR), the Posterior Tibia Translation (PTT) of the lateral tibial compartment, and the ACLR graft stress developed around the femoral tunnel insertion site. We observed the following: a) LET reduces ETR and PTT compared to isolated ACLR, b) combined ACLR-LET is more sensitive to LET graft pretension with lower values showcasing performance closer to the healthy joint, c) LET reduces ACLR graft forces for the same pretension values, d) LET exhibits significant overconstraint for higher pretension values. In general, these findings are in agreement with relevant clinical studies and accentuate the potential of the developed framework as a tool that can assist orthopaedists during surgery planning. We provide open access for the FE models of this study to enhance research transparency, reproducibility and extensibility.

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

Knee instability caused by altered graft mechanical properties after anterior cruciate ligament reconstruction: the early onset of osteoarthritis?

Anterior cruciate ligament (ACL) rupture is a very common knee joint injury. Torn ACLs are currently reconstructed using tendon autografts. However, half of the patients develop osteoarthritis (OA) within 10 to 14 years postoperatively. Proposedly, this is caused by altered knee kine(ma)tics originating from changes in graft mechanical properties during the in vivo remodeling response. Therefore, the main aim was to use subject-specific finite element knee models and investigate the influence of decreasing graft stiffness and/or increasing graft laxity on knee kine(ma)tics and cartilage loading. In this research, 4 subject-specific knee geometries were used, and the material properties of the ACL were altered to either match currently used grafts or mimic in vivo graft remodeling, i.e., decreasing graft stiffness and/or increasing graft laxity. The results confirm that the in vivo graft remodeling process increases the knee range of motion, up to >300 percent, and relocates the cartilage contact pressures, up to 4.3 mm. The effect of remodeling-induced graft mechanical properties on knee stability exceeded that of graft mechanical properties at the time of surgery. This indicates that altered mechanical properties of ACL grafts, caused by in vivo remodeling, can initiate the early onset of osteoarthritis, as observed in many patients clinically.

Strain estimation in aortic roots from 4D echocardiographic images using medial modeling and deformable registration

Even though the central role of mechanics in the cardiovascular system is widely recognized, estimating mechanical deformation and strains in-vivo remains an ongoing practical challenge. Herein, we present a semi-automated framework to estimate strains from four-dimensional (4D) echocardiographic images and apply it to the aortic roots of patients with normal trileaflet aortic valves (TAV) and congenital bicuspid aortic valves (BAV). The method is based on fully nonlinear shell-based kinematics, which divides the strains into in-plane (shear and dilatational) and out-of-plane components. The results indicate that, even for size-matched non-aneurysmal aortic roots, BAV patients experience larger regional shear strains in their aortic roots. This elevated strains might be a contributing factor to the higher risk of aneurysm development in BAV patients. The proposed framework is openly available and applicable to any tubular structures.

Validation of a Finite Element Simulation for Predicting Individual Knee Joint Kinematics

Goal: We introduce an in-vivo validated finite element (FE) simulation approach for predicting individual knee joint kinematics. Our vision is to improve clinicians' understanding of the complex individual anatomy and potential pathologies to improve treatment and restore physiological joint kinematics. Methods: Our 3D FE modeling approach for individual human knee joints is based on segmentation of anatomical structures extracted from routine static magnetic resonance (MR) images. We validate the predictive abilities of our model using static MR images of the knees of eleven healthy volunteers in dedicated knee poses, which are achieved using a customized MR-compatible pneumatic loading device. Results: Our FE simulations reach an average translational accuracy of 2 mm and an average angular accuracy of 1[Formula: see text] compared to the reference knee pose. Conclusions: Reaching high accuracy, our individual FE model can be used in the decision-making process to restore knee joint stability and functionality after various knee injuries.

Open Knee(s): A Free and Open Source Library of Specimen-Specific Models and Related Digital Assets for Finite Element Analysis of the Knee Joint

There is a growing interest in the use of virtual representations of the knee for musculoskeletal research and clinical decision making, and to generate digital evidence for design and regulation of implants. Accessibility to previously developed models and related digital assets can dramatically reduce barriers to entry to conduct simulation-based studies of the knee joint and therefore help accelerate scientific discovery and clinical innovations. Development of models for finite element analysis is a demanding process that is both time consuming and resource intensive. It necessitates expertise to transform raw data to reliable virtual representations. Modeling and simulation workflow has many processes such as image segmentation, surface geometry generation, mesh generation and finally, creation of a finite element representation with relevant loading and boundary conditions. The outcome of the workflow is not only the end-point knee model but also many other digital by-products. When all of these data, derivate assets, and tools are freely and openly accessible, researchers can bypass some or all the steps required to build models and focus on using them to address their research goals. With provenance to specimen-specific anatomical and mechanical data and traceability of digital assets throughout the whole lifecycle of the model, reproducibility and credibility of the modeling practice can be established. The objective of this study is to disseminate Open Knee(s), a cohort of eight knee models (and relevant digital assets) for finite element analysis, that are based on comprehensive specimen-specific imaging data. In addition, the models and by-products of modeling workflows are described along with model development strategies and tools. Passive flexion served as a test simulation case, demonstrating an end-user application. Potential roadmaps for reuse of Open Knee(s) are also discussed.

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.

Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.

Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases

Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Arbitrary Prestrain Values for Ligaments Cause Numerical Issues in a Multibody Model of an Ankle Joint

Experimental studies report that ligaments of the ankle joint are prestrained. The prestrain is an important aspect of modern biomechanical analysis, which can be included in the models by: applying symmetrical, arbitrary prestrains to the ligaments, assuming a strain-free location for the joint or by using experimental prestrain data. The aim of the study was to comparatively analyze these approaches. In total, 4 prestraining methods were considered. In order to do so, a symmetrical model of the ankle with six nonlinear cables and two sphere–sphere contact pairs was assumed. The model was solved in statics under moment loads up to 5 Nm. The obtained results showed that the arbitrary prestrains caused an unbalanced load for the model at rest, and in turn modified its rest location in an unpredictable way. Due to the imbalance, it was impossible to enforce the assumed prestrains and thus cartilage prestrain was required to stabilize the model. The prestraining had a significant effect on the angular displacements and the load state of the model. The findings suggest that the prestrain values are patient specific and arbitrary prestrains will not be valid for most models.

About prestretch in homogenized constrained mixture models simulating growth and remodeling in patient-specific aortic geometries

Evolution of mechanical and structural properties in the Ascending Thoracic Aorta (ATA) is the results of complex mechanobiological processes. In this work, we address some numerical challenges in order to elaborate computational models of these processes. For that, we extend the state of the art of homogenized constrained mixture (hCM) models. In these models, prestretches are assigned to the mixed constituents in order to ensure local mechanical equilibrium macroscopically, and to maintain a homeostatic level of tension in collagen fibers microscopically. Although the initial prestretches were assumed as homogeneous in idealized straight tubes, more elaborate prestretch distributions need to be considered for curved geometrical models such as patient-specific ATA. Therefore, we introduce prestretches having a three-dimensional gradient across the ATA geometry in the homeostatic reference state. We test different schemes with the objective to ensure stable growth and remodeling (G&R) simulations on patient-specific curved vessels. In these simulations, aneurysm progression is triggered by tissue changes in the constituents such as mass degradation of intramural elastin. The results show that the initial prestretches are not only critical for the stability of numerical simulations, but they also affect the G&R response. Eventually, we submit that initial conditions required for G&R simulations need to be identified regionally for ensuring realistic patient-specific predictions of aneurysm progression.

Simulation-based reasoning of residual tissue deformations in a two-chamber test of a lymphedematous leg

A two-chamber inflation-deflation test was recently proposed as a diagnostic method to determine parameters of the intermittent pneumatic compression used as an effective therapeutic modality for lymphedematous limbs. It is crucial that the recorded trends for residual tissue deformations are understood in terms of specific properties of subcutaneous tissue and skin to support diagnostic process. This paper presents a mechanical model of lymphedematous legs in two-chamber tests. The cylindrical geometry composed of layers of skin, modeled as hyperelastic medium, and subcutaneous tissue, modeled as fluid saturated hyperporoelastic medium, is assumed. The results of finite element simulations show the possibility of such combinations of the properties of skin (rigidity) and subcutaneous tissue (rigidity and permeability), which ensures that the model predictions resemble the evolution of tissue residual deformations observed in the two-chamber test. The stiffness and permeability appeared to be the most crucial tissue property determining trend lines of residual deformations. The analysis of the components of displacement of solid matrix and pore fluid pressure explains the mechanisms that are responsible for particular tissue behavior. The moderate role of skin and limitations related to the mechanical and geometrical model assumptions are indicated. Recommendations for treating lymphedema using intermittent compression therapy in relation to the results of the two-chamber test and properties of tissues are discussed.

Toward Elucidating the Physiological Impacts of Residual Stresses in the Colorectum

Irritable bowel syndrome afflicts 10-20% of the global population, causing visceral pain with increased sensitivity to colorectal distension and normal bowel movements. Understanding and predicting these biomechanics will further advance our understanding of visceral pain and complement the existing literature on visceral neurophysiology. We recently performed a series of experiments at three longitudinal segments (colonic, intermediate, and rectal) of the distal 30 mm of colorectums of mice. We also established and fitted constitutive models addressing mechanical heterogeneity in both the through-thickness and longitudinal directions of the colorectum. Afferent nerve endings, strategically located within the submucosa, are likely nociceptors that detect concentrations of mechanical stresses to evoke the perception of pain from the viscera. In this study, we aim to: (1) establish and validate a method for incorporating residual stresses into models of colorectums, (2) predict the effects of residual stresses on the intratissue mechanics within the colorectum, and (3) establish intratissue distributions of stretches and stresses within the colorectum in vivo. To these ends we developed two-layered, composite finite element models of the colorectum based on our experimental evidence and validated our approaches against independent experimental data. We included layer- and segment-specific residual stretches/stresses in our simulations via the prestrain algorithm built into the finite element software febio. Our models and modeling approaches allow researchers to predict both organ and intratissue biomechanics of the colorectum and may facilitate better understanding of the underlying mechanical mechanisms of visceral pain.

Mechanical characterisation of the human dura mater, falx cerebri and superior sagittal sinus

The cranial meninges have been shown to play a pivotal role in traumatic brain injury mechanopathology. However, while the mechanical response of the brain and its many subregions have been studied extensively, the meninges have conventionally been overlooked. This paper presents the first comparative mechanical analysis of human dura mater, falx cerebri and superior sagittal sinus tissues. Biaxial tensile analysis identified that these tissues are mechanically heterogeneous, in contrast to the assumption that the tissues are mechanically homogeneous which is typically employed in FE model design. A thickness of 0.91 ± 0.05 (standard error) mm for the falx cerebri was also identified. This data can aid in improving the biofidelity of the influential falx structure in FE models. Additionally, the use of a collagen hybridizing peptide on the superior sagittal sinus suggests this structure is particularly susceptible to the effects of circumferential stretch, which may have important implications for clinical treatment of dural venous sinus pathologies. Collectively, this research progresses understanding of meningeal mechanical and structural characteristics and may aid in elucidating the behaviour of these tissues in healthy and diseased conditions. STATEMENT OF SIGNIFICANCE: This study presents the first evaluation of human falx cerebri and superior sagittal sinus mechanical, geometrical and structural properties, along with a comparison to cranial dura mater. To mechanically characterise the tissues, biaxial tensile testing is conducted on the tissues. This analysis identifies, for the first time, mechanical stiffness differences between these tissues. Additionally, geometrical analysis identifies that there are thickness differences between the tissues. The evaluation of human meningeal tissues allows for direct implementation of the novel data to finite element head injury models to enable improved biofidelity of these influential structures in traumatic brain injury simulations. This work also identifies that the superior sagittal sinus may be easily damaged during clinical angioplasty procedures, which may inform the treatment of dural sinus pathologies.

A computational model of glioma reveals opposing, stiffness-sensitive effects of leaky vasculature and tumor growth on tissue mechanical stress and porosity

A biphasic computational model of a growing, vascularized glioma within brain tissue was developed to account for unique features of gliomas, including soft surrounding brain tissue, their low stiffness relative to brain tissue, and a lack of draining lymphatics. This model is the first to couple nonlinear tissue deformation with porosity and tissue hydraulic conductivity to study the mechanical interaction of leaky vasculature and solid growth in an embedded glioma. The present model showed that leaky vasculature and elevated interstitial fluid pressure produce tensile stress within the tumor in opposition to the compressive stress produced by tumor growth. This tensile effect was more pronounced in softer tissue and resulted in a compressive stress concentration at the tumor rim that increased when tumor was softer than host. Aside from generating solid stress, fluid pressure-driven tissue deformation decreased the effective stiffness of the tumor while growth increased it, potentially leading to elevated stiffness in the tumor rim. A novel prediction of reduced porosity at the tumor rim was corroborated by direct comparison with estimates from our in vivo imaging studies. Antiangiogenic and radiation therapy were simulated by varying vascular leakiness and tissue hydraulic conductivity. These led to greater solid compression and interstitial pressure in the tumor, respectively, the former of which may promote tumor infiltration of the host. Our findings suggest that vascular leakiness has an important influence on in vivo solid stress, stiffness, and porosity fields in gliomas given their unique mechanical microenvironment.

Mechanical Properties of the Cranial Meninges: A Systematic Review

The meninges are membranous tissues that are pivotal in maintaining homeostasis of the central nervous system. Despite the importance of the cranial meninges in nervous system physiology and in head injury mechanics, our knowledge of the tissues' mechanical behavior and structural composition is limited. This systematic review analyzes the existing literature on the mechanical properties of the meningeal tissues. Publications were identified from a search of Scopus, Academic Search Complete, and Web of Science and screened for eligibility according to Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. The review details the wide range of testing techniques employed to date and the significant variability in the observed experimental findings. Our findings identify many gaps in the current literature that can serve as a guide for future work for meningeal mechanics investigators. The review identifies no peer-reviewed mechanical data on the falx and tentorium tissues, both of which have been identified as key structures in influencing brain injury mechanics. A dearth of mechanical data for the pia-arachnoid complex also was identified (no experimental mechanics studies on the human pia-arachnoid complex were identified), which is desirable for biofidelic modeling of human head injuries. Finally, this review provides recommendations on how experiments can be conducted to allow for standardization of test methodologies, enabling simplified comparisons and conclusions on meningeal mechanics.

The Macro- and Micro-Mechanics of the Colon and Rectum II: Theoretical and Computational Methods

Abnormal colorectal biomechanics and mechanotransduction associate with an array of gastrointestinal diseases, including inflammatory bowel disease, irritable bowel syndrome, diverticula disease, anorectal disorders, ileus, and chronic constipation. Visceral pain, principally evoked from mechanical distension, has a unique biomechanical component that plays a critical role in mechanotransduction, the process of encoding mechanical stimuli to the colorectum by sensory afferents. To fully understand the underlying mechanisms of visceral mechanical neural encoding demands focused attention on the macro- and micro-mechanics of colon tissue. Motivated by biomechanical experiments on the colon and rectum, increasing efforts focus on developing constitutive frameworks to interpret and predict the anisotropic and nonlinear biomechanical behaviors of the multilayered colorectum. We will review the current literature on computational modeling of the colon and rectum as well as the mechanical neural encoding by stretch sensitive afferent endings, and then highlight our recent advances in these areas. Current models provide insight into organ- and tissue-level biomechanics as well as the stretch-sensitive afferent endings of colorectal tissues yet an important challenge in modeling theory remains. The research community has not connected the biomechanical models to those of mechanosensitive nerve endings to create a cohesive multiscale framework for predicting mechanotransduction from organ-level biomechanics.

A backward pre-stressing algorithm for efficient finite element implementation of in vivo material and geometrical parameters into fibril-reinforced mixture models of articular cartilage

Classical continuum mechanics has been widely used for implementation of the material models of articular cartilage (AC) mainly with the aid of the finite element (FE) method, which, in many cases, considers the stress-free configuration as the initial configuration. On the contrary, the AC experimental tests typically begin with the pre-stressed state of both material and geometrical properties. Indeed, imposing the initial pre-stress onto AC models with the in vivo values as the initial state would result in nonphysiologically expansion of the FE mesh due to the soft nature of AC. This change in the model configuration can also affect the material behavior kinematically in the mixture models of cartilage due to the intrinsic compressibility of the tissue. Although several different fixed-point backward algorithms, as the most straightforward pre-stressing methods, have already been developed to incorporate these initial conditions into FE models iteratively, such methods focused merely on the geometrical parameters, and they omitted the material variations of the anisotropic mixture models of AC. To address this issue, we propose an efficient algorithm generalizing the backward schemes to restore stress-free conditions by optimizing both the involving variables, and we hypothesize that it can affect the results considerably. To this end, a comparative simulation was implemented on an advanced and validated multiphasic model by the new and conventional algorithms. The results are in support of the hypothesis, as in our illustrative general AC model, the material parameters experienced a maximum error of 16% comparing to the initial in vivo data when the older algorithm was employed, and it led to a maximum variation of 44% in the recorded stresses comparing to the results of the new method. We conclude that our methodology enhanced the model fidelity, and it is applicable in most of the existing FE solvers for future mixture studies with accurate stress distributions.

Computational frame of ligament in situ strain in a full knee model

The biomechanical function of connective tissues in a knee joint is to stabilize the kinematics-kinetics of the joint by augmenting its stiffness and limiting excessive coupled motion. The connective tissues are characterized by an in vivo reference configuration (in situ strain) that would significantly contribute to the mechanical response of the knee joint. In this work, a novel iterative method for computing the in situ strain at reference configuration was presented. The framework used an in situ strain gradient approach (deformed reference configuration) and a detailed finite element (FE) model of the knee joint. The effect of the predicted initial configuration on the mechanical response of the joint was then investigated under joint axial compression, passive flexion, and coupled rotations (adduction and internal), and during the stance phase of gait. The inclusion of the reference configuration has a minimal effect on the knee joint mechanics under axial compression, passive flexion, and at two instances (0% and 50%) of the stance phase of gait. However, the presence of the ligaments in situ strains significantly increased the joint stiffness under passive adduction and internal rotations, as well as during the other simulated instances (25%, 75% and 100%) of the stance phase of gait. Also, these parameters substantially altered the local loading state of the ligaments and resulted in better agreement with the literature during joint flexion. Therefore, the proposed computational framework of ligament in situ strain will help to overcome the challenges in considering this crucial biological aspect during knee joint modeling. Besides, the current construct is advantageous for a better understanding of the mechanical behavior of knee ligaments under physiological and pathological states and provide relevant information in the design of reconstructive treatments and artificial grafts.

Mapping cellular-scale internal mechanics in 3D tissues with thermally responsive hydrogel probes

Local tissue mechanics play a critical role in cell function, but measuring these properties at cellular length scales in living 3D tissues can present considerable challenges. Here we present thermoresponsive, smart material microgels that can be dispersed or injected into tissues and optically assayed to measure residual tissue elasticity after creep over several weeks. We first develop and characterize the sensors, and demonstrate that internal mechanical profiles of live multicellular spheroids can be mapped at high resolutions to reveal broad ranges of rigidity within the tissues, which vary with subtle differences in spheroid aggregation method. We then show that small sites of unexpectedly high rigidity develop in invasive breast cancer spheroids, and in an in vivo mouse model of breast cancer progression. These focal sites of increased intratumoral rigidity suggest new possibilities for how early mechanical cues that drive cancer cells towards invasion might arise within the evolving tumor microenvironment.

Estimation of joint contact pressure in the index finger using a hybrid finite element musculoskeletal approach

The knowledge of local stress distribution in hand joints is crucial to understand injuries and osteoarthritis occurrence. However, determining cartilage contact stresses remains a challenge, requiring numerical models including both accurate anatomical components and realistic tendon force actuation. Contact forces in finger joints have frequently been calculated but little data is available on joint contact pressures. This study aimed to develop and assess a hybrid biomechanical model of the index finger to estimate in-vivo joint contact pressure during a static maximal strength pinch grip task. A finite element model including bones, cartilage, tendons, and ligaments was developed, with tendon force transmission based on a tendon-pulley system. This model was driven by realistic tendon forces estimated from a musculoskeletal model and motion capture data for six subjects. The hybrid model outputs agreed well with the experimental measurement of fingertip forces and literature data on the physiological distribution of tendon forces through the index finger. Mean contact pressures were 6.9 ± 2.7 MPa, 6.2 ± 1.0 MPa and 7.2 ± 1.3 MPa for distal, proximal interphalangeal and metacarpophalangeal joints, respectively. Two subjects had higher mean contact pressure in the distal joint than in the other two joints, suggesting a mechanical cause for the prevalence of osteoarthritis in the index distal joint. The inter-subject variability in joint contact pressure could be explained by different neuromuscular strategies employed for the task. This first application of an effective hybrid model to the index finger is promising for estimating hand joint stresses under daily grip tasks and simulating surgical procedures.

In vivo estimation of optic nerve sheath stiffness using noninvasive MRI measurements and finite element modeling

The optic nerve sheath (ONS) is biomechanically important. It is acted on by tension due to ocular movements, and by fluid shifts and/or alterations in intracranial pressure (ICP) in human disease, specifically in pathologies leading to intracranial hypertension. It has also been hypothesized that the ONS is acted on by altered ICP in astronauts exposed chronically to microgravity. However, a non-invasive method to quantify ONS biomechanical properties is not presently available; knowledge of such properties is desirable to allow characterization of the biomechanical forces exerted on the optic nerve head and other ocular structures due to the ONS. Thus, the primary objective of this study was to characterize the biomechanical properties (stiffness) of the human ONS in vivo as a necessary step towards investigating the role of ICP in various conditions, including Spaceflight Associated Neuro-ocular Syndrome (SANS). We acquired non-invasive magnetic resonance imaging (MRI) scans of ostensibly healthy subjects (n = 18, age = 30.4 ± 11.6 [mean ± SD] years) during supine and 15-degree head-down-tilt (HDT) postures, and extracted ONS contours from these scans. We then used finite element modeling to quantify ONS expansion due to postural changes and an inverse approach to estimate ONS stiffness. Using this non-invasive procedure, we estimated an in vivo ONS stiffness of 39.2 ± 21.9 kPa (mean ± SD), although a small subset of individuals had very stiff ONS that precluded accurate estimates of their stiffness values. ONS stiffness was not correlated with age and was higher in males than females.

A comparative study of methods used to generate the arterial fiber structure in a clinically relevant numerical analysis

The advanced constitutive material models of artery wall require the definition of the mean collagen fiber directions in the material configuration. There are several proposed methods; however, it is unclear how much does the fiber structures obtained by these methods differ one from the other and how much this difference may affect the results of the structural analysis of a clinically relevant scenario. Therefore, in this paper, we address this issue by presenting the results of the comparative study of our developed and currently state-of-the-art fiber definition methods. In addition, we present the verification of our developed numerical model that incorporates the extended Holzapfel-Gasser-Ogden (HGO) constitutive material model and the generalized prestressing algorithm (GPA). In the case of the patient-specific internal carotid artery (ICA), the percentage error of the mean fiber directions defined by different methods does not exceed 17.73% (at least 0.05%, at most 81.82%) and has negligible effect on the stress levels, as the percentage error of the mean circumferential Cauchy stress does not exceed 0.1%. Both fiber definition methods produce comparable fiber structure, but our proposed method has an advantage, as it does not depend on method and software used to model the arterial wall mechanics.

A Formulation for Fluid Structure-Interactions in FEBio Using Mixture Theory

Many physiological systems involve strong interactions between fluids and solids, posing a signicant challenge when modeling biomechanics. The objective of this study was to implement a fluid-structure interaction (FSI) solver in the free, open-source finite element code FEBio (febio.org), that combined the existing solid mechanics and rigid body dynamics solver with a recently-developed computational fluid dynamics (CFD) solver. A novel Galerkin-based finite element FSI formulation was introduced based on mixture theory, where the FSI domain was described as a mixture of fluid and solid constituents that have distinct motions. The mesh was defined on the solid domain, specialized to have zero mass, negligible stiffness and zero frictional interactions with the fluid, whereas the fluid was modeled as isothermal and compressible. The mixture framework provided the foundation for evaluating material time derivatives in a material frame for the solid and in a spatial frame for the fluid. Similar to our recently reported CFD solver, our FSI formulation did not require stabilization methods to achieve good convergence, producing a compact set of equations and code implementation. The code was successfully verified against benchmark problems and an analytical solution for squeeze-film lubrication. It was validated against experimental measurements of the flow rate in a peristaltic pump, and illustrated using non-Newtonian blood flow through a bifurcated carotid artery with a thick arterial wall. The successful formulation and implementation of this FSI solver enhances the multiphysics modeling capabilities in FEBio relevant to the biomechanics and biophysics communities.

A Plugin Framework for Extending the Simulation Capabilities of FEBio

The FEBio software suite is a set of software tools for nonlinear finite element analysis in biomechanics and biophysics. FEBio employs mixture theory to account for the multiconstituent nature of biological materials, integrating the field equations for irreversible thermodynamics, solid mechanics, fluid mechanics, mass transport with reactive species, and electrokinetics. This communication describes the development and application of a new "plugin" framework for FEBio. Plugins are dynamically linked libraries that allow users to add new features and to couple FEBio with other domain-specific software applications without modifying the source code directly. The governing equations and simulation capabilities of FEBio are reviewed. The implementation, structure, use, and application of the plugin framework are detailed. Several example plugins are described in detail to illustrate how plugins enrich, extend, and leverage existing capabilities in FEBio, including applications to deformable image registration, constitutive modeling of biological tissues, coupling to an external software package that simulates angiogenesis using a discrete computational model, and a nonlinear reaction-diffusion solver. The plugin feature facilitates dissemination of new simulation methods, reproduction of published results, and coupling of FEBio with other domain-specific simulation approaches such as compartmental modeling, agent-based modeling, and rigid-body dynamics. We anticipate that the new plugin framework will greatly expand the range of applications for the FEBio software suite and thus its impact.

On incorporating osmotic prestretch/prestress in image-driven finite element simulations of cartilage

Medical imaging performed in vivo captures geometries under Donnan osmotic loading, even when the articulating joint is otherwise mechanically unloaded. Hence patient-specific finite element (FE) models constructed from such medical images of cartilage represent osmotically induced prestretched/prestressed states. When applying classical modeling approaches to patient-specific simulations of cartilage a theoretical inconsistency arises: the in-vivo imaged geometry (used to construct the model) is not an unloaded, stress-free reference configuration. Furthermore when fitting nonlinear constitutive models that include osmotic swelling (to obtain material parameters), if one assumes that experimental data-generated from osmotically loaded cartilage-begin from a stress-free reference configuration the fitted stress-stretch relationship (parameters) obtained will actually describe a different behavior. In this study we: (1) establish a practical computational method to include osmotically induced prestretch/prestress in image-driven simulations of cartilage; and (2) investigate the influence of considering the prestretched/prestressed state both when fitting fiber-reinforced, biphasic constitutive models of cartilage that include osmotic swelling and when simulating cartilage responses. Our results highlight the importance of determining the prestretched/prestressed state within cartilage induced by osmotic loading in the imaged configuration prior to solving boundary value problems of interest. With our new constitutive model and modeling methods, we aim to improve the fidelity of FE-based, patient-specific biomechanical simulations of joints and cartilage. Improved simulations can provide medical researchers with new information often unavailable in a clinical setting, information that may contribute to better insight into the pathophysiology of cartilage diseases.

A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta

Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs.

Computational predictions of damage propagation preceding dissection of ascending thoracic aortic aneurysms

Dissections of ascending thoracic aortic aneurysms (ATAAs) cause significant morbidity and mortality worldwide. They occur when a tear in the intima-media of the aorta permits the penetration of the blood and the subsequent delamination and separation of the wall in 2 layers, forming a false channel. To predict computationally the risk of tear formation, stress analyses should be performed layer-specifically and they should consider internal or residual stresses that exist in the tissue. In the present paper, we propose a novel layer-specific damage model based on the constrained mixture theory, which intrinsically takes into account these internal stresses and can predict appropriately the tear formation. The model is implemented in finite-element commercial software Abaqus coupled with user material subroutine. Its capability is tested by applying it to the simulation of different exemplary situations, going from in vitro bulge inflation experiments on aortic samples to in vivo overpressurizing of patient-specific ATAAs. The simulations reveal that damage correctly starts from the intimal layer (luminal side) and propagates across the media as a tear but never hits the adventitia. This scenario is typically the first stage of development of an acute dissection, which is predicted for pressures of about 2.5 times the diastolic pressure by the model after calibrating the parameters against experimental data performed on collected ATAA samples. Further validations on a larger cohort of patients should hopefully confirm the potential of the model in predicting patient-specific damage evolution and possible risk of dissection during aneurysm growth for clinical applications.

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.

An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling

Continued advances in computational power and methods have enabled image-based biomechanical modeling to become an important tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is identification of a stress-free reference configuration based on in vivo images of loaded and often prestrained or residually stressed soft tissues and organs. Fortunately, iterative methods have been proposed to solve this inverse problem, among them Sellier's method. This method is particularly appealing because it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. By means of several practical examples, however, we demonstrate that in its original formulation Sellier's method is not optimally fast and may not converge for problems with large deformations. Fortunately, we can also show that a simple, inexpensive augmentation of Sellier's method based on Aitken's delta-squared process can not only ensure convergence but also significantly accelerate the method.