A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

Alteration in cartilage matrix stiffness as an indicator and modulator of osteoarthritis

Osteoarthritis (OA) is characterized by cartilage degeneration and destruction, leading to joint ankylosis and disability. The major challenge in diagnosing OA at early stage is not only lack of clinical symptoms but also the insufficient histological and immunohistochemical signs. Alteration in cartilage stiffness during OA progression, especially at OA initiation, has been confirmed by growing evidences. Moreover, the stiffness of cartilage extracellular matrix (ECM), pericellular matrix (PCM) and chondrocytes during OA development are dynamically changed in unique and distinct fashions, revealing possibly inconsistent conclusions when detecting cartilage matrix stiffness at different locations and scales. In addition, it will be discussed regarding the mechanisms through which OA-related cartilage degenerations exhibit stiffened or softened matrix, highlighting some critical events that generally incurred to cartilage stiffness alteration, as well as some typical molecules that participated in constituting the mechanical properties of cartilage. Finally, in vitro culturing chondrocytes in various stiffness-tunable scaffolds provided a reliable method to explore the matrix stiffness-dependent modulation of chondrocyte metabolism, which offers valuable information on optimizing implant scaffolds to maximally promote cartilage repair and regeneration during OA. Overall, this review systematically and comprehensively elucidated the current progresses in the relationship between cartilage stiffness alteration and OA progression. We hope that deeper attention and understanding in this researching field will not only develop more innovative methods in OA early detection and diagnose but also provide promising ideas in OA therapy and prognosis.

A Fast, Robust Method for Quantitative Assessment of Collagen Fibril Architecture from Transmission Electron Micrographs

Collagen is the most abundant protein in mammals; it exhibits a hierarchical organization and provides structural support to a wide range of soft tissues, including blood vessels. The architecture of collagen fibrils dictates vascular stiffness and strength, and changes therein can contribute to disease progression. While transmission electron microscopy (TEM) is routinely used to examine collagen fibrils under normal and pathological conditions, computational tools that enable fast and minimally subjective quantitative assessment remain lacking. In the present study, we describe a novel semi-automated image processing and statistical modeling pipeline for segmenting individual collagen fibrils from TEM images and quantifying key metrics of interest, including fibril cross-sectional area and aspect ratio. For validation, we show first-of-their-kind illustrative results for adventitial collagen in the thoracic aorta from three different mouse models.

A novel knee joint model in FEBio with inhomogeneous fibril-reinforced biphasic cartilage simulating tissue mechanical responses during gait: data from the osteoarthritis initiative

We developed a novel knee joint model in FEBio to simulate walking. Knee cartilage was modeled using a fibril-reinforced biphasic (FRB) formulation with depth-wise collagen architecture and split-lines to account for cartilage structure. Under axial compression, the knee model with FRB cartilage yielded contact pressures, similar to reported experimental data. Furthermore, gait analysis with FRB cartilage simulated spatial and temporal trends in cartilage fluid pressures, stresses, and strains, comparable to those of a fibril-reinforced poroviscoelastic (FRPVE) material in Abaqus. This knee joint model in FEBio could be used for further studies of knee disorders using physiologically relevant loading.

Computational assessment on the impact of collagen fiber orientation in cartilages on healthy and arthritic knee kinetics/kinematics

BACKGROUND

The inhomogeneous distribution of collagen fiber in cartilage can substantially influence the knee kinematics. This becomes vital for understanding the mechanical response of soft tissues, and cartilage deterioration including osteoarthritis (OA). Though the conventional computational models consider geometrical heterogeneity along with fiber reinforcements in the cartilage model as material heterogeneity, the influence of fiber orientation on knee kinetics and kinematics is not fully explored. This work examines how the collagen fiber orientation in the cartilage affects the healthy (intact knee) and arthritic knee response over multiple gait activities like running and walking.

METHODS

A 3D finite element knee joint model is used to compute the articular cartilage response during the gait cycle. A fiber-reinforced porous hyper elastic (FRPHE) material is used to model the soft tissue. A split-line pattern is used to implement the fiber orientation in femoral and tibial cartilage. Four distinct intact cartilage models and three OA models are simulated to assess the impact of the orientation of collagen fibers in a depth wise direction. The cartilage models with fibers oriented in parallel, perpendicular, and inclined to the articular surface are investigated for multiple knee kinematics and kinetics.

FINDINGS

The comparison of models with fiber orientation parallel to articulating surface for walking and running gait has the highest elastic stress and fluid pressure compared with inclined and perpendicular fiber-oriented models. Also, the maximum contact pressure is observed to be higher in the case of intact models during the walking cycle than for OA models. In contrast, the maximum contact pressure is higher during running in OA models than in intact models. Additionally, parallel-oriented models produce higher maximum stresses and fluid pressure for walking and running gait than proximal-distal-oriented models. Interestingly, during the walking cycle, the maximum contact pressure with intact models is approximately three times higher than on OA models. In contrast, the OA models exhibit higher contact pressure during the running cycle.

INTERPRETATION

Overall, the study indicates that collagen orientation is crucial for tissue responsiveness. This investigation provides insights into the development of tailored implants.

Magnetic resonance imaging assessments for knee segmentation and their use in combination with machine/deep learning as predictors of early osteoarthritis diagnosis and prognosis

Knee osteoarthritis (OA) is a prevalent and disabling disease that can develop over decades. This disease is heterogeneous and involves structural changes in the whole joint, encompassing multiple tissue types. Detecting OA before the onset of irreversible changes is crucial for early management, and this could be achieved by allowing knee tissue visualization and quantifying their changes over time. Although some imaging modalities are available for knee structure assessment, magnetic resonance imaging (MRI) is preferred. This narrative review looks at existing literature, first on MRI-developed approaches for evaluating knee articular tissues, and second on prediction using machine/deep-learning-based methodologies and MRI as input or outcome for early OA diagnosis and prognosis. A substantial number of MRI methodologies have been developed to assess several knee tissues in a semi-quantitative and quantitative fashion using manual, semi-automated and fully automated systems. This dynamic field has grown substantially since the advent of machine/deep learning. Another active area is predictive modelling using machine/deep-learning methodologies enabling robust early OA diagnosis/prognosis. Moreover, incorporating MRI markers as input/outcome in such predictive models is important for a more accurate OA structural diagnosis/prognosis. The main limitation of their usage is the ability to move them in rheumatology practice. In conclusion, MRI knee tissue determination and quantification provide early indicators for individuals at high risk of developing this disease or for patient prognosis. Such assessment of knee tissues, combined with the development of models/tools from machine/deep learning using, in addition to other parameters, MRI markers for early diagnosis/prognosis, will maximize opportunities for individualized risk assessment for use in clinical practice permitting precision medicine. Future efforts should be made to integrate such prediction models into open access, allowing early disease management to prevent or delay the OA outcome.

A chemo-mechano-biological modeling framework for cartilage evolving in health, disease, injury, and treatment

BACKGROUND AND OBJECTIVE

Osteoarthritis (OA) is a pervasive and debilitating disease, wherein degeneration of cartilage features prominently. Despite extensive research, we do not yet understand the cause or progression of OA. Studies show biochemical, mechanical, and biological factors affect cartilage health. Mechanical loads influence synthesis of biochemical constituents which build and/or break down cartilage, and which in turn affect mechanical loads. OA-associated biochemical profiles activate cellular activity that disrupts homeostasis. To understand the complex interplay among mechanical stimuli, biochemical signaling, and cartilage function requires integrating vast research on experimental mechanics and mechanobiology-a task approachable only with computational models. At present, mechanical models of cartilage generally lack chemo-biological effects, and biochemical models lack coupled mechanics, let alone interactions over time.

METHODS

We establish a first-of-its kind virtual cartilage: a modeling framework that considers time-dependent, chemo-mechano-biologically induced turnover of key constituents resulting from biochemical, mechanical, and/or biological activity. We include the "minimally essential" yet complex chemical and mechanobiological mechanisms. Our 3-D framework integrates a constitutive model for the mechanics of cartilage with a novel model of homeostatic adaptation by chondrocytes to pathological mechanical stimuli, and a new application of anisotropic growth (loss) to simulate degradation clinically observed as cartilage thinning.

RESULTS

Using a single set of representative parameters, our simulations of immobilizing and overloading successfully captured loss of cartilage quantified experimentally. Simulations of immobilizing, overloading, and injuring cartilage predicted dose-dependent recovery of cartilage when treated with suramin, a proposed therapeutic for OA. The modeling framework prompted us to add growth factors to the suramin treatment, which predicted even better recovery.

CONCLUSIONS

Our flexible framework is a first step toward computational investigations of how cartilage and chondrocytes mechanically and biochemically evolve in degeneration of OA and respond to pharmacological therapies. Our framework will enable future studies to link physical activity and resulting mechanical stimuli to progression of OA and loss of cartilage function, facilitating new fundamental understanding of the complex progression of OA and elucidating new perspectives on causes, treatments, and possible preventions.

A fast, robust method for quantitative assessment of collagen fibril architecture from transmission electron micrographs

Collagen is the most abundant protein in mammals; it exhibits a hierarchical organization and provides structural support to a wide range of soft tissues, including blood vessels. The architecture of collagen fibrils dictates vascular stiffness and strength, and changes therein can contribute to disease progression. While transmission electron microscopy (TEM) is routinely used to examine collagen fibrils under normal and pathological conditions, computational tools that enable fast and minimally subjective quantitative assessment remain lacking. In the present study, we describe a novel semi-automated image processing and statistical modeling pipeline for segmenting individual collagen fibrils from TEM images and quantifying key metrics of interest, including fibril cross-sectional area and aspect ratio. For validation, we show illustrative results for adventitial collagen in the thoracic aorta from three different mouse models.

Poroviscoelasto-plasticity of agarose-based hydrogels

Agarose gels are excellent candidates for tissue engineering as they are tunable, viscoelastic, and show a pronounced strain-stiffening response. These characteristics make them ideal to create in vitro environments to grow cells and develop tissues. As in many other biopolymers, viscoelasticity and poroelasticity coexist as time-dependent behaviors in agarose gels. While the viscoelastic behavior of these hydrogels has been considered using both phenomenological and continuum models, there remains a lack of connection between the underlying physics and the macroscopic material response. Through a finite element analysis and complimentary experiments, we evaluated the complex time-dependent mechanical response of agarose gels in various conditions. We then conceptualized these gels as a dynamic network where the global dissociation/association rate of intermolecular bonds is described as a combination of a fast rate native to double helices forming between aligned agarose molecules and a slow rate of the agarose molecules present in the clusters. Using the foundation of the transient network theory, we developed a physics-based constitutive model that accurately describes agarose behavior. Integrating experimental results and model prediction, we demonstrated that the fast dissociation/association rate follows a nonlinear force-dependent response, whose exponential evolution agrees with Eyring's model based on the transition state theory. Overall, our results establish a more accurate understanding of the time-dependent mechanics of agarose gels and provide a model that can inform design of a variety of biopolymers with a similar network topology.

Hydrated Collagen: Where Physical Chemistry, Medical Imaging, and Bioengineering Meet

It is well-known that collagen is the most abundant protein in the human body; however, what is not often appreciated is its fascinating physical chemistry and molecular physics. In this Perspective, we aim to expose some of the physicochemical phenomena associated with the hydration of collagen and to examine the role collagen's hydration water plays in determining its biological function as well as applications ranging from radiology to bioengineering. The main focus is on the Magic-Angle Effect, a phenomenon observed in Nuclear Magnetic Resonance (NMR) spectroscopy and Magnetic Resonance Imaging (MRI) of anisotropic collagenous tissues such as articular cartilage and tendon. While the effect has been known in NMR and MRI for decades, its exact molecular mechanism remains a topic of debate and continuing research in scientific literature. We survey some of the latest research aiming to develop a comprehensive molecular-level model of the Magic-Angle Effect. We also touch on other fields where understanding of collagen hydration is important, particularly nanomechanics and mechanobiology, biomaterials, and piezoelectric sensors.

A specialized protocol for mechanical testing of isolated networks of type II collagen

The mechanical responses of most soft biological tissues rely heavily on networks of collagen fibers, thus quantifying the mechanics of both individual collagen fibers and networks of these fibers advances understanding of biological tissues in health and disease. The mechanics of type I collagen are well-studied and quantified. Yet no data exist on the tensile mechanical responses of individual type II collagen fibers nor of isolated networks comprised of type II collagen. We aimed to establish methods to facilitate studies of networked and individual type II collagen fibers within the native networked structure, specifically to establish best practices for isolating and mechanically testing type II collagen networks in tension. We systematically investigated mechanical tests of networks of type II collagen undergoing uniaxial extension, and quantified ranges for each of the important variables to help ensure that the experiment itself does not affect the measured mechanical parameters. Specifically we determined both the specimen (establishing networks of isolated collagen, the footprint and thickness of the specimen) and the mechanical test (both the device and the strain rate) to establish a repeatable and practical protocol. Mechanical testing of isolated networks of type II collagen fibers leveraging this protocol will lead to better understanding of the mechanics both of these networks and of the individual fibers. Such understanding may aid in developing and testing therapeutics, understanding inter-constituent interactions (and their roles in bulk-tissue biomechanics), investigating mechanical/biochemical modifications to networked type II collagen, and proposing, calibrating, and validating constitutive models for finite element analyses.

Associations of human femoral condyle cartilage structure and composition with viscoelastic and constituent-specific material properties at different stages of osteoarthritis

The relationships between structure and function in human knee femoral cartilage are not well-known at different stages of osteoarthritis. Thus, our aim was to characterize the depth-dependent composition and structure (proteoglycan content, collagen network organization and collagen content) of normal and osteoarthritic human femoral condyle cartilage (n = 47) and relate them to their viscoelastic and constituent-specific mechanical properties that are obtained through dynamic sinusoidal testing and fibril-reinforced poroelastic material modeling of stress-relaxation testing, respectively. We characterized the proteoglycan content using digital densitometry, collagen network organization (orientation angle and anisotropy) using polarized light microscopy and collagen content using Fourier transform infrared spectroscopy. In the superficial cartilage (0-10 % of thickness), the collagen network disorganization and proteoglycan loss were associated with the smaller initial fibril network modulus - a parameter representing the pretension of the collagen network. Furthermore, the proteoglycan loss was associated with the greater strain-dependent fibril network modulus - a measure of nonlinear mechanical behavior. The proteoglycan loss was also associated with greater cartilage viscosity at a low loading frequency (0.005 Hz), while the collagen network disorganization was associated with greater cartilage viscosity at a high loading frequency (1 Hz). Our results suggest that proteoglycan loss and collagen network disorganization reduce the pretension of the collagen network while proteoglycan degradation also increases the nonlinear mechanical behavior of the collagen network. Further, the results also highlight that proteoglycan loss and collagen disorganization increase the viscosity of femoral cartilage, but their contribution to increased viscosity occurs in completely different loading frequencies.

Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics

The analysis of tissue mechanics in biomedical applications demands nonlinear constitutive models able to capture the energy dissipation mechanisms, such as damage, that occur during tissue deformation. Furthermore, implementation of sophisticated material models in finite element models is essential to improve medical devices and diagnostic tools. Building on previous work toward microstructure-driven models of collagenous tissue, here we show a constitutive model based on fiber orientation and waviness distributions for skin that captures not only the anisotropic strain-stiffening response of this and other collagen-based tissues, but, additionally, accounts for tissue damage directly as a function of changes in the microstructure, in particular changes in the fiber waviness distribution. The implementation of this nonlinear constitutive model as a user subroutine in the popular finite element package Abaqus enables large-scale finite element simulations for biomedical applications. We showcase the performance of the model in fracture simulations during pure shear tests, as well as simulations of needle insertion into skin relevant to auto-injector design.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

Predicting the micromechanics of embedded nerve fibers using a novel three-layered model of mouse distal colon and rectum

Mechanotransduction plays a central role in evoking pain from the distal colon and rectum (colorectum) where embedded sensory nerve endings convert micromechanical stresses and strains into neural action potentials. The colorectum displays strong through-thickness and longitudinal heterogeneity with collagen concentrated in the submucosa thus indicating the significant load-bearing role of this layer. The density of sensory nerve endings is also significantly the greatest in the submucosa, suggesting a nociceptive function. Thus biomechanical heterogeneity in the colorectum influences the micromechanical stresses and strains surrounding afferent endings embedded within different layers of the colorectum which is critical for the mechanotransduction of various mechanical stimuli. In this study we aimed to: (1) calibrate and validate a three-layered computational model of the colorectum; (2) predict intra-tissue distributions of stresses and strains during mechanical stimulation of the colorectum ex vivo (i.e. circumferential stretching, punctuate probing, and mucosal shearing); and (3) establish a methodology to calculate local micromechanical stresses and strains surrounding afferent nerve endings embedded in the colorectum. We established three-layered FE models that include mucosa, submucosa, and muscular layers, and incorporated residual stretches, to calculate intra-tissue stresses and strains when the colorectum undergoes the mechanical stimuli used to characterize afferent neural encoding ex vivo. Finally, we established a methodology for detailed calculations of the local micromechanical stresses and strains surrounding afferent endings embedded in the colorectum and demonstrated this with a representative example. Our novel methodologies will bridge the existing neurophysiological and biomechanical evidence from experiments to advance our mechanistic understanding of colorectal mechanotransduction.

A Nonparametric Approach for Estimating Three-Dimensional Fiber Orientation Distribution Functions (ODFs) in Fibrous Materials

Many biological tissues contain an underlying fibrous microstructure that is optimized to suit a physiological function. The fiber architecture dictates physical characteristics such as stiffness, diffusivity, and electrical conduction. Abnormal deviations of fiber architecture are often associated with disease. Thus, it is useful to characterize fiber network organization from image data in order to better understand pathological mechanisms. We devised a method to quantify distributions of fiber orientations based on the Fourier transform and the Qball algorithm from diffusion MRI. The Fourier transform was used to decompose images into directional components, while the Qball algorithm efficiently converted the directional data from the frequency domain to the orientation domain. The representation in the orientation domain does not require any particular functional representation, and thus the method is nonparametric. The algorithm was verified to demonstrate its reliability and used on datasets from microscopy to show its applicability. This method increases the ability to extract information of microstructural fiber organization from experimental data that will enhance our understanding of structure-function relationships and enable accurate representation of material anisotropy in biological tissues.

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.

Magnetic Resonance Imaging-based biomechanical simulation of cartilage: A systematic review

MRI-based mathematical and computational modeling studies can contribute to a better understanding of the mechanisms governing cartilage's mechanical performance and cartilage disease. In addition, distinct modeling of cartilage is needed to optimize artificial cartilage production. These studies have opened up the prospect of further deepening our understanding of cartilage function. Furthermore, these studies reveal the initiation of an engineering-level approach to how cartilage disease affects material properties and cartilage function. Aimed at researchers in the field of MRI-based cartilage simulation, research articles pertinent to MRI-based cartilage modeling were identified, reviewed, and summarized systematically. Various MRI applications for cartilage modeling are highlighted, and the limitations of different constitutive models used are addressed. In addition, the clinical application of simulations and studied diseases are discussed. The paper's quality, based on the developed questionnaire, was assessed, and out of 79 reviewed papers, 34 papers were determined as high-quality. Due to the lack of the best constitutive models for various clinical conditions, researchers may consider the effect of constitutive material models on the cartilage disease simulation. In the future, research groups may incorporate various aspects of machine learning into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification, such as gait analysis.

Constitutive modeling using structural information on collagen fiber direction and dispersion in human superficial femoral artery specimens of different ages

Arterial mechanics plays an important role in vascular pathophysiology and repair, and advanced imaging can inform constitutive models of vascular behavior. We have measured the mechanical properties of 14 human superficial femoral arteries (SFAs) (age 12-70, mean 48±19 years) using planar biaxial extension, and determined the preferred collagen fiber direction and dispersion using multiphoton microscopy. The collagen fiber direction and dispersion were evaluated using second-harmonic generation imaging and modeled using bivariate von Mises distributions. The microstructures of elastin and collagen were assessed using two-photon fluorescence imaging and conventional bidirectional histology. The mechanical and structural data were used to describe the SFA mechanical behavior using two- and four-fiber family invariant-based constitutive models. Older SFAs were stiffer and mechanically more nonlinear than younger specimens. In the adventitia, collagen fibers were undulated and diagonally-oriented, while in the media, they were straight and circumferentially-oriented. The media was rich in collagen that surrounded the circumferentially-oriented smooth muscle cells, and the elastin was present primarily in the internal and external elastic laminae. Older SFAs had a more circumferential collagen fiber alignment, a decreased circumferential-radial fiber dispersion, but the same circumferential-longitudinal fiber dispersion as younger specimens. Both the two- and the four-fiber family constitutive models were able to capture the experimental data, and the fits were better for the four-fiber family formulation. Our data provide additional details on the SFA intramural structure and inform structurally-based constitutive models.

Computational Modeling of Mouse Colorectum Capturing Longitudinal and Through-thickness Biomechanical Heterogeneity

Mechanotransduction, the encoding of local mechanical stresses and strains at sensory endings into neural action potentials at the viscera, plays a critical role in evoking visceral pain, e.g., in the distal colon and rectum (colorectum). The wall of the colorectum is structurally heterogeneous, including two major composites: the inner consists of muscular and submucosal layers, and the outer consists of circular muscular, intermuscular, longitudinal muscular, and serosal layers. In fact the colorectum presents biomechanical heterogenity across both the longitudinal and through-thickness directions thus highlighting the differential roles of sensory nerve endings within different regions of the colorectum in visceral mechanotransduction. We determined constitutive models and model parameters for individual layers of the colorectum from three longitudinal locations (colonic, intermediate, and distal) using nonlinear optimization to fit our experimental results from biaxial extension tests on layer-separated colorectal tissues (mouse model, 7×7 mm2, Siri et al., Am. J. Physiol. Gastrointest. Liver Physiol. 316, G473-G481 and 317, G349-G358), and quantified the thicknesses of the layers. In this study we also quantified the residual stretches stemming from separating colorectal specimens into inner and outer composites and we completed new pressure-diameter mechanical testing to provide an additional validation case. We implemented the constitutive equations and created two-layered, 3-D finite element models using FEBio (University of Utah), and incorporated the residual stretches. We validated the modeling framework by comparing FE-predicted results for both biaxial extension testing of bulk specimens of colorectum and pressure-diameter testing of bulk segments against corresponding experimental results independent of those used in our model fitting. We present the first theoretical framework to simulate the biomechanics of distal colorectum, including both longitudinal and through-thickness heterogeneity, based on constitutive modeling of biaxial extension tests of colon tissues from mice. Our constitutive models and modeling framework facilitate analyses of both fundamental questions (e.g., the impact of organ/tissue biomechanics on mechanotransduction of the sensory nerve endings, structure-function relationships, and growth and remodeling in health and disease) and specific applications (e.g., device design, minimally invasive surgery, and biomedical research).

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 3-D constitutive model for finite element analyses of agarose with a range of gel concentrations

Hydrogels have seen widespread application across biomedical sciences and there is considerable interest in using hydrogels, including agarose, for creating in vitro three-dimensional environments to grow cells and study mechanobiology and mechanotransduction. Recent advances in the preparation of agarose gels enable successful encapsulation of viable cells at gel concentrations as high as 5%. Agarose with a range of gel concentrations can thus serve as an experimental model mimicking changes in the 3-D microenvironment of cells during disease progression and can facilitate experiments aimed at probing the corresponding mechanobiology, e.g. the evolving mechanobiology of chondrocytes during the progression of osteoarthritis. Importantly, whether stresses (forces) or strains (displacements) drive mechanobiology and mechanotransduction is currently unknown. We can use experiments to quantify mechanical properties of hydrogels, and imaging to estimate microstructure and even strains; however, only computational models can estimate intra-gel stresses in cell-seeded agarose constructs because the required in vitro experiments are currently impossible. Finite element modeling is well-established for (computational) mechanical analyses, but accurate constitutive models for modeling the 3-D mechanical environments of cells within high-stiffness agarose with varying gel concentrations are currently unavailable. In this study we aimed to establish a 3-D constitutive model of high-stiffness agarose with a range of gel concentrations. We applied a multi-step, physics-based optimization approach to separately fit subsets of model parameters and help achieve robust convergence. Our constitutive model, fitted to experimental data on progressive stress-relaxations, was able to predict reaction forces determined from independent experiments on cyclical loading. Our model has broad applications in finite element modeling aimed at interpreting mechanical experiments on agarose specimens seeded with cells, particularly in predicting distributions of intra-gel stresses. Our model and fitted parameters enable more accurate finite element simulations of high-stiffness agarose constructs, and thus better understanding of experiments aimed at mechanobiology, mechanotransduction, or other applications in tissue engineering.

Anisotropic Diffusivity Tensor in Articular Cartilage: Effective Medium Approach

Due to the avascular nature of articular cartilage, molecular transport occurs via interstitial fluid flow as well as via diffusion. Diffusion in cartilage has been studied experimentally, but no mathematical models have been developed to interpret the experimental results and the observed isotropy or anisotropy in the different cartilage zones. Here, we propose a model for the determination of the diffusivity tensor of uncharged macromolecules in articular cartilage, accounting for the inhomogeneity and anisotropy arising from fiber arrangement, volumetric fraction, and radius. We study a representative element of volume (REV) comprising a fiber surrounded by fluid-saturated proteoglycan matrix. The REV permeability tensor is evaluated using a previously developed model, while the REV diffusivity tensor is obtained by incorporating the hydrodynamic effect and the steric effect of the fiber-reinforced matrix. Both effects are represented by anisotropic second-order tensors. The overall diffusivity tensor is obtained as the averaging integral of the REV diffusivity, weighted by the probability distribution of fiber orientation. The model's predictions of the trend of the magnitude of the diffusivity of spheroidal macromolecules as a function of molecular radius agree with published experimental results. For large linear macromolecules, the model underestimates the diffusivity magnitude (i.e., the equivalent isotropic diffusivity). The model correctly predicts the anisotropic behavior for linear macromolecules, although it underestimates the numerical value of the diffusivity anisotropy ratio of large linear macromolecules in the superficial zone, and overestimates it in the deep zone. In summary, this model constitutes a first step toward understanding the relation between diffusivity and permeability in articular cartilage.

Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests

It has been experimentally proposed that the discrete regions of articular cartilage, along with different subchondral bone tissues, known as the bone-cartilage unit, are biomechanically altered during osteoarthritis degeneration. However, a computational framework capturing all of the dominant changes in the multiphasic parameters has not yet been developed. This article proposes a new finite element model of the bone-cartilage unit by combining several validated, nonlinear, depth-dependent, fibril-reinforced, and swelling models, which can computationally simulate the variations in the dominant parameters during osteoarthritis degeneration by indentation and unconfined compression tests. The mentioned dominant parameters include the proteoglycan depletion, collagen fibrillar softening, permeability, and fluid fraction increase for approximately non-advanced osteoarthritis. The results depict the importance of subchondral bone tissues in fluid distribution within the bone-cartilage units by decreasing the fluid permeation and pressure (up to a maximum of 100 kPa) during osteoarthritis, supporting the notion that subchondral bones might play a role in the pathogenesis of osteoarthritis. Furthermore, the osteoarthritis composition-based studies shed light on the significant biomechanical role of the calcified cartilage, which experienced a maximum change of 70 kPa in stress, together with relative load contributions of articular cartilage constituents during osteoarthritis, in which the osmotic pressure bore around 70% of the loads after degeneration. To conclude, the new insights provided by the results reveal the significance of the multiphasic osteoarthritis simulation and demonstrate the functionality of the proposed bone-cartilage unit model.

Elastic, Viscoelastic and Fibril-Reinforced Poroelastic Material Properties of Healthy and Osteoarthritic Human Tibial Cartilage

Articular cartilage constituents (collagen, proteoglycans, fluid) are significantly altered during osteoarthritis (OA). A fibril-reinforced poroelastic (FRPE) material model can separate the contribution of each constituent on the mechanical response of cartilage. Yet, these properties and their OA related alterations are not known for human tibial cartilage. To answer this gap in the knowledge, we characterized the FRPE as well as elastic and viscoelastic properties of healthy and osteoarthritic human tibial cartilage. Tibial osteochondral explants (n = 27) harvested from 7 cadavers were mechanically tested in indentation followed by a quantification of elastic, viscoelastic and FRPE properties. Then they were histopathologically OARSI graded for the severity of OA. FRPE modeling revealed that non-fibrillar matrix modulus was higher in the healthy group compared to the early OA (p = 0.003) and advanced OA (p < 0.001) groups. The initial fibril network modulus was also higher in the healthy group compared to the early OA (p = 0.009) and advanced OA (p < 0.001) groups. The permeability correlated with the OARSI grade (p = 0.002, r = 0.56). For the first time, the FRPE properties were characterized for human tibial cartilage. This knowledge is crucial to improve the accuracy of computational knee joint models.

Maximum shear strain-based algorithm can predict proteoglycan loss in damaged articular cartilage

Post-traumatic osteoarthritis (PTOA) is a common disease, where the mechanical integrity of articular cartilage is compromised. PTOA can be a result of chondral defects formed due to injurious loading. One of the first changes around defects is proteoglycan depletion. Since there are no methods to restore injured cartilage fully back to its healthy state, preventing the onset and progression of the disease is advisable. However, this is problematic if the disease progression cannot be predicted. Thus, we developed an algorithm to predict proteoglycan loss of injured cartilage by decreasing the fixed charge density (FCD) concentration. We tested several mechanisms based on the local strains or stresses in the tissue for the FCD loss. By choosing the degeneration threshold suggested for inducing chondrocyte apoptosis and cartilage matrix damage, the algorithm driven by the maximum shear strain showed the most substantial FCD losses around the lesion. This is consistent with experimental findings in the literature. We also observed that by using coordinate system-independent strain measures and selecting the degeneration threshold in an ad hoc manner, all the resulting FCD distributions would appear qualitatively similar, i.e., the greatest FCD losses are found at the tissue adjacent to the lesion. The proposed strain-based FCD degeneration algorithm shows a great potential for predicting the progression of PTOA via biomechanical stimuli. This could allow identification of high-risk defects with an increased risk of PTOA progression.

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.

GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations

Finite element (FE) simulations are increasingly valuable in assessing and improving the performance of biomedical devices and procedures. Due to high computational demands such simulations may become difficult or even infeasible, especially when considering nearly incompressible and anisotropic material models prevalent in analyses of soft tissues. Implementations of GPGPU-based explicit FEs predominantly cover isotropic materials, e.g. the neo-Hookean model. To elucidate the computational expense of anisotropic materials, we implement the Gasser-Ogden-Holzapfel dispersed, fiber-reinforced model and compare solution times against the neo-Hookean model. Implementations of GPGPU-based explicit FEs conventionally rely on single-point (under) integration. To elucidate the expense of full and selective-reduced integration (more reliable) we implement both and compare corresponding solution times against those generated using underintegration. To better understand the advancement of hardware, we compare results generated using representative Nvidia GPGPUs from three recent generations: Fermi (C2075), Kepler (K20c), and Maxwell (GTX980). We explore scaling by solving the same boundary value problem (an extension-inflation test on a segment of human aorta) with progressively larger FE meshes. Our results demonstrate substantial improvements in simulation speeds relative to two benchmark FE codes (up to 300[Formula: see text] while maintaining accuracy), and thus open many avenues to novel applications in biomechanics and medicine.

T2 MR imaging vs. computational modeling of human articular cartilage tissue functionality

The detection of early stages of cartilage degeneration remains diagnostically challenging. One promising non-invasive approach is to functionally assess the tissue response to loading by serial magnetic resonance (MR) imaging in terms of T2 mapping under simultaneous mechanical loading. As yet, however, it is not clear which cartilage component contributes to the tissue functionality as assessed by quantitative T2 mapping. To this end, quantitative T2 maps of histologically intact cartilage samples (n=8) were generated using a clinical 3.0-T MR imaging system. Using displacement-controlled quasi-static indentation loading, serial T2 mapping was performed at three defined strain levels and loading-induced relative changes were determined in distinct regions-of-interest. Samples underwent conventional biomechanical testing (by unconfined compression) as well as histological assessment (by Mankin scoring) for reference purposes. Moreover, an anisotropic hyperelastic constitutive model of cartilage was implemented into a finite element (FE) code for cross-referencing. In efforts to simulate the evolution of compositional and structural intra-tissue changes under quasi-static loading, the indentation-induced changes in quantitative T2 maps were referenced to underlying changes in cartilage composition and structure. These changes were parameterized as cartilage fluid, proteoglycan and collagen content as well as collagen orientation. On a pixel-wise basis, each individual component correlation with T2 relaxation times was determined by Spearman's ρ_s and significant correlations were found between T2 relaxation times and all four tissue parameters for all indentation strain levels. Thus, the biological changes in functional MR Imaging parameters such as T2 can further be characterized to strengthen the scientific basis of functional MRI techniques with regards to their perspective clinical applications.