On the multiscale modeling of heart valve biomechanics in health and disease

Local and global growth and remodeling in calcific aortic valve disease and aging

Aging and calcific aortic valve disease (CAVD) are the main factors leading to aortic stenosis. Both processes are accompanied by growth and remodeling pathways that play a crucial role in aortic valve pathophysiology. Herein, a computational growth and remodeling (G&R) framework was developed to investigate the effects of aging and calcification on aortic valve dynamics. Particularly, an algorithm was developed to couple the global growth and stiffening of the aortic valve due to aging and the local growth and stiffening due to calcification with the aortic valve transient dynamics. The aortic valve dynamics during baseline were validated with available data in the literature. Subsequently, the changes in aortic valve dynamic patterns during aging and CAVD progression were studied. The results revealed the patterns in geometric orifice area reduction and an increase in the valve stress during local and global growth and remodeling of the aortic valve. The proposed algorithm provides a framework to couple mechanobiology models of disease growth with tissue-scale transient structural mechanics models to study the biomechanical changes during cardiovascular disease growth and aging.

A Coupled Multiscale Approach to Modeling Aortic Valve Mechanics in Health and Disease

Mechano-biological processes in the aortic valve span multiple length scales ranging from the molecular and cell to tissue and organ levels. The valvular interstitial cells residing within the valve cusps sense and actively respond to leaflet tissue deformations caused by the valve opening and closing during the cardiac cycle. Abnormalities in these biomechanical processes are believed to impact the matrix-maintenance function of the valvular interstitial cells, thereby initiating valvular disease processes such as calcific aortic stenosis. Understanding the mechanical behavior of valvular interstitial cells in maintaining tissue homeostasis in response to leaflet tissue deformation is therefore key to understanding the function of the aortic valve in health and disease. In this study, we applied a multiscale computational homogenization technique (also known as “FE2”) to aortic valve leaflet tissue to study the three-dimensional mechanical behavior of the valvular interstitial cells in response to organ-scale mechanical loading. We further considered calcific aortic stenosis with the aim of understanding the likely relationship between the valvular interstitial cell deformations and calcification. We find that the presence of calcified nodules leads to an increased strain profile that drives further growth of calcification.

The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid-Structure Interaction Simulation

Built on the hybrid immersed boundary/finite element (IB/FE) method, fluid-structure interaction (FSI) simulations of aortic valve (AV) dynamics are performed with three different constitutive laws and two different fiber architectures for the AV leaflets. An idealized AV model is used and mounted in a straight tube, and a three-element Windkessel model is further attached to the aorta. After obtaining ex vivo biaxial tensile testing of porcine AV leaflets, we first determine the constitutive parameters of the selected three constitutive laws by matching the analytical stretch-stress relations derived from constitutive laws to the experimentally measured data. Both the average error and relevant R-squared value reveal that the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions could be more suitable for characterizing the mechanical behaviors of the AV leaflets. We then thoroughly compare the simulation results from both structural mechanics and hemodynamics. Compared to the other two constitutive laws, the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions shows the larger leaflet displacements at the opened state, the largest forward jet flow, the smaller regurgitant flow. We further analyze hemodynamic parameters of the six different cases, including the regurgitant fraction, the mean transvalvular pressure gradient, the effective orifice area, and the energy loss of the left ventricle. We find that the fiber architecture with body-fitted orientation shows better dynamic behaviors in the leaflets, especially with the constitutive law using exponential terms for both the fiber and cross-fiber directions. In conclusion, both constitutive laws and fiber architectures can affect AV dynamics. Our results further suggest that the strain energy function with exponential terms for both the fiber and cross-fiber directions could be more suitable for describing the AV leaflet mechanical behaviors. Future experimental studies are needed to identify competent constitutive laws for the AV leaflets and their associated fiber orientations with controlled experiments. Although limitations exist in the present AV model, our results provide important information for selecting appropriate constitutive laws and fiber architectures when modeling AV dynamics.

Feasibility of two-dimensional speckle-tracking echocardiography of aortic valve in patients with calcific aortic valve disease

Calcific aortic valve (AV) disease is associated with increased stiffness and reduced motion of AV leaflets, has a progressive course, and can develop into aortic stenosis (AS). Our aim was to evaluate whether two-dimensional speckle-tracking echocardiography (STE) may be used for the assessment of AV stiffness. We applied STE to AV leaflets in patients with various degrees of degenerative changes of AV and measured strain as an absolute value of the radial deformation of AV leaflets. Deformation of AV expressed as averaged AV strain was greatest in patients with a normal AV (23.4 ± 6.4%), compared to those with aortic sclerosis (12.9 ± 3.2%), moderate-to-severe AS (11.9 ± 4%), and severe AS (10.9 ± 3.5%) (p < 0.01). A non-linear relationship and moderate correlation of AV strain with transvalvular hemodynamic parameters was observed. In patients with mild-to-moderate AS, the strain of AV leaflets also correlated negatively with AV calcification (r = -0.59, p = 0.008). Good inter-observer agreement was obtained for averaged AV strain with a coefficient of variation of 0.15 and an interclass correlation coefficient of 0.94 (p < 0.0001). In this study we demonstrated that deformation of AV leaflets as assessed by STE might be a potential method for a non-invasive evaluation of AV biomechanical properties and of the progression of calcific aortic disease. Further development of the two-dimensional speckle tracking technique specifically for valve structures is needed to enable a better quantification of leaflet deformation.

Subject-specific multiscale modeling of aortic valve biomechanics

A Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.36-0.87$$\end{document}0.36-0.87) with a strong correlation with the organ length-scale radial strain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^{2}= 0.95$$\end{document}R2=0.95); conversely, circumferential cell strains spanned a very narrow range (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.75-0.88$$\end{document}0.75-0.88) showing no correlation with the circumferential strain at the organ level (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^{2}= 0.02$$\end{document}R2=0.02). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.

Multimodal cardiovascular model for hemodynamic analysis: Simulation study on mitral valve disorders

Valvular heart diseases are a prevalent cause of cardiovascular morbidity and mortality worldwide, affecting a wide spectrum of the population. In-silico modeling of the cardiovascular system has recently gained recognition as a useful tool in cardiovascular research and clinical applications. Here, we present an in-silico cardiac computational model to analyze the effect and severity of valvular disease on general hemodynamic parameters. We propose a multimodal and multiscale cardiovascular model to simulate and understand the progression of valvular disease associated with the mitral valve. The developed model integrates cardiac electrophysiology with hemodynamic modeling, thus giving a broader and holistic understanding of the effect of disease progression on various parameters like ejection fraction, cardiac output, blood pressure, etc., to assess the severity of mitral valve disorders, naming Mitral Stenosis and Mitral Regurgitation. The model mimics an adult cardiovascular system, comprising a four-chambered heart with systemic, pulmonic circulation. The simulation of the model output comprises regulated pressure, volume, and flow for each heart chamber, valve dynamics, and Photoplethysmogram signal for normal physiological as well as pathological conditions due to mitral valve disorders. The generated physiological parameters are in agreement with published data. Additionally, we have related the simulated left atrium and ventricle dimensions, with the enlargement and hypertrophy in the cardiac chambers of patients with mitral valve disorders, using their Electrocardiogram available in Physionet PTBI dataset. The model also helps to create 'what if' scenarios and relevant analysis to study the effect in different hemodynamic parameters for stress or exercise like conditions.

Perspectives on Sharing Models and Related Resources in Computational Biomechanics Research

The role of computational modeling for biomechanics research and related clinical care will be increasingly prominent. The biomechanics community has been developing computational models routinely for exploration of the mechanics and mechanobiology of diverse biological structures. As a result, a large array of models, data, and discipline-specific simulation software has emerged to support endeavors in computational biomechanics. Sharing computational models and related data and simulation software has first become a utilitarian interest, and now, it is a necessity. Exchange of models, in support of knowledge exchange provided by scholarly publishing, has important implications. Specifically, model sharing can facilitate assessment of reproducibility in computational biomechanics and can provide an opportunity for repurposing and reuse, and a venue for medical training. The community's desire to investigate biological and biomechanical phenomena crossing multiple systems, scales, and physical domains, also motivates sharing of modeling resources as blending of models developed by domain experts will be a required step for comprehensive simulation studies as well as the enhancement of their rigor and reproducibility. The goal of this paper is to understand current perspectives in the biomechanics community for the sharing of computational models and related resources. Opinions on opportunities, challenges, and pathways to model sharing, particularly as part of the scholarly publishing workflow, were sought. A group of journal editors and a handful of investigators active in computational biomechanics were approached to collect short opinion pieces as a part of a larger effort of the IEEE EMBS Computational Biology and the Physiome Technical Committee to address model reproducibility through publications. A synthesis of these opinion pieces indicates that the community recognizes the necessity and usefulness of model sharing. There is a strong will to facilitate model sharing, and there are corresponding initiatives by the scientific journals. Outside the publishing enterprise, infrastructure to facilitate model sharing in biomechanics exists, and simulation software developers are interested in accommodating the community's needs for sharing of modeling resources. Encouragement for the use of standardized markups, concerns related to quality assurance, acknowledgement of increased burden, and importance of stewardship of resources are noted. In the short-term, it is advisable that the community builds upon recent strategies and experiments with new pathways for continued demonstration of model sharing, its promotion, and its utility. Nonetheless, the need for a long-term strategy to unify approaches in sharing computational models and related resources is acknowledged. Development of a sustainable platform supported by a culture of open model sharing will likely evolve through continued and inclusive discussions bringing all stakeholders at the table, e.g., by possibly establishing a consortium.

Tricuspid valve leaflet strains in the beating ovine heart

The tricuspid leaflets coapt during systole to facilitate proper valve function and, thus, ensure efficient transport of deoxygenated blood to the lungs. Between their open state and closed state, the leaflets undergo large deformations. Quantification of these deformations is important for our basic scientific understanding of tricuspid valve function and for diagnostic or prognostic purposes. To date, tricuspid valve leaflet strains have never been directly quantified in vivo. To fill this gap in our knowledge, we implanted four sonomicrometry crystals per tricuspid leaflet and six crystals along the tricuspid annulus in a total of five sheep. In the beating ovine hearts, we recorded crystal coordinates alongside hemodynamic data. Once recorded, we used a finite strain kinematic framework to compute the temporal evolutions of area strain, radial strain, and circumferential strain for each leaflet. We found that leaflet strains were larger in the anterior leaflet than the posterior and septal leaflets. Additionally, we found that radial strains were larger than circumferential strains. Area strains were as large as 97% in the anterior leaflet, 31% in the posterior leaflet, and 31% in the septal leaflet. These data suggest that tricuspid valve leaflet strains are significantly larger than those in the mitral valve. Should our findings be confirmed they could suggest either that the mechanobiological equilibrium of tricuspid valve resident cells is different than that of mitral valve resident cells or that the mechanotransductive apparatus between the two varies. Either phenomenon may have important implications for the development of tricuspid valve-specific surgical techniques and medical devices.

Investigation of raphe function in the bicuspid aortic valve and its influence on clinical criteria-A patient-specific finite element study

The aortic valve is normally composed of 3 cusps. In one common lesion, 2 cusps are fused together. The conjoined area of the fused cusps is termed raphe. Occurring in 1% to 2% of the population, the bicuspid aortic valve (BAV) is the most common congenital cardiac malformation. The majority of BAV patients eventually require surgery. There is a lack in the literature regarding modeling of the raphe (geometry and material properties), its role and its influence on BAV function. The present study aims to propose improvements on these aspects. Three patient-specific finite element models of BAVs were created based on 3D trans-esophageal echocardiography measurements, and assuming age-dependent material properties. The raphe was initially given the same material properties as its underlying cusps. Two levels of validation were performed; one based on the anatomical validation of the pressurized geometry in diastole (involving 7 anatomical measures), as simulated starting from the unpressurized geometry, and the other based on a functional assessment using clinical measurements in both systole and diastole (involving 16 functional measures). The pathology was successfully reproduced in the FE models of all 3 patients. To further investigate the role of the raphe, 2 additional scenarios were considered; (1) the raphe was considered as almost rigid, (2) the raphe was totally removed. The results confirmed the interpretation of the raphe as added stiffness in the fused cusp's rotation with respect to the aortic wall, as well as added support for stress distribution from the fused cusps to the aortic wall.

The Three-Dimensional Microenvironment of the Mitral Valve: Insights into the Effects of Physiological Loads

INTRODUCTION

In the mitral valve (MV), numerous pathological factors, especially those resulting from changes in external loading, have been shown to affect MV structure and composition. Such changes are driven by the MV interstitial cell (MVIC) population via protein synthesis and enzymatic degradation of extracellular matrix (ECM) components.

METHODS

While cell phenotype, ECM composition and regulation, and tissue level changes in MVIC shape under stress have been studied, a detailed understanding of the three-dimensional (3D) microstructural mechanisms are lacking. As a first step in addressing this challenge, we applied focused ion beam scanning electron microscopy (FIB-SEM) to reveal novel details of the MV microenvironment in 3D.

RESULTS

We demonstrated that collagen is organized into large fibers consisting of an average of 605 ± 113 fibrils, with a mean diameter of 61.2 ± 9.8 nm. In contrast, elastin was organized into two distinct structural subtypes: (1) sheet-like lamellar elastin, and (2) circumferentially oriented elastin struts, based on both the aspect ratio and transmural tilt. MVICs were observed to have a large cytoplasmic volume, as evidenced by the large mean surface area to volume ratio 3.68 ± 0.35, which increased under physiological loading conditions to 4.98 ± 1.17.

CONCLUSIONS

Our findings suggest that each MVIC mechanically interacted only with the nearest 3-4 collagen fibers. This key observation suggests that in developing multiscale MV models, each MVIC can be considered a mechanically integral part of the local fiber ensemble and is unlikely to be influenced by more distant structures.

Can We Grow Valves Inside the Heart? Perspective on Material-based In Situ Heart Valve Tissue Engineering

In situ heart valve tissue engineering using cell-free synthetic, biodegradable scaffolds is under development as a clinically attractive approach to create living valves right inside the heart of a patient. In this approach, a valve-shaped porous scaffold "implant" is rapidly populated by endogenous cells that initiate neo-tissue formation in pace with scaffold degradation. While this may constitute a cost-effective procedure, compatible with regulatory and clinical standards worldwide, the new technology heavily relies on the development of advanced biomaterials, the processing thereof into (minimally invasive deliverable) scaffolds, and the interaction of such materials with endogenous cells and neo-tissue under hemodynamic conditions. Despite the first positive preclinical results and the initiation of a small-scale clinical trial by commercial parties, in situ tissue formation is not well understood. In addition, it remains to be determined whether the resulting neo-tissue can grow with the body and preserves functional homeostasis throughout life. More important yet, it is still unknown if and how in situ tissue formation can be controlled under conditions of genetic or acquired disease. Here, we discuss the recent advances of material-based in situ heart valve tissue engineering and highlight the most critical issues that remain before clinical application can be expected. We argue that a combination of basic science - unveiling the mechanisms of the human body to respond to the implanted biomaterial under (patho)physiological conditions - and technological advancements - relating to the development of next generation materials and the prediction of in situ tissue growth and adaptation - is essential to take the next step towards a realistic and rewarding translation of in situ heart valve tissue engineering.

Multiscale mechanics of the cervical facet capsular ligament, with particular emphasis on anomalous fiber realignment prior to tissue failure

The facet capsular ligaments encapsulate the bilateral spinal facet joints and are common sources of painful injury due to afferent innervation. These ligaments exhibit architectural complexity, which is suspected to contribute to the experimentally observed lack of co-localization between macroscopic strain and microstructural tissue damage. The heterogeneous and multiscale nature of this ligament, combined with challenges in experimentally measuring its microscale mechanics, hinders the ability to understand sensory mechanisms under normal or injurious loading. Therefore, image-based, subject-specific, multiscale finite-element models were constructed to predict the mechanical responses of the human cervical facet capsular ligament under uniaxial tensile stretch. The models precisely simulated the force-displacement responses for all samples ([Formula: see text]) and showed promise in predicting the magnitude and location of peak regional strains at two different displacements. Yet, there was a loss of agreement between the model and experiment in terms of fiber organization at large tissue stretch, possibly due to a lack of accounting for tissue failure. The mean fiber stretch ratio predicted by the models was found to be significantly higher in regions that exhibited anomalous fiber realignment experimentally than in regions with normal realignment ([Formula: see text]). The development of microstructural abnormalities was associated with the predicted fiber-level stretch ([Formula: see text]), but not with the elemental maximum principal stress or maximum principal strain by logistic regression. The multiscale models elucidate a potential mechanical basis for predicting injury-prone tissue domains and for defining the relationships between macroscopic ligament stretch and microscale pathophysiology in the subfailure regime.

Modeling the Deformation of the Elastin Network in the Aortic Valve

This paper is concerned with proposing a suitable structurally motivated strain energy function, denoted by Weelastin network, for modeling the deformation of the elastin network within the aortic valve (AV) tissue. The AV elastin network is the main noncollagenous load-bearing component of the valve matrix, and therefore, in the context of continuum-based modeling of the AV, the Weelastin network strain energy function would essentially serve to model the contribution of the “isotropic matrix.” To date, such a function has mainly been considered as either a generic neo-Hookean term or a general exponential function. In this paper, we take advantage of the established structural analogy between the network of elastin chains and the freely jointed molecular chain networks to customize a structurally motivated Weelastin network function on this basis. The ensuing stress–strain (force-stretch) relationships are thus derived and fitted to the experimental data points reported by (Vesely, 1998, “The Role of Elastin in Aortic Valve Mechanics,” J. Biomech., 31, pp. 115–123) for intact AV elastin network specimens under uniaxial tension. The fitting results are then compared with those of the neo-Hookean and the general exponential models, as the frequently used models in the literature, as well as the “Arruda–Boyce” model as the gold standard of the network chain models. It is shown that our proposed Weelastin network function, together with the general exponential and the Arruda–Boyce models provide excellent fits to the data, with R2 values in excess of 0.98, while the neo-Hookean function is entirely inadequate for modeling the AV elastin network. However, the general exponential function may not be amenable to rigorous interpretation, as there is no structural meaning attached to the model. It is also shown that the parameters estimated by the Arruda–Boyce model are not mathematically and structurally valid, despite providing very good fits. We thus conclude that our proposed strain energy function Weelastin network is the preferred choice for modeling the behavior of the AV elastin network and thereby the isotropic matrix. This function may therefore be superimposed onto that of the anisotropic collagen fibers family in order to develop a structurally motivated continuum-based model for the AV.

Modelling mitral valvular dynamics-current trend and future directions

Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed.

Fiber-reinforced computational model of the aortic root incorporating thoracic aorta and coronary structures

Cardiovascular diseases are still the leading causes of death in the developed world. The decline in the mortality associated with circulatory system diseases is accredited to development of new diagnostic and prognostic tools. It is well known that there is an inter relationship between the aortic valve impairment and pathologies of the aorta and coronary vessels. However, due to the limitations of the current tools, the possible link is not fully elucidated. Following our previous model of the aortic root including the coronaries, in this study, we have further developed the global aspect of the model by incorporating the anatomical structure of the thoracic aorta. This model is different from all the previous studies in the sense that inclusion of the coronary structures and thoracic aorta into the natural aortic valve introduces the notion of globality into the model enabling us to explore the possible link between the regional pathologies. The developed model was first validated using the available data in the literature under physiological conditions. Then, to provide a support for the possible association between the localized cardiovascular pathologies and global variations in hemodynamic conditions, we simulated the model for two pathological conditions including moderate and severe aortic valve stenoses. The findings revealed that malformations of the aortic valve are associated with development of low wall shear stress regions and helical blood flow in thoracic aorta that are considered major contributors to aortic pathologies.

Consistent trilayer biomechanical modeling of aortic valve leaflet tissue

Aortic valve tissue exhibits highly nonlinear, anisotropic, and heterogeneous material behavior due to its complex microstructure. A thorough understanding of these characteristics permits us to develop numerical models that can shed insight on the function of the aortic valve in health and disease. Herein, we take a closer look at consistently capturing the observed physical response of aortic valve tissue in a continuum mechanics framework. Such a treatment is the first step in developing comprehensive multiscale and multiphysics models. We highlight two important aspects of aortic valve tissue behavior: the role of the collagen fiber microstructure and the native prestressing. We propose a model that captures these two features as well as the heterogeneous layer-scale topology of the tissue. We find the model can reproduce the experimentally observed multiscale mechanical behavior in a manner that provides intuition on the underlying mechanics.

A coupled mitral valve-left ventricle model with fluid-structure interaction

Understanding the interaction between the valves and walls of the heart is important in assessing and subsequently treating heart dysfunction. This study presents an integrated model of the mitral valve (MV) coupled to the left ventricle (LV), with the geometry derived from in vivo clinical magnetic resonance images. Numerical simulations using this coupled MV-LV model are developed using an immersed boundary/finite element method. The model incorporates detailed valvular features, left ventricular contraction, nonlinear soft tissue mechanics, and fluid-mediated interactions between the MV and LV wall. We use the model to simulate cardiac function from diastole to systole. Numerically predicted LV pump function agrees well with in vivo data of the imaged healthy volunteer, including the peak aortic flow rate, the systolic ejection duration, and the LV ejection fraction. In vivo MV dynamics are qualitatively captured. We further demonstrate that the diastolic filling pressure increases significantly with impaired myocardial active relaxation to maintain a normal cardiac output. This is consistent with clinical observations. The coupled model has the potential to advance our fundamental knowledge of mechanisms underlying MV-LV interaction, and help in risk stratification and optimisation of therapies for heart diseases.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

In Vivo Multiscale and Spatially-Dependent Biomechanics Reveals Differential Strain Transfer Hierarchy in Skeletal Muscle

Biological tissues have a complex hierarchical architecture that spans organ to subcellular scales and comprises interconnected biophysical and biochemical machinery. Mechanotransduction, gene regulation, gene protection, and structure-function relationships in tissues depend on how force and strain are modulated from macro to micro scales, and vice versa. Traditionally, computational and experimental techniques have been used in common model systems (e.g., embryos) and simple strain measures were applied. But the hierarchical transfer of mechanical parameters like strain in mammalian systems is largely unexplored in vivo. Here, we experimentally probed complex strain transfer processes in mammalian skeletal muscle tissue over multiple biological scales using complementary in vivo ultrasound and optical imaging approaches. An iterative hyperelastic warping technique quantified the spatially-dependent strain distributions in tissue, matrix, and subcellular (nuclear) structures, and revealed a surprising increase in strain magnitude and heterogeneity in active muscle as the spatial scale also increased. The multiscale strain heterogeneity indicates tight regulation of mechanical signals to the nuclei of individual cells in active muscle, and an emergent behavior appearing at larger (e.g. tissue) scales characterized by dramatically increased strain complexity.

Heart Valve Biomechanics and Underlying Mechanobiology

Heart valves control unidirectional blood flow within the heart during the cardiac cycle. They have a remarkable ability to withstand the demanding mechanical environment of the heart, achieving lifetime durability by processes involving the ongoing remodeling of the extracellular matrix. The focus of this review is on heart valve functional physiology, with insights into the link between disease-induced alterations in valve geometry, tissue stress, and the subsequent cell mechanobiological responses and tissue remodeling. We begin with an overview of the fundamentals of heart valve physiology and the characteristics and functions of valve interstitial cells (VICs). We then provide an overview of current experimental and computational approaches that connect VIC mechanobiological response to organ- and tissue-level deformations and improve our understanding of the underlying functional physiology of heart valves. We conclude with a summary of future trends and offer an outlook for the future of heart valve mechanobiology, specifically, multiscale modeling approaches, and the potential directions and possible challenges of research development. © 2016 American Physiological Society. Compr Physiol 6:1743-1780, 2016.

Micro and nanotechnologies in heart valve tissue engineering

Due to the increased morbidity and mortality resulting from heart valve diseases, there is a growing demand for off-the-shelf implantable tissue engineered heart valves (TEHVs). Despite the significant progress in recent years in improving the design and performance of TEHV constructs, viable and functional human implantable TEHV constructs have remained elusive. The recent advances in micro and nanoscale technologies including the microfabrication, nano-microfiber based scaffolds preparation, 3D cell encapsulated hydrogels preparation, microfluidic, micro-bioreactors, nano-microscale biosensors as well as the computational methods and models for simulation of biological tissues have increased the potential for realizing viable, functional and implantable TEHV constructs. In this review, we aim to present an overview of the importance and recent advances in micro and nano-scale technologies for the development of TEHV constructs.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

Computational modeling of cardiac fibroblasts and fibrosis

Altered fibroblast behavior can lead to pathologic changes in the heart such as arrhythmia, diastolic dysfunction, and systolic dysfunction. Computational models are increasingly used as a tool to identify potential mechanisms driving a phenotype or potential therapeutic targets against an unwanted phenotype. Here we review how computational models incorporating cardiac fibroblasts have clarified the role for these cells in electrical conduction and tissue remodeling in the heart. Models of fibroblast signaling networks have primarily focused on fibroblast cell lines or fibroblasts from other tissues rather than cardiac fibroblasts, specifically, but they are useful for understanding how fundamental signaling pathways control fibroblast phenotype. In the future, modeling cardiac fibroblast signaling, incorporating -omics and drug-interaction data into signaling network models, and utilizing multi-scale models will improve the ability of in silico studies to predict potential therapeutic targets against adverse cardiac fibroblast activity.

Coupled Simulation of Heart Valves: Applications to Clinical Practice

The last few decades have seen great advances in the understanding of heart valves, and consequently, in the development of novel treatment modalities and surgical procedures for valves afflicted by disease. This is due in part to the profound advancements in computing technology and noninvasive medical imaging techniques that have made it possible to numerically model the complex heart valve systems characterized by distinct features at different length scales and various interacting processes. In this article, we highlight the importance of explicitly coupling these multiple scales and diverse processes to accurately simulate the true behavior of the heart valves, in health and disease. We examine some of the computational modeling studies that have a direct consequence on clinical practice.

Quantification and simulation of layer-specific mitral valve interstitial cells deformation under physiological loading

Within each of the four layers of mitral valve (MV) leaflet tissues there resides a heterogeneous population of interstitial cells that maintain the structural integrity of the MV tissue via protein biosynthesis and enzymatic degradation. There is increasing evidence that tissue stress-induced MV interstitial cell (MVIC) deformations can have deleterious effects on their biosynthetic states that are potentially related to the reduction of tissue-level maintenance and to subsequent organ-level failure. To better understand the interrelationships between tissue-level loading and cellular responses, we developed the following integrated experimental-computational approach. Since in vivo cellular deformations are not directly measurable, we quantified the in-situ layer-specific MVIC deformations for each of the four layers under a controlled biaxial tension loading device coupled to multi-photon microscopy. Next, we explored the interrelationship between the MVIC stiffness and deformation to layer-specific tissue mechanical and structural properties using a macro-micro finite element computational model. Experimental results indicated that the MVICs in the fibrosa and ventricularis layers deformed significantly more than those in the atrialis and spongiosa layers, reaching a nucleus aspect ratio of 3.3 under an estimated maximum physiological tension of 150N/m. The simulated MVIC moduli for the four layers were found to be all within a narrow range of 4.71-5.35kPa, suggesting that MVIC deformation is primarily controlled by each tissue layer's respective structure and mechanical behavior rather than the intrinsic MVIC stiffness. This novel result further suggests that while the MVICs may be phenotypically and biomechanically similar throughout the leaflet, they experience layer-specific mechanical stimulatory inputs due to distinct extracellular matrix architecture and mechanical behaviors of the four MV leaflet tissue layers. This also suggests that MVICs may behave in a layer-specific manner in response to mechanical stimuli in both normal and surgically modified MVs.

Bicuspid aortic valves experience increased strain as compared to tricuspid aortic valves

OBJECTIVE

To determine whether the leaflets of bicuspid aortic valve (BAV) experience increased strain when compared to tricuspid aortic valve (TAV) leaflets.

BACKGROUND

The population at highest risk of aortic valve calcification (AVC) are individuals with BAVs. Currently, efforts to medically treat AVC are hampered by a limited understanding of the biomechanical forces involved in the molecular pathogenesis of AVC.

METHODS

Surgically created BAVs and control TAVs were placed into a left heart simulator. Strains were calculated by comparing the distances between points on the aortic valve (AoV) leaflet during various time points during a simulated cardiac cycle.

RESULTS

The fused leaflets of BAVs experience significantly more strain during systole when compared to TAVs. Specifically, BAVs experience 24% strain (P < .0001) in the radial direction, parallel to the direction of blood flow, as compared to TAVs. There was peak difference of 4% (P < .001) in the circumferential direction.

DISCUSSION

Based upon the data presented here, we are in the process of identifying how increased strain activates calcification-associated pathways in AoV cells. Future studies will examine whether these stretch responsive pathways can be blocked to inhibit calcification of BAVs.

Computational modeling of cardiac valve function and intervention

In the past two decades, major advances have been made in the clinical evaluation and treatment of valvular heart disease owing to the advent of noninvasive cardiac imaging modalities. In clinical practice, valvular disease evaluation is typically performed on two-dimensional (2D) images, even though most imaging modalities offer three-dimensional (3D) volumetric, time-resolved data. Such 3D data offer researchers the possibility to reconstruct the 3D geometry of heart valves at a patient-specific level. When these data are integrated with computational models, native heart valve biomechanical function can be investigated, and preoperative planning tools can be developed. In this review, we outline the advances in valve geometry reconstruction, tissue property modeling, and loading and boundary definitions for the purpose of realistic computational structural analysis of cardiac valve function and intervention.

Ex Vivo characterization of canine liver tissue viscoelasticity after high-intensity focused ultrasound ablation

The potential of elasticity imaging to detect high-intensity focused ultrasound (HIFU) lesions on the basis of their distinct biomechanical properties is promising. However, information on the quantitative mechanical properties of the tissue and the optimal intensity at which to determine the best contrast parameters is scarce. In this study, fresh canine livers were ablated using combinations of ISPTA intensities of 5.55, 7.16 and 9.07 kW/cm(2) and durations of 10 and 30 s ex vivo, resulting in six groups of ablated tissues. Biopsy samples were then interrogated using dynamic shear mechanical testing within the range of 0.1-10 Hz to characterize the tissue's post-ablation viscoelastic properties. All mechanical parameters were found to be frequency dependent. Compared with unablated cases, all six groups of ablated tissues had statistically significant higher complex shear modulus and shear viscosity. However, among the ablated groups, both complex shear modulus and shear viscosity were found to monotonically increase in groups 1-4 (5.55 kW/cm(2) for 10 s, 7.16 kW/cm(2) for 10 s, 9.07 kW/cm(2) for 10 s, and 5.55 kW/cm(2) for 30 s, respectively), but to decrease in groups 5 and 6 (7.16 kW/cm(2) for 30 s, and 9.07 kW/cm(2) for 30 s, respectively). For groups 5 and 6, the temperature was expected to exceed the boiling point, and therefore, the decreased stiffening could be due to the compromised integrity of the tissue microstructure. Future studies will entail estimation tissue mechanical properties in vivo and perform real-time monitoring of tissue alterations during ablation.

The use of sonication treatment to decellularize aortic tissues for preparation of bioscaffolds

A novel decellularization method using sonication treatment is described. Sonication treatment is the combination of physical and chemical agents. These methods will disrupt cell membrane and release cell contents to external environments. The cell removal was facilitated by subsequent rinsing of sodium dodecyl sulfate detergents. Sonication treatment is used in the preparation of complete decellularized bioscaffolds. The aim of this study is to confirm the usefulness of sonication treatment for preparation of biological scaffolds. In this study, samples of aortic tissues are decellularized by sonication treatment at frequency of 170 kHz in 0.1% and 2% sodium dodecyl sulfate detergents for 10-h treatment time. The relation between decellularization and sonication parameters such as dissolved oxygen concentration, conductivity, and pH is investigated. Histological analysis and biomechanical testing is performed to evaluate cell removal efficiency as well as changes in biomechanical properties. Minimal inflammation response elicit by bioscaffolds is confirmed by xenogeneic implantation and immunohistochemistry. Sonication treatment is able to produce complete decellularized tissue suggesting that these treatments could be applied widely as one of the decellularization method.

A viscoelastic property study in canine liver before and after HIFU ablation in vitro

Elasticity imaging techniques have shown great potential in detecting High Intensity Focused Ultrasound (HIFU) lesions based on their distinct biomechanical properties. However, quantitative tissue viscoelastic properties and the optimal power to obtain the best contrast parameters remain scarce. In the present study, fresh canine livers were ablated ex vivo using six different acoustic powers and time durations, covering an energy range of 80-330 J. Biopsy samples were then extracted and examined, using rheometry, to obtain the viscoelastic properties post-ablation in vitro. All mechanical parameters were found to be frequency dependent. Both the shear complex modulus and viscosity exhibited monotonic increase for the first 4 groups (80-240 J), relatively lower HIFU powers. Similar parameters from groups 5-6 (300-330 J) showed relative decrease, still higher than unablated group 0. The tangent of the stress-strain phase shift was found to vary from unablated group 0 to ablated groups 1-6. However, no measurable difference amongst the ablated groups was found. Decreased stiffening at high powers compared to the baseline could likely be due to compromised structural integrity in the pulverized tissue well beyond the boiling point. The findings here can be used to optimize the efficient monitoring and treatment of tumors using any thermally-based methods where strong tissue damage is expected and/or warranted, respectively.

Quantifying the interfibrillar spacing and fibrillar orientation of the aortic extracellular matrix using histology image processing: toward multiscale modeling

An essential part of understanding tissue microstructural mechanics is to establish quantitative measures of the morphological changes. Given the complex, highly localized, and interactive architecture of the extracellular matrix, developing techniques to reproducibly quantify the induced microstructural changes has been found to be challenging. In this paper, a new method for quantifying the changes in the fibrillar organization is developed using histology images. A combinatorial frequency-spatial image processing approach was developed based on the Fourier and Hough transformations of histology images to measure interfibrillar spacing and fibrillar orientation, respectively. The method was separately applied to the inner and outer wall thickness of native- and elastin-isolated aortic tissues under different loading states. Results from both methods were interpreted in a complementary manner to obtain a more complete understanding of morphological changes due to tissue deformations at the microscale. The observations were consistent in quantifying the observed morphological changes during tissue deformations and in explaining such changes in terms of tissue-scale phenomena. The findings of this study could pave the way for more rigorous modeling of structure-property relationships in soft tissues, with implications extendable to cardiovascular constitutive modeling and tissue engineering.

The mechanobiology of mitral valve function, degeneration, and repair

In degenerative valve disease, the highly organized mitral valve leaflet matrix stratification is progressively destroyed and replaced with proteoglycan rich, mechanically inadequate tissue. This is driven by the actions of originally quiescent valve interstitial cells that become active contractile and migratory myofibroblasts. While treatment for myxomatous mitral valve disease in humans ranges from repair to total replacement, therapies in dogs focus on treating the consequences of the resulting mitral regurgitation. The fundamental gap in our understanding is how the resident valve cells respond to altered mechanical signals to drive tissue remodeling. Despite the pathological similarities and high clinical occurrence, surprisingly little mechanistic insight has been gleaned from the dog. This review presents what is known about mitral valve mechanobiology from clinical, in vivo, and in vitro data. There are a number of experimental strategies already available to pursue this significant opportunity, but success requires the collaboration between veterinary clinicians, scientists, and engineers.

In vivo dynamic strains of the ovine anterior mitral valve leaflet

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.

Substrates for cardiovascular tissue engineering

Cardiovascular tissue engineering aims to find solutions for the suboptimal regeneration of heart valves, arteries and myocardium by creating 'living' tissue replacements outside (in vitro) or inside (in situ) the human body. A combination of cells, biomaterials and environmental cues of tissue development is employed to obtain tissues with targeted structure and functional properties that can survive and develop within the harsh hemodynamic environment of the cardiovascular system. This paper reviews the up-to-date status of cardiovascular tissue engineering with special emphasis on the development and use of biomaterial substrates. Key requirements and properties of these substrates, as well as methods and readout parameters to test their efficacy in the human body, are described in detail and discussed in the light of current trends toward designing biologically inspired microenviroments for in situ tissue engineering purposes.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.