Continuum mixture models of biological growth and remodeling: past successes and future opportunities

A biochemomechanical model of collagen turnover in arterial adaptations to hemodynamic loading

The production, removal, and remodeling of fibrillar collagen is fundamental to mechanical homeostasis in arteries, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have proven able to predict salient features of the progression of certain vascular adaptations as well as disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically within the range of 10-70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Developing the genotype-to-phenotype relationship in evolutionary theory: A primer of developmental features

For decades, there have been repeated calls for more integration across evolutionary and developmental biology. However, critiques in the literature and recent funding initiatives suggest this integration remains incomplete. We suggest one way forward is to consider how we elaborate the most basic concept of development, the relationship between genotype and phenotype, in traditional models of evolutionary processes. For some questions, when more complex features of development are accounted for, predictions of evolutionary processes shift. We present a primer on concepts of development to clarify confusion in the literature and fuel new questions and approaches. The basic features of development involve expanding a base model of genotype-to-phenotype to include the genome, space, and time. A layer of complexity is added by incorporating developmental systems, including signal-response systems and networks of interactions. The developmental emergence of function, which captures developmental feedbacks and phenotypic performance, offers further model elaborations that explicitly link fitness with developmental systems. Finally, developmental features such as plasticity and developmental niche construction conceptualize the link between a developing phenotype and the external environment, allowing for a fuller inclusion of ecology in evolutionary models. Incorporating aspects of developmental complexity into evolutionary models also accommodates a more pluralistic focus on the causal importance of developmental systems, individual organisms, or agents in generating evolutionary patterns. Thus, by laying out existing concepts of development, and considering how they are used across different fields, we can gain clarity in existing debates around the extended evolutionary synthesis and pursue new directions in evolutionary developmental biology. Finally, we consider how nesting developmental features in traditional models of evolution can highlight areas of evolutionary biology that need more theoretical attention.

An updated Lagrangian constrained mixture model of pathological cardiac growth and remodelling

Progressive left ventricular (LV) growth and remodelling (G&R) is often induced by volume and pressure overload, characterized by structural and functional adaptation through myocyte hypertrophy and extracellular matrix remodelling, which are dynamically regulated by biomechanical factors, inflammation, neurohormonal pathways, etc. When prolonged, it can eventually lead to irreversible heart failure. In this study, we have developed a new framework for modelling pathological cardiac G&R based on constrained mixture theory using an updated reference configuration, which is triggered by altered biomechanical factors to restore biomechanical homeostasis. Eccentric and concentric growth, and their combination have been explored in a patient-specific human LV model under volume and pressure overload. Eccentric growth is triggered by overstretching of myofibres due to volume overload, i.e. mitral regurgitation, whilst concentric growth is driven by excessive contractile stress due to pressure overload, i.e. aortic stenosis. Different biological constituent's adaptations under pathological conditions are integrated together, which are the ground matrix, myofibres and collagen network. We have shown that this constrained mixture-motivated G&R model can capture different phenotypes of maladaptive LV G&R, such as chamber dilation and wall thinning under volume overload, wall thickening under pressure overload, and more complex patterns under both pressure and volume overload. We have further demonstrated how collagen G&R would affect LV structural and functional adaption by providing mechanistic insight on anti-fibrotic interventions. This updated Lagrangian constrained mixture based myocardial G&R model has the potential to understand the turnover processes of myocytes and collagen due to altered local mechanical stimuli in heart diseases, and in providing mechanistic links between biomechanical factors and biological adaption at both the organ and cellular levels. Once calibrated with patient data, it can be used for assessing heart failure risk and designing optimal treatment therapies. STATEMENT OF SIGNIFICANCE: Computational modelling of cardiac G&R has shown high promise to provide insight into heart disease management when mechanistic understandings are quantified between biomechanical factors and underlying cellular adaptation processes. The kinematic growth theory has been dominantly used to phenomenologically describe the biological G&R process but neglecting underlying cellular mechanisms. We have developed a constrained mixture based G&R model with updated reference by taking into account different mechanobiological processes in the ground matrix, myocytes and collagen fibres. This G&R model can serve as a basis for developing more advanced myocardial G&R models further informed by patient data to assess heart failure risk, predict disease progression, select the optimal treatment by hypothesis testing, and eventually towards a truly precision cardiology using in-silico models.

A Biochemomechanical Model of Collagen Turnover in Arterial Adaptations to Hemodynamic Loading

The production, removal, and remodeling of fibrillar collagen is fundamental to arterial homeostasis, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have demonstrated a capability to predict salient features of the progression of certain vascular adaptations and disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically taken within the range of 10â€"70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Computer simulation of the wound process (review of literature)

Relevance. Computer simulation is a mathematical modeling process performed on a computer that is designed to predict the behavior or results of a real or physical system. Computer simulation has a number of advantages over classical models of animal experiments: the cheapness of the method (the need to acquire and maintain animals disappears by itself), the speed of obtaining results, the absence of bioethical problems, the ability to change the conditions of the experiment, etc.

he purpose of this study is to review the methods of computer simulation of the wound process, to identify the shortcomings of the models and propose ways to solve them, as well as to select the best existing model for describing wound regeneration.

Material and methods. In the course of this work, an analysis was made of foreign and domestic literature on the problem of computer modeling of the wound process.

Results. After analyzing the relevant literature on this topic, the problem is seen precisely in the insufficiently studied process of wound regeneration, since many different cells, cytokines, growth factors, enzymes, fibrillar proteins, etc. take part in it. The models that currently exist describe wound regeneration only in an extremely generalized way, which does not allow us to apply them in clinical situations. Analyzing literature sources, we came to the conclusion that both numerical approaches, both cellular-biochemical (the first type of models) and phenomenological (the second type) are applicable in the case of wound modeling and can be used very successfully. The problem is that on the basis of one approach it is impossible to display a complete picture of wound healing, in this way it is possible to predict only individual regeneration parameters necessary for certain purposes due to the complexity and versatility of this typical pathophysiological process.

Conclusion. Computer modeling of wounds is still a controversial and complex topic. Existing models are not intended to describe all the processes occurring in a healing wound. It is much more productive to describe the various phenomena during healing separately. This is due to the fact that many elements are involved in the regeneration of the skin, which are almost impossible to take into account in full. The available models are of exclusively scientific value, consisting in attempts to understand all complex processes and interactions. Practical application is difficult, since existing models require specific input data that require highly specialized equipment. If we abstract from all this, then the best existing model of the first type is the model of the authors Yangyang Wang, Christian F. Guerrero-Juarez, Yuchi Qiu and co-authors, in addition to it, any of the described phenomenological models will do. 

Nuclear pore complexes concentrate on Actin/LINC/Lamin nuclear lines in response to mechanical stress in a SUN1 dependent manner

Formation of robust actomyosin stress fibers (SF) in response to cell stretch plays a key role in the transfer of information from the cytoplasm into the nucleus. Actin/LINC/Lamin (ALL) nuclear lines provide mechanical linkage between the actin cytoskeleton and the lamin nucleoskeleton across the nuclear envelope. To understand the establishment of ALL lines, we used live cell imaging of cells exposed to cyclic stretch. We discovered that nuclear pore complexes (NPCs) concentrate along ALL lines that are generated in response to uniaxial cyclic stretch. The ALL-associated NPCs display increased fluorescence intensity of nucleoporins Pom121, TPR and Nup153 relative to nucleoporins that are distal to the ALL lines. Here we test the hypothesis that a LINC complex component of ALL lines, SUN1 is involved in the integration of NPCs with ALL lines. We generated CRISPR SUN1 knockdown and knockout cell lines and show that SUN1 is essential for normal integration of NPCs to ALL lines. Loss or elimination of SUN1 significantly diminishes NPC/ALL line integration, demonstrating a key role for SUN1 in the recruitment or stabilization of NPCs to a discrete subdomain of the nuclear envelope at ALL lines. This work provides new insight into the mechanism by which cells respond to mechanical force through nuclear envelope remodeling.

Phosphorylation of the small heat shock protein HspB1 regulates cytoskeletal recruitment and cell motility

The small heat shock protein HspB1, also known as Hsp25/27, is a ubiquitously expressed molecular chaperone that responds to mechanical cues. Uniaxial cyclic stretch activates the p38 mitogen-activated protein kinase (MAPK) signaling cascade and increases the phosphorylation of HspB1. Similar to the mechanosensitive cytoskeletal regulator zyxin, phospho-HspB1 is recruited to features of the stretch-stimulated actin cytoskeleton. To evaluate the role of HspB1 and its phosphoregulation in modulating cell function, we utilized CRISPR/Cas9-edited HspB1-null cells and determined they were altered in behaviors such as actin cytoskeletal remodeling, cell spreading, and cell motility. In our model system, expression of WT HspB1, but not nonphosphorylatable HspB1, rescued certain characteristics of the HspB1-null cells including the enhanced cell motility of HspB1-null cells and the deficient actin reinforcement of stretch-stimulated HspB1-null cells. The recruitment of HspB1 to high-tension structures in geometrically constrained cells, such as actin comet tails emanating from focal adhesions, also required a phosphorylatable HspB1. We show that mechanical signals activate posttranslational regulation of the molecular chaperone, HspB1, and are required for normal cell behaviors including actin cytoskeletal remodeling, cell spreading, and cell migration.

On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics

This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius-Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Constrained Mixture Models of Soft Tissue Growth and Remodeling - Twenty Years After

Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or clinical intervention. Such approaches also can be used to design improved tissue engineered constructs to repair, replace, or regenerate tissues. Focusing on blood vessels as archetypes of soft tissues, this paper reviews a constrained mixture theory introduced twenty years ago and explores its usage since by contrasting simulations of diverse vascular conditions. The discussion is framed within the concept of mechanical homeostasis, with consideration of solid-fluid interactions, inflammation, and cell signaling highlighting both past accomplishments and future opportunities as we seek to understand better the evolving composition, geometry, and material behaviors of soft tissues under complex conditions.

Mechanical stress influences the morphology and function of human uterosacral ligament fibroblasts and activates the p38 MAPK pathway

Introduction and hypothesis

Pelvic organ prolapse (POP) is a common condition in older women that affects quality of life. Mechanical injury of the pelvic floor support system contributes to POP development. In our study, we aimed to examine the mechanical damage to human uterosacral ligament fibroblasts (hUSLFs) to preliminarily explore the mechanism of mechanical transduction in POP.

Methods

hUSLFs were derived from POP and non-POP patients. Mechanical stress was induced by the FX-5000 T-cell stress loading system. Student’s t-test was used for comparisons between different groups.

Results

We found that hUSLFs from POP patients were larger and longer than those from non-POP patients and exhibited cytoskeleton F-actin rearrangement. Collagen I and III expression levels were lower and matrix metalloproteinase 1 (MMP1) levels were higher in POP patients than in non-POP patients. Additionally, the apoptosis rate was significantly increased in POP patients compared to non-POP patients. After mechanical stretching, hUSLFs underwent a POP-like transformation. Cells became longer, and the cytoskeleton became thicker and rearranged. The extracellular matrix (ECM) was remodelled because of the upregulation of collagen I and III expression and downregulation of MMP1 expression. Mechanical stress also induced hUSLF apoptosis. Notably, we found that the p38 MAPK pathway was activated by mechanical stretching.

Conclusions

Mechanical stress induced morphological changes in ligament fibroblasts, leading to cytoskeleton and ECM remodelling and cell apoptosis. p38 MAPK might be involved in this process, providing novel insights into the mechanical biology of and possible therapies for this disease.

Computational models of cardiac hypertrophy

Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.

Investigation of Pathophysiological Aspects of Aortic Growth, Remodeling, and Failure Using a Discrete-Fiber Microstructural Model

Aortic aneurysms are inherently unpredictable. One can never be sure whether any given aneurysm may rupture or dissect. Clinically, the criteria for surgical intervention are based on size and growth rate, but it remains difficult to identify a high-risk aneurysm, which may require intervention before the cutoff criteria, versus an aneurysm than can be treated safely by more conservative measures. In this work, we created a computational microstructural model of a medial lamellar unit (MLU) incorporating (1) growth and remodeling laws applied directly to discrete, individual fibers, (2) separate but interacting fiber networks for collagen, elastin, and smooth muscle, (3) active and passive smooth-muscle cell mechanics, and (4) failure mechanics for all three fiber types. The MLU model was then used to study different pathologies and microstructural anomalies that may play a role in vascular growth and failure. Our model recapitulated many aspects of arterial remodeling under hypertension with no underlying genetic syndrome including remodeling dynamics, tissue mechanics, and failure. Syndromic effects (smooth muscle cell (SMC) dysfunction or elastin fragmentation) drastically changed the simulated remodeling process, tissue behavior, and tissue strength. Different underlying pathologies were able to produce similarly dilatated vessels with different failure properties, providing a partial explanation for the imperfect nature of aneurysm size as a predictor of outcome.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel-Gasser-Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

Cellular Automata Modeling of Stem-Cell-Driven Development of Tissue in the Nervous System

Mathematical and computational modeling enables biologists to integrate data from observations and experiments into a theoretical framework. In this review, we describe how developmental processes associated with stem-cell-driven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the single-cell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.

Mechanobiological Stability of Biological Soft Tissues

Like all other materials, biological soft tissues are subject to general laws of physics, including those governing mechanical equilibrium and stability. In addition, however, these tissues are able to respond actively to changes in their mechanical and chemical environment. There is, therefore, a pressing need to understand such processes theoretically. In this paper, we present a new rate-based constrained mixture formulation suitable for studying mechanobiological equilibrium and stability of soft tissues exposed to transient or sustained changes in material composition or applied loading. These concepts are illustrated for canonical problems in arterial mechanics, which distinguish possible stable versus unstable mechanobiological responses. Such analyses promise to yield insight into biological processes that govern both health and disease progression.

3D bone models to study the complex physical and cellular interactions between tumor and the bone microenvironment

As the complexity of interactions between tumor and its microenvironment has become more evident, a critical need to engineer in vitro models that veritably recapitulate the 3D microenvironment and relevant cell populations has arisen. This need has caused many groups to move away from the traditional 2D, tissue culture plastic paradigms in favor of 3D models with materials that more closely replicate the in vivo milieu. Creating these 3D models remains a difficult endeavor for hard and soft tissues alike as the selection of materials, fabrication processes, and optimal conditions for supporting multiple cell populations makes model development a nontrivial task. Bone tissue in particular is uniquely difficult to model in part because of the limited availability of materials that can accurately capture bone rigidity and architecture, and also due to the dependence of both bone and tumor cell behavior on mechanical signaling. Additionally, the bone is a complex cellular microenvironment with multiple cell types present, including relatively immature, pluripotent cells in the bone marrow. This prospect will focus on the current 3D models in development to more accurately replicate the bone microenvironment, which will help facilitate improved understanding of bone turnover, tumor-bone interactions, and drug response. These studies have demonstrated the importance of accurately modelling the bone microenvironment in order to fully understand signaling and drug response, and the significant effects that model properties such as architecture, rigidity, and dynamic mechanical factors have on tumor and bone cell response.

A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue

Most mathematical models of the growth and remodeling of load-bearing soft tissues are based on one of two major approaches: a kinematic theory that specifies an evolution equation for the stress-free configuration of the tissue as a whole or a constrained mixture theory that specifies rates of mass production and removal of individual constituents within stressed configurations. The former is popular because of its conceptual simplicity, but relies largely on heuristic definitions of growth; the latter is based on biologically motivated micromechanical models, but suffers from higher computational costs due to the need to track all past configurations. In this paper, we present a temporally homogenized constrained mixture model that combines advantages of both classical approaches, namely a biologically motivated micromechanical foundation, a simple computational implementation, and low computational cost. As illustrative examples, we show that this approach describes well both cell-mediated remodeling of tissue equivalents in vitro and the growth and remodeling of aneurysms in vivo. We also show that this homogenized constrained mixture model suggests an intimate relationship between models of growth and remodeling and viscoelasticity. That is, important aspects of tissue adaptation can be understood in terms of a simple mechanical analog model, a Maxwell fluid (i.e., spring and dashpot in series) in parallel with a "motor element" that represents cell-mediated mechanoregulation of extracellular matrix. This analogy allows a simple implementation of homogenized constrained mixture models within commercially available simulation codes by exploiting available models of viscoelasticity.

Mechanical signals activate p38 MAPK pathway-dependent reinforcement of actin via mechanosensitive HspB1

Mechanical force induces protein phosphorylations, subcellular redistributions, and actin remodeling. We show that mechanical activation of the p38 MAPK pathway leads to phosphorylation of HspB1 (hsp25/27), which redistributes to cytoskeletal structures, and contributes to the actin cytoskeletal remodeling induced by mechanical stimulation.

Despite the importance of a cell’s ability to sense and respond to mechanical force, the molecular mechanisms by which physical cues are converted to cell-instructive chemical information to influence cell behaviors remain to be elucidated. Exposure of cultured fibroblasts to uniaxial cyclic stretch results in an actin stress fiber reinforcement response that stabilizes the actin cytoskeleton. p38 MAPK signaling is activated in response to stretch, and inhibition of p38 MAPK abrogates stretch-induced cytoskeletal reorganization. Here we show that the small heat shock protein HspB1 (hsp25/27) is phosphorylated in stretch-stimulated mouse fibroblasts via a p38 MAPK-dependent mechanism. Phosphorylated HspB1 is recruited to the actin cytoskeleton, displaying prominent accumulation on actin “comet tails” that emanate from focal adhesions in stretch-stimulated cells. Site-directed mutagenesis to block HspB1 phosphorylation inhibits the protein’s cytoskeletal recruitment in response to mechanical stimulation. HspB1-null cells, generated by CRISPR/Cas9 nuclease genome editing, display an abrogated stretch-stimulated actin reinforcement response and increased cell migration. HspB1 is recruited to sites of increased traction force in cells geometrically constrained on micropatterned substrates. Our findings elucidate a molecular pathway by which a mechanical signal is transduced via activation of p38 MAPK to influence actin remodeling and cell migration via a zyxin-independent process.

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues

Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data.

The characterization of decellularized human skeletal muscle as a blueprint for mimetic scaffolds

The use of decellularized skeletal muscle (DSM) as a cell substrate and scaffold for the repair of volumetric muscle loss injuries has shown therapeutic promise. The performance of DSM materials motivated our interest in exploring the chemical and physical properties of this promising material. We suggest that these properties could serve as a blueprint for the development of next generation engineered materials with DSM mimetic properties. In this study, whole human lower limb rectus femoris (n = 10) and upper limb supraspinatus muscle samples (n = 10) were collected from both male and female tissue donors. Skeletal muscle samples were decellularized and nine property values, capturing key compositional, architectural, and mechanical properties, were measured and statistically analyzed. Mean values for each property were determined across muscle types and sexes. Additionally, the influence of muscle type (upper vs lower limb) and donor sex (male vs female) on each of the DSM material properties was examined. The data suggests that DSM materials prepared from lower limb rectus femoris samples have an increased modulus and contain a higher collagen content then upper limb supraspinatus muscles. Specifically, lower limb rectus femoris DSM material modulus and collagen content was approximately twice that of lower limb supraspinatus DSM samples. While muscle type did show some influence on material properties, we did not find significant trends related to sex. The material properties reported herein may be used as a blueprint for the data-driven design of next generation engineered scaffolds with muscle mimetic properties, as well as inputs for computational and physical models of skeletal muscle.

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.

Mathematical modeling of cardiac growth and remodeling

This review provides an overview of the current state of mathematical models of cardiac growth and remodeling (G&R). We concisely describe the experimental observations associated with cardiac G&R and discuss existing mathematical models that describe this process. To facilitate the discussion, we have organized the G&R models in terms of (1) the physical focus (biochemical vs mechanical) and (2) the process that they describe (myocyte hypertrophy vs extracellular matrix remodeling). The review concludes with a discussion of some possible directions that can advance the existing state of cardiac G&R mathematical modeling. WIREs Syst Biol Med 2016, 8:211-226. doi: 10.1002/wsbm.1330 For further resources related to this article, please visit the WIREs website.

A triphasic constrained mixture model of engineered tissue formation under in vitro dynamic mechanical conditioning

While it has become axiomatic that mechanical signals promote in vitro engineered tissue formation, the underlying mechanisms remain largely unknown. Moreover, efforts to date to determine parameters for optimal extracellular matrix (ECM) development have been largely empirical. In the present work, we propose a two-pronged approach involving novel theoretical developments coupled with key experimental data to develop better mechanistic understanding of growth and development of dense connective tissue under mechanical stimuli. To describe cellular proliferation and ECM synthesis that occur at rates of days to weeks, we employ mixture theory to model the construct constituents as a nutrient-cell-ECM triphasic system, their transport, and their biochemical reactions. Dynamic conditioning protocols with frequencies around 1 Hz are described with multi-scale methods to couple the dissimilar time scales. Enhancement of nutrient transport due to pore fluid advection is upscaled into the growth model, and the spatially dependent ECM distribution describes the evolving poroelastic characteristics of the scaffold-engineered tissue construct. Simulation results compared favorably to the existing experimental data, and most importantly, distinguish between static and dynamic conditioning regimes. The theoretical framework for mechanically conditioned tissue engineering (TE) permits not only the formulation of novel and better-informed mechanistic hypothesis describing the phenomena underlying TE growth and development, but also the exploration/optimization of conditioning protocols in a rational manner.

A computational analysis of cell-mediated compaction and collagen remodeling in tissue-engineered heart valves

One of the most critical problems in heart valve tissue engineering is the progressive development of valvular insufficiency due to leaflet retraction. Understanding the underlying mechanisms of this process is crucial for developing tissue-engineered heart valves (TEHVs) that maintain their functionality in the long term. In the present study, we adopted a computational approach to predict the remodeling process in TEHVs subjected to dynamic pulmonary and aortic pressure conditions, and to assess the risk of valvular insufficiency. In addition, we investigated the importance of the intrinsic cell contractility on the final outcome of the remodeling process. For valves implanted in the aortic position, the model predictions suggest that valvular insufficiency is not likely to occur as the blood pressure is high enough to prevent the development of leaflet retraction. In addition, the collagen network was always predicted to remodel towards a circumferentially aligned network, which is corresponding to the native situation. In contrast, for valves implanted in the pulmonary position, our model predicted that there is a high risk for the development of valvular insufficiency, unless the cell contractility is very low. Conversely, the development of a circumferential collagen network was only predicted at these pressure conditions when cell contractility was high. Overall, these results, therefore, suggest that tissue remodeling at aortic pressure conditions is much more stable and favorable compared to tissue remodeling at pulmonary pressure conditions.

Competition between cap and basal actin fiber orientation in cells subjected to contact guidance and cyclic strain

In vivo, adhesive cells continuously respond to a complex range of physical cues coming from the surrounding microenvironment by remodeling their cytoskeleton. Topographical and mechanical cues applied separately have been shown to affect the orientation of the actin stress fibers. Here we investigated the combined effects of contact guidance by topographical cues and uniaxial cyclic strain on actin cytoskeleton orientation of vascular derived cells. We devised a modular setup of stretchable circular and elliptic elastomeric microposts, capable to expose the cells to both contact guidance and uniaxial cyclic strain. A competition occurs between these cues when both contact guidance and strain are oriented along the same direction. For the first time we show that this competition originates from the distinct response of perinuclear basal and actin cap fibers: While basal fibers follow the contact guidance cue, actin cap fibers respond to the cyclic strain by strain avoidance. We also show that nuclear orientation follows actin cap fiber orientation, suggesting that actin cap fibers are responsible for cellular reorientation. Taken together, these findings may have broad implications in understanding the response of cells to combined topographical and mechanical cues.

Micro-poromechanics model of fluid-saturated chemically active fibrous media

We have developed a micromechanics based model for chemically active saturated fibrous media that incorporates fiber network microstructure, chemical potential driven fluid flow, and micro-poromechanics. The stress-strain relationship of the dry fibrous media is first obtained by considering the fiber behavior. The constitutive relationships applicable to saturated media are then derived in the poromechanics framework using Hill's volume averaging. The advantage of this approach is that the resultant continuum model accounts for the discrete nature of the individual fibers while retaining a form suitable for porous materials. As a result, the model is able to predict the influence of micro-scale phenomena, such as the fiber pre-strain caused by osmotic effects and evolution of fiber network structure with loading, on the overall behavior and in particular, on the poromechanics parameters. Additionally, the model can describe fluid-flow related rate-dependent behavior under confined and unconfined conditions and varying chemical environments. The significance of the approach is demonstrated by simulating unconfined drained monotonic uniaxial compression under different surrounding fluid bath molarity, and fluid-flow related creep and relaxation at different loading-levels and different surrounding fluid bath molarity. The model predictions conform to the experimental observations for saturated soft fibrous materials. The method can potentially be extended to other porous materials such as bone, clays, foams and concrete.

Bone tissue regeneration: the role of scaffold geometry

A review of how the geometrical design of scaffolds influences the bone tissue regeneration process.

A coupled model of neovessel growth and matrix mechanics describes and predicts angiogenesis in vitro

During angiogenesis, sprouting microvessels interact with the extracellular matrix (ECM) by degrading and reorganizing the matrix, applying traction forces, and producing deformation. Morphometric features of the resulting microvascular network are affected by the interaction between the matrix and angiogenic microvessels. The objective of this study was to develop a continuous-discrete modeling approach to simulate mechanical interactions between growing neovessels and the deformation of the matrix in vitro. This was accomplished by coupling an existing angiogenesis growth model which uses properties of the ECM to regulate angiogenic growth with the nonlinear finite element software FEBio (www.febio.org). FEBio solves for the deformation and remodeling of the matrix caused by active stress generated by neovessel sprouts, and this deformation was used to update the ECM into the current configuration. After mesh resolution and parameter sensitivity studies, the model was used to accurately predict vascular alignment for various matrix boundary conditions. Alignment primarily arises passively as microvessels convect with the deformation of the matrix, but active alignment along collagen fibrils plays a role as well. Predictions of alignment were most sensitive to the range over which active stresses were applied and the viscoelastic time constant in the material model. The computational framework provides a flexible platform for interpreting in vitro investigations of vessel-matrix interactions, predicting new experiments, and simulating conditions that are outside current experimental capabilities.

LIM proteins in actin cytoskeleton mechanoresponse

The actin cytoskeleton assembles into branched networks or bundles to generate mechanical force for critical cellular processes such as establishment of polarity, adhesion, and migration. Stress fibers (SFs) are contractile actomyosin structures that physically couple to the extracellular matrix through integrin-based focal adhesions (FAs), thereby transmitting force into and across the cell. Recently, LIN-11, Isl1, and MEC-3 (LIM) domain proteins have been implicated in mediating this cytoskeletal mechanotransduction. Among the more well-studied LIM domain adapter proteins is zyxin, a dynamic component of both FAs and SFs. Here we discuss recent research detailing the mechanisms by which SFs adjust their structure and composition to balance mechanical forces and suggest ways that zyxin and other LIM domain proteins mediate mechanoresponse.

Interstitial growth and remodeling of biological tissues: tissue composition as state variables

Growth and remodeling of biological tissues involves mass exchanges between soluble building blocks in the tissue's interstitial fluid and the various constituents of cells and the extracellular matrix. As the content of these various constituents evolves with growth, associated material properties, such as the elastic modulus of the extracellular matrix, may similarly evolve. Therefore, growth theories may be formulated by accounting for the evolution of tissue composition over time in response to various biological and mechanical triggers. This approach has been the foundation of classical bone remodeling theories that successfully describe Wolff's law by establishing a dependence between Young's modulus and bone apparent density and by formulating a constitutive relation between bone mass supply and the state of strain. The goal of this study is to demonstrate that adding tissue composition as state variables in the constitutive relations governing the stress-strain response and the mass supply represents a very general and straightforward method to model interstitial growth and remodeling in a wide variety of biological tissues. The foundation for this approach is rooted in the framework of mixture theory, which models the tissue as a mixture of multiple solid and fluid constituents. A further generalization is to allow each solid constituent in a constrained solid mixture to have its own reference (stress-free) configuration. Several illustrations are provided, ranging from bone remodeling to cartilage tissue engineering and cervical remodeling during pregnancy.