Tissue growth and remodeling

Modeling Fatigue Failure of Cartilage and Fibrous Biological Tissues Using Constrained Reactive Mixture Theory

Fatigue failure in biological soft tissues plays a critical role in the etiology of chronic soft tissue injuries and diseases such as osteoarthritis (OA). Understanding failure mechanisms is hindered by the decades-long timescales over which damage takes place. Analyzing the factors contributing to fatigue failure requires the help of validated computational models developed for soft tissues. This study presents a framework for fatigue failure of fibrous biological tissues based on reaction kinetics, where the composition of intact and fatigued material regions can evolve via degradation and breakage over time, in response to energy-based fatigue and damage criteria. Using reactive constrained mixture theory, material region mass fractions are governed by the axiom of mass balance. Progression of fatigue is controlled by an energy-based reaction rate, with user-selected probability functions defining the damage propensity of intact and fatigued material regions. Verification of this reactive theory, which is implemented in the open-source FEBio finite element software, is provided in this study. Validation is also demonstrated against experimental data, showing that predicted damage can be linked to results from biochemical assays. The framework is also applied to study fatigue failure during frictional contact of cartilage. Simulating previous experiments suggests that frictional effects slightly increase fatigue progression, but the main driver is cyclic compressive contact loading. This study demonstrated the ability of theoretical models to complement and extend experimental findings, advancing our understanding of the time progression of fatigue in biological tissues.

Langevin picture of subdiffusion in nonuniformly expanding medium

Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in a static medium to a uniformly and even nonuniformly expanding medium. The dynamic mechanism of the anomalous diffusion in the nonuniformly expanding medium has only been investigated by the approach of continuous-time random walk. To study more physical observables and to supplement the physical models of the anomalous diffusion in the expanding mediums, we characterize the nonuniformly expanding medium with a spatiotemporal dependent scale factor a(x,t) and build the Langevin picture describing the particle's motion in the nonuniformly expanding medium. Besides the existing comoving and physical coordinates, by introducing a new coordinate and assuming that a(x,t) is separable at a long-time limit, we build the relation between the nonuniformly expanding medium and the uniformly expanding one and further obtain the moments of the comoving and physical coordinates. Different forms of the scale factor a(x,t) are considered to uncover the combined effects of the particle's intrinsic diffusion and the nonuniform expansion of medium. The theoretical analyses and simulations provide the foundation for studying more anomalous diffusion phenomena in the expanding mediums.

Instabilities in a growing system of active particles: scalar and vectorial systems

The physics of micron-scale biological colonies usually benefits from different out-of-equilibrium sources. In bacterial colonies and cellular tissues, the growth process is among the important active sources that determine the dynamics. In this article, we study the generic dynamical instabilities associated with the growth phenomena that may arise in both scalar and vectorial systems. In vectorial systems, where the rotational degrees of particles play a role, a phenomenological growth-mediated torque can affect the rotational dynamics of individual particles. We show that such a growth-mediated torque can result in active traveling waves in the bulk of a growing system. In addition to the bulk properties, we analyze the instabilities in the shape of growing interfaces in both scalar and vectorial systems.

Pathological beige remodeling induced by cancer cachexia depends on the disease severity and involves mainly the trans-differentiation of mature white adipocytes

In cancer associated cachexia (CAC), white adipose tissue undergoes morphofunctional and inflammatory changes that lead to tissue dysfunction and remodeling. In addition to metabolic changes in white adipose tissues (WAT), adipose tissue atrophy has been implicated in several clinical complications and poor prognoses associated with cachexia. Adipocyte atrophy may be associated with increased beige remodeling in human CAC as evidenced by the "beige remodeling" observed in preclinical models of CAC. Even though beige remodeling is associated with CAC-induced WAT dysfunction, there are still some open questions regarding their cellular origins. In this study, we investigated the development of beige remodeling in CAC from a broader perspective. In addition, we used a grading system to identify the scAT as being affected by mice weight loss early and intensely. Using different in vitro and ex-vivo techniques, we demonstrated that Lewis LLC1 cells can induce a switch from white to beige adipocytes, which is specific to this type of tumor cell. During the more advanced stages of CAC, beige adipocytes are mainly formed from the transdifferentiation of cells. According to our results, humanizing the CAC classification system is an efficient approach to defining the onset of the syndrome in a more homogeneous manner. Pathological beige remodeling occurred early in the disease course and exhibited phenotypic characteristics specific to LLC cells' secretomes. Developing therapeutic strategies that recruit beige adipocytes in vivo may be better guided by an understanding of the cellular origins of beige adipocytes emitted by CAC.

Turtle Shell Kinesis Underscores Constraints and Opportunities in the Evolution of the Vertebrate Musculoskeletal System

Species groups that feature traits with a low number of potentially variable (evolvable) character states are more likely to repeatedly evolve similar phenotypes, that is, convergence. To evaluate this phenomenon, this present paper addresses anatomical alterations in turtles that convergently evolved shell kinesis, for example, the movement of shell bones to better shield the head and extremities. Kinesis constitutes a major departure from the evolutionarily conserved shell of modern turtles, yet it has arisen independently at least 8 times. The hallmark signature of kinesis is the presence of shell bone articulations or "hinges," which arise via similar skeletal remodeling processes in species that do not share a recent common ancestor. Still, the internal biomechanical components that power kinesis may differ in such distantly related species. Complex diarthrodial joints and modified muscle connections expand the functional boundaries of the limb girdles and neck in a lineage-specific manner. Some lineages even exhibit mobility of thoracic and sacral vertebrae to facilitate shell closure. Depending on historical contingency and structural correlation, a myriad of anatomical alterations has yielded similar functional outcomes, that is, many-to-one mapping, during the convergent evolution of shell kinesis. The various iterations of this intricate phenotype illustrate the potential for the vertebrate musculoskeletal system to undergo evolutionary change, even when constraints are imposed by the development and structural complexity of a shelled body plan. Based on observations in turtles and comparisons to other vertebrates, a hypothetical framework that implicates functional interactions in the origination of novel musculoskeletal traits is presented.

Epithelial tissue confinement inhibits cell growth and leads to volume-reducing divisions

Cell proliferation is a central process in tissue development, homeostasis, and disease, yet how proliferation is regulated in the tissue context remains poorly understood. Here, we introduce a quantitative framework to elucidate how tissue growth dynamics regulate cell proliferation. Using MDCK epithelial monolayers, we show that a limiting rate of tissue expansion creates confinement that suppresses cell growth; however, this confinement does not directly affect the cell cycle. This leads to uncoupling between rates of cell growth and division in epithelia and, thereby, reduces cell volume. Division becomes arrested at a minimal cell volume, which is consistent across diverse epithelia in vivo. Here, the nucleus approaches the minimum volume capable of packaging the genome. Loss of cyclin D1-dependent cell-volume regulation results in an abnormally high nuclear-to-cytoplasmic volume ratio and DNA damage. Overall, we demonstrate how epithelial proliferation is regulated by the interplay between tissue confinement and cell-volume regulation.

Langevin picture of anomalous diffusion processes in expanding medium

The expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of a particle's motion in an expanding medium has only been investigated in the framework of a continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in an expanding medium, and conduct detailed analyses in the framework of the Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in the expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in an expanding medium under the framework of the Langevin equation.

PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data

We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.

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

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

Skeletal repatterning enhances the protective capacity of the shell in African hinge-back tortoises (Kinixys)

Changes in the structural association of skeletal traits are crucial to the evolution of novel forms and functions. In vertebrates, such rearrangements often occur gradually and may precede or coincide with the functional activation of skeletal traits. To illustrate this process, we examined the ontogeny of African hinge-back tortoises (Kinixys spp.). Kinixys species feature a moveable "hinge" on the dorsal shell (carapace) that enables shell closure (kinesis) when the hind limbs are withdrawn. This hinge, however, is absent in juveniles. Herein, we describe how this unusual phenotype arises via alterations in the tissue configuration and shape of the carapace. The ontogenetic repatterning of osseous and keratinous tissue coincided with shifts in morphological integration and the establishment of anterior (static) and posterior (kinetic) carapacial modules. Based on ex vivo skeletal movement and raw anatomy, we propose that Kinixys employs a "sliding hinge" shell-closing system that overcomes thoracic rigidity and enhances the protective capacity of the carapace. Universal properties of the vertebrate skeleton, such as plasticity, modularity, and secondary maturation processes, contributed to adaptive evolutionary change in Kinixys. We discuss a hypothetical model to explain the delayed emergence of skeletal traits and its relevance to the origins of novel form-to-function relationships.

Bayesian calibration of a computational model of tissue expansion based on a porcine animal model

Tissue expansion is a technique used clinically to grow skin in situ to correct large defects. Despite its enormous potential, lack of fundamental knowledge of skin adaptation to mechanical cues, and lack of predictive computational models limit the broader adoption and efficacy of tissue expansion. In our previous work, we introduced a finite element model of tissue expansion that predicted key patterns of strain and growth which were then confirmed by our porcine animal model. Here we use the data from a new set of experiments to calibrate the computational model within a Bayesian framework. Four 10×10cm2 patches were tattooed in the dorsal skin of four 12 weeks-old minipigs and a total of six patches underwent successful tissue expander placement and inflation to 60cc for expansion times ranging from 1 h to 7 days. Six patches that did not have expanders implanted served as controls for the analysis. We find that growth can be explained based on the elastic deformation. The predicted area growth rate is k∈[0.02,0.08] [h-1]. Growth is anisotropic and reflects the anisotropic mechanical behavior of porcine dorsal skin. The rostral-caudal axis shows greater deformation than the transverse axis, and the time scale of growth in the rostral-caudal direction is given by rate parameters k1∈[0.04,0.1] [h-1] compared to k2∈[0.01,0.05] [h-1] in the transverse direction. Moreover, the calibration results underscore the high variability in biological systems, and the need to create probabilistic computational models to predict tissue adaptation in realistic settings. STATEMENT OF SIGNIFICANCE: Tissue expansion is a widely used technique in reconstructive surgery because it triggers growth of skin for the correction of large skin lesions and for breast reconstruction after mastectomy. Despite of its potential, complications and undesired outcomes persist due to our incomplete understanding of skin mechanobiology. Here we quantify the deformation and growth fields induced by an expander over 7 days in a porcine animal model and use these data to calibrate a computational model of skin growth using finite element simulations and a Bayesian framework. The calibrated model is a leap forward in our understanding skin growth, we now have quantitative understanding of this process: area growth is anisotropic and it is proportional to stretch with a characteristic rate constant of k∈[0.02,0.08] [h-1].

Sinonasal Tissue Remodelling during Chronic Rhinosinusitis

The purpose of this review is to summarise contemporary knowledge of sinonasal tissue remodelling during chronic rhinosinusitis (CRS), a chronic disease involving long-term inflammation of the paranasal sinuses and nasal passage. The concept of tissue remodelling has significant clinical relevance because of its potential to cause irreversibility in chronic airway tissues. Recent studies have indicated that early surgical treatment of CRS may improve clinical outcome. Tissue remodelling has been described in the literature extensively with no consensus on how remodelling is defined. This review describes various factors implicated in establishing remodelling in sinonasal tissues with a special mention of asthma as a comorbid condition. Some of the main histological features of remodelling include basement membrane thickening and collagen modulation. This may be an avenue of research with regard to targeted therapy against remodelling in CRS.

Damage Function of a Quasi-Brittle Material, Damage Rate, Acceleration and Jerk during Uniaxial Compression: Model and Application to Analysis of Trabecular Bone Tissue Destruction

A diversity of quasi-brittle materials can be observed in various engineering structures and natural objects (rocks, frozen soil, concrete, ceramics, bones, etc.). In order to predict the condition and safety of these objects, a large number of studies aimed at analyzing the strength of quasi-brittle materials has been conducted and presented in publications. However, at the modeling level, the problem of estimating the rate and acceleration of destruction of a quasi-brittle material under loading remains relevant. The purpose of the study was to substantiate the function of damage to a quasi-brittle material under uniaxial compression, determine the rate, acceleration and jerk of the damage process, and also to apply the results obtained to predicting the destruction of trabecular bone tissue. In accordance with the purpose of the study, the basic concepts of fracture mechanics and standard methods of mathematical modeling were used. The proposed model is based on the application of the previously obtained differentiable damage function without parameters. The results of the study are presented in the form of plots and analytical relations for computing the rate, acceleration and jerk of the damage process. Examples are given. The predicted peak of the combined effect of rate, acceleration and jerk of the damage process are found to be of practical interest as an additional criterion for destruction. The simulation results agree with the experimental data known from the available literature.

Growth-profile configuration for specific deformations of tubular organs: A study of growth-induced thinning and dilation of the human cervix

Growth is a significant factor that results in deformations of tubular organs, and particular deformations associated with growth enable tubular organs to perform certain physiological functions. Configuring growth profiles that achieve particular deformation patterns is critical for analyzing potential pathological conditions and for developing corresponding clinical treatments for tubular organ dysfunctions. However, deformation-targeted growth is rarely studied. In this article, the human cervix during pregnancy is studied as an example to show how cervical thinning and dilation are generated by growth. An advanced hyperelasticity theory called morphoelasticity is employed to model the deformations, and a growth tensor is used to represent growth in three principle directions. The computational results demonstrate that both negative radial growth and positive circumferential growth facilitate thinning and dilation. Modeling such mixed growth represents an advancement beyond commonly used uniform growth inside tissues to study tubular deformations. The results reveal that complex growth may occur inside tissues to achieve certain tubular deformations. Integration of further biochemical and cellular activities that initiate and mediate such complex growth remains to be explored.

Spider Silk-Augmented Scaffolds and Adipose-Derived Stromal Cells Loaded with Uniaxial Cyclic Strain: First Investigations of a Novel Approach for Tendon-Like Constructs

Tendon injuries still pose a challenge to reconstructive surgeons. Tendon tissue is a bradytrophic tissue and has a poor tendency to heal. Autologous tendon grafts are, therefore, still the gold standard in restorative operations but are associated with significant donor side morbidity. The experimental approach of the present study focused on the use of the biomaterial spider silk as a biocompatible and very stable carrier matrix in combination with a collagen type I hydrogel and adipose-derived stromal cells. The constructs were differentiated by axial strain to tendon-like tissue using a custom-made bioreactor. Macroscopically, tendon-like tissue could be detected which histologically showed high cell vitality even in long-term cultivation. In addition, cell morphology comparable to tenocytes could be detected in the bioreactor-stimulated tendon-like constructs compared to the controls. Immunohistochemically, tendon tissue-specific markers could be detected. Therefore, the developed tendon-like construct represents a promising approach towards patient specific tendon reconstruction, but further studies are needed.

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.

Mechanical stimuli for left ventricular growth during pressure overload

BACKGROUND

The mechanical stimulus (i.e. stress or stretch) for growth occurring in the pressure-overloaded left ventricle (LV) is not exactly known.

OBJECTIVE

To address this issue, we investigate the correlation between local ventricular growth (indexed by local wall thickness) and the local acute changes in mechanical stimuli after aortic banding.

METHODS

LV geometric data were extracted from 3D echo measurements at baseline and 2 weeks in the aortic banding swine model (n = 4). We developed and calibrated animal-specific finite element (FE) model of LV mechanics against pressure and volume waveforms measured at baseline. After the simulation of the acute effects of pressure-overload, the local changes of maximum, mean and minimum myocardial stretches and stresses in three orthogonal material directions (i.e., fiber, sheet and sheet-normal) over a cardiac cycle were quantified. Correlation between mechanical quantities and the corresponding measured local changes in wall thickness was quantified using the Pearson correlation number (PCN) and Spearman rank correlation number (SCN).

RESULTS

At 2 weeks after banding, the average septum thickness decreased from 10.6 ± 2.92mm to 9.49 ± 2.02mm, whereas the LV free-wall thickness increased from 8.69 ± 1.64mm to 9.4 ± 1.22mm. The FE results show strong correlation of growth with the changes in maximum fiber stress (PCN = 0.5471, SCN = 0.5111) and changes in the mean sheet-normal stress (PCN= 0.5266, SCN = 0.5256). Myocardial stretches, however, do not have good correlation with growth.

CONCLUSION

These results suggest that fiber stress is the mechanical stimuli for LV growth in pressure-overload.

Modeling Tissue Expansion with Isogeometric Analysis: Skin Growth and Tissue Level Changes in the Porcine Model

BACKGROUND

Tissue expansion relies on the ability of skin to grow in response to sustained mechanical strain. This study focuses on correlation of cellular and histologic changes with skin growth and deformation during tissue expansion.

METHODS

Tissue expanders were placed underneath the skin of five Yucatan minipigs and inflated with one fill of 60 cc of saline 1 hour, 24 hours, 3 days, and 7 days before the animals were killed, or two fills of either 30 cc or 60 cc at 10 and 3 days or 14 and 7 days before the animals were killed. Skin biopsy specimens and three-dimensional photographs were used to calculate skin growth and stretch according to the authors' novel finite element analysis model.

RESULTS

The mitotic index of keratinocytes in the basal layer increased 1 hour after stimulus was applied (4 percent) (p = 0.022), peaked at approximately day 3 (26 percent) (p < 0.0001), and tapered by day 7 (12.5 percent) (p = 0.012) after tissue expansion. The authors demonstrated that it is the volume per fill rather than the total volume in the expander that scales the magnitude of response. Lastly, the authors demonstrated that the ratio of deformation attributable to growth versus stretch (Fgrowth/Fstretch) after 60 cc of tissue expansion fill was 1.03 at 1 hour, 0.82 at 1 day, 0.85 at day 3, and 0.95 at 7 days.

CONCLUSIONS

Peak cell proliferation occurred 3 days after tissue expansion fill and is scaled in response to stimulus magnitude. The growth component of deformation equilibrates to the stretch component at day 7, as cell proliferation has started to translate to skin growth.

Fast, Rate-Independent, Finite Element Implementation of a 3D Constrained Mixture Model of Soft Tissue Growth and Remodeling

Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated evolutions when imposed perturbations are slow relative to the adaptive process. We demonstrate quadratic convergence and verify the model via comparisons with semi-analytical solutions for arterial mechanics. We further examine the enlargement of aortic aneurysms for which we identify new mechanobiological insights into factors that affect the nearby non-aneurysmal segment as it responds to the changing mechanics within the diseased segment. Because this new 3D approach can be implemented within many existing finite element solvers, constrained mixture models of growth and remodeling can now be used more widely.

Effect of fabric on the accuracy of computed tomography-based finite element analyses of the vertebra

Quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra are widely used in studying spine biomechanics and mechanobiology, but their accuracy has not been fully established. Although the models typically assign material properties based only on local bone mineral density (BMD), the mechanical behavior of trabecular bone also depends on fabric. The goal of this study was to determine the effect of incorporating measurements of fabric on the accuracy of FE predictions of vertebral deformation. Accuracy was assessed by using displacement fields measured via digital volume correlation-applied to time-lapse microcomputed tomography (μCT)-as the gold standard. Two QCT-based FE models were generated from human L1 vertebrae (n = 11): the entire vertebral body and a cuboid-shaped portion of the trabecular centrum [dimensions: (20-30) × (15-20) × (15-20) mm3]. For axial compression boundary conditions, there was no difference (p = 0.40) in the accuracy of the FE-computed displacements for models using material properties based on local values of BMD versus those using material properties based on local values of fabric and volume fraction. However, when using BMD-based material properties, errors were higher for the vertebral-body models (8.4-50.1%) than cuboid models (1.5-19.6%), suggesting that these properties are inaccurate in the peripheral regions of the centrum. Errors also increased when assuming that the cuboid region experienced uniaxial loading during axial compression of the vertebra. These findings indicate that a BMD-based constitutive model is not sufficient for the peripheral region of the vertebral body when seeking accurate QCT-based FE modeling of the vertebra.

Mechanical Roles in Formation of Oriented Collagen Fibers

Collagen is a structural protein that is widely present in vertebrates, being usually distributed in tissues in the form of fibers. In living organisms, fibers are organized in different orientations in various tissues. As the structural base in connective tissue and load-bearing tissue, the orientation of collagen fibers plays an extremely important role in the mechanical properties and physiological and biochemical functions. The study on mechanics role in formation of oriented collagen fibers enables us to understand how discrete cells use limited molecular materials to create tissues with different structures, thereby promoting our understanding of the mechanism of tissue formation from scratch, from invisible to tangible. However, the current understanding of the mechanism of fiber orientation is still insufficient. In addition, existing fabrication methods of oriented fibers are varied and involve interdisciplinary study, and the achievements of each experiment are favorable to the construction and improvement of the fiber orientation theory. To this end, this review focuses on the preparation methods of oriented fibers and proposes a model explaining the formation process of oriented fibers in tendons based on the existing fiber theory. Impact statement As the structural base in connective tissue and load-bearing tissue, the orientation of collagen fibers plays an extremely important role in the mechanical properties and physiological and biochemical functions. However, the current understanding of the mechanism of fiber orientation is still insufficient, which is greatly responsible for the challenge of functional tissue repair and regeneration. Understanding the mechanism of fiber orientation can promote the successful application of fiber orientation scaffolds in tissue repair and regeneration, as well as providing an insight for the mechanism of tissue histomorphology.

A review of accelerated wound healing approaches: biomaterial- assisted tissue remodeling

Nowadays, due to a growing number of tissue injuries, in particular, skin wounds, induction and promotion of tissue healing responses can be considered as a crucial step towards a complete regeneration. Recently, biomaterial design has been oriented towards promoting a powerful, effective, and successful healing. Biomaterials with wound management abilities have been developed for different applications such as providing a native microenvironment and supportive matrices that induce the growth of tissue, creating physical obstacles against microbial contamination, and to be used as delivery systems for therapeutic reagents. Until now, numerous strategies aiming to accelerate the wound healing process have been utilized and studied with their own pros and cons. In this review, tissue remodeling phenomena, wound healing mechanisms, and their related factors will be discussed. In addition, different methods for induction and acceleration of healing via cell therapy, bioactive therapeutic delivery, and/or biomaterial-based approaches will be reviewed.

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain hyperelasticity and the kinematics of the continuum is described by both a position vector and by a remodelling tensor which, in the present context, is an orthogonal tensor representing the fibre reorientation process. By imposing suitable thermodynamical restrictions on the constitutive equation, we obtain an evolution equation of the remodelling tensor governed by the Eshelby torque, whose stationary solutions are studied in absence of any external source terms. It is shown that the fibres reorient themselves in a configuration that minimises the elastic energy and get aligned along a direction that may or may not be of principal strain. The explicit analysis of the Hessian of the strain energy density allows us to discriminate among the stationary solutions, which ones are stable. Examples are given for passive reorientation processes driven by applied strains or external boundary tractions. Applications of the proposed theory to biological tissues, nematic or magneto-electro active elastomers are foreseen.

Extra-cellular matrix rigidity may dictate the fate of injury outcome

After injury, while regeneration can be observed in hydra, planaria and some vertebrates, regeneration is rare in mammals and particularly in humans. In this paper, we investigate the mechanisms by which biological tissues recover after injury. We explore this question on adipose tissue, using the mathematical framework recently developed in Peurichard et al., J. Theoret. Biol. 429 (2017), pp. 61-81. Our assumption is that simple mechanical cues between the Extra-Cellular Matrix (ECM) and differentiated cells can explain adipose tissue morphogenesis and that regeneration requires after injury the same mechanisms. We validate this hypothesis by means of a two-dimensional Individual Based Model (IBM) of interacting adipocytes and ECM fiber elements. The model successfully generates regeneration or scar formation as functions of few key parameters, and seems to indicate that the fate of injury outcome could be mainly due to ECM rigidity.

Critical roles of time-scales in soft tissue growth and remodeling

Most soft biological tissues exhibit a remarkable ability to adapt to sustained changes in mechanical loads. These macroscale adaptations, resulting from mechanobiological cellular responses, are important determinants of physiological behaviors and thus clinical outcomes. Given the complexity of such adaptations, computational models can significantly increase our understanding of how contributions of different cell types or matrix constituents, and their rates of turnover and evolving properties, ultimately change the geometry and biomechanical behavior at the tissue level. In this paper, we examine relative roles of the rates of tissue responses and external loading and present a new rate-independent approach for modeling the evolution of soft tissue growth and remodeling. For illustrative purposes, we also present numerical results for arterial adaptations. In particular, we show that, for problems defined by particular characteristic times, this approximate theory captures well the predictions of a fully general constrained mixture theory at a fraction of the computational cost.

Programmable Hydrogels for Cell Encapsulation and Neo-Tissue Growth to Enable Personalized Tissue Engineering

Biomimetic and biodegradable synthetic hydrogels are emerging as a promising platform for cell encapsulation and tissue engineering. Notably, synthetic-based hydrogels offer highly programmable macroscopic properties (e.g., mechanical, swelling and transport properties) and degradation profiles through control over several tunable parameters (e.g., the initial network structure, degradation kinetics and behavior, and polymer properties). One component to success is the ability to maintain structural integrity as the hydrogel transitions to neo-tissue. This seamless transition is complicated by the fact that cellular activity is highly variable among donors. Thus, computational models provide an important tool in tissue engineering due to their unique ability to explore the coupled processes of hydrogel degradation and neo-tissue growth across multiple length scales. In addition, such models provide new opportunities to develop predictive computational tools to overcome the challenges with designing hydrogels for different donors. In this report, programmable properties of synthetic-based hydrogels and their relation to the hydrogel's structural properties and their evolution with degradation are reviewed. This is followed by recent progress on the development of computational models that describe hydrogel degradation with neo-tissue growth when cells are encapsulated in a hydrogel. Finally, the potential for predictive models to enable patient-specific hydrogel designs for personalized tissue engineering is discussed.

Computer modeling tools to understand the causes of preterm birth

The mechanical integrity of the soft tissue structures supporting the fetus may play a role in maintaining a healthy pregnancy and triggering the onset of labor. Currently, the level of mechanical loading on the uterus, cervix, and fetal membranes during pregnancy is unknown, and it is hypothesized that the over-stretch of these tissues contributes to the premature onset of contractility, tissue remodeling, and membrane rupture, leading to preterm birth. The purpose of this review article is to introduce and discuss engineering analysis tools to evaluate and predict the mechanical loads on the uterus, cervix, and fetal membranes. Here we will explore the potential of using computational biomechanics and finite element analysis to study the causes of preterm birth and to develop a diagnostic tool that can predict gestational outcome. We will define engineering terms and identify the potential engineering variables that could be used to signal an abnormal pregnancy. We will discuss the translational ability of computational models for the better management of clinical patients. We will also discuss the process of model validation and the limitations of these models. We will explore how we can borrow from parallel engineering fields to push the boundary of patient care so that we can work toward eliminating preterm birth.

Mechanical control of growth: ideas, facts and challenges

In his classic book On Growth and Form, D'Arcy Thompson discussed the necessity of a physical and mathematical approach to understanding the relationship between growth and form. The past century has seen extraordinary advances in our understanding of biological components and processes contributing to organismal morphogenesis, but the mathematical and physical principles involved have not received comparable attention. The most obvious entry of physics into morphogenesis is via tissue mechanics. In this Review, we discuss the fundamental role of mechanical interactions between cells induced by growth in shaping a tissue. Non-uniform growth can lead to accumulation of mechanical stress, which in the context of two-dimensional sheets of tissue can specify the shape it assumes in three dimensions. A special class of growth patterns - conformal growth - does not lead to the accumulation of stress and can generate a rich variety of planar tissue shapes. Conversely, mechanical stress can provide a regulatory feedback signal into the growth control circuit. Both theory and experiment support a key role for mechanical interactions in shaping tissues and, via mechanical feedback, controlling epithelial growth.

Growth Description for Vessel Wall Adaptation: A Thick-Walled Mixture Model of Abdominal Aortic Aneurysm Evolution

(1) Background: Vascular tissue seems to adapt towards stable homeostatic mechanical conditions, however, failure of reaching homeostasis may result in pathologies. Current vascular tissue adaptation models use many ad hoc assumptions, the implications of which are far from being fully understood; (2) Methods: The present study investigates the plausibility of different growth kinematics in modeling Abdominal Aortic Aneurysm (AAA) evolution in time. A structurally motivated constitutive description for the vessel wall is coupled to multi-constituent tissue growth descriptions; Constituent deposition preserved either the constituent’s density or its volume, and Isotropic Volume Growth (IVG), in-Plane Volume Growth (PVG), in-Thickness Volume Growth (TVG) and No Volume Growth (NVG) describe the kinematics of the growing vessel wall. The sensitivity of key modeling parameters is explored, and predictions are assessed for their plausibility; (3) Results: AAA development based on TVG and NVG kinematics provided not only quantitatively, but also qualitatively different results compared to IVG and PVG kinematics. Specifically, for IVG and PVG kinematics, increasing collagen mass production accelerated AAA expansion which seems counterintuitive. In addition, TVG and NVG kinematics showed less sensitivity to the initial constituent volume fractions, than predictions based on IVG and PVG; (4) Conclusions: The choice of tissue growth kinematics is of crucial importance when modeling AAA growth. Much more interdisciplinary experimental work is required to develop and validate vascular tissue adaption models, before such models can be of any practical use.

Simple mechanical cues could explain adipose tissue morphology

The mechanisms by which organs acquire their functional structure and realize its maintenance (or homeostasis) over time are still largely unknown. In this paper, we investigate this question on adipose tissue. Adipose tissue can represent 20 to 50% of the body weight. Its investigation is key to overcome a large array of metabolic disorders that heavily strike populations worldwide. Adipose tissue consists of lobular clusters of adipocytes surrounded by an organized collagen fiber network. By supplying substrates needed for adipogenesis, vasculature was believed to induce the regroupment of adipocytes near capillary extremities. This paper shows that the emergence of these structures could be explained by simple mechanical interactions between the adipocytes and the collagen fibers. Our assumption is that the fiber network resists the pressure induced by the growing adipocytes and forces them to regroup into clusters. Reciprocally, cell clusters force the fibers to merge into a well-organized network. We validate this hypothesis by means of a two-dimensional Individual Based Model (IBM) of interacting adipocytes and extra-cellular-matrix fiber elements. The model produces structures that compare quantitatively well to the experimental observations. Our model seems to indicate that cell clusters could spontaneously emerge as a result of simple mechanical interactions between cells and fibers and surprisingly, vasculature is not directly needed for these structures to emerge.

Bone fracture healing in mechanobiological modeling: A review of principles and methods

Bone fracture is a very common body injury. The healing process is physiologically complex, involving both biological and mechanical aspects. Following a fracture, cell migration, cell/tissue differentiation, tissue synthesis, and cytokine and growth factor release occur, regulated by the mechanical environment. Over the past decade, bone healing simulation and modeling has been employed to understand its details and mechanisms, to investigate specific clinical questions, and to design healing strategies. The goal of this effort is to review the history and the most recent work in bone healing simulations with an emphasis on both biological and mechanical properties. Therefore, we provide a brief review of the biology of bone fracture repair, followed by an outline of the key growth factors and mechanical factors influencing it. We then compare different methodologies of bone healing simulation, including conceptual modeling (qualitative modeling of bone healing to understand the general mechanisms), biological modeling (considering only the biological factors and processes), and mechanobiological modeling (considering both biological aspects and mechanical environment). Finally we evaluate different components and clinical applications of bone healing simulation such as mechanical stimuli, phases of bone healing, and angiogenesis.

Response of mandibular condyles of juvenile and adult rats to abnormal occlusion and subsequent exemption

OBJECTIVE

The adaptation capacities of the mandibular condyle in response to mechanical stimuli might be different between juveniles and adults, but has not been compared. This study aimed to investigate whether abnormal molar occlusion and subsequent molar extraction could lead to different remodeling responses in the mandibular condyles of juvenile and adult rats.

METHODS

Abnormal molar occlusion (AMO) was established in the 5- and 16-wk old rats by moving their maxillary left and mandibular right third molars distally. AMO was removed in the molar extraction group at 4 weeks but remained in the AMO group. All rats were sacrificed at 8 weeks. Micro-computed tomography, histomorphology, immunohistochemistry and real-time PCR were adopted to evaluate the remodeling of condylar subchondral bone.

RESULTS

Condylar subchondral bone loss and increased osteoclastic activities were observed in both juvenile and adult AMO groups, while increased osteoblastic activities were only seen in the juvenile AMO group. Decreased bone mineral density, bone volume fraction and trabecular thickness, but increased trabecular separation, number and surface of osteoclasts and mRNA levels of TRAP, cathepsin-K, RANKL in the juvenile AMO group were all reversed after molar extraction (all P<0.05). However, these parameters showed no difference between adult AMO and extraction groups (all P>0.05).

CONCLUSIONS

Abnormal molar occlusion led to degenerative remodeling in the mandibular condyles of both juvenile and adult rats, while exemption of abnormal occlusion caused significant rescue of the degenerative changes only in the juvenile rats.

Effective equations governing an active poroelastic medium

In this work, we consider the spatial homogenization of a coupled transport and fluid–structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The ‘active’ nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection–reaction–diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits.

Distinct biological events generated by ECM proteolysis by two homologous collagenases

It is well established that the expression profiles of multiple and possibly redundant matrix-remodeling proteases (e.g., collagenases) differ strongly in health, disease, and development. Although enzymatic redundancy might be inferred from their close similarity in structure, their in vivo activity can lead to extremely diverse tissue-remodeling outcomes. We observed that proteolysis of collagen-rich natural extracellular matrix (ECM), performed uniquely by individual homologous proteases, leads to distinct events that eventually affect overall ECM morphology, viscoelastic properties, and molecular composition. We revealed striking differences in the motility and signaling patterns, morphology, and gene-expression profiles of cells interacting with natural collagen-rich ECM degraded by different collagenases. Thus, in contrast to previous notions, matrix-remodeling systems are not redundant and give rise to precise ECM-cell crosstalk. Because ECM proteolysis is an abundant biochemical process that is critical for tissue homoeostasis, these results improve our fundamental understanding its complexity and its impact on cell behavior.

The Effect of Size and Geometry of Poly(acrylamide) Brush-Based Micropatterns on the Behavior of Cells

In this study, the fabrication, detailed characterization, and application of long-term stable micropatterned bio-interfaces of passivating poly(acrylamide) (PAAm) brushes on transparent gold for application in the study of cell-surface interactions is reported. The micropatterns were fabricated by microcontact printing of an initiator for surface-initiated atom transfer radical polymerization (SI-ATRP), SI-ATRP of acrylamide, and subsequently backfilling of the unfunctionalized areas of 400-2500 μm(2) size and systematically altered number of corners with octadecanethiol. As verified by surface plasmon resonance spectroscopy, the physisorption of fibronectin (FN) was restricted to the adhesive areas. Exploiting this platform, the effect of micropattern geometry and size of cell-adhesive FN areas surrounded by passivating PAAm brushes on transparent gold substrates on the attachment of cells and cytoskeleton alignment was investigated at the single-cell level. Exceptional long-term stability of the patterned PAAm brushes and arrays of adhesive areas, in which human pancreatic tumor cells (Patu 8988T) and fibroblast cells (NIH 3T3) were confined for more than one week, was observed. Adhesive areas of 1600 μm(2) or less constrained the cell shape and caused focal adhesions to accumulate in the corners of the pattern. These changes were most obvious for the PatuT cells in adhesive areas of ∼900 μm(2), in which the actin filaments were aligned, following the boundary of the pattern, and merged in the focal adhesions concentrated in the corners of the pattern. NIH 3T3 cells possessed a larger cell area, which led to an optimal cytoskeleton alignment in adhesive patterns of ∼1600 μm(2). The alignment of the cytoskeleton was found to be less pronounced in cells on larger adhesive areas, where the PatuT cells spread similarly to cells on unpatterned substrates. By contrast, the NIH 3T3 cells were found to stretch even on larger adhesive areas, spanning from one corner to the other. The long-term stability under cell culture conditions of the patterns introduced here will also be useful for long-term studies of single and multiple cells, cell motility in toxicity assays, and stem cell differentiation.

Surface and interfacial creases in a bilayer tubular soft tissue

Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as their morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability; therefore nonlinear finite element simulations are carried out to replicate the poststability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.

Optical-Based Analysis of Soft Tissue Structures

Fibrous structures are an integral and dynamic feature of soft biological tissues that are directly related to the tissues' condition and function. A greater understanding of mechanical tissue behavior can be gained through quantitative analyses of structure alone, as well as its integration into computational models of soft tissue function. Histology and other nonoptical techniques have traditionally dominated the field of tissue imaging, but they are limited by their invasiveness, inability to provide resolution on the micrometer scale, and dynamic information. Recent advances in optical modalities can provide higher resolution, less invasive imaging capabilities, and more quantitative measurements. Here we describe contemporary optical imaging techniques with respect to their suitability in the imaging of tissue structure, with a focus on characterization and implementation into subsequent modeling efforts. We outline the applications and limitations of each modality and discuss the overall shortcomings and future directions for optical imaging of soft tissue structure.

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.

Pushing, pulling, and squeezing our way to understanding mechanotransduction

Mechanotransduction is often described in the context of force-induced changes in molecular conformation, but molecular-scale mechanical stimuli arise in vivo in the context of complex, multicellular tissue structures. For this reason, we highlight and review experimental methods for investigating mechanotransduction across multiple length scales. We begin by discussing techniques that probe the response of individual molecules to applied force. We then move up in length scale to highlight techniques aimed at uncovering how cells transduce mechanical stimuli into biochemical activity. Finally, we discuss approaches for determining how these stimuli arise in multicellular structures. We expect that future work will combine techniques across these length scales to provide a more comprehensive understanding of mechanotransduction.

A mixture approach to investigate interstitial growth in engineering scaffolds

Controlling biological growth within a cell-laden polymeric scaffold is a critical challenge in the tissue engineering community. Indeed, construct growth must often be balanced with scaffold degradation and is often coupled to varying degrees of deformation that originate from swelling, external forces and the effects of confinement. These factors have been shown to affect growth in many ways, but to date, our understanding is mostly qualitative. While cell sensing, molecular transport and scaffold/tissue interactions are believed to be important players, it will be critical to quantify, predict and control these effects in order to eventually optimize tissue growth in the laboratory. The aim of this paper was thus to provide a theoretical framework to better understand how the scaffold-mediated mechanisms of transport, deposition (and possibly degradation) and elasticity affect the overall growth of a tissue subjected to finite deformations. We propose a formulation in which the macroscopic evolutions in tissue size, density as well as the appearance of residual stresses can be directly related to changes in internal composition by considering three fundamental principles: mechanical equilibrium, chemical equilibrium and molecular incompressibility. The resulting model allows us to pay particular attention to features that are critical to the interaction between growth and deformation: osmotic pressure and swelling, the strain mismatch between old and newly deposited material as well as the mechano-sensitive cell-mediated production. We show that all of these phenomena may indeed strongly affect the overall growth of a construct under finite deformations.

A theoretical model of the endothelial cell morphology due to different waveforms

Endothelial cells are key units in the regulatory biological process of blood vessels. They represent an interface to transmit variations on the fluid dynamic changes. They are able to adapt its cytoskeleton, by means of microtubules reorientation and F-actin reorganization, due to new mechanical environments. Moreover, they are responsible for initiating a huge cascade of biological processes, such as the release of endothelins (ET-1), in charge of the constriction of the vessel and growth factors such as TGF-β and PDGF. Although a huge efforts have been made in the experimental characterization and description of these two issues the computational modeling has not gained such an attention. In this work we study the 3D remodeling of endothelial cells based on the main features of blood flow. In particular we study how different oscillatory shear index and the time average wall shear stresses modify the endothelial cell shape. We found our model fitted the experimental works presented before in in vitro studies. We also include our model within a computational fluid dynamics simulation of a carotid artery to evaluate endothelial cell shape index which is a key predictor of atheroma plaque formation. Moreover, our approach can be coupled with models of collagen and smooth muscle cell growth, where remodeling and the associated release of chemical substance are involved.

Bone tissue regeneration: the role of scaffold geometry

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

Fiber-assisted molding (FAM) of surfaces with tunable curvature to guide cell alignment and complex tissue architecture

A simple and robust method termed "fiber-assisted molding (FAM)" is presented to create biomimetic three-dimensional surfaces with controllable curvature and helical twist. The alignment of muscle fibrils and the assembly of helically patterned extracellular matrix by cells demonstrate the potential of this method for tissue engineering and other materials science applications.