Gradient-enhanced continuum models of healing in damaged soft tissues

Nonlocal damage evaluation of a sigmoid-based damage model for fibrous biological soft tissues

The comprehension and modeling of the mechanical behavior of soft biological tissues are essential due to their clinical applications. This knowledge is essential for predicting tissue responses accurately and enhancing our ability to compute the behavior of biological structures and bio-prosthetic devices under specific loading conditions. The current research is centered on modeling the initiation and progression of soft tissues damage, which typically exhibit intricate anisotropic and nonlinear elastic characteristics. For this purpose, the following study presents a comparative analysis of the computational performance of two distinct damage modeling techniques. The first technique employs a well-established damage model, based on a piece-wise exponential damage function as proposed by Calvo et al. (Int J Numer Methods Eng 69:2036-2057, 2007. https://doi.org/10.1002/nme.1825 ). The second approach adopts a sigmoid function, as proposed by López-Campos et al. (Comput Methods Biomech Biomed Eng 23(6):213-223. https://doi.org/10.1080/10255842.2019.1710742 ). The aim of this study is to verify the validity of the López-Campos sigmoid-based damage model to be used in finite element simulation, the implementation of which is unknown. For this proposal, both models were implemented within a commercial Finite Element software package, and their responses to local and non-local damage algorithms were assessed in depth through two standard benchmark tests: a plate with a hole and a ball burst. The results of this study indicate that, for a wide range of cases, such as in-plane stresses, out-plane stresses, stress concentration and contact, all over large displacement conditions, the López-Campos damage model shows a good response to non-local algorithms achieving mesh independence and convergence in all these cases. The results obtained are in line with those obtained for the Calvo's damage model, showing, in addition, larger deformations under in-plane stress and stress concentration conditions and a lower number of iterations under out-plane stress and contact conditions. Consequently, the López-Campos' damage model emerges as a valuable and useful tool in the field of mechanical damage research in biological systems.

Post-angioplasty remodeling of coronary arteries investigated via a chemo-mechano-biological in silico model

This work presents the application of a chemo-mechano-biological constitutive model of soft tissues for describing tissue inflammatory response to damage in collagen constituents. The material model is implemented into a nonlinear finite element formulation to follow up a coronary standard balloon angioplasty for one year. Numerical results, compared with available in vivo clinical data, show that the model reproduces the temporal dynamics of vessel remodeling associated with subintimal damage. Such dynamics are bimodular, being characterized by an early tissue resorption and lumen enlargement, followed by late tissue growth and vessel constriction. Applicability of the modeling framework in retrospective studies is demonstrated, and future extension towards prospective applications is discussed.

Sensitivity analysis of the mechanical properties on atherosclerotic arteries rupture risk with an artificial neural network method

Considering the differences between individuals, in this paper, an uncertainty analysis model for predicting rupture risk of atherosclerotic arteries is established based on a back-propagation artificial neural network. The influence of isotropy and anisotropy on the rupture risk of atherosclerotic arteries is analyzed, and the results demonstrate the effectiveness of the artificial neural network in predicting the rupture risk. Moreover, the rupture risk of atherosclerotic arteries at different inflation sizes are simulated. This study contributes to a better understanding of the underlying mechanisms of atherosclerotic arteries rupture and promotes the advancement of artificial neural networks in atherosclerosis research.

Arterial tissues and their inflammatory response to collagen damage: A continuum in silico model coupling nonlinear mechanics, molecular pathways, and cell behavior

Damage in soft biological tissues causes an inflammatory reaction that initiates a chain of events to repair the tissue. This work presents a continuum model and its in silico implementation that describe the cascade of mechanisms leading to tissue healing, coupling mechanical as well as chemo-biological processes. The mechanics is described by means of a Lagrangian nonlinear continuum mechanics framework and follows the homogenized constrained mixtures theory. Plastic-like damage, growth and remodeling as well as homeostasis are taken into account. The chemo-biological pathways account for two molecular and four cellular species, and are activated by damage of collagen molecules in fibers. To consider proliferation, differentiation, diffusion and chemotaxis of species, diffusion-advection-reaction equations are employed. To the best of authors' knowledge, the proposed model combines for the first time such high number of chemo-mechano-biological mechanisms in a consistent continuum biomechanical framework. The resulting set of coupled differential equations describe balance of linear momentum, evolution of kinematic variables as well as mass balance equations. They are discretized in time according to a backward Euler finite difference scheme, and in space through a finite element Galerkin discretization. The features of the model are firstly demonstrated presenting the species dynamics and highlighting the influence of damage intensities on the growth outcome. In terms of a biaxial test, the chemo-mechano-biological coupling and the model's applicability to reproduce normal as well as pathological healing are shown. A last numerical example underlines the model's applicability to complex loading scenarios and inhomogeneous damage distributions. Concluding, the present work contributes towards comprehensive in silico models in biomechanics and mechanobiology.

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. 

Multiscale mechanobiology: Coupling models of adhesion kinetics and nonlinear tissue mechanics

The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues, such as fiber alignment and stiffness, as well as exert active stresses needed for wound closure. Here, we develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate that this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues.

A Review on Damage and Rupture Modelling for Soft Tissues

Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.

Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing

Healing in soft biological tissues is a chain of events on different time and length scales. This work presents a computational framework to capture and couple important mechanical, chemical and biological aspects of healing. A molecular-level damage in collagen, i.e., the interstrand delamination, is addressed as source of plastic deformation in tissues. This mechanism initiates a biochemical response and starts the chain of healing. In particular, damage is considered to be the stimulus for the production of matrix metalloproteinases and growth factors which in turn, respectively, degrade and produce collagen. Due to collagen turnover, the volume of the tissue changes, which can result either in normal or pathological healing. To capture the mechanisms on continuum scale, the deformation gradient is multiplicatively decomposed in inelastic and elastic deformation gradients. A recently proposed elasto-plastic formulation is, through a biochemical model, coupled with a growth and remodeling description based on homogenized constrained mixtures. After the discussion of the biological species response to the damage stimulus, the framework is implemented in a mixed nonlinear finite element formulation and a biaxial tension and an indentation tests are conducted on a prestretched flat tissue sample. The results illustrate that the model is able to describe the evolutions of growth factors and matrix metalloproteinases following damage and the subsequent growth and remodeling in the respect of equilibrium. The interplay between mechanical and chemo-biological events occurring during healing is captured, proving that the framework is a suitable basis for more detailed simulations of damage-induced tissue response.

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.