Gradient-enhanced continuum models of healing in damaged soft tissues

He, Yiqian; Zuo, Di; Hackl, Klaus; Yang, Haitian; Mousavi, S. Jamaleddin; Avril, Stéphane

doi:10.1007/s10237-019-01155-z

Cited by 17 publications

(13 citation statements)

References 34 publications

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“…The first advantage of the presented model is that it can assess nonlocal damage with uncertain material parameters, including internal length scales. In our previous works, 12,13 it was proved that the internal length scales have obvious effects on the localization of damage, for example, a larger internal length scales lead to a larger lower level of damage and activated zone. In this paper, the influence of uncertain internal length scales can be analyzed by the proposed model.…”

Section: Discussionmentioning

confidence: 99%

“…In this part, series of tests on 286 elements are performed. The mesh‐dependence had been already examined in our previous works 12,13 . Here we investigate the influence of the shear modulus and the internal length scales on the damage analysis in deterministic problem.…”

Section: Numerical Examplesmentioning

confidence: 94%

“…The developed damage models can be divided into three approaches 9 : (1) models based on continuum damage mechanics, (2) models based on the theory of pseudo‐elasticity, and (3) the softening hyperelasticity approach. Among the continuum damage models, a gradient‐enhanced non‐local damage model was proposed by Dimitrijevic and Hackl, 10,11 and a nonlocal continuum healing model that combines the gradient‐enhanced damage model and a temporally homogenized growth and remodeling model was originally presented in our previous works 12,13 . This model has the following advantages: (1) good mesh independence is achieved in the simulation of damage evolution with growth and remodeling; and (2) the nonlocal damage process is realized by introducing the gradient‐enhanced variable, thus allowing the effect of internal length scales of soft tissues to be considered.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity analysis of non‐local damage in soft biological tissues

Zuo

Avril

Ran

et al. 2020

Numer Methods Biomed Eng

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Computational modeling can provide insight into understanding the damage mechanisms of soft biological tissues. Our gradient‐enhanced damage model presented in a previous publication has shown advantages in considering the internal length scales and in satisfying mesh independence for simulating damage, growth and remodeling processes. Performing sensitivity analyses for this model is an essential step towards applications involving uncertain patient‐specific data. In this paper, a numerical analysis approach is developed. For that we integrate two existing methods, that is, the gradient‐enhanced damage model and the surrogate model‐based probability analysis. To increase the computational efficiency of the Monte Carlo method in uncertainty propagation for the nonlinear hyperelastic damage analysis, the surrogate model based on Legendre polynomial series is employed to replace the direct FEM solutions, and the sparse grid collocation method (SGCM) is adopted for setting the collocation points to further reduce the computational cost in training the surrogate model. The effectiveness of the proposed approach is illustrated by two numerical examples, including an application of artery dilatation mimicking to the clinical problem of balloon angioplasty.

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Section: Discussionmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Sensitivity analysis of non‐local damage in soft biological tissues

Zuo

Avril

Ran

et al. 2020

Numer Methods Biomed Eng

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“…Based on the proposed model, the effects of some important factors in 3D healing can be considered; for instance, the rate of healing, the value of intrinsic length scales, the value of the homeostatic stress, etc. The deformation due to growth can also be computed to illustrate the change of inelastic deformation in healing [35].…”

Section: Discussionmentioning

confidence: 99%

“…Regarding applications, the two-dimensional isotropic healing model presented previously by the same authors was suitable for problems that can be simplified using a plane-strain or plane-stress assumption, such as balloon angioplasty [35]. However, in many problems, three-dimensional effects have to be taken into account, such as the three-dimensional evolution of damage and anisotropic effects due to collagen fibres, and the three-dimensional healing model presented in this paper appears essential to deal with general applications involving patient-specific problems for instance.…”

Section: Discussionmentioning

confidence: 99%

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

Zuo

Avril

Yang

et al. 2020

J. R. Soc. Interface.

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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.

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

Gierig

Wriggers

Marino

2021

Biomech Model Mechanobiol

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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.

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Gradient-enhanced continuum models of healing in damaged soft tissues

Cited by 17 publications

References 34 publications

Sensitivity analysis of non‐local damage in soft biological tissues

Sensitivity analysis of non‐local damage in soft biological tissues

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

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

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