A Computational Model for Biological Tissues Considering the Influence of Injury on Growth and Remodelling

Gierig, Meike; Marino, Michele; Wriggers, Peter

doi:10.1002/pamm.201900259

Cited by 1 publication

(2 citation statements)

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“…For in the free energy ( 10 ), a constitutive equation is introduced for the volumetric deformation via a penalty-type approach, see Gierig et al. ( 2019 ): where is a parameter. In the limit , incompressibility is enforced.…”

Section: Methodsmentioning

confidence: 99%

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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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Section: Methodsmentioning

confidence: 99%

“…In line with this assumption, the property of a nearly constant density, (t) ≈ 0 (0) , is inserted into (5) yielding the constraint det( ) ≈ 0 0 (0) . For W L in the free energy (10), a constitutive equation is introduced for the volumetric deformation via a penalty-type approach, see Gierig et al (2019):…”

Section: Growth Formulationmentioning

confidence: 99%