Abstract
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.
Highlights
When a soft biological tissue is injured, e.g., after trauma or surgical procedures, repair mechanisms within the tissue occur to rebuild functionality and integrity of the tissue
Soft biological tissue is mainly comprised of cells embedded in a non-cellular structure that is comprised of numerous molecules (Hay 1981; Alberts et al 2002)
The damage mechanism modeled is interstrand delamination what can be regarded as a source of plastic-like deformations in collagen due to the irreversible sliding between polypeptide strands
Summary
When a soft biological tissue is injured, e.g., after trauma or surgical procedures, repair mechanisms within the tissue occur to rebuild functionality and integrity of the tissue. In contrast to the previously mentioned models, the recently available experimental evidence that collagen damage is related to plastic deformations associated with interstrand delamination is incorporated and coupled with alterations in the mechanics of injured tissues. This mechanism is elected and used as damage stimulus. With respect to a number of existing approaches (Buganza Tepole and Kuhl 2016; Escuer et al 2019; Li et al 2019; Nolan and Lally 2018), the proposed framework includes a consistent continuum-based biomechanical description and coupling of damage evolution, biological events and tissue growth and remodeling. The kinematics of damage-induced tissue growth and remodeling is introduced consistently with the pre-existing elasto-plastic tissue state, determining the evolving configuration of healing biostructures in the respect of mechanical equilibrium
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