A finite element model for mixed porohyperelasticity with transport, swelling, and growth

The purpose of this manuscript is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. We combine the theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid/fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To illustrate the capabilities of this model, several example finite element test problems are considered using model geometry and material parameters based on experimental data from a porcine coronary artery. Multiple growth laws are considered, including time-driven, concentrationdriven, and stress-driven growth. Time-driven growth is compared against an exact analytical solution to validate the model. For concentration-dependent growth, changing the diffusivity (representing a change in drug) fundamentally changes growth behavior. We further demonstrate that for stress-dependent, solid-only growth of an artery, growth of an MPHETS model results in a more uniform hoop stress than growth in a hyperelastic model for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To our knowledge, this manuscript provides the first full description of an MPHETS model with growth. The developed computational framework can be used in concert with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues

In vivo measurement of skin surface strain and sub-surface layer deformation induced by natural tissue stretching.

Stratum corneum and epidermal layers change in terms of thickness and roughness with gender, age and anatomical site. Knowledge of the mechanical and tribological properties of skin associated with these structural changes are needed to aid in the design of exoskeletons, prostheses, orthotics, body mounted sensors used for kinematics measurements and in optimum use of wearable on-body devices. In this case study, optical coherence tomography (OCT) and digital image correlation (DIC) were combined to determine skin surface strain and sub-surface deformation behaviour of the volar forearm due to natural tissue stretching. The thickness of the epidermis together with geometry changes of the dermal-epidermal junction boundary were calculated during change in the arm angle, from flexion (90°) to full extension (180°). This posture change caused an increase in skin surface Lagrange strain, typically by 25% which induced considerable morphological changes in the upper skin layers evidenced by reduction of epidermal layer thickness (20%), flattening of the dermal-epidermal junction undulation (45-50% reduction of flatness being expressed as Ra and Rz roughness profile height change) and reduction of skin surface roughness Ra and Rz (40-50%). The newly developed method, DIC combined with OCT imaging, is a powerful, fast and non-invasive methodology to study structural skin changes in real time and the tissue response provoked by mechanical loading or stretching

Computational modelling of wound healing insights to develop new treatments

About 1% of the population will suffer a severe wound during their life. Thus, it is really important to develop new techniques in order to properly treat these injuries due to the high socioeconomically impact they suppose. Skin substitutes and pressure based therapies are currently the most promising techniques to heal these injuries. Nevertheless, we are still far from finding a definitive skin substitute for the treatment of all chronic wounds. As a first step in developing new tissue engineering tools and treatment techniques for wound healing, in silico models could help in understanding the mechanisms and factors implicated in wound healing. Here, we review mathematical models of wound healing. These models include different tissue and cell types involved in healing, as well as biochemical and mechanical factors which determine this process. Special attention is paid to the contraction mechanism of cells as an answer to the tissue mechanical state. Other cell processes such as differentiation and proliferation are also included in the models together with extracellular matrix production. The results obtained show the dependency of the success of wound healing on tissue composition and the importance of the different biomechanical and biochemical factors. This could help to individuate the adequate concentration of growth factors to accelerate healing and also the best mechanical properties of the new skin substitute depending on the wound location in the body and its size and shape. Thus, the feedback loop of computational models, experimental works and tissue engineering could help to identify the key features in the design of new treatments to heal severe wounds

Constitutive modelling of skin ageing

The objective of this chapter is to review the main biomechanical and structural aspects associated with both intrinsic and extrinsic skin ageing, and to present potential research avenues to account for these effects in mathematical and computational models of the skin. This will be illustrated through recent work of the authors which provides a basis to those interested in developing mechanistic constitutive models capturing the mechanobiology of skin across the life course