Stretching skin: The physiological limit and beyond

Abstract

The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

Mathematical and computational modelling of skin biophysics: a review

“…An attractive feature of computational models is the ability to quantify physical parameters required to obtain a specific outcome. For example, Prof. Kuhl's group at Stanford University has pioneered the development of mechanobiological adaptation models for skin to optimize the outcome of reconstructive surgery procedures in children [61][62][63][64][65][66][67] Streamline plots representing the maximum (coloured) and minimum (white) principal strain vectors in a finite deformation 2D plane-strain image-based finite-element model of the skin subjected to 20% in-plane compression (adapted from [20]). Grey arrows indicate the direction and location of the applied load.…”

Virtual testing of advanced composites, cellular materials and biomaterials: A review

“…The application of virtual testing in understanding the mechanics of skin is progressing rapidly. Tepole and co-workers [151,152] published their recent implementation of such an approach for skin growth, expansion and stretching. A typical implementation of skin growth in a child is shown in Figure 28 for increasing skin area.…”

“…A typical implementation of skin growth in a child is shown in Figure 28 for increasing skin area. The authors developed a computational model, based on a nonlinear continuum mechanics, for stretch-induced skin growth during tissue expansion [151,152]. Skin growth was multiplicatively decomposed into elastic and growth deformation gradient parts.…”

Evaluating the mechanical properties of biomaterials

“…More complicated models may take into account specifi c features of the material composition 8 or microstructure, including anisotropy in orientated tissues, 11,12 and porosity and trabecular architecture in cancellous bone. 13 Figure 9.1 shows the response to uniaxial tests (plotted as engineering stress σ o vs stretch) in tension and in compression of some of the best-known models.…”