Constitutive Modelling of Skin Growth

Skin, like all biological materials, adapts to mechanical cues. When expanded beyond its physiological regime over extended time periods, skin grows. This intuitive knowledge has been leveraged clinically in a widely used surgical technique called tissue expansion, in which a surgeon inserts a balloon-like device and inflates it gradually over months to grow skin for reconstructive purposes. However, it is currently not possible to anticipate how much of the deformation due to the expander is growth and how much of it is elastic strain, and tissue expansion protocols remain arbitrary, based on each physician’s experience and training, leading to an unacceptable frequency of complications. Here we show a continuum mechanics framework to describe skin growth based on the multiplicative split of the deformation gradient in to growth and elastic tensors. We present the corresponding finite element implementation, in which the growth component is an internal variable stored and updated at the integration points of the finite element mesh. The model is applied to study the deformation and growth patterns of skin for different expander shapes, as well as in patient specific scenarios, showing excellent qualitative agreement with clinical experience. Experimental methods to calibrate and validate the translation of the model to the clinical setting are briefly discussed. We expect that the proposed modeling framework will increase our fundamental understanding of how skin grows in response to stretch, and it will soon lead to personalized treatment plans to achieve the desired patterns of skin growth while minimizing complications.