Computational Biophysics of the Skin

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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. 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.

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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.

Wound healing is a complex process spanning several temporal and spatial scales and requiring precise coordination of cell populations through mechanical and biochemical regulatory networks.

The dermis, which is the load bearing layer of the skin, is rebuilt after injury by fibroblasts through collagen deposition and active contraction. Fibroblast activity is controlled by cytokine gradients established during the initial inflammatory response, as well as by mechanical cues. However, even though we know the individual components of the wound healing system, in particular the factors associated with fibroblast-driven remodeling, we are still unable to achieve perfect skin regeneration and, instead, wounds lead to scars with inferior mechanical properties compared to healthy skin.

Computational Biophysics of the Skin

Computational models offer the unique ability to quantitatively analyze the dynamics of wound healing in order to attain a deeper understanding of this system. Here we show a continuum framework to describe the essential bio-chemo-mechanical couplings during wound healing, together with a finite element implementation of a model problem.

We account for nonlinear mechanical behavior and anisotropy of skin through a microstructure-based strain energy function, as well as the split of the deformation gradient into elastic and permanent deformations. These microstructure features evolve in time according to the spatiotemporal evolution of cell and cytokine concentration fields, which obey reaction diffusion differential equations.

The model problem exhibits emergent features of wound healing dynamics, such as wound contraction by fibroblasts in the periphery of the injury. Moreover, the proposed framework can be readily extended to more comprehensive regulatory networks and used to simulate other realistic geometries. Thus, we expect that the formulation presented here will enable further advances in wound healing research. 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.

A computational insight into skin formation

The mechanical properties of skin have been studied for several decades; yet, to this day reported stiffness values for full-thickness skin or individual layers such as the epidermis, papillary dermis, reticular dermis, and subcutis vary drastically. In vivo and ex vivo measurement techniques include extension, indentation, and suction tests. At the same time, several new imaging modalities emerged that visualize tissue microstructure at length scales ranging from the cell to the organ level.

Informed by the experimental characterization of mechanobiological skin properties, computational skin models aim at predicting the soft tissue response under various physiological conditions such as skin growth, scar tissue formation, and surgical interventions.

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The identification of corresponding model parameters plays a major role in improving the predictive capabilities of such constitutive models. Here, we first provide an overview of the most common measurement techniques and imaging modalities. We then discuss popular methods used for model parameter identification based on inverse methods.

Biophysics of Computation I

Human skin is a complex material that exhibits a non-linear stress-strain response, anisotropy, and viscoelasticity. In addition, skin in vivo is under an anisotropic pre-stress, which varies according to location and person. While several methods have been developed to measure the in vivo mechanical response of skin, many of these are incapable of characterising the anisotropy. Few also attempt to measure the in vivo stress. To quantify the anisotropy, it is necessary to apply deformations to the skin in a number of directions.

Biophysics and Quantitative Biology

This chapter provides an overview of a method where a rich set of deformations are applied to the surface of the skin and the nonlinear, anisotropic, and viscoelastic response is characterised using finite element analyses and nonlinear optimisation. The in vivo stress is also estimated.

Different constitutive models were tested as to their suitability to represent skin. Material parameters and pre-stresses were identified for points on the anterior forearm, upper arm, and the face. The complex mechanical properties of skin have been studied intensively over the past decades. They are intrinsically linked to the structure of the skin at several length scales, from the macroscopic layers epidermis, dermis and hypodermis down to the microstructural organization at the molecular level. Understanding the link between this microscopic organization and the mechanical properties is of significant interest in the cosmetic and medical fields.

These recent observations have provided novel information on the role of structural components of the skin in its mechanical properties, mainly the collagen fibers in the dermis, while the contribution of others, such as elastin fibers, remains elusive. Skin tension lines are natural lines of tension that occur within the skin as a result of growth and remodeling mechanisms.

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Research in the twentieth century showed clearly, through destructive mechanical testing, that the orientation of skin tension lines greatly affects the mechanical response of skin in situ. Scientists also use quantitative and computational biophysics tools to answer questions about the cell: to predict protein folding or observe interactions between biological macromolecules in vivo. But computational tools cannot answer one of the most fiercely debated questions among biophysicists: What is biophysics? The US government is investing in the twinned discipline, and pharmaceutical companies seek biophysics-trained candidates.

But no two biophysicists necessarily perform the same tasks. Because biophysics changes over time and with technology, definitions do not remain permanent anyway, she says. Scientists pursue both theoretical and practical biophysics. Such work can translate to drug discovery leads.

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The other side to biophysics is more theoretical. Klaus Schulten , director of the theoretical biophysics group at the University of Illinois, Urbana-Champaign, and self-proclaimed "world champion of biological simulations," says that biophysicists work to describe the matter in cells and how they carry out their functions. Structure-based approaches to drug design have helped fuel theoretical biophysics, according to Brian Shoichet , associate professor of molecular pharmacology and biochemistry at Northwestern University.

Some will argue, however, that such biological simulations become studies in other fields: "I wouldn't consider clinical simulations biophysics, because you start to step away from the physics and more toward physiology," Alvarez says.