Computational models of skin mechanics and mechanobiology [electronic resource]

Skin is our interface to the world, it protects our internal machinery, regulates our temperature, fluid exchange, and resists constant wear and tear. Skin has remarkable mechanical properties, it is a thin structure that can undergo large deformations without rupturing, letting us move around, interact with the objects in our surroundings, and express ourselves. Additionally, our integument is a living system and it can adapt to mechanical and environmental cues. In summary, mechanical integrity of skin is crucial to our survival. Understanding the mechanics and mechanobiology of skin is also important for the clinician since disruption of mechanical homeostasis appears often in disease and repair. This dissertation focuses on the problems of plastic and reconstructive surgery in which skin adapts to mechanical scenarios. These include tissue expansion, flap design and wound healing. Tissue expansion is a well-known technique to resurface large defects by growing skin in vivo. Skin grows in response to overstretch. Despite its numerous advantages and wide-spread, this technique does not lack complications and suboptimal outcomes. A major reason lies in the lack of quantitative tools to understand the fundamental aspects of skin growth to overstretch that can be then used to predict and guide preoperative planning. In this thesis, I show how applying the classical theories of mechanics and incorporating the description of finite growth by the multiplicative split of the deformation gradient into growth and elastic contributions, it is possible to get biological insight into the dynamics of skin growth in response to mechanical deformations. Furthermore, this approach is suitable for an efficient computational implementation using finite elements. I show how simulations can predict the effect of different expander geometries and sizes which are variables of clinical significance. The same set of tools can be used in patient specific scenarios. I demonstrate the use of computational simulations on geometries obtained from computer tomography scans of pediatric patients. In order to validate and calibrate the model, I designed and conducted animal experiments in collaboration with surgeons at Northwestern University. We established a novel experimental protocol that uses multi-view stereo and B-spline isogeometric analysis to capture the kinematics of expanded porcine integument. We show experimentally how overstretch triggers the growth of new skin. We compared different expander shapes and inflation protocols. We also quantified for the first time the development of residual stresses over a sizable patch of tissue. Tissue expansion is at the core of this dissertation, however, once new skin is grown there are two other processes of mechanical interest that become relevant: flap design and wound healing. These phenomena are also relevant for a vast majority of plastic and reconstructive surgery procedures and not only tissue expansion. I present the comparison of different flap designs on grown skin patches and show that the double back cut flap produces an overall lower stress distribution for the same size of defect as compared to the advancement flap. I also show how the orientation of the underlying collagen network plays an important role in the preoperative planning. Finally, another major concern regarding the restoration of mechanical homeostasis of skin is the process of wound healing and scarring. I present a generic framework for the coupled mechano-chemo-biological problem of wound healing. Starting from the mechanics perspective, I use state-of-the-art constitutive laws of skin to model it as an anisotropic hyperelastic material in terms of structurally motivated parameters. The load bearing properties of skin are attributed to the collagen content. When skin is wounded, the collagen architecture is abruptly disrupted. During healing, different cell populations act in coordination through various cell-signaling pathways in order to lay down and remodel the collagen microstructure. In the proposed framework, micro-structural parameters such as the collagen content become part of the evolving fields that have to be characterized as they change over time and space. I incorporate the mechanobiology coupling by making these parameters a function of cellular response. In turn, I introduce a new set of reaction-diffusion partial differential equations to model the dynamics of cell density fields and the chemical signals that regulate the cell behavior. The generic framework I propose is implemented in a monolithic finite element formulation. Simulations of a model problem of cutaneous wound healing shows good agreement with experiments from the literature, offering promise to more detailed simulations and experimental validation and calibration. In conclusion, the body of work presented in this dissertation is a significant step towards the better understanding of skin mechanics not only as a structure, but as a living tissue that can grow and heal. The computational tools developed are ultimately aimed at applications in clinically relevant problems of plastic and reconstructive surgery.

Keywords: Mechanical Engineering.
Advisor: Kuhl Ellen
Pinsky Peter M. (Peter Michael)
Steele C. R. (Charles R.) advisor. Thesis advisor