Multiscale and Multiphysics Modeling of Pressure Driven Ischemia and Ulcer Formation in the Skin

Vivek Dharmangadan Sree, Purdue University

Abstract

Pressure ulcers (PU) are localized damage to skin and underlying tissue that forms in response to ischemia and subsequent hypoxia from external applied mechanical loads such as pressure, pressure in combinations with friction and shear. PUs are devastating injuries that disproportionately affect the older adult population. The initiating factor of pressure ulcers is local ischemia, or lack of perfusion at the microvascular level, following tissue compression against bony prominences. In turn, lack of blood flow leads to a drop in oxygen concentration, i.e, hypoxia, that ultimately leads to cell death, tissue necrosis, and disruption of tissue continuity. Despite our qualitative understanding of the initiating mechanisms of pressure ulcers, we are lacking quantitative knowledge of the relationship between applied pressure, skin mechanical properties as well as structure, and tissue hypoxia. This gap in our understanding is, at least in part, due to the limitations of current imaging technologies that cannot simultaneously image the microvascular architecture, while quantifying tissue deformation. We overcome this limitation in our work by combining realistic microvascular geometries with detailed mechanical constitutive models into a microscale finite element model of the skin. By solving boundary value problems on a representative volume element via the finite element method, we can predict blood volume fractions in response to physiological skin loading conditions (i.e., shear and compression). We then use blood volume fraction as a homogenized variable to couple tissue-level skin mechanics to an oxygen diffusion model. With our model we find that moderate levels of pressure applied to the outer skin surface lead to oxygen concentration contours indicative of tissue hypoxia. In the second part of the thesis we explore the possibility of interlinking the model of tissue hypoxia with a cell regulatory network that governs the dynamics of PU formation. While there is a general understanding of the biological elements involved in this process and their interdependence within the biological PU signaling network, this system’s spatio-temporal dynamics in conjugation with realistic geometries have not yet been studied. Here we first present a 0D mathematical description of the PU regulatory network consisting of two cell types - keratinocytes and neutrophils- and six chemical species - TNFα, KC, ROS , DAMPs, O2 and XO. Extension of this regulatory network from a set of ordinary differential equations to realistic spatial domains is demonstrated by coupling each species’ dynamic equations to reaction diffusion partial differential equations. This model is further coupled to mechanical deformation of the spatial domain by including a pressure-sensitive oxygen perfusion term from the vascular deformations. The total model provides solutions to the regulatory network dynamics at the tissue scale with spatio-temporal detail on the evolution of each species. The model predicts patterns of PU formation in response to moderate loads, as seen clinically and experimentally. Future work will include rigorous calibration and validation of this model, which may render our work an important tool toward developing better prevention and treatment tools for pressure ulcers specifically targeted toward the older adult patient population.

Degree

M.Sc.

Advisors

Buganza, Purdue University.

Subject Area

Mechanics|Physiology|American history|History|Mathematics

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