Modeling the Effects of Dehydration on Cellular Growth and Wound Repair

Abstract

Dehydration is a common problem among athletes and the elderly, both of whom get injured more frequently than the average adult. Dehydration has been linked to reduced circulation, a reduced amount of water being absorbed into the cellular matrix, increased inflammation, decreased blood pressure, decreased volume of plasma, increased heart rate, decreased cellular density, and increase adhesion constant, depending on the severity and duration of dehydration. A comprehensive and functioning model describing the impacts of dehydration on tissue growth could be used when studying and designing treatment plans for groups vulnerable to dehydration and to inform decisions on environments for growing cell cultures and tissue in vitro. Previous models have described hydration and water replacement in the human body or the process of tissue growth or wound repair. This model integrates the effects of dehydration with the parameters of wound repair to create a more comprehensive model. This resulting model is a combination and modification of a continuum and a partial differential equation model. The continuum model is modified to consider more of the effects of dehydration on the tissue with the intent to increase the accuracy of the model. The overlapping parameters and relationships are used to link the models together. The combined model is then modified with unitless parameters that represent the severity and duration of dehydration to create the final model. The model found that while the simulated subject is fully hydrated, intralayer elastic couplings are the largest factor that increases cell density, being to a power of nine. The influence of the tangential diffusion of cells is only to a power of one and comparatively uninfluential. The grouped effect of cell crowding and cell synthesis and apoptosis to decrease cellular density is to a power of negative nine, so mathematically it balances out the effect of the elastic couplings. The influence of the tangential velocity of cells is the next most influential component to decrease the cellular density, at a power of five. During severe dehydration, the cell crowding component and the elastic component changed by a power of four, the cell crowding component becoming less negative and the elastic couplings component increasing. Both the tangential diffusion and tangential velocity decreased by a power of two. Unexpectedly, the cellular density changed very little with varying simulations of dehydration. Despite this, the model shows that dehydration slows the rate of wound healing and it suggests that the severity of dehydration is more detrimental than the duration of dehydration.