A simple stochastic model to explain the sigmoid nature of the strain-time cellular tolerance curve

Abstract

Using animal and tissue-engineered experimental models, we previously found that a decreasing sigmoidal function is adequate for describing the diminishing tolerance of skeletal muscle tissue/cells for static mechanical strains delivered over time. Compressive loads at the tissue scale, which are associated with weight-bearing, appear to stretch the plasma membrane (PM) of cells at the mesoscopic–microscopic scales. The permeability of such stretched PMs may then increase, which could alter the control mechanisms and consequently the homeostasis of the deformed cells. The present paper is aimed at demonstrating this suggested deformation–diffusion damage pathway – which is particularly relevant to the aetiology of deep tissue injury – at the level of a single cell, using simple stochastic computer modeling which is supported by experimental confocal microscopy imaging data. The modeling and confocal studies better explain the strain-time injury threshold previously proposed by our group, and in particular, they provide an explanation for the nature of the rapid decrease of the threshold curve. The simulations revealed that there was a clear trend of nearly inverse relationship between the level of stretch applied to the PM and the time for accumulation of cytotoxic contents of a diffusing biomolecule. Taken together with the confocal data, which correspondingly demonstrated increased permeability of the PM of statically stretched cells to a fluorescent dye, the present results point to cell-level deformation–diffusion damage as a factor that should be looked at more closely in aetiological research of pressure ulcers.