An Analytic Model of Tissue Self-Healing and Its Network Implementation: Application to Fibrosis and Aging

Abstract

Here we present a model capable of self-healing and explore its ability to resolve pathological alterations in biological tissue. We derive a simple analytic model consisting of an agent representing a cell that exhibits anabolic or catabolic activity, and which interacts with its tissue substrate according to tissue stiffness. When perturbed, this system returns toward a stable fixed point, a process corresponding to self-healing. We implemented this agent-substrate mechanism numerically on a hexagonal elastic network representing biological tissue. Agents, representing fibroblasts, were placed on the network and allowed to migrate around while they remodeled the network elements according to their activity which was determined by the stiffnesses of network elements that each agent encountered during its random walk. Initial injury to the network was simulated by increasing the stiffness of a single central network element above baseline. This system also exhibits a fixed point represented by the uniform baseline state. During the approach to the fixed point, interactions between the agents and the network create a transient spatially extended halo of stiffer network elements around the site of initial injury, which aids in overall injury repair. Non-equilibrium constraints generated by persistent injury prohibit the network to return to baseline and results in progressive stiffening, mimicking the development of fibrosis. Additionally, reducing anabolic or catabolic rates delay self-healing, reminiscent of aging. Our model thus embodies what may be the simplest set of attributes required of a spatiotemporal self-healing system, and so may help understand altered self-healing in chronic fibrotic diseases and aging.

Keywords: agents; fixed point; network; random walk; repair.