Eden Model Simulation of Re-Epithelialization and Angiogenesis of an Epidermal Wound

Abstract

Among the vital processes of cutaneous wound healing are epithelialization and angiogenesis. The former leads to the successful closure of the wound while the latter ensures that nutrients are delivered to the wound region during and after healing is completed. These processes are regulated by various cytokines and growth factors that subtend their proliferation and migration into the wound region until full healing is attained. Wound epithelialization can be enhanced by the administration of epidermal stem cells (ESC) or impaired by the presence of an infection. This paper uses the Eden model of a growing cluster to independently simulate the processes of epithelialization and angiogenesis in a cutaneous wound for different geometries. Further, simulations illustrating bacterial infection are provided. Our simulation results demonstrate contraction and closure for any wound geometry due to a collective migration of epidermal cells from the wound edge in fractal form and the diffusion of capillary sprouts with the laying down of capillary blocks behind moving tips into the wound area.

Fractal models of the PbTe nanocluster structures on a solid surface

“…Fractal nanofilms with a percolation structure and good filling of nanoclusters can be modeled in the directed percolation approximation [ ]. This technique allows generating Eden clusters [12]. Models of nanoclusters were developed on the basis of the fractals indicated in Table 1.…”

Topology and Local Geometry of the Eden Model

“…That is, over time, the shape of the resulting structure looks more and more like a rescaling of a certain convex set which depends only on the model parameters-so, in the case of the Eden model, only on the dimension. 1 The shape theorem restricts all nondeterministic behavior to a collar near the boundary of this convex set which is vanishingly small compared to the whole structure, but whose thickness measured in tiles tends to infinity. As far as we know, not much previous attention has been dedicated to the local geometry in this region for any first-passage percolation model.…”

Topology and local geometry of the Eden model

“…That is, over time, the shape of the resulting structure looks more and more like a rescaling of a certain convex set which depends only on the model parameters-so, in the case of the Eden model, only on the dimension. 1 The shape theorem restricts all "random" behavior to a region near the boundary of this convex set which is vanishingly small compared to the whole structure, but grows larger and larger when its width is measured in tiles. As far as we know, not much previous attention has been dedicated to the local geometry in this region for any first-passage percolation model.…”

“…The EGM itself has specifically been proposed as a model for wound regeneration [1] and the growth of bacterial colonies [34]. Similar systems with additional parameters or modified rules for the addition (or subtraction) of tiles have been proposed to model a wide variety of phenomena, such as the magnetic Eden model for aggregations of particles with a fixed spin in a medium 2 [3,6,22]; cellular automata [11]; tumor growth [35]; and urban growth [23,33], among others.…”

“…Similar systems with additional parameters or modified rules for the addition (or subtraction) of tiles have been proposed to model a wide variety of phenomena, such as the magnetic Eden model for aggregations of particles with a fixed spin in a medium 2 [3,6,22]; cellular automata [11]; tumor growth [35]; and urban growth [23,33], among others. 1 While this convex set looks round in simulations in dimension d = 2, it is known not to be a Euclidean ball for d > 34 [21,8]. 2 Constrast with the Ising model, in which the spins of the particles are allowed to change over time.…”