Numerical Simulation of the Evolution of Wound Healing in the 3D Environment

Abstract

Numerical simulation of the wound healing behaviour by considering the coupled reaction-diffusion, transport and viscoelastic system is vital in investigating the mechanical stress field induced by cell migration. In this work, numerical simulation is viewed in three-dimensional space during a time course of wound healing. Over the years, many authors have developed two-dimensional mathematical models of wound healing, as supported by the background in the introduction below. But we know that a three-dimensional case realistically captures the tissue deformations. The two-dimensional simulation is restricted to observing the motion in two directions only. Hence, the interest is in the three-dimensional case. Therefore, to our knowledge, this is the first article to consider the numerical simulation of the coupled reaction-diffusion, transport and viscoelastic system during wound healing in a three-dimensional environment. Firstly, the two-dimensional evolution of wound healing is developed to compare our results with published data. Then the work is extended to three-dimensional wound healing, which is the main focus.

One-step three-parameter optimized hybrid block method for solving first order initial value problems of ordinary differential equations

“…Similarly, other types of differential equations such as fractional-order differential equation, Caputo fractional-order derivative, Fuzzy Volterra integral equation have been treated using diverse approach such as establishing the existence and stability of solution [4,5,6,7,8]; Laplace Adomain Decomposition method [9]; Haar Wavelets method [10]; and finite difference method [11,12,13,14] among others.…”