Mathematical modelling, parameter estimation and computational simulation for skin wound healing under Copaiferalangsdorffi treatments

Abstract

We present three mathematical models which simulate the wound healing time for 10% oil-resin (10% OR), 10% hydroalcoholic extract (10% EH) (Copaifera langsdorffii drugs), Lanette cream (LC) and Collagenase treatments. Wound healing is a complex process consisting of inflammatory, proliferative and remodelling phases. The experiments were made on rats with wounds on their backs. The mathematical models consider the interplay among neutrophils, macrophages, which play an essential role in skin wound healing, pro-inflammatory (IL-6) and anti-inflammatory (IL-10) cytokines. The ordinary differential equations (ODE) models reproduce the cellular dynamics of wound healing on the skin, suggesting levels of macrophages and neutrophils cellularity, consistent with the values of total cellularity obtained in the laboratory. The partial differential equations (PDE) model replicate the dispersion along the wound radius, suggesting that the balance of the interleukins is better modelled on copaíba-based treatments (CBT). The cell density is directly influenced by neutrophils in the wound bed and by macrophages at the wound edge. It was possible to find the time for wound healing for all treatments by inserting the diffusive terms.