ABSTRACT
The inflammatory phase is an important event in the skin wound healing process. The deposition of granulation tissue in the wound bed and the rebuilding of the vascular network occur as inflammation diminishes. An angiogenic component in the formation of granulation tissue is the secretion of vascular endothelial growth factor, which assists in the chemotaxis, proliferation, and replication of fibroblasts. In this paper, we develop a mathematical model of skin wound healing angiogenic factors based on inflammatory cells (macrophages and neutrophils) and mediators (interleukin 6 and interleukin 10). We highlight the importance of this process in vascular endothelial growth factor release and in the formation of new capillary tips. We used a mathematical model of partial differential equations based on the reaction-diffusion-advection equations. In order to calibrate the parameters, we considered an in vivo model composed by four treatments: hydroalcoholic extract and oil-resin of Copaifera langsdorffii at 10% concentration, collagenase, and Lanette cream. Using the laboratory data for the wound edge, our mathematical model estimated the values of vascular endothelial growth factor concentration, and tips density in the center of the wound with a maximum error of 2.9%, and predicted healing time required for each treatment. The region of viability for the parameters, in the proposed model, was found through numerical simulations from the Interleukin 6 and 10 dysregulation and we obtained that, among the parameters analyzed, the greatest influencer in the dynamics of the system is the one, which represents the production of Interleukin 10 during phagocytosis.
Subject(s)
Interleukin-10 , Vascular Endothelial Growth Factor A , Rats , Animals , Interleukin-6 , Wound Healing/physiology , Vascular Endothelial Growth Factors , SkinABSTRACT
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.
