MATHEMATICAL MODELLING OF THE INFLAMMATORY PHASE OF SKIN WOUND HEALING IN RATS

The skin wound healing is a complex process divided into three overlapping and interdependent phases (inflammatory, proliferative and remodelling). The inflammatory response must occur rapidly to avoid chronic inflammation and it depends on biochemical, molecular and cellular events. The effective crosstalk between leukocytes and cytokines (proinflammatory and anti-inflammatory) lead to correct healing of the lesions. We considered a system of ordinary differential equations to model the inflammatory phase of skin wound healing process under treatments with oleoresin and hydroalcoholic cream extract from Copaifera langsdorffii. The model can exhibit two stable steady states corresponding to healthy or unhealthy skin, nevertheless this study has been concentrated in a parameter search to healthy state in order to verify the treatment efficiency comparing the results of the oleoresin against hydroalcoholic extract. Thus, we have analysed the roles among the main leukocytes (neutrophils and macrophages), present in the inflammatory phase, and the inflammatory cytokines: interleukin 6 (IL-6) and interleukin 10 (IL-10). The model solution reproduced the dynamics of the neutrophils and macrophages during inflammatory phase, however there was a lack between numeric and biological results suggesting the necessity to improve the model. One possible strategy to enhance this model is to consider the interaction between the pro-inflammatory cytokine and macrophages in the mathematical model.