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.

我们提出了三种数学模型，分别模拟了10％的油脂树脂（10％的OR），10％的水醇提取物（10％的EH）的伤口愈合时间（Copaifera langsdorffii药物），Lanette乳霜（LC）和胶原酶治疗。伤口愈合是一个复杂的过程，包括炎症，增生和重塑阶段。实验是在大鼠背上有伤口的情况下进行的。数学模型考虑了嗜中性粒细胞，巨噬细胞之间的相互作用，它们在皮肤伤口愈合，促炎（IL-6）和抗炎（IL-10）细胞因子中起着至关重要的作用。普通微分方程（ODE）模型再现了皮肤伤口愈合的细胞动力学，表明巨噬细胞和嗜中性粒细胞的细胞水平与实验室获得的总细胞水平一致。偏微分方程（PDE）模型沿伤口半径复制了弥散，提示白细胞介素的平衡可以更好地模拟基于Copaíba的治疗（CBT）。细胞密度直接受创床中嗜中性粒细胞和创口边缘巨噬细胞的影响。通过插入扩散项，可以找到所有治疗方法的伤口愈合时间。