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

Mathematical and numerical analyses of cellular, molecular and angiogenic parameters of a rat skin wound healing model

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.

Kinetic modeling: A tool for temperature shift and feeding optimization in cell culture process development

Mammalian cells have dominated the biopharmaceutical industry for biotherapeutic protein production and tremendous efforts have been devoted to enhancing productivity during the cell culture process development. However, determining the optimal process conditions is still a huge challenge. Constrained by the limited resources and timeline, usually it is impossible to fully explore the optimal range of all process parameters (temperature, pH, dissolved oxygen, basal and feeding medium, additives, etc.). Kinetic modeling, which finds out the global optimum by systematically screening all potential conditions for cell culture process, provides a solution to this dilemma. However, studies on optimizing temperature shift and feeding strategies simultaneously using this approach have not been reported. In this study, we built up a kinetic model of fed-batch culture process for simultaneous optimization of temperature shift and feeding strategies. The fitting results showed high accuracy and demonstrated that the kinetic model can be used to describe the mammalian cell culture performance. In addition, five more fed-batch experiments were conducted to test this model's predicting power on different temperature shift and feeding strategies. It turned out that the predicted data matched well with experimental ones on viable cell density (VCD), metabolites, and titer for the entire culture duration and allowed selecting the same best condition with the experimental results. Therefore, adopting this approach can potentially reduce the number of experiments required for culture process optimization.