Author(s)

Namrata Gupta, Madhvi Shakya

Department of Applied Mathematics, Maulana Azad National Institute of Technology, Bhopal, India.

During wound healing, the metabolic activity associated with each phase must occur in the proper sequence, at a specific time, and continue for a specific duration at an optimal intensity. Any disturbance in appropriate thermal environment may complicate the wound healing process and may give rise to wound infection. In the presented paper a transient state two-dimensional mathematical model has been developed to analyse thermal variations in skin and subcutaneous tissue (SST) region of human limb. Due to circular shape of human limb, model has been developed in polar coordinates. The domain of the study consists of two types of tissues: abnormal tissues and normal tissues. The post surgery peripheral tissue of human limb during healing time is considered as abnormal tissues. The effect of variable density of blood vessels in dermal layer of both tissues on the physical and physiological parameters is incorporated in the model. The effect of healing on physiological parameters of abnormal tissue is incorporated by considering the physiological parameters to be function of time “t”. The effect of different climatic conditions is considered in the model. Taking into account the variable core temperature due to anatomy of arteries and variable physiological parameters in dermal layer of peripheral region, the well known Pennes’ bio heat equation is used to analyse the time-dependent temperature distribution of both normal and abnormal tissues. Comparison between temperature profiles of both normal and abnormal tissue has been done using finite element approach with bilinear shape functions in polar coordinates. A computer program in MATLAB has been developed to simulate the results.

Bio-Heat Equation, Surgical Wound Healing, Finite Element Technique, Crank-Nicolson Method, Skin and Subcutaneous Tissue Region

Gupta, N. and Shakya, M. (2016) A Two-Dimensional Mathematical Model to Analyze Thermal Variations in Skin and Subcutaneous Tissue Region of Human Limb during Surgical Wound Healing. Applied Mathematics, 7, 145-158. doi: 10.4236/am.2016.72014.