Analytical solution of the Pennes equation for burn-depth determination from infrared thermographs

• Published in: Mathematical medicine and biology Vol. 27; no. 1; pp. 21 - 38
• Main Authors: Romero-Méndez, Ricardo, Jiménez-Lozano, Joel N., Sen, Mihir, González, F. Javier
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01-03-2010
• Subjects: Algorithms; burns; Burns - diagnosis; Burns - pathology; Humans; Models, Biological; Pennes equation; Skin Temperature - physiology; thermographs; Thermography - methods
• ISSN: 1477-8599; 1477-8602
• DOI: 10.1093/imammb/dqp010

A serious problem in emergency medicine is the correct evaluation of skin burn depth to make the appropriate choice of treatment. In clinical practice, there is no difficulty in classifying first- and third-degree burns correctly. However, differentiation between the IIa (superficial dermal) and IIb (deep dermal) wounds is problematic even for experienced practitioners. In this work, the use of surface skin temperature for the determination of the depth of second-degree burns is explored. An analytical solution of the 3D Pennes steady-state equation is obtained assuming that the ratio between burn depth and the burn size is small. The inverse problem is posed in a search space consisting of geometrical parameters associated with the burned region. This space is searched to minimize the error between the analytical and experimental skin surface temperatures. The technique is greatly improved by using local one-dimensionality to provide the shape of the burned region. The feasibility of using this technique and thermography to determine skin burn depth is discussed.