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Mathematical Medicine and Biology Advance Access published online on July 17, 2009
Mathematical Medicine and Biology, doi:10.1093/imammb/dqp010
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Ricardo Romero-Méndez{dagger}

Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí, San Luis Potosí, SLP, Mexico

Joel N. Jiménez-Lozano and Mihir Sen

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

F. Javier González

Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí, San Luis Potosí, SLP, Mexico

{dagger} Email: rromerom{at}uaslp.mx

Received on October 8, 2008. Revised on February 25, 2009. Accepted on March 24, 2009.

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.

Keywords: thermographs; Pennes equation; burns


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