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

Abstract

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.

Numerical analysis of interrelations between skin surface temperature and burn wound shape

“…The process of wound healing can be also analyzed. The problems close to the presented ones are also discussed in [4] and [5].…”

Determination of Burn Depth on the Basis of Skin Surface Temperature – Solution of Inverse Problem Using the Gradient Method

“…where T e /n , e=1, 2 denotes the normal derivative, n is the normal outward vector, for 2D problem: n= [cos 1 …”

“…For example, for 2D problem presented in Figure 2: K 1 =48, K=108. It should be pointed out that taking into account the boundary conditions, at the contact surface between sub-domains Ω 1 and Ω 2 (nodes 2869 in Figure 2) the double boundary nodes should be introduced. The remaining double nodes (shown in Figure 2) for example 3-4, 24-25 correspond to different boundary conditions, namely nodes 4, 25 are connected with the Robin condition, while nodes 3, 25 are connected with the Neumann condition.…”

“…A very important problem in the burns therapy is a correct evaluation of skin burn depth [1,2,3,4]. One of the possibilities depends on the measurements of the temperature distribution at the skin surface (thermographs) and the solution of the problem using an inverse approach.…”

Sensitivity Analysis of Temperature Field and Parameter Identification in Burned and Healthy Skin Tissue

“…A very important problem in burn therapy is the estimation of the temperature field in the injured and surrounding healthy tissue [1][2][3][4]. The information concerning the skin surface temperature allows one to observe the process of burn wounds healing.…”