M. Dziewoński

Numerical Modelling of Hyperthermia and Hypothermia Processes

In the paper the results of different numerical solutions of bioheat transfer problems are presented. The base of numerical algorithms constitute the models containing the bioheat transfer equation (or equations) and the adequate geometrical, physical, boundary and initial conditions. In the first part of the paper the solutions concerning the transient temperature field in the biological tissue subjected to the strong external heat sources (freezing, burns) are presented. Next, the examples of sensitivity analysis application in the range of bioheat transfer are discussed. In the final part of the paper the inverse problems are formulated and the example concerning the identification of thermal parameters is shown.

Identification of cast steel latent heat by means of gradient method

The inverse problem consisting of the identification of volumetric latent heat of steel cast is presented. Additionally, it is assumed that the courses of temperature at the set of points from casting and/or mould are known. Thermal processes proceeding in a casting domain are described using the one-domain formulation. The substitute thermal capacity of steel cast (this parameter is directly connected with the latent heat) is approximated by the fourth-degree polynomial. To solve the inverse problem, the least squares criterion containing the sensitivity coefficients is applied. The solution of the problem is found using the numerical methods (FDM, explicit scheme). In the final part of this paper, the numerical solutions concerning the different input data are presented. The disturbed data are also taken into account. [Received 16 May 2007; Accepted 17 July 2007]

Evolutionary Computation in Inverse Problems

Evolutionary computations in identification of multiple material defects (voids and cracks) in mechanical systems and identification of shape and position of a tumor region in the biological tissue domain are presented. The identification belongs to inverse problems and is treated here as an output (measurement) error minimization, which is solved using numerical optimization methods. The output error is defined in the form of a functional of boundary displacements or temperature fields. An evolutionary algorithm is employed to minimize of the functional. Numerical tests of internal defects identification and some anomalies in the tissue are presented.

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

In the chapter, problems connected with the numerical modeling of bioheat transfer processes are presented. In particular the non-homogeneous system of a burn wound and healthy tissue is considered. The heat exchange between sub-domains and environment is described by a system of partial differential equations (the Pennes equations) supplemented by adequate boundary conditions. The first goal of the research is the estimation of the changes of temperature fields due to perturbations in thermal parameters using the direct method of sensitivity analysis. Both the basic problem and additional ones concerning the sensitivity with respect to selected parameters are solved using the boundary element method. The second goal is the problem of burn wound shape identification. The additional information necessary to solve such a task results from the knowledge of temperature distribution on the external surface of skin tissue. At the stage of solving the inverse problem, a gradient method has been used. In the final part of the chapter the results of computations are shown.

The BEM-FDM model of thermal processes proceeding in the domain of the human finger.

PURPOSE The problem of the numerical modeling of thermal processes proceeding in the non-homogeneous domain of the human finger is discussed. The domain considered constitutes the assembling of soft and bone tissues and the system of supplying blood vessels (arteries and veins). The mathematical description of the process analyzed corresponds to the so-called vascular models. METHODS At the stage of numerical modeling the algorithm being the composition of the boundary element method (BEM) and the finite difference method (FDM) is applied. RESULTS The algorithm presented allows one to determine the steady state temperature field in the finger domain in natural convection conditions. To verify the effectiveness and exactness of the method of the problem solution, the thermal imaging measurements of the finger surface temperature have been done. CONCLUSIONS The compatibility of numerical and experimental results (the natural convection conditions) has proved to be quite satisfactory. It is possible to use the algorithm proposed for the modeling of thermal processes proceeding in the conditions of low or high ambient temperatures and the big values of heat transfer coefficients. The impact of protective clothing on the temperature field in the domain of the finger can also be analyzed.

Scanning Method of Temperature Distribution of Human Body by Device Registering Encircling Images

This chapter is related to a scanning method for measuring a skin surface temperature distribution of a patient’s body with a burn wound. Results can be used for medical diagnostics in order to evaluate the skin burn depth. Within the project entitled “The diagnostic system supporting the healing process of burn and chronic wounds” funded by The Polish National Centre of Research and Development, the diagnostic device for recording thermal images was created. The chapter concerns the description of merging algorithm of these images which is based on the mathematical formulas. In the final part of this chapter, some simulation results are shown.

Prototype of the Device Registering Encircling Images

Within the project entitled ”The diagnostic system supporting the healing process of burn and chronic wounds” funded by The Polish National Centre of Research and Development the diagnostic system and device for recording thermal images/videos was created. The paper concerns the description of the prototype of the device registering encircling thermograms and video images.