Abstract
Here, the Dual Reciprocity Boundary Element Method is used to solve the 3D Pennes Bioheat Equation, which together with a Genetic Algorithm, produces an inverse model capable of obtaining the location and the size of a tumour, having as data input the temperature distribution measured on the skin surface. Given that the objective function, which is solved inversely, involves the DRBEM (Dual Reciprocity Boundary Element Method) the Genetic Algorithm in its usual form becomes slower, in such a way that it was necessary to develop functions based the solution history in order that the process becomes quicker and more accurate. Results for 8 examples are presented including cases with convection and radiation boundary conditions. Cases involving noise in the readings of the equipment are also considered. This technique is intended to assist health workers in the diagnosis of tumours.
Highlights
There exist various techniques for the localization of tumours: Invasive techniques, which need surgery and non-invasive techniques, such as ultra sound, MRI and thermal methods
Bueno et al / Inverse model for locating skin tumours in 3D using the genetic algorithm with the Dual Reciprocity Boundary Element Method Initially a rectangular tumour with dimensions 0.02 x 0.02 x 0.01 m3 and with its centre located at coordinates (0.00; 0.00; 0.01) corresponding to the coordinates x, z and y respectively, as shown in fig. 3
If the chromosome indicates a tumour which is in a position in which part of the tumour would be outside the search space, this will be automatically eliminated by the fitness function because the temperature distribution will be discontinuous and completely different from a real distribution
Summary
There exist various techniques for the localization of tumours: Invasive techniques, which need surgery and non-invasive techniques, such as ultra sound, MRI and thermal methods. A steady-state mathematical model based on the Bioheat Equation developed by Pennes (1948), simulating heat transfer throughout the human body, was developed by Wissler (1961) These results were compared with experimental data and were considered satisfactory. DRBEM is essentially a generalized way of constructing particular solutions that can be used to solve non-linear and time-dependent problems as well as to represent any integral source distribution (Partridge et al, 1992) Considering these observations Partridge and Wrobel (2007) developed an inverse procedure using the Genetic Algorithm, through which the size and location of a skin tumour could be obtained from temperatures measured at the skin surface in a two dimensional model. In this way the results obtained are more complete and satisfactory
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