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Analytical solution to the transient 1D bioheat equation in a multilayer region with spatial dependent heat sources

Publication ,  Journal Article
Rodrigues, DB; Da Silva Pereira, PJ; Limão-Vieira, PM; Maccarini, PF
Published in: Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011
June 13, 2011

An analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat equation in a multilayer region with spatial dependent heat sources is derived. Multilayer regions with 1D Cartesian, cylindrical or spherical geometries and composed of different types of biological tissues characterised by temperature-invariant physiological parameters are considered. Boundary conditions of first, second and third kinds to the temperature at the inner and outer surfaces are also assumed. In this work, the bioheat transfer model is applied to obtain the temperature profiles in a tumor bed and a surrounding healthy tissue using two spatial dependent heat source terms to simulate a magnetic fluid hyperthermia technique in the cancer treatment. The influence of these two heat sources, described by polynomial and exponential functions, on temperature is investigated.

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Published In

Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011

DOI

Publication Date

June 13, 2011

Start / End Page

96 / 103
 

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Rodrigues, D. B., Da Silva Pereira, P. J., Limão-Vieira, P. M., & Maccarini, P. F. (2011). Analytical solution to the transient 1D bioheat equation in a multilayer region with spatial dependent heat sources. Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011, 96–103. https://doi.org/10.2316/P.2011.723-092
Rodrigues, D. B., P. J. Da Silva Pereira, P. M. Limão-Vieira, and P. F. Maccarini. “Analytical solution to the transient 1D bioheat equation in a multilayer region with spatial dependent heat sources.” Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011, June 13, 2011, 96–103. https://doi.org/10.2316/P.2011.723-092.
Rodrigues DB, Da Silva Pereira PJ, Limão-Vieira PM, Maccarini PF. Analytical solution to the transient 1D bioheat equation in a multilayer region with spatial dependent heat sources. Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011. 2011 Jun 13;96–103.
Rodrigues, D. B., et al. “Analytical solution to the transient 1D bioheat equation in a multilayer region with spatial dependent heat sources.” Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011, June 2011, pp. 96–103. Scopus, doi:10.2316/P.2011.723-092.
Rodrigues DB, Da Silva Pereira PJ, Limão-Vieira PM, Maccarini PF. Analytical solution to the transient 1D bioheat equation in a multilayer region with spatial dependent heat sources. Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011. 2011 Jun 13;96–103.

Published In

Proceedings of the 8th IASTED International Conference on Biomedical Engineering, Biomed 2011

DOI

Publication Date

June 13, 2011

Start / End Page

96 / 103