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International Heat Transfer Conference 16

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)


João Freire
IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Pedro J. M. Coelho
Technical University of Lisbon Instituto Superior Tecnico AV Rovisco Pais 1049-001, Lisbon, Portugal

DOI: 10.1615/IHTC16.bma.021406
pages 487-494

KEY WORDS: Bio and medical applications, Radiation, Radiative transfer equation, Discrete ordinates method, Cylindrical coordinates


A short pulse laser is applied to the investigate the influence of cutaneous tumours in the human skin on the reflected signal using two-dimensional axisymmetric coordinates. This approach extends previous works that relied on a one-dimensional approximation. The transient radiative transfer equation is solved using the discrete ordinates method. A 2nd order Runge-Kutta method is employed for time discretization and the CLAM scheme is employed for spatial discretization. The skin is treated as a multi-layered medium with different optical properties in each skin layer, and the Henyey-Greenstein scattering phase function is employed. The numerical solution of the transient radiative transfer equation in 2D axisymmetric problems is firstly validated for homogeneous media. The code is then applied to normal skin, and the 2D predictions are compared with 1D results to show the limitations of the latter approximation when the diameter of the laser beam is small. Finally, the temporal variation of the reflectance in healthy skin tissue is compared with the reflected signals in cancerous tissues. The variation of the reflectance with the size of the tumour is also studied. The results demonstrate that different skin carcinomas of the same size yield reflected signals of different magnitude, allowing their identification, even though this is more difficult at early stages of growth. The reflectance also changes with the size of the tumour, i.e., with the stage of growth.

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