Calculation of the heat released by a highly conducting spheroidal particle inside a biological tissue after absorption of a brief radiation pulse

Laplace’s transform technique is used to solve the equations that govern the cooling of a spheroidal particle embedded in a biological tissue, viewed here as a homogeneous conducting medium. The particle, of sub-micrometer dimensions, is supposedly made of a material with high thermal conductivity that absorbs an incident, brief electromagnetic pulse. These ideal characteristics can be met with carbonaceous materials. They are exploited to derive a formal solution of the heat equation. It is shown that the temperature field can be determined everywhere once the Laplace transform of the particle temperature has been determined. How the methodology works is illustrated with the case of a prolate spheroid. Different aspect ratios of the particle are considered, from spherical to cigar shape. A few interesting parameters come out of the calculations. The way these parameters influence the cooling evolution is discussed in connection with applications in photothermal therapy.