In this study, we present a fast analytical approach for laser induced temperature increase in biological tissue. The whole problem consists of two main steps. These steps are the light propagation and heat transfer in tissue. We first obtain a detailed analytical solution for the diffusion equation based on an integral approach for specific boundary conditions. Secondly, we also solve the Pennes' bio-heat transfer equation analytically using the separation of variables technique and obtain the temperature induced by optical absorption of tissue. Here, heat source term consists of the local absorption and photon density, which will be determined from the diffusion equation. We find a very comprehensive solution for the diffusion equation by using an integral method for the Robin boundary condition. In other words, we obtain a particular Green's function in a different way. Next, we use this solution as a source term in the Pennes’ bio-heat equation by utilizing the heat convection boundary condition. It is important to note that these boundary conditions are good approximations for imaging of biological tissue. As a result, we obtain spatio-temporal temperature distribution inside the medium. First, our approach is validated by a numerical approach using a Finite Element Method (FEM). Next, we also validate our method by performing phantom and tissue experiments. Experimental data corresponding to spatio-temporal temperature distribution are recorded using magnetic resonance thermometry. The analytical results obtained by our method are in a very good agreement with ones obtained by the FEM and experiment.
Hakan Erkol, Farouk Nouizi, Alex T. Luk, Mehmet B. Unlu, and Gultekin Gulsen, "A new analytical approach for heat generation in tissue due to laser excitation
(Conference Presentation)," Proc. SPIE 9706, Optical Interactions with Tissue and Cells XXVII, 97060L (Presented at SPIE BiOS: February 15, 2016; Published: 26 April 2016); https://doi.org/10.1117/12.2213684.4848609620001.
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