Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method

Fabrizio Martelli; Angelo Sassaroli; Samuele Del Bianco; Yukio Yamada; Giovanni Zaccanti

doi:10.1103/PhysRevE.67.056623

Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method

Fabrizio Martelli, Angelo Sassaroli, Samuele Del Bianco, Yukio Yamada, and Giovanni Zaccanti

Phys. Rev. E 67, 056623 – Published 27 May 2003

Abstract

An exact solution of the time-dependent diffusion equation for the case of a two- and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.

Received 20 May 2002

DOI:https://doi.org/10.1103/PhysRevE.67.056623

Authors & Affiliations

Fabrizio Martelli^*, Angelo Sassaroli^2,†, Samuele Del Bianco¹, Yukio Yamada³, and Giovanni Zaccanti¹

¹Dipartimento di Fisica dell’Università degli Studi di Firenze and Istituto Nazionale per la Fisica della Materia, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
²Institute for Human Science and Biomedical Engineering, National Institute of Advanced Industrial Science and Technology, Namiki 1-2, Tsukuba, Ibaraki 305-8564, Japan
³Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, Chofugaoka, 1-5-1 Chofu, Tokyo 182-8585, Japan

^*Email address: fabrizio.martelli@unifi.it
^†Present address: Department of Biomedical Engineering, Bioengineering Center, Tufts University, 4 Colby Street, Medford, Massachusetts 02155.

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Vol. 67, Iss. 5 — May 2003

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