Finite difference methods for solving the transport equation in the problems of optical biomedical diagnostics

Leonid P. Bass (Login required)
M.V. Keldysh Institute of Applied Mathematics RAS, Moscow, Russia

Olga V. Nikolaeva
M.V. Keldysh Institute of Applied Mathematics RAS, Moscow, Russia

Alexander V. Bykov
Opto-Electronics and Measurement Techniques Lab., University of Oulu, Finland

Mikhail Yu. Kirillin
Institute of Applied Physics RAS, Nizhny Novgorod, Russia

Paper #3176 received 5 Apr 2017; revised manuscript received 14 Apr 2017; accepted for publication 17 Apr 2017; published online 30 Apr 2017.

DOI: 10.18287/JBPE17.03.010311


The present paper is a retrospective review of the development of the approach to numerical modeling of radiation propagation in biological tissues, based on the use of finite difference methods for the solution of the radiative transfer equation (RTE) and its application to the problems of biomedical diagnostics. The advantage of finite difference methods is the possibility to obtain the solution of the direct problem of radiation propagation in turbid media, when the exact analytical solution is impossible. In turn, the possibility to solve the RTE opens wide perspectives for the solution of inverse problem and reconstruction of structural and functional characteristics of objects from the detected scattered radiation. We present a review of the finite difference methods applied to the solution of angiography problems and investigation of blood using optical biomedical diagnostic technologies.


radiative transfer equation; finite difference techniques; Monte Carlo simulations; stationary problem; non-stationary problem

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