Blood perfusion estimation in heterogeneous tissue using BEM based algorithm

The estimation of space-dependent perfusion coefficient in homogeneous and non-homogeneous tissue has been investigated. While initial and Dirichlet boundary conditions are known, additional heat-flux measurement data is needed to render a unique solution. A numerical approach based on Boundary Element Method (BEM) combined with two different optimization routines and first-order Tikhonov regularization using L-Curve method has been developed. Efficiency of the algorithm, effect of initial guess, noise, perfusion distribution and non-homogeneous tissue on retrieving the perfusion coefficient has been studied on two test examples using exact as well as noisy data. Results show very good agreement with the true perfusion function under exact and low-noisy data, using Levenberg–Marquardt (LM) method combined with first-order regularization process. If the true perfusion function first-derivative is large, the function can be successfully retrieved only in the region near the boundary measurement, which is especially noticeable for a non-monotonic function in non-homogeneous tissue. This study represents the base for further research on the field of successful non-invasive blood perfusion determination in non-homogeneous tissue.