Frequency domain optical tomography in human tissue

In this paper, a reconstruction algorithm for frequency-domain optical tomography in human tissue is presented. A fast and efficient multigrid finite difference (MGFD) method is adopted as a forward solver to obtain the simulated detector responses and the required imaging operator. The solutions obtained form MGFD method for 3D problems with weakly discontinuous coefficients are compared with analyzed solutions to determine the accuracy of the numerical method. Simultaneous reconstruction of both absorption and scattering coefficients for tissue-like media is accomplished by solving a perturbation equation using the Born approximation. This solution is obtained by a conjugate gradient descent method with Tikhonov regularization. Two examples are given to show the quality of the reconstruction results. Both involve the examination of anatomically accurate optical models of tissue derived from segmented 3D magnetic resonance images to which have been assigned optical coefficients to the designated tissue types. One is a map of a female breast containing two small 'added pathologies', such as tumors. The other is a map of the brain containing a 'local bleeding' area, representing a hemorrhage. The reconstruction results show that the algorithm is computationally practical and can yield qualitatively correct geometry of the objects embedded in the simulated human tissue. Acceptable results are obtained even when 10% noise is present in the data.