We have computed optical images of the female breast based on analysis of tomographic data obtained from simulated time-independent optical measurements of anatomically accurate maps derived from segmented 3-D magnetic resonance (MR) images. Images were segmented according to the measured MR contrast levels for fat and parenchymal tissue from T1 weighted acquistions. Computed images were obtained from analysis of solutions to the forward problem for breasts containing "added pathologies," representing tumors, to breasts lacking these inclusions. Both breast size and its optical properties have been examined over a range of values, including large and small breasts and optical scattering lengths smaller and larger than those expected in tissue. In each case, two small simulated tumors (approximately 0.1% of breast volume) were "added" to the background tissue. Values of absorption and scattering coefficients of the tumors have been examined that are both greater and less than the surrounding tissue.
Detector responses and the required imaging operators were computed by numerically solving the diffusion equation for inhomogeneous media. Detectors were distributed uniformly, in a circular fashion, around the breast in a plane positioned parallel and half-way between the chest wall and the nipple. A total of 20 sources were used, and for each 20 detectors. Reconstructed images were obtained by solving a linear perturbation equation derived from transport theory. Three algorithms were tested to solve the perturbation equation, and include the methods of Conjugate Gradient Descent (CGD), Projection onto Convex Sets (POCS), and Simultaneous Algebraic Reconstruction Technique (SART). Results obtained wshowed that in each case, high quality reconstructions were obtained. The computed images correctly obtained showed that in each case high quality reconstructions were obtained. The computed images correctly resolved and identified the spatial position of the two tumors. Additional studies showed that computed images were stable to large systematic errors in the imaging operators and to added noise. Further, examination of the computed detector readings indicate that images of tissue up to approximately 10 cm in thickness should be possible.
The results reported are the first to demonstrate that high quality images of small added inclusions can be obtained from anatomically accurate models of thick tissues having arbitrary boundaries based on the analysis of diffusely scattered light.