Performance of fitting procedures in curved geometry for retrieval of the optical properties of tissue from time-resolved measurements.

By use of the solution of the diffusion equation for cylindrical and spherical geometry, two fitting procedures for retrieval of the optical properties from time-resolved measurements have been implemented. The fitting procedures are based on the Levenberg-Marquardt algorithm, in which the fitting parameters are the absorption coefficient, the reduced scattering coefficient, and an amplitude factor. Monte Carlo data generated for cylindrical and spherical geometry were fitted by these fitting procedures, and the retrieved optical properties were compared with those obtained from the inversion procedure with a mismatched geometry of a semi-infinite medium. The effects of refractive-index mismatch and of different boundary conditions of the diffusion equation were also studied, together with the effects of several sources of error that are typically found in time-resolved measurements. The advantages and drawbacks of these fitting procedures, including many details in several situations of interest in the field of tissue optics, are discussed. The results also offer a guideline to understanding the effects of mismatching in curved geometry as functions of source-detector distance and radii of cylinders or spheres.