Optimizing wavelength choice for quantitative optoacoustic imaging using the Cramer-Rao lower bound

Several papers have recently addressed the issue of estimating chromophore concentration in optoacoustic imaging (OAI) using multiple wavelengths. The choice of wavelengths obviously affects the accuracy and precision of the estimates. One might assume that the wavelengths that maximize the extinction coefficients of the chromophores would be the most suitable. However, this may not always be the case since the distribution of light intensity in the medium is also wavelength dependent. In this paper, we explore a method for optimizing the choice of wavelengths based on the Cramer-Rao lower bound (CRLB) on the variance of the chromophore concentration. This lower bound on variance can be evaluated numerically for different wavelengths using the variation of the extinction coefficients and scattering coefficients with wavelength. The wavelengths that give the smallest variance will be considered optimal for multi-wavelength OAI to estimate the chromophore concentrations. The expression for the CRLB has been derived analytically for estimating the concentration of multiple chromophores for several simple phantom models for the case when the optoacoustic signal is proportional to the product of the optical absorption and the illumination function. This approach could be easily extended to other geometries.