Multi-wavelength approach to optoacoustic molecular imaging (OMI) using Cramer-Rao lower bound (CRLB)

Several papers recently have addressed the issue of estimating chromophore concentration in PAT using multiple wavelengths. The question is how does one choose the multiple wavelengths for imaging in PAT that would give the most accurate results. Previous work was based on the knowledge of the wavelength dependence of the extinction coefficient of chromophores but did not directly address this question. One would assume that the wavelength that maximizes the extinction coefficient of the chromophorewould be the most suitable. However, this may not always be the case, especially if the extinction peak of the chromophore is fairly broad. In this paper, we derive an expression for the variance of the measured signal based on the Cramer-Rao lower bound (CRLB). 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 wavelength that gives the smallest variance will be optimal for multi-wavelength PAT to estimate the chromophore concentration. The expression for CRLB has been derived analytically for estimating the concentration of a oxy or deoxyhemoglobin contained in a background tissue-like solution using the knowledge of the illumination function in a specific geometry using a photoacoustic microscope. This approach could also be extended to the estimation of concentrations of multiple chromophores and for other geometries.