Estimating blood oxygenation from photoacoustic images: can a simple linear spectroscopic inversion ever work?

Linear spectroscopic inversions, in which photoacoustic amplitudes are assumed to be directly proportional to absorption coefficients, are widely used in photoacoustic imaging to estimate blood oxygen saturation because of their simplicity. Unfortunately, they do not account for the spatially varying wavelength-dependence of the light fluence within the tissue, which introduces "spectral coloring," a potentially significant source of error. However, accurately correcting for spectral coloring is challenging, so we investigated whether there are conditions, e.g., sets of wavelengths, where it is possible to ignore the spectral coloring and still obtain accurate oxygenation measurements using linear inversions. Accurate estimates of oxygenation can be obtained when the wavelengths are chosen to (i) minimize spectral coloring, (ii) avoid ill-conditioning, and (iii) maintain a sufficiently high signal-to-noise ratio (SNR) for the estimates to be meaningful. It is not obvious which wavelengths will satisfy these conditions, and they are very likely to vary for different imaging scenarios, making it difficult to find general rules. Through the use of numerical simulations, we isolated the effect of spectral coloring from sources of experimental error. It was shown that using wavelengths between 500 nm and 1000 nm yields inaccurate estimates of oxygenation and that careful selection of wavelengths in the 620- to 920-nm range can yield more accurate oxygenation values. However, this is only achievable with a good prior estimate of the true oxygenation. Even in this idealized case, it was shown that considerable care must be exercised over the choice of wavelengths when using linear spectroscopic inversions to obtain accurate estimates of blood oxygenation. This suggests that for a particular imaging scenario, obtaining accurate and reliable oxygenation estimates using linear spectroscopic inversions requires careful modeling or experimental studies of that scenario, taking account of the instrumentation, tissue anatomy, likely sO range, and image formation process.