Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A two-dimensional (2-D) radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimization scheme is then used to recover 2-D absorption and scattering coefficients distributions from simulated photoacoustic measurements. It is shown that the functional gradients, which are a challenge to compute efficiently using MC models, can be calculated directly from the coefficients of the harmonic angular basis used in the forward and adjoint models. This work establishes a framework for transport-based quantitative photoacoustic tomography that can fully exploit emerging highly parallel computing architectures.
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 wavelengthdependence 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 2 range, and image formation process.
In photoacoustic tomography (PAT) the image contrast is due to optical absorption, and because of this PAT images are sensitive to changes in blood oxygen saturation (sO 2 ). However, this is not a linear relationship due to the presence of a non-uniform light fluence distribution. In this paper we systematically evaluate the conditions in which an approximate linear inversion scheme -which assumes the internal fluence distribution is unchanged when the absorption coefficient changes -can give accurate estimates of sO 2 . A numerical phantom of highly vascularised tissue is used a test case for this assumption. It is shown that using multiple wavelengths over a broad range of the near-infrared spectrum yields inaccurate estimates of oxygenation, while a careful selection of wavelengths in the 620-920nm range is likely to yield more accurate oxygenation values. (We demonstrate that a 1D fluence correction, obtained from the average decay rate in the image, can further improve the estimates.) However, opting to use these longer wavelengths involves sacrificing signal-to-noise ratio in the image, as the absorption of blood is low in this range. This results in an inherent trade-off between uncertainty in the sO 2 estimates due to fluence variation and error due to noise. This study shows that the depth to which sO 2 can be estimated accurately using a linear approximation is limited in vivo, even with idealised measurements, to at most 3mm. In practice, there will be even greater uncertainties affecting the estimates, eg. due to bandlimited or partial-view acoustic detection.
We introduce a new Monte-Carlo technique to estimate the radiance distribution in a medium according to the radiative transport equation (RTE). We demonstrate how to form gradients of the forward model, and thus how to employ this technique as part of the inverse problem in Diffuse Optical Tomography (DOT). Use of the RTE over the more typical application of the diffusion approximation permits accurate modelling in the case of short source-detector separation and regions of low scattering, in addition to providing time-domain information without extra computational effort over continuous-wave solutions.
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