Weighting scheme for robust depth normalization in reflectance time-domain diffuse optical tomography

Significance: Reflectance mode diffuse optical tomography (DOT) is limited in its depth sensitivity. Current approaches to improve depth sensitivity need some prior knowledge to correctly localize deep inclusions. It has been shown that time-domain (TD) measurements can enhance depth sensitivity, but reconstructions still tend to be biased toward the surface, and TD modeling of diffuse light is computationally burdensome. Efficient TD modeling of diffuse light and prior-free reflectance DOT is critical to streamline the adoption of the technology into clinics. Aim: Our aim is to develop an efficient simulation tool for TD fluence in tissue as well a weighted reconstruction algorithm that uses TD measurements to enhance both the depth sensitivity and spatial selectivity of DOT without relying on any prior knowledge of the tissue structure or inclusion location. Approach: To overcome the computational burden of TD modeling of diffuse light, we solve the diffusion approximation in the Fourier domain for many frequencies parallelizing our solver across mesh nodes, sources, and frequencies. Using only the sensitivity matrix calculated from this modeled fluence, we calculate a weighting matrix that optimizes the spatial selectivity and depth sensitivity of our measurements. This weighting matrix was used in a Levenburg-Marquardt algorithm to retrieve the three-dimensional absorption profile of single inclusions at different depths, two complex scenes with inclusion(s) that spanned the depth of the sample, and computational phantoms adapted from publicly available breast lesion magnetic resonance imaging data. Results: We found in our simulations that our weighted scheme enables enhanced spatial selectivity for diffuse measurements as well as flattening the net sensitivity across the depth of the sample for DOT. We were able to accurately localize inclusions up to 40 mm deep without using prior knowledge of inclusion depth to normalize the sensitivity. Investigations of the effect of shot noise and Monte-Carlo-generated data on our reconstructions revealed we are still able to localize inclusions up to 30 mm deep for realistic noise levels. The complex targets were also well reconstructed up to 40 mm for noise-free measurements and up to 30 mm for the same noise levels. We found our regularization parameters had limited dependence on the geometry or ground truth optical property distribution. For all our reconstructions, we only tuned the regularizer used to find the weighting matrix based on the noise level. Conclusions: We demonstrate by simulation a weighting scheme for diffuse measurements and DOT that greatly enhances spatial selectivity and depth sensitivity, with no explicit depth prior. As well as this, we demonstrate the robustness of our approach by reconstructing complex targets with the same initial parameters used throughout.