Analytical model for rapid simulation of ultrasound optical tomography images based on mean photon path lengths

Ultrasound optical tomography enables noninvasive characterization of tissue and lesions up to 5 cm below the skin surface, by enhancing diffuse optical tomography with ultrasound focusing resolution and an increased number of measurement points. For optimal clinical imaging, it is essential to be able to reconstruct tissue optical properties in real time during in vivo measurements, and therefore, it is necessary to have fast analytical models for ultrasound-modulated light fluence calculation. We derive a simple analytical model for tagged light fluence calculation based on mean photon pathlengths. The continuous-wave diffusion equation and the perturbation approach are used for modeling light propagation through a diffusive medium with inhomogeneous absorption. We introduce, forwhat we believe to be the first time, a concept of conditional mean photon pathlengths and the partial pathlengths approach with its derivation. The proposed analytical model is validated against a previously developed tagged light Monte Carlo simulator. The tagged light transmittance from the analytical model differs <10% on average compared to the Monte Carlo simulator, and the output is obtained with a speed of the order of 10³ times faster (∼30 s instead of ∼20 h). This substantial improvement in computational efficiency will enable real-time inverse problem solving. The results also show potential for further refinement of the proposed analytical model and for the development of in vivo clinical applications, e.g., including the characterization of suspicious breast lesions or the measurement of oxygen saturation in tissues.