Direct estimation of the reduced scattering coefficient from experimentally measured time-resolved reflectance via Monte Carlo based lookup tables

Efficient computation of the steady-state and time-domain solutions of the photon diffusion equation in layered turbid media

Accurate and efficient forward models of photon migration in heterogeneous geometries are important for many applications of light in medicine because many biological tissues exhibit a layered structure of independent optical properties and thickness. However, closed form analytical solutions are not readily available for layered tissue-models, and often are modeled using computationally expensive numerical techniques or theoretical approximations that limit accuracy and real-time analysis. Here, we develop an open-source accurate, efficient, and stable numerical routine to solve the diffusion equation in the steady-state and time-domain for a layered cylinder tissue model with an arbitrary number of layers and specified thickness and optical coefficients. We show that the steady-state ([Formula: see text] ms) and time-domain ([Formula: see text] ms) fluence (for an 8-layer medium) can be calculated with absolute numerical errors approaching machine precision. The numerical implementation increased computation speed by 3 to 4 orders of magnitude compared to previously reported theoretical solutions in layered media. We verify our solutions asymptotically to homogeneous tissue geometries using closed form analytical solutions to assess convergence and numerical accuracy. Approximate solutions to compute the reflected intensity are presented which can decrease the computation time by an additional 2-3 orders of magnitude. We also compare our solutions for 2, 3, and 5 layered media to gold-standard Monte Carlo simulations in layered tissue models of high interest in biomedical optics (e.g. skin/fat/muscle and brain). The presented routine could enable more robust real-time data analysis tools in heterogeneous tissues that are important in many clinical applications such as functional brain imaging and diffuse optical spectroscopy.

Reconstruction of optical coefficients in turbid media using time-resolved reflectance and calibration-free instrument response functions

Measurements of time-resolved reflectance from a homogenous turbid medium can be employed to retrieve the absolute values of its optical transport coefficients. However, the uncertainty in the temporal shift of the experimentally determined instrument response function (IRF) with respect to the real system response can lead to errors in optical property reconstructions. Instrument noise and measurement of the IRF in a reflectance geometry can exacerbate these errors. Here, we examine three reconstruction approaches that avoid requiring direct measurements of photon launch times. They work by (a) fitting relative shapes of the reflectance profile with a pre-determined constraint on the scattering coefficient, (b) calibrating launch-time differences via a reference sample, and (c) freely fitting for the launch-time difference within the inverse problem. Analysis methods that can place a tight bound on the scattering coefficient can produce errors within 5-15% for both absorption and scattering at source-detector separations of 10 and 15 mm. Including the time-shift in the fitting procedure also recovered optical coefficients to under 20% but showed large crosstalk between extracted scattering and absorption coefficients. We find that the uncertainty in the temporal shift greatly impacts the reconstructed reduced scattering coefficient compared to absorption.