Simultaneous retrieval of optical and geometrical parameters of multilayered turbid media via state-estimation algorithms

Two-layered blood-lipid phantom and method to determine absorption and oxygenation employing changes in moments of DTOFs

Near-infrared spectroscopy (NIRS) is an established technique for measuring tissue oxygen saturation (StO₂), which is of high clinical value. For tissues that have layered structures, it is challenging but clinically relevant to obtain StO₂ of the different layers, e.g. brain and scalp. For this aim, we present a new method of data analysis for time-domain NIRS (TD-NIRS) and a new two-layered blood-lipid phantom. The new analysis method enables accurate determination of even large changes of the absorption coefficient (Δµ_a) in multiple layers. By adding Δµ_a to the baseline µ_a, this method provides absolute µ_a and hence StO₂ in multiple layers. The method utilizes (i) changes in statistical moments of the distributions of times of flight of photons (DTOFs), (ii) an analytical solution of the diffusion equation for an N-layered medium, (iii) and the Levenberg-Marquardt algorithm (LMA) to determine Δµ_a in multiple layers from the changes in moments. The method is suitable for NIRS tissue oximetry (relying on µ_a) as well as functional NIRS (fNIRS) applications (relying on Δµ_a). Experiments were conducted on a new phantom, which enabled us to simulate dynamic StO₂ changes in two layers for the first time. Two separate compartments, which mimic superficial and deep layers, hold blood-lipid mixtures that can be deoxygenated (using yeast) and oxygenated (by bubbling oxygen) independently. Simultaneous NIRS measurements can be performed on the two-layered medium (variable superficial layer thickness, L), the deep (homogeneous), and/or the superficial (homogeneous). In two experiments involving ink, we increased the nominal µ_a in one of two compartments from 0.05 to 0.25 cm^-1, L set to 14.5 mm. In three experiments involving blood (L set to 12, 15, or 17 mm), we used a protocol consisting of six deoxygenation cycles. A state-of-the-art multi-wavelength TD-NIRS system measured simultaneously on the two-layered medium, as well as on the deep compartment for a reference. The new method accurately determined µ_a (and hence StO₂) in both compartments. The method is a significant progress in overcoming the contamination from the superficial layer, which is beneficial for NIRS and fNIRS applications, and may improve the determination of StO₂ in the brain from measurements on the head. The advanced phantom may assist in the ongoing effort towards more realistic standardized performance tests in NIRS tissue oximetry. Data and MATLAB codes used in this study were made publicly available.

A Monte Carlo study of near infrared light propagation in the human head with lesions-a time-resolved approach

Several clinical conditions leading to traumatic brain injury can cause hematomas or edemas inside the cerebral tissue. If these are not properly treated in time, they are prone to produce long-term neurological disabilities, or even death. Low-cost, portable and easy-to-handle devices are desired for continuous monitoring of these conditions and Near Infrared Spectroscopy (NIRS) techniques represent an appropriate choice. In this work, we use Time-Resolved (TR) Monte Carlo simulations to present a study of NIR light propagation over a digital MRI phantom. Healthy and injured (hematoma/edema) situations are considered. TR Diffuse Reflectance simulations for different lesion volumes and interoptode distances are performed in the frontal area and the left parietal area. Results show that mean partial pathlengths, photon measurement density functions and time dependent contrasts are sensitive to the presence of lesions, allowing their detection mainly for intermediate optodes separations, which proves that these metrics represent robust means of diagnose and monitoring. Conventional Continuous Wave (CW) contrasts are also presented as a particular case of the time dependent ones, but they result less sensitive to the lesions, and have higher associated uncertainties.

A comparison between plausible models in layered turbid media with geometrical variations applying a Bayesian selection criterion

One possible application of Near Infrared techniques is to analyze human brain metabolic activity. Currently used models take into account the layered structure of the human head but, usually, they do not consider the non-planar surface of some of the boundaries, i.e. gray matter, which results in a much more complex structure, thus leading to more sophisticated models and longer calculation times. The main objective of this work is to determine if it is worth to replace a planar layered structure by a non-planar one. To this end we implement a Bayesian-based quantitative methodology for choosing between two competitive models describing light propagation in layered turbid media. Experiments of time-resolved diffuse reflectance measurements are performed in layered phantoms and complemented with numerical calculations. The resulting Distributions of Time of Flight of both models are compared using Bayesian model selection analysis. The non-planar interface was introduced in the simulations by a simple surface parametrization. Results suggest that, under certain conditions, a multilayer model with planar boundaries is good enough.

Implementation of the extended Kalman filter for determining the optical and geometrical properties of turbid layered media by time-resolved single distance measurements

In this article we propose an implementation of the extended Kalman filter (EKF) for the retrieval of optical and geometrical properties in two-layered turbid media assuming a dynamic setting, where absorption of each layer was changed in different steps. Prior works implemented the EKF in frequency-domain with several pairs of light sources and detectors and for static parameters estimation problems. Here we explore the use of the EKF in single distance, time-domain measurements, together with a corresponding forward model. Results show good agreement between retrieved and nominal values, with rather narrow analytical credibility intervals, indicating that the recovery process has low uncertainty, especially for the absorption coefficients.