Frequency domain measurements on turbid media with strong absorption using the PN approximation

Small separation frequency-domain near-infrared spectroscopy for the recovery of tissue optical properties at millimeter depths

Millimeter-depth sensitivity with frequency domain near-infrared spectroscopy has been challenging due to the breakdown of the diffusion equation for source-detection separations < 1cm. To overcome this challenge, we employ a Monte-Carlo lookup table-based inverse algorithm to fit small separation (3-6 mm) frequency-domain near-infrared spectroscopy (FDNIRS) data for absorption and reduced scattering coefficients. We verify this small separation FDNIRS method through a series of in vitro and in vivo studies. In vitro, we observed a root mean squared percent error (RMSE) in estimation of the reduced scattering coefficient and absorption coefficient of 2.8% and 7.6%, respectively, in liquid phantoms consisting of Intralipid and Indian ink, and a RMSE in estimation of oxygen saturation and total hemoglobin concentrations of 7.8 and 11.2%, respectively, in blood-mixed liquid phantoms. Next, we demonstrate one particularly valuable in vivo application of this technique wherein we non-invasively measure the optical properties of the mouse brain (n = 4). We find that the measured resting state cerebral oxygen saturation and hemoglobin concentration are consistent with literature reported values, and we observe expected trends during a hyper-/hypoxia challenge that qualitatively mimic changes in partial pressure of oxygen (pO₂) measured simultaneously with an invasive pO₂ sensor. Further, through simulations of the mouse head geometry, we demonstrate that the skull and scalp exert minimal influence on the estimate oxygen saturation, while leading to small but systematic underestimation of total hemoglobin concentration. In total, these results demonstrate the robustness of small separation FDNIRS to assess tissue optical properties at millimeter depth resolution.

Novel analytical solution for the radiance in an anisotropically scattering medium

We report on a novel analytical solution of the three-dimensional radiative transport equation for the case of an infinitely extended anisotropically scattering medium that is illuminated by an isotropic point light source. The resulting expression for the radiance can be evaluated efficiently and accurately and exhibits significant improvements with respect to the convergence and the numerical stability compared to the solutions found in the literature so far. The equations obtained were successfully verified by comparisons with the Monte Carlo method.

Green's function of the time-dependent radiative transport equation in terms of rotated spherical harmonics

The time-dependent radiative transport equation is solved for the three-dimensional spatially uniform infinite medium which is illuminated by a point unidirectional source using a spherical harmonics transform under rotation. Apart from the numerical evaluation of a spherical Hankel transform which connects the spatial distance with the radial distance in Fourier space, the dependence on all variables is found analytically. For the special case of a harmonically modulated source, even the spherical Hankel transform can be carried out analytically. Additionally, a special solution for the isotropically scattering infinite medium is given. The Monte Carlo method is used for a successful verification of the derived solution.

Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation

In this study, we investigate the performance of early-photon fluorescence tomography based on a heterogeneous mouse model. The telegraph equation is used to accurately describe the propagation of light in tissues at short times. The optimal time gate for early photons is determined by singular value analysis at first. Then, fluorescent targets located in different organs of the mouse model are investigated. The simulation results demonstrate that the reconstructed tomographic images based on early photons yield improvement in spatial resolution and quantification than the quasi-CW measurements. Meanwhile, compared with the homogeneous model, the use of the heterogeneous model can improve the accuracy of fluorescence distribution and quantification in early-photon fluorescence tomography.