Theoretical investigation of photon partial pathlengths in multilayered turbid media

Abstract

Functional near infrared spectroscopy (fNIRS) is a valuable tool for assessing oxy- and deoxyhemoglobin concentration changes (Δ[HbO] and Δ[HbR], respectively) in the human brain. To this end, photon pathlengths in tissue are needed to convert from light attenuation to Δ[HbO] and Δ[HbR]. Current techniques describe the human head as a homogeneous medium, in which case these pathlengths are easily computed. However, the head is more appropriately described as a layered medium; hence, the partial pathlengths in each layer are required. The current way to do this is by means of Monte Carlo (MC) simulations, which are time-consuming and computationally expensive. In this work, we introduce an approach to theoretically calculate these partial pathlengths, which are computed several times faster than MC simulations. Comparison of our approach with MC simulations show very good agreement. Results also suggest that these analytical expressions give much more specific information about light absorption in each layer than in the homogeneous case.

Light diffusion in layered media: A numerical study in the spatial and time-domains

“…An advantage of the routine presented is that computing the fluence at 10 arbitrarily specified spatial locations takes only 3x longer than the times reported in Table 2. Although it can be difficult to directly compare computational times of different routines, as they depend highly on the computational resources and effort put into them, we were able to simulate the steady-state fluence 500-1,000x faster than previously reported 19,46 . We note that these times are achieved on a personal laptop using a single core.…”

“…Several solutions for photon diffusion in layered media have been reported, but present technical difficulties for numerical computation. We have investigated a previously developed model 21,35 that has received wide interest 28,[44][45][46] . However, the model relies on numerical inverse transforms for obtaining the photon fluence for both steady-state and time-domain simulations which limits the numerical accuracy and speed.…”

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

“…An advantage of the routine presented is that computing the fluence at 10 arbitrarily specified spatial locations takes only 3× longer than the times reported in Table 2. Although it can be difficult to directly compare computational times of different routines, as they depend highly on the computational resources and effort put into them, we were able to simulate the steady-state fluence 500-1000× faster than previously reported 21,51 . We note that these times are achieved on a personal laptop using a single core.…”

“…Several solutions for photon diffusion in layered media have been reported, but present technical difficulties for numerical computation. We have investigated a previously developed model 23 , 37 that has received wide interest 30 , 47 , 48 , 51 . However, the model relies on numerical inverse transforms for obtaining the photon fluence for both steady-state and time-domain simulations which limits the numerical accuracy and speed.…”

Theoretical computation of photon mean partial pathlengths in multilayered turbid media

“…Although different strategies have been implemented to overcome this issue 4 , the intrinsic model remains homogeneous, and the retrieved signal is susceptible of being corrupted by spurious influences from other tissues. Recently, some of the authors have developed a method to analytically compute the MPPLs in turbid media, consisting of up to four layers, in a matter of a few milliseconds 5 . In this way we have been able to demonstrate that the MPPLs strongly depend on the optical properties of each layer, as well as on its thicknesses and on the source-detector separation ρ, something which remains frequently neglected when using homogeneous models.…”