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

Abstract

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.

Fig. 1.

Diagrams of the phantom showing top view (a) and side view (b), and the corresponding model (c). The three containers are labeled: Deep, Superficial, and Third container, which is movable. Units are mm.

Fig. 2.

Changes in moments (ΔA, Δm₁, and ΔV) for all combinations of Δµ_a,Sup and Δµ_a,Deep (a). Error norm (χ²) for all combinations of Δµ_a,Sup and Δµ_a,Deep (white cross marks true values) when using changes in three moments (b) or using only Δm₁ and ΔV (c). Baseline parameters are µ_a,Sup = µ_a,Deep = 0.13 cm^-1, µ′_s = 10 cm^-1, L = 12 mm, and n = 1.33.

Fig. 3.

Determined Δµ_a,Sup and Δµ_a,Deep for different assumed values of baseline parameters: µ_a (a), µ′_s (b), n (c), and L (d). Green lines mark true values: Δµ_a,Sup = 0 and Δµ_a,Deep = 0.05 cm^-1, µ_a = 0.1 cm^-1, µ′_s = 10 cm^-1, L = 15 mm, and n = 1.33.

Fig. 4.

(a) Determined µ_a for two experiments involving ink, for three nominal µ_a (0.05, 0.15, and 0.25 cm^-1 at 750 nm). (b) Determined µ′_s for 20 Δµ_a steps for Exp. #1. Results were obtained using measurements on each compartment (Pos. #1 or #3 in Fig. 1), analyzed using the curve-fitting method with a homogeneous model.

Fig. 5.

(a) Normalized IRFs and DTOFs (when targeted µ_a = 0.10 cm^-1 at 750 nm in both compartments), for two source-detector pairs on Pos. #1 and #2, at 768 nm. (b) Changes in moments (ΔA, Δm₁, and ΔV) for 20 Δµ_a steps, measured on Pos. #2 (two-layered), at 768 nm.

Fig. 6.

Determined µ_a for 20 Δµ_a steps in first (a) and second (b) experiments involving ink, at 768 nm. Measurements on a compartment with increasing µ_a (Pos. #1 or Pos. #3) were analyzed using the curve-fitting method with a homogeneous model (black crosses). Measurements on two-layered medium (Pos. #2) were analyzed using the same method (green circles) and the method based on changes in moments with a two-layered model (red and blue crosses).

Fig. 7.

(a) DTOFs measured on Pos. #2 at different µ_a in two compartments, at 705 nm. Changes in moments, Δm₁ (b) and ΔV (c), measured on Pos. #1 and #2, for three experiments involving blood. Filled triangles indicate when yeast was added, separately in deep and superficial compartments, and hollow triangles denote the start of bubbling oxygen in the deep compartment (these triangles are also shown in Fig. 9 to 12).

Fig. 8.

Determined µ_a (a) and µ′_s (b) at maximum and minimum StO₂ for three experiments involving blood, measured on the deep compartment. The molar absorption coefficients (ε) [78] and the µ_a of water [79] were used for calculating the concentrations of HbO₂ and Hb.

Fig. 9.

Determined µ_a at 705 nm in first (a), second (b), and third (c) experiments involving blood. Measurements were analyzed using the curve-fitting method with a homogeneous model (Homog.) and using the changes in moments with a two-layered model (2-L). For visualization, a moving average window (10 data points) was applied to all curves. Triangles at the top are explained in caption of Fig. 7.

Fig. 10.

Reduced scattering coefficient µ′_s in three experiments involving blood, at 705 nm (a) and 805 nm (b). Measurements were analyzed using the curve-fitting method with a homogeneous model and the corresponding determined µ_a values are black and green curves in Fig. 9. Triangles at the top are explained in caption of Fig. 7.

Fig. 11.

Concentrations of HbO₂ and Hb in three experiments (three rows) involving blood. Curve-fitting method (Homog.) was used for measurements on Pos. #1 and on Pos. #2, and the latter was also analyzed with method based on moments (2-L. Deep and 2-L. Sup). For visualization, a moving average window (10 data points) was applied to all curves. Triangles at the top are explained in caption of Fig. 7.

Fig. 12.

Determined StO₂ in first (a), second (b), and third (c) experiments involving blood for two measurements and two methods of data analysis. The concentrations corresponding to the four StO₂ curves are shown in Fig. 11. A moving average window (10 data points) was applied to all curves. Triangles at the top are explained in caption of Fig. 7.

Fig. 13.

Comparison of StO₂ time traces (from Fig. 12) for first (a), second (b), and third (c) experiments involving blood. Measurements on deep compartment were analyzed using curve-fitting method with homogeneous model (plotted along x-axis). Measurements on two-layered medium were analyzed using method based on moments with two-layered model (along y-axis).