Algorithmic depth compensation improves quantification and noise suppression in functional diffuse optical tomography

Abstract

Accurate depth localization and quantitative recovery of a regional activation are the major challenges in functional diffuse optical tomography (DOT). The photon density drops severely with increased depth, for which conventional DOT reconstruction yields poor depth localization and quantitative recovery. Recently we have developed a depth compensation algorithm (DCA) to improve the depth localization in DOT. In this paper, we present an approach based on the depth-compensated reconstruction to improve the quantification in DOT by forming a spatial prior. Simulative experiments are conducted to demonstrate the usefulness of this approach. Moreover, noise suppression is a key to success in DOT which also affects the depth localization and quantification. We present quantitative analysis and comparison on noise suppression in DOT with and without depth compensation. The study reveals that appropriate combination of depth-compensated reconstruction with the spatial prior can provide accurate depth localization and improved quantification at variable noise levels.

Fig. 1

Setups of simulative experiments: (a) experiment I, (b) experiment II, and (c) experiment III.

Fig. 2

For experiment I, a depth cross section (y-z plane, x = 0) of the (a) actual absorber, (b) reconstructed DOT image without depth compensation, and (c) reconstructed DOT image with depth compensation. The dash circles in (b) and (c) mark the ROIs with half-maximum threshold.

Fig. 3

For experiment II: Figs. 3(a), 3(c), 3(e) are depth cross sections along the diagonal plane at y = x, which is marked by the dash line in (b), of the (a) actual and reconstructed absorbers (c) without and (e) with depth compensation being utilized. Figures 3(b), 3(d), 3(f) are lateral cross sections in the x-y plane of the (b) actual and recovered absorbers (d) without and (f) with depth compensation applied, respectively.

Fig. 4

For experiment III: a depth cross section along the diagonal plane at y = x of the (a) actual absorbers, (b) reconstructed DOT image without depth compensation, and (c) reconstructed DOT image with depth compensation.

Fig. 5

Reconstructed depths of the absorber, using the setup of Experiment I in Fig. 1(a), with variable α and γ values when data were (a) noise-free and (b) with 1% random noise. Conventional DOT without depth compensation is equivalent to γ = 0. In (b) the reconstructed depths become divergent roughly after α = 10⁻³, which is attributed to the 1% random noise. The expected depth of the absorber is at z = −2 cm.

Fig. 6

Quantified (a) Δµ_{a_max}, (b) Δµ_{a_ROI} and (c) V_ROI values of the absorber, with the given setup in Experiment I, when α and γ values are varied. The expected Δµ_a value is 0.2 cm⁻¹. The expected volume of the absorber is 1.7 cm³. Conventional DOT without depth compensation is equivalent to γ = 0.

Fig. 7

For phantom experiment, a depth cross section (y-z plane, x = 0) of the reconstructed DOT image (a) without depth compensation, and (b) with depth compensation. The cylindrical absorber was located at z = −2.0 cm which had an actual Δµ_a of 0.15 cm⁻¹.