Diffuse optical reconstructions of functional near infrared spectroscopy data using maximum entropy on the mean

Abstract

Functional near-infrared spectroscopy (fNIRS) measures the hemoglobin concentration changes associated with neuronal activity. Diffuse optical tomography (DOT) consists of reconstructing the optical density changes measured from scalp channels to the oxy-/deoxy-hemoglobin concentration changes within the cortical regions. In the present study, we adapted a nonlinear source localization method developed and validated in the context of Electro- and Magneto-Encephalography (EEG/MEG): the Maximum Entropy on the Mean (MEM), to solve the inverse problem of DOT reconstruction. We first introduced depth weighting strategy within the MEM framework for DOT reconstruction to avoid biasing the reconstruction results of DOT towards superficial regions. We also proposed a new initialization of the MEM model improving the temporal accuracy of the original MEM framework. To evaluate MEM performance and compare with widely used depth weighted Minimum Norm Estimate (MNE) inverse solution, we applied a realistic simulation scheme which contained 4000 simulations generated by 250 different seeds at different locations and 4 spatial extents ranging from 3 to 40[Formula: see text] along the cortical surface. Our results showed that overall MEM provided more accurate DOT reconstructions than MNE. Moreover, we found that MEM was remained particularly robust in low signal-to-noise ratio (SNR) conditions. The proposed method was further illustrated by comparing to functional Magnetic Resonance Imaging (fMRI) activation maps, on real data involving finger tapping tasks with two different montages. The results showed that MEM provided more accurate HbO and HbR reconstructions in spatial agreement with the main fMRI cluster, when compared to MNE.

Figure 1

fNIRS measurement montage 1 and the anatomical model considered for DOT forward model estimation. (a) Anatomical 3D MRI segmented in five tissues, namely, scalp (green), skull (brown), CSF (light green), gray matter (purple) and white matter (black). (b) Optical fluence of one optode calculated through Monte Carlo simulation of Photons within this head model, using MCXLab. (c) Sensitivity profile of the whole montage in volume space. (d) Sensitivity profile, i.e. the summation of sensitivity map of all channels, along the cortical surface. Green dots represent detectors, including one proximity detector $0.7\text{cm}$ for each source, and red dots represent sources. (e) double-density montage 1 considered for this acquisition. There were 50 channels in total, 12 of $3.8\text{cm}$ (black), 24 of $3\text{cm}$ (blue), 6 of $1.5\text{cm}$ (yellow) and 8 of close distance (0.7 cm) channels. Figure created by Brainstorm using the NIRSTORM plugin developed by our team (https://github.com/Nirstorm).

Figure 2

Workflow describing our proposed realistic fNIRS simulation framework. (a) 100 Superficial seeds (black dots), 100 Middle seeds (red dots), 50 Deep seeds (blue dots) with spatial extent of $Se=3,5,7,9$ neighbourhood order within the field of view. (b) Convolution of a canonical HRF model with an experimental block paradigm (60s before and 50s after the onset). (c) Simulated theoretical HbO/HbR fluctuations along the cortical surface within the corresponding generator. (d) Realistic simulations obtained by applying the fNIRS forward model and addition of the average of 10 trials of real fNIRS background measurements at 830 nm. Time course of $\mathrm{\Delta }OD$ of all channels with SNR of 5, 3, 2 and 1 respectively are presented. Figure created by Brainstorm using the NIRSTORM plugin developed by our team (https://github.com/Nirstorm).

Figure 3

Evaluation of the performances of MEM and MNE using realistic simulations involving superficial seeds for different spatial extent ($Se=3,5,7,9$). Boxplot representation of the distribution of four validation metrics for three depth weighted strategies of MEM and two depth weighted strategies of MNE, namely: MEM(0.3, 0.3) in blue, MEM(0.3, 0.5) in green, MEM(0.5, 0.5) in red, MNE(0.3) in magenta and MNE(0.5) in black. Results were obtained after DOT reconstruction of 830nm $\mathrm{\Delta }OD$. Figure created by MATLAB version (R2016a) https://www.mathworks.com/products/matlab.html.

Figure 4

Comparisons of the reconstruction maps using MEM and MNE in realistic simulations. Three theoretical regions with spatial extent $Se=5$ ($11{\text{c}m}^2$) were selected near the ‘hand knob’ at different depth. The first column presents the locations and the size of the generator along the cortical surface. (a) Superficial seed case with reconstructed maps reconstructed using all MEM and MNE implementations considered in this study. (b) Middle seed case with reconstructed maps reconstructed using all MEM and MNE implementations considered in this study. (c) Deep seed case with reconstructed maps reconstructed using all MEM and MNE implementations considered in this study. $20\%$ inflated and zoomed maps are presented on the left corner of each figure. $100\%$ inflated right hemisphere are presented on the right side. All the maps were normalized by their own global maximum and no threshold was applied. Figure created by Brainstorm using the NIRSTORM plugin developed by our team (https://github.com/Nirstorm).

Figure 5

Effects of depth weighting on the depth and size of the simulated generators. First row demonstrates the validation matrices, AUC, SD and SE, as a function of depth of generators. We selected 250 generators created from all 250 seeds with a spatial extent of $SD=5$. Depth was calculated by the average of minimum Euclidean distance from each vertex, within each generator, to the head surface. Second row demonstrates the validation matrices, AUC, SD and SE, as a function of size of generators. Involving 400 generators which constructed from 100 superficial seeds with 4 different spatial extend of $Se=3,5,7,9$. Line fittings were performed via a 4 knots spline function to estimate the smoothed trend and the shade areas represent $95\%$ confident interval. Color coded points represent the values of validation matrices of all involved generators. Figure created by MATLAB version (R2016a) https://www.mathworks.com/products/matlab.html.

Figure 6

Evaluation of the performances of MEM and MNE at four different SNR levels. Boxplot representation of the distribution of four validation metrics for MEM(0.3, 0.5) and MNE(0.5) involving superficial seeds with spatial extent $Se=5$. SNR levels ($SNR=1,2,3,5$) are represented using different colors. Figure created by MATLAB version (R2016a) https://www.mathworks.com/products/matlab.html.

Figure 7

Application of MEM versus MNE reconstruction of HbR during a finger tapping task on one healthy subject. (a) Reconstructed maps of HbR (e.g. $20\%$ inflation on the left and $100\%$ inflation on the right side.) from MEM and MNE with different depth compensations. Each map was normalized by its own global maximum. (b) fMRI Z-map results projected along the cortical surface. (c) Reconstructed time courses of HbR within the hand knob region from MEM and MNE. Note that the hand knob region, represented by the black profile, was also matched well with the mean cluster of fMRI activation map on primary motor cortex. No statistical threshold was applied on fNIRS reconstructions. Figure created by Brainstorm using the NIRSTORM plugin developed by our team (https://github.com/Nirstorm).