# Diffuse Optical Tomography Using Bayesian Filtering in the Human Brain
## 3 Results and Discussion
### Imaging Results  
DOT systems are characterized by high temporal resolution (-500 ms) as compared to fMRI systems (-2000 ms), meaning that slow physiological oscillations are rapidly sampled, causing nearby time points in the DOT signal to be highly correlated. Serial correlations violate common statistical assumptions of the independence of repeated measurements over time and contribute to inaccurate estimations of type I errors, making a statistical analysis that is based on a GLM impossible. Applying the Bayesian filtering on raw DOT data reduces serial correlations between consecutive points over time, hence providing data independence, which will allow for the use of a GLM that is commonly used in the neuroimaging field for mapping cerebral activations. Figure 4 shows T-maps of brain activation for both the blood-oxygen level-dependent (BOLD) signal and the HbO signal (\(p<0.001\), corrected  
Figure 2: The top left graphic shows a time series of an average of the optical channels (2048) over time. The blue plot shows raw diffuse optical tomography (DOT) data and the red plot shows DOT data after filtering with the Bayesian algorithm at a wavelength of 760 nm. The right top graphic shows the respiration recorded continuously at 4 kHz using AD Instrument ML870/PowerLab16/30. The bottom graphic depicts power spectrum densities for the unfiltered signal (**a**) and the signal extracted by the Bayesian-filtering method (**b**). Note the respiration frequency (*) has been isolated from the raw DOT data. false discovery rate, FDR). The figure depicts an increased statistical significance in Bayesian filtered DOT images. Brain activation maps generated from unfiltered or band pass filtered (0.01-0.3 Hz) wavelengths have not been represented in this work, because they did not show significant changes (T: 1.282, no significant voxels, \(p\leq 0.05\), uncorrected; and, T: 1.645, no significant voxels, \(p\leq 0.05\), uncorrected, respectively). A conjunction analysis was performed for the example shown in Figure 4. The spatial conjunction that is shown in Table 1 depicts common anatomical regions between the hemoglobin molecule HbO and BOLD signal measured by DOT and fMRI equipment, respectively. As a result, 296 voxels with a size of \(2\times 2\times 2\) are activated by the BOLD signal, where 174 voxels are common with the HbO signal (\(\sim\)59%). As fMRI has been the most commonly used technique in neuroimaging studies, we assume that the information that is provided by fMRI is reliable. Both the literature [24; 25; 26] as well as T-maps of fMRI help to corroborate the implication of frontal areas for the cognitive task, allowing for the comparison of T- maps from both fMRI and DOT modalities. Figure 3: Representation of the average of the optical channels (2048) over time. The blue plot shows raw DOT data, the red plot shows DOT data filtered with a band pass filter, and the black plot shows DOT data after applying the Bayesian filter algorithm for 760 nm (**a**) and 830 nm (**b**). Abscissas axes correspond to normalized arbitrary units and the ordinate axis represents the experimental time in frames. The results show that DOT detects the same areas as fMRI at a functional level. These results can be used to corroborate the reliability of Bayesian filtering applied on the frontal cortex through a cognitive task crossing barrier, such as the presence of frontal sinus where scalp-brain distance vary across the subject [13]. Additionally, cognitive signals generate more subtle relative activation changes, unlike motor or visual tasks. Even so, we still obtain increased statistical significance using cognitive changes in a strict sense, as has been shown in prior works [21]. Our results show that band pass filtering alone does not provide statistical significance in the T-maps; therefore, the comparison with fMRI cannot do it. Previous studies have used this linear filtering to detect brain activations in the frontal lobe [8; 27; 28].