## 4 Discussion
In our preliminary study, we evaluated the variable importance for the prediction, and found that the subject's age showed the highest rank (1.0) while the right and left SO2 showed the second (0.77) and third (0.73) highest rank, respectively [25]. It should be noted that these parameters with high variable importance showed high correlation coefficients. Combination of MRI image and TRS measurement may be useful to predict cognitive dysfunction. In order to develop a deep learning based-diagnostic method of cognitive dysfunction, further study is necessary based on the present study. The OPLs in the right PFC negatively correlated with VSRAD scores (Severity, Extent, and Ratio), indicating that the shorter the OPL, the greater the VSRAD scores which means greater degree of brain atrophy [16; 17]. This might be caused by an increase of subarachnoid space due to brain atrophy; an increase of cerebrospinal fluid (CSF) layer in subarachnoid space caused a shortening of OPL since light scattering of CSF is much less than that of brain tissue. However, these findings are inconsistent with our previous TRS study on chronic stroke patients; we observed that the OPLs on the affected side, where subarachnoid space increased due to cortical atrophy in chronic stroke, was longer than that on the normal side [26]. It should be noted, however, that VSRAD scores does not indicate the degree of the PFC atrophy selectively. Therefore, further study, such as selective measurements of the degree of atrophy of the PFC, is necessary to clarify the relation between OPLs and brain atrophy. Interestingly, there was a difference in correlation of OPLs and VSRAD between left and right PFC. Some evidence suggests that neurodegeneration related to aging and disease may preferentially affect the left-usually language- and motor-dominant-hemisphere; however, a recent meta-analysis provided no evidence for increased left-hemisphere vulnerability [27]. Further work is needed to provide a better understanding of the role of gray matter asymmetries. We discuss the relation between the brain atrophy and the OPL from the view point of light propagation in the head. According to the numerical study of light propagation inside a human head model by [PERSON] et al. [28], the OPL between the source and detector depends on the reduced scattering coefficient of the CSF layer (\(\mu^{\prime}_{s\text{-}CSF}\)), which corresponds to the subarachnoid space. The head model consists of four layers, i.e., the superficial layer including the scalp and skull (thickness of 10 mm), the CSF layer (2 mm), the gray matter (4 mm) and the white matter (6 mm). Light injected from the source propagates through the four layers to reach the detector with the partial optical pathlengths of \(l_{\text{sup}}\), \(l_{CSF}\), \(l_{\text{{{{{{I}}}}\text{{{{{I}}}}\text{{{{{I}}}}\text{{{{I}}}\text{{{{I}}} \text{{{{I}}}\text{{{{I  
propagation pattern inside the head model can be schematically described as in Figure 2a where the thickness of the CSF layer is exaggerated to see its effect on light propagation. The propagation path from the source, S, to the detector, D, depicts a so-called banana shape as a semitransparent yellow region. In this case, the typical propagation path expressed by the red zig-zag lines crosses the interface between the superficial and CSF layers at positions \"a\" and \"d\" with a relatively short distance between them. When \(\mu^{\prime}\)\({}_{s\text{-}CSF}\) = 0.01 mm\({}^{-1}\), the CSF layer exhibits very weak (or almost no) scattering, and the light propagation pattern can be described as in Figure 2b. The propagation pattern in Figure 2b is widened from the banana shape in Figure 2a due to the presence of the almost non-scattering CSF layer, and the typical propagation path crosses the interface between the superficial and CSF layers at positions \"a\" and \"d\" with a longer distance between them than the distance between \"a\" and \"d\".