## 4 Discussion  
The fat fractions of fibroglandular tissue in the normal breast measured by DECT and MRI in the first part of the study were comparable (Figure 3). The differences between the two measurements could be caused by differences in the body position: DECT was acquired with the subject in a supine position, whereas MRI was acquired with the subject in the prone position. Unlike MRI, DECT can be measured in the same supine position as that used in TD-DOS. Therefore, DECT was adopted as the method for comparison with TD-DOS in the second part of the study. The tumors of patients with breast cancer and the contralateral normal breasts were measured by both methods, to assess the validity of the in vivo TD-DOS lipid and water content measurements. There were two patients whose fat fractions measured by DECT were slightly over 100%. The fat fraction can show values under 0% or over 100% due to the limitation of the calculation algorithm when the CT number measurement by DECT is close to the that in pure soft tissue or in pure fat. Our TD-DOS system measures hemoglobin, lipid, and water contents, while the DECT measures fat fraction and the remaining components as fat-free content. The fat-free fraction of living tissue is composed of water, protein, carbohydrates, and minerals, but in this breast study, the fat-free fraction was regarded as a parameter related to water content [22]. The correlation between TD-DOS and DECT was moderate for lipid content and very strong for water content (Figure 5). These results show that TD-DOS captures the characteristics of the lipid and water contents of the breast. Although the correlation for lipid was lower than that for water content, a moderate correlation was still found for the lipid. However, the 95% CI of the slope and the intercept for the lipid were wider than those for water due to the small number of patients with very low lipid levels (n = 3). The absorption peaks of lipid and water are around 936 and 976 nm, respectively. The accuracy for lipid may be lower than that for water because the absorption coefficient at 936 nm is affected by water absorption, which is also high at this wavelength. A similar trend was also shown in the absorption coefficient results from phantoms with various proportions of water and lipid in our previous study [14]. The absorption coefficient at 976 nm reflected the relative amount of water in the phantom, whereas the absorption coefficient at 936 nm did not necessarily reflect the relative amount of lipid in the phantom. [PERSON] et al. used seven wavelengths from 635 to 1060 nm to measure collagen as an important biomarker in a pathological classification [32]. They stated that 635 and 1060 nm were very effective wavelengths for collagen identification. They also reported that the presence or absence of collagen affects the calculation of other parameters [33]. The level of collagen varies with age, body mass index (BMI), and breast density [17; 34], and is reported to be involved in tumor development and progression [32]. It is difficult to measure collagen with the wavelengths of 760-1000 nm used in this study, as the absorption of collagen is lower than that of water and lipid at those wavelengths, and the spectral peak positions of lipid and collagen are similar within this wavelength range [33]. In future study, we need to investigate whether or not individual differences in collagen affect the lipid results calculated from similar spectra using water/lipid phantoms with added collagen. There was much less dynamic range in TD-DOS than DECT for both lipid and water. The regression slope between the TD-DOS and DECT measurements of the breast tissues was 0.5-0.6, lower than that of a water/lipid phantom [14]. There are several possible reasons for this. For DECT measurement, a semicircular ROI with depth 2 cm, including the breast surface, was set on a 1-mm-thick DECT image. In contrast, the optical path of TD-DOS is spatial and banana-shaped [35], and the measurement region differs from the ROI used on the DECT images.