## 2 Materials and Methods
### Time-Domain Diffuse Optical Spectroscopy (TD-DOS) Measurement  
Our TD-DOS system (TRS-21-6W) uses the time-correlated single photon counting (TCSPC) method to measure the temporal profile of the detected light. The TRS-21-6W consists of two light source units, two photodetector units, a single photon counting (SPC) circuit, and optical fiber bundles. The light source units (custom-designed, Hamamatsu Photonics K.K., Hamamatsu, Japan) contain three laser diodes per unit (762 nm, 802 nm, and 838 nm for unit 1; 908 nm, 936 nm, and 976 nm for unit 2). Each laser diode emits a pulse 100 ps to 200 ps wide (full width at half maximum) at a repetition rate of 5 MHz. The specimen is irradiated with the pulsed laser through a 1-mm diameter source optical fiber bundle with a numerical aperture (NA) of 0.29 (Sumita Optical Glass, Inc., Saitama, Japan). The light propagating through the specimen is collected by a 3-mm diameter detection fiber bundle with an NA of 0.29 (Sumita Optical Glass, Inc.), and is guided to two photodetector units containing different photomultiplier tubes (GaAs and InGaAs PMT, Hamamatsu Photonics K.K.). The detected light is converted into an electrical signal by the photodetector units, and processed with a custom-designed SPC circuit consisting of a constant fraction discriminator, time-to-amplitude converter, an analog-to-digital converter, and histogram memory. The processed signal is acquired as a temporal profile of detected light. The TRS-21-6W can quantify the optical properties of a specimen measured in the reflectance and transmittance geometry by analyzing the temporal profile according to photon diffusion theory. An estimated profile is calculated by convolving the instrument response function (IRF) with an analytical solution of the photon diffusion equation for a homogeneous medium, and then the \(\mu_{s}^{\prime}\) and \(\mu_{a}\) of the specimen are determined by fitting the estimated profile to the measured profile with a non-linear least squares method based on the Levenberg-Marquardt algorithm. The details of analyzing the temporal profiles have been described previously [14]. The major chromophores in breast tissue at near-infrared wavelengths are oxy-hemoglobin (O\({}_{2}\)Hb), deoxy-hemoglobin (HHb), water, and lipid [27], and the absorption coefficient at the wavelength \(\lambda\) is expressed as follows:  
\[\mu_{a}(\lambda)=\varepsilon_{O_{2}Hb}(\lambda)C_{O_{2}Hb}+\varepsilon_{HHb}( \lambda)C_{HHb}+\mu_{a,water}^{100\%}(\lambda)V_{water}+\mu_{a,lipid}^{100\%}( \lambda)V_{lipid}, \tag{1}\]  
where \(\varepsilon_{m}(\lambda)\) and \(C_{m}\) are the molar extinction coefficient at the wavelength \(\lambda\), and the concentration of the substance \(m\), respectively, and \(\mu_{a,n}^{100\%}(\lambda)\) and \(V_{n}\) are the absorption coefficient of the pure solution at the wavelength \(\lambda\) and the volume fraction of the substance \(n\), respectively. Since \(\varepsilon_{m}(\lambda)\) and \(\mu_{a,n}^{100\%}(\lambda)\) can be measured with a spectrophotometer, the concentrations and volume fractions are determined from \(\mu_{a}(\lambda)\) by solving the system of linear equations in Equation (1). Total hemoglobin (HHb) is derived as the sum of O\({}_{2}\)Hb and HHb. Tissue oxygen saturation (StO\({}_{2}\)) is defined as the ratio of O\({}_{2}\)Hb to tHb. The molar extinction coefficients of O\({}_{2}\)Hb and HHb were taken from the literature by [PERSON] et al. [28]. The absorption spectrum of lipid that we used was reported by [PERSON] et al. [29]. They measured the absorption spectrum of clear purified oil obtained from lard above 36 \({}^{\circ}\)C. Differences in