## Materials and Methods
### Prediction of Hepatic First-Pass Metabolism  
Microsomal metabolism stability studies were conducted to predict the fraction of TU that could escape hepatic first-pass metabolism (\(F_{\text{H}}\)). Stability studies were performed using human liver microsomes. The in vitro intrinsic clearance (\(Cl_{\text{int}}\), mL/min/mg protein) was calculated using the in vitro half-life (\(t_{\text{1/2 inv}}\)) of TU depletion in human liver microsomes according to Equation (1) [17; 18]. \[Cl_{\text{int}}=\frac{0.693}{\text{{in vitro}}\ t_{\text{1/2}}}.\frac{\text{mL }}{\text{{mg}}}.\frac{\text{{incubation medium}}}{\text{{mg}},\text{{ microsomes}}} \tag{1}\]  
Microsomal incubations were performed as previously described [17]. Briefly, the reaction mixture consisted of human microsomal proteins and MgCl\({}_{\text{2}}\) dissolved in solution a of potassium phosphate buffer (\(\text{KH}_{\text{2}}\text{PO}_{\text{4}}\)/\(\text{K}_{\text{2}}\text{HPO}_{\text{4}}\), pH 7.4). TU was accurately weighed and dissolved in aqueous acetonitrile (50% _v/v_). Reaction tubes containing the reaction mixture were placed in a temperature-controlled orbital shaker at 37 \({}^{\circ}\)C and shaken at 200 rpm (Thermo Scientific MaxQ4000, Waltham, MA, USA). Following a pre-incubation period of 3 min, the reaction was initiated by the addition of TU and the NADPH solution in the potassium phosphate buffer. TU solution in potassium phosphate buffer without NADPH was added to another set of reaction tubes as a control. The concentration of acetonitrile in the final mixture was less than 1%. The final concentrations of TU, human liver microsomes, MgCl\({}_{\text{2}}\), \(\text{KH}_{\text{2}}\text{PO}_{\text{4}}\)/\(\text{K}_{\text{2}}\text{HPO}_{\text{4}}\), and NADHP were 1 uM, 0.5 mg/mL, 10 mM, 84.7 mM, and 1 mM, respectively. Two-hundred microlitre aliquots were withdrawn at 0 min, 10 min, 20 min, and 30 min and placed in a test tube that contained 300 uL ice-cold acetonitrile to stop the reaction. Samples were then processed on the same day for high-performance liquid chromatography (HPLC) analysis as described below. All experiments were performed in triplicates. \(Cl_{\text{int}}\) was then corrected by the fraction of drug unbound in the incubation medium (\(f_{\text{u,mic}}\)) according to Equation (2) to find the unbound intrinsic clearance (\(Cl_{\text{u,int}}\)) [19]. \[Cl_{\text{u,int}}=\frac{Cl_{\text{int}}}{f_{\text{u,mic}}} \tag{2}\]  
The experimental determination of \(f_{\text{u,mic}}\) for highly lipophilic drugs is quite challenging due to significant non-specific binding [20]. In addition, predictive tools for \(f_{\text{u,mic}}\), such as those suggested by [PERSON] et al. [21] and [PERSON] and [PERSON] [22], were demonstrated to be unreliable for drugs with a logP value \(\geq\) 5 such as TU (logP = 9.15 [23]) [20]. Therefore, the binding of TU to microsomal proteins was assumed to be similar to that of plasma proteins, corrected by protein concentration [18]. Based on this,\(f_{\text{u,mic}}\) was calculated by Equation (3) [24]. \[f_{\text{u,mic}}=\frac{1}{\left(\frac{C_{\text{mic}}}{C_{\text{pp}}}\ \times\ \frac{\left(1-f_{\text{u,p}}\right)}{f_{\text{u,p}}}\right)+1} \tag{3}\]  
where \(C_{\text{mic}}\) is the microsomal protein concentration (0.5 mg/mL), \(C_{\text{pp}}\) is the concentration of human plasma proteins (70 mg/mL [25]), and \(f_{\text{u,p}}\) is the fraction of TU unbound in human plasma. The value of \(f_{\text{u,p}}\) for TU was estimated by the online prediction tool ([[https://drumap.nibiohn.go.jp/](https://drumap.nibiohn.go.jp/)]([https://drumap.nibiohn.go.jp/](https://drumap.nibiohn.go.jp/))) [26]. The calculated value of \(Cl_{\text{u,inc}}\) was then scaled, based on human physiological factors of 32 mg microsomes/g liver and 22 g liver/kg body weight [18; 27; 28], to find the hepatic intrinsic clearance (\(Cl_{\text{H,inc}}\), mL/min/kg).