*3.2. Pharmacokinetic Modeling*

The one-compartment model was successfully applied to describe each group in terms of the plasma concentration-time profile after a single oral administration of 2 mg/kg tadalafil. Among the various compartment models, the one-compartment model, which is the simplest and best suited to the observed pharmacokinetic profile of tadalafil, was used to compare the observed pharmacokinetic profile with the fitted pharmacokinetic profile. The one-compartment modeling supports the results of the non-compartment analysis that changed by the co-administration of ticagrelor. The modeling-based comparison allows for greater confidence in the metabolic inhibition effect by comparing the observed pharmacokinetic profile with the fitted pharmacokinetic profile, as well as by matching with the parameters of the non-compartment analysis. Additionally, the model-based approach was used to evaluate a more specific and quantified absorption, elimination, and distribution of tadalafil in vivo.

As shown in Figure 1, the dashed lines and dotted marks mean the predicted plasma concentration and observed plasma concentration, respectively. The dashed lines showed similar patterns to the dotted marks. Figure 3 indicates the residual plot of the fold error versus time or observed plasma concentration. It shows the acceptable residual values (fold error <2) at most of the analyzed points, which indicates that the one-compartment model is suitable for the explanation of the plasma concentration profile of tadalafil [35,40].

**Figure 3.** Residual plots written with the pharmacokinetic modeling values of non-pretreated rats (Group N) and ticagrelor-pretreated rats (Group T). (**A**) Fold error vs. time; (**B**) fold error vs. plasma concentration.

Table 2 lists the parameters of the one-compartment model. In the one-compartment model, Ke and V/F were decreased significantly in Group T compared to Group N. The Ke of Group T (0.13 ± 0.03 <sup>h</sup>−1) were decreased compared with that of Group N (0.17 ± 0.05 <sup>h</sup>−1) (*p* < 0.05). Moreover, the V/F of Group T (3.36 ± 0.95 L/kg) was significantly decreased compared with that of Group N (4.39 ± 0.78 L/kg) (*p* < 0.05). These reductions led to a decrease in the clearance of tadalafil. In addition, the Ka of Group T was also decreased, but there was no statistical significance (*p* = 0.1933) (Figure 4). However, this slight reduction was due to the delay in absorption, and it is clear that the absorption increased because of the high Cmax. These results were consistent with those from the non-compartment analysis, indicating that the more absorption and the low clearance caused the increased exposure of tadalafil.

**Table 2.** The one-compartment model parameters of tadalafil in non-pretreated rats (Group N) and ticagrelor-pretreated rats (Group T). Values are represented as mean ± SD (n = 10).


a Ratio = *Value o f Group T Value o f Group N* ; Absorption rate constant from the gu<sup>t</sup> compartment to the central compartment (Ka); elimination rate constant from the central compartment to the gu<sup>t</sup> compartment (Ke); the central volume of distribution (V/F).

**Figure 4.** Comparisons of the one-compartment model parameters of tadalafil in non-pretreated rats (Group N) and ticagrelor-pretreated rats (Group T). Boxes mean 25th and 75th percentiles of data and whiskers mean 5th and 95th percentiles of data. The median and mean values are displayed as a solid line (–) and a plus mark (+) in boxes, respectively. (**A**) Ka; (**B**) Ke; (**C**) V/F. Absorption rate constant from the gu<sup>t</sup> compartment to the central compartment (Ka); elimination rate constant from the central compartment to the gu<sup>t</sup> compartment (Ke); the central volume of distribution (V/F).

In addition, the results from the modeling indicate that ticagrelor is a weak CYP3A inhibitor. The weak inhibitor is defined as a substance that increases the AUC value of the CYP substrate by 1.25-fold to 2-fold, or that it reduces the clearance of the CYP substrate by 20–50%, and ticagrelor is also classified as this inhibitor [22,41]. Changes in the AUC (1.61-fold) and clearance (37%) of tadalafil by co-administration with ticagrelor were within the range, supporting the above classification. Therefore, we inferred that ticagrelor acts as a weak CYP3A inhibitor, a ffecting the pharmacokinetic profiles of tadalafil, a CYP3A substrate. Furthermore, co-administration of tadalafil with ticagrelor or other CYP3A inhibitors, such as ketoconazole and diltiazem, would also be expected to increase tadalafil exposure [42].

In a clinical aspect, tadalafil shows robust safety and tolerability [12]. However, the co-administration of tadalafil with ticagrelor to elderly men may cause unexpected side e ffects. The half-life of tadalafil in normal healthy men is reported to be approximately 17.5 h after administration, whereas that of elderly men is about 21.6 h [43]. This half-life in elderly men is likely to increase further due to co-administration with ticagrelor, which may increase the incidence of side e ffects, such as headaches and dyspepsia. In addition, patients receiving nitrate medication for treatment of angina are recommended to postpone the nitrate treatment for at least 48 h after administration of tadalafil, but this may need to be longer to prevent serious hypotension [44]. Therefore, most patients receiving these drugs are older, so co-administration of tadalafil should be carefully considered.
