The present popPK analysis identified that changes in apparent absorption rate and apparent bioavailability, rather than changes in renal elimination, are the primary causes of the slight DDI that was found for adefovir as a victim when co-administered with other transporter probe substrates. Although the identified nonlinear renal clearance of adefovir is not saturated at the standard dose, further dose reduction in the existing transporter phenotyping cocktail might avoid even minor DDIs.

In this evaluation, plasma and urine data could be reasonably explained by a one-compartment model with first-order absorption (including lag time) and a combination of Michaelis-Menten-type nonlinear renal and linear nonrenal elimination. Despite previous studies reported that adefovir plasma levels declined biexponentially [10, 25, 26], our investigation did not reveal an observable biphasic decline in the semi-log plots (Supplemental Fig. 1s). Introducing a second compartment to the one-compartment base model did not significantly improve the BIC score (drop in BIC by 1.44), residual unexplained variability, or VPCs. Therefore, the one-compartment model was chosen as the final model.

The estimates for PK parameters of adefovir we present here are in line with the previous NCA conducted on the same dataset [3]. According to the final model, the individual apparent volume of distribution (V/F) for adefovir was calculated based on the individual EBEs of V divided by individual EBEs of F. The median of these individual values was 369 L and 308 L in the reference and test periods, respectively. These values are comparable to the geometric mean values obtained from the previous NCA study, which reported 368 L and 307 L for the corresponding periods [3]. Additionally, the median (range) CLR and t1/2 values for adefovir during the reference and test periods in this evaluation are in accordance with those reported in the NCA study [3]. According to the NCA, during the reference period, the geometric mean (95% CI) CLR and the geometric mean (95% CI) t1/2 of adefovir were 12.3 (6.06–24.9) L/h and 6.38 (4.68–8.72) h, respectively. In the test period, these values were 11.3 (7.26–17.8) L/h and 6.58 (5.05–8.57) h, respectively [3].

In our analysis, after normalizing for body weight, median individual values for V/F, CLR, and CL/F are 4.89 L/kg, 0.175 L/h/kg, and 0.493 L/h/kg, respectively. Moreover, the median urinary recovery over 24 h is 46.4%. These findings align with the characteristics reported in the summary of product characteristics for HEPSERA® (adefovir dipivoxil) tablets [23] and are consistent with observations by Sokal et al. [26]. Sokal et al. studied adolescents aged 12–17 years, finding mean ± SD values of 0.739 ± 0.192 L/h/kg for CL/F, 7.16 ± 1.6 L/kg for V/F, and 6.84 ± 0.97 h for t/2 after a single oral dose of 10 mg adefovir dipivoxil [26]. However, our results were slightly lower than those reported by Hughes et al. [15] in infants and children (3 months–18 years) after a 1.5 mg/kg adefovir dipivoxil dose, showing a median CL/F of 1.0 L/h/kg and a median V/F of 8.1 L/kg. Conversely, our estimates of CL/F and V/F were slightly higher than those reported by Shiffman et al. [27] in patients with mild renal impairment (creatinine clearance ≥ 50 to < 80 mL/min), reflecting a mean CL/F of 0.270 L/h/kg and a mean V/F of 2.6 L/kg [27]. These discrepancies may stem from physiological variations due to factors such as growth, development, and disease.

In the study by Cundy et al. [10], a comparable mean ± SD value for CLR was observed at 0.205 ± 0.078 L/h/kg. Nevertheless, they reported a lower V at 0.418 ± 0.076 L/kg, a shorter t1/2 of 1.6 ± 0.5 h, and a reduced CL of 0.223 ± 0.053 L/h/kg compared to our study. This discrepancy was noted following the intravenous administration of adefovir at 1 or 3 mg/kg/day in HIV-infected patients [10]. Considering adefovir dipivoxil, an ester prodrug of adefovir, may rapidly convert to adefovir after administration [28], it is not probable that adefovir dipivoxil pharmacokinetics play an important role in estimating the PK parameters of adefovir. Therefore, the underlying mechanisms of this difference remain unclear.

While Sun et al. [14] and Huang et al. [25] reported 1/2 values similar to those in our study, Sun et al. presented notably low mean values for / (7.0 mL/kg) and CL/ (0.63 mL/h/kg) following a 10 mg oral dose of adefovir dipivoxil [14]. These values diverge from the mean serum concentration–time curves presented in their manuscript, prompting us to consider a potential unit mislabeling in the published results—suggesting “L” may be more appropriate than “mL.” Should this correction prove accurate, it would better align with the results of our current study. In contrast, Huang et al. reported a higher CL (1.00 L/h/kg) and a higher V (10.7 L/kg) after a 10 mg dose of adefovir dipivoxil [25]. We attribute this discrepancy to an error in their article, where they indicate, “open circles represent observed adefovir dipivoxil concentrations” [25]. It appears they inadvertently used adefovir dipivoxil as the moiety for concentrations instead of adefovir, inflating both and CL in their analysis. Overall, published data on adefovir pharmacokinetics show a remarkable variability in clearance and volume of distribution.

To evaluate the influence of co-treatment on PK parameters, we employed two approaches. Firstly, we independently evaluated PK parameters for reference and test periods. Additionally, we integrated co-treatment effect as a covariate on the PK parameters. The relative differences in PK parameters between these periods, as estimated by both methods, are consistent and resulted in an equivalent reduction of the OFV. To allow for greater flexibility in identifying potentially more fundamental distinctions in the description of PK processes between periods, we finally conducted a separate assessment of PK parameters for each of the reference and test periods, respectively. After a detailed assessment of the parameters in various PK processes using the popPK model, a higher apparent bioavailability, but a slower apparent absorption rate of adefovir when co-administered with the cocktail, has been identified. These findings indicate potential changes in the apparent absorption of adefovir dipivoxil or prodrug conversion, contributing to increased systemic exposure during co-administration with the cocktail, as observed in the previous DDI study [3]. Based on sporadic studies, a potential mechanism to explain this result may stem from the co-administered drugs exerting inhibitory effects on the intestinal multidrug resistance-associated protein 2 (MRP2, ABCC2). This protein mediates unidirectional transport of adefovir to the intestinal lumen within enterocytes [29,30,31]; thus, inhibition may enhance the bioavailability of adefovir. Furthermore, the model-based approach did not support the inclusion of Vmax for reference and test periods separately. Additionally, no significant difference was observed in the median CLR between reference and test periods. This suggests that CLR remains unaffected by the other concomitantly administered probe drugs and may reliably reflect changes in the renal OAT1 activity, which is rate limiting for adefovir renal excretion [2, 9, 10].

The final model, incorporating a nonlinear renal elimination, provides an appropriate description of the data, as supported by the supplemental figures. The adefovir renal clearance plot (Supplemental Fig. 3s) indicates a deviation from linearity in urinary excretion at high concentrations, which is well described by the nonlinear renal clearance model. The residual plot (Supplemental Fig. 4s) illustrates clearly biased descriptions of urinary excretion with a linear model at high concentrations, supporting that the linear clearance model is inadequate. Furthermore a model with nonlinear renal elimination offers a physiologically plausible representation for adefovir renal elimination. Adefovir primarily undergoes OAT1-mediated tubular secretion, a process that could potentially saturate and complement kidney filtration. Calculated as CLR – fu*GFR (with a median GFR of 6.28 L/h in this study) [2], adefovir secretion accounts for over 50% of CLR in this study, aligning with findings in previous reports [10, 24]. The population estimate (95% CI) for Km in nonlinear renal elimination is 170 (122–295) nmol/L, which is lower than in vitro studies (mean ± SD 23.8 ± 4.2 µmol/L) [11, 12]. This disparity may stem from challenges in replicating the dynamic in vivo environment in controlled in vitro settings and differences in techniques. Despite this, it exceeds the observed adefovir Cmax range (5.56–91.0 nmol/L). Thus, this mechanism is expected to have little influence on systemic exposure and is considered clinically insignificant at therapeutic doses. However, this result suggests that a reduction of adefovir dose as part of the transporter probe cocktail may be considered in future studies to prevent relevant transporters to be saturated, and to minimize any impact on other cocktail components.

As discussed in the “Introduction” section, indeed there is some prior evidence for nonlinearity on adefovir pharmacokinetics [14, 15], albeit nonlinear renal clearance has not been shown yet [10, 25,26,27, 32,33,34]. The possible reason might be that such finding requires a popPK evaluation to gain a more detailed understanding of the role of individual PK processes for the pharmacokinetics of adefovir, while most of previous studies assessed the PK of adefovir by noncompartmental methods, which may provide insufficient information of individual PK processes [10, 14, 27]. Another possible reason could be that the extent of saturability in adefovir’s elimination, based on the recommended single dose of 10 mg, was relatively small. Therefore, both plasma measurements and urine collection might be necessary for a sound estimation of the nonlinearity. This could explain why Jihan Huang reported first-order elimination for adefovir in their popPK study [25].

The model could not be improved further by incorporating the AGFR as a component of CLR in addition to nonlinear renal clearance. Although it might better reflect the physiological conditions of the renal excretion of adefovir, which involves both active tubular secretion and glomerular filtration, this approach resulted in unstable parameter estimates of Km and Vmax (RSEs > 1000%). As a result, we were unable to estimate the Km value of true renal secretion, which might become more saturated at therapeutic adefovir concentrations.

Another limitation of this study is that it only included healthy adults who received a standard dose. To gain a comprehensive understanding of the nonlinear renal elimination of adefovir, future studies would need to include more dose levels, particularly higher doses, in diverse populations with varying degrees of renal function.