Novel Mechanistic PBPK Model to Predict Renal Clearance in Varying Stages of CKD by Incorporating Tubular Adaptation and Dynamic Passive Reabsorption

Abstract

Chronic kidney disease (CKD) has significant effects on renal clearance (CL_r ) of drugs. Physiologically-based pharmacokinetic (PBPK) models have been used to predict CKD effects on transporter-mediated renal active secretion and CL_r for hydrophilic nonpermeable compounds. However, no studies have shown systematic PBPK modeling of renal passive reabsorption or CL_r for hydrophobic permeable drugs in CKD. The goal of this study was to expand our previously developed and verified mechanistic kidney model to develop a universal model to predict changes in CL_r in CKD for permeable and nonpermeable drugs that accounts for the dramatic nonlinear effect of CKD on renal passive reabsorption of permeable drugs. The developed model incorporates physiologically-based tubular changes of reduced water reabsorption/increased tubular flow rate per remaining functional nephron in CKD. The final adaptive kidney model successfully (absolute fold error (AFE) all < 2) predicted renal passive reabsorption and CL_r for 20 permeable and nonpermeable test compounds across the stages of CKD. In contrast, use of proportional glomerular filtration rate reduction approach without addressing tubular adaptation processes in CKD to predict CL_r generated unacceptable CL_r predictions (AFE = 2.61-7.35) for permeable compounds in severe CKD. Finally, the adaptive kidney model accurately predicted CL_r of para-amino-hippuric acid and memantine, two secreted compounds, in CKD, suggesting successful integration of active secretion into the model, along with passive reabsorption. In conclusion, the developed adaptive kidney model enables mechanistic predictions of in vivo CL_r through CKD progression without any empirical scaling factors and can be used for CL_r predictions prior to assessment of drug disposition in renal impairment.

Figure 1

Schematic presentation of the mechanistic kidney model structure, together with the corresponding renal tubular flow rate (TFR; in mL/min) for each individual tubular subsegment (a total of 12) of the model. Three sets of physiologically‐based TFR shown here are for healthy subjects (glomerular filtration rate (GFR) 120 mL/min, in green) and for the representative patients with chronic kidney disease (CKD) who have residual GFR of 10 mL/min using the adaptive model (in red) and the proportional model (in blue). The dynamic physiologically‐based mechanistic kidney model shown here is parameterized by 33 volume parameters, 22 surface area parameters, 12 peritubular renal blood flow parameters, 12 renal TFR parameters, 3 basolateral uptake clearance parameters, and 3 apical efflux clearance parameters to fully capture the disposition of drugs/metabolites between renal tubules, cells, and vasculature. CL, clearance.

Figure 2

Sensitivity analyses of simulated renal clearance (CL_r, in mL/min) at multiple stages of chronic kidney disease (CKD) reflected as varying glomerular filtration rate (GFR, in mL/min) using proportional model (shown in blue‐green) vs. adaptive model (shown in yellow‐red). Three sets of sensitivity analyses were conducted, (1) CL_r of neutral drugs with varying permeability values (P _app = 1–100 × 10^‐6 cm/s, all values shown are in 10^‐6 cm/s) but a constant plasma unbound fraction (f _u,p = 1) and peritubular renal blood flow (RBF = 1,000 mL/min, the average of healthy human subjects) were simulated using proportional model (a), adaptive model (b), and both models (c) across a wide range of GFR values from 5 mL/min to 120 mL/min, (2) renal clearances of highly permeable neutral drugs (P _app = 100 × 10^‐6 cm/s) with varying f _u,p (0.1–1) but a constant peritubular RBF (1,000 mL/min) were simulated using the proportional model (d), the adaptive model (e), and both models (f) across a range of GFR from 5 mL/min to 120 mL/min, (3) CL_r of a highly permeable neutral drugs (P _app = 100 × 10^‐6 cm/s) with varying peritubular RBF (300–1,000 mL/min) but a constant f _u,p (1) were simulated using proportional model (g), adaptive model (h), and both models (i) across a range of GFR from 5 mL/min to 120 mL/min. In panel a (proportional model), the decrease in CL_r between GFR of 120 mL/min and GFR of 5 mL/min is 24‐fold for all permeability values. In contrast, in panel b (adaptive model), the CL_r decreases by 22‐fold for a drug with a permeability of 1 between GFR of 120 mL/min and GFR of 5 mL/min, whereas the CL_r decreases by 1.5‐fold for a drug with a permeability of 100 between GFR of 120 mL/min and GFR of 5 mL/min, demonstrating a high sensitivity of the CL_r reduction to drug permeability.

Figure 3

Simulation (Sim) and verification of renal clearance (CL_r) of three drugs and their corresponding glucuronide metabolites at multiple stages of chronic kidney disease (CKD) reflected by varying glomerular filtration rate (GFR). Observed (Obs) CL_r data are shown as black solid squares depicting the group mean value with error bar showing the 95% confidence interval. The simulated CL_r of different test compounds at varying stages of CKD are shown with red curves for the adaptive model and blue dashed curves for the proportional model (a–c, g–i). The performance of the adaptive and proportional models was evaluated at CKD stages 4 and 5 where GFR ≤ 30 mL/min using calculated absolute fold‐error (AFE)_A (shown in red) and AFE_P (shown in blue), respectively (d–f, j–l). The experimentally determined apparent permeability (P _app), plasma unbound fraction (f _u,p), and observed CL_r data of rotigotine a, d, acetaminophen b, e, and lamotrigine c, f were collected from literature and summarized in Table S2 . The P _app and f _u,p values of all glucuronide metabolites g–l were assumed to be 0.1 × 10^‐6 cm/s and 1, respectively, based on their physicochemical properties. The observed CL_r data of all metabolites were from the same subjects in the same studies of their respective parent drugs (Table S2 ). The simulation results are shown on linear scale in Figure S1 .

Figure 4

Simulation (Sim) and verification of renal clearance (CL_r) of six nonpermeable compounds at multiple stages of chronic kidney disease (CKD) reflected by varying glomerular filtration rate (GFR). Observed (Obs) CL_r data of the test compounds are shown as black open circles and are from individual subjects in the reported studies. The simulated CL_r of different test compounds at varying stages of CKD are shown with red curves for the adaptive model and blue dashed curves for the proportional model (a–c, g–i). The performance of the adaptive model and proportional model was evaluated at CKD stages 4 and 5 (GFR ≤ 30 mL/min) using calculated absolute fold‐error (AFE)_A (shown in red) and AFE_P (shown in blue), respectively (d–f, j–l). The experimentally determined apparent permeability (P _app), plasma unbound fraction (f _u,p), and observed CL_r data of melagatran a, d, sotalol b, e, gabapentin c, f, nadolol g, j, ribavirin h, k, and doxycycline i, l were collected from literature and summarized in Table S2 . The simulation results are shown on linear scale in Figure S1 .

Figure 5

Simulation (Sim) and verification of renal drug clearance (CL_r) of six permeable and highly renally reabsorbed compounds at multiple stages of chronic kidney disease (CKD) reflected by varying glomerular filtration rate (GFR). Observed (Obs) CL_r data of the test compounds are from individual subjects when available and are shown as black open circles. If only group mean data were available, data are shown as black solid squares with 95% confidence interval as the error bar. The simulated CL_r of different test compounds at varying stages of CKD are shown with red curves for the adaptive model and blue dashed curves for the proportional model (a–c, g–i). The performance of adaptive and proportional model was evaluated at CKD stages 4 and 5 (GFR ≤ 30 mL/min) using calculated absolute fold‐error (AFE)_A (shown in red) and AFE_P (shown in blue), respectively (d–f, j–l). The plasma unbound fraction (f _u,p) and observed CL_r data of pefloxacin a, d, metronidazole b, e, and minocycline c, f, digitoxin g, j, cicletanine h, k, and pirfenidone I, l were collected from literature and summarized in Table S2 . The apparent permeability (P _app) values of pefloxacin, metronidazole, and minocycline were experimentally determined, whereas the P _app values of other drugs were optimized using the f _u,p and observed CL_r in healthy subjects, assuming no active secretion. The same optimized P _app values were used for extrapolated simulations at varying stages of CKD. The simulation results in linear plot are shown in the Figure S1 .

Figure 6

Sensitivity analyses of simulated renal clearance (CL_r in mL/min) at multiple stages of chronic kidney disease (CKD) reflected by varying glomerular filtration rates (GFR in mL/min) using adaptive model (shown in yellow‐red). (a) The sensitivity analyses of adaptive model‐simulated CL_r of neutral unbound permeable drugs (f _u,p = 1, P _app = 30 × 10^‐6 cm/s) with a constant unbound intrinsic apical efflux transport clearance (CL_efflux = 150 mL/min) and different unbound intrinsic basolateral uptake transport clearances (CL_uptake = 10–3,000 mL/min) across a range of GFRs (5–120 mL/min). (b) The sensitivity analyses of adaptive model‐simulated CL_r of neutral unbound permeable drugs (f _u,p = 1, P _app = 30 × 10^‐6 cm/s) with a constant unbound intrinsic basolateral uptake transport clearance (CL_uptake = 150 mL/min) and different unbound intrinsic apical efflux transport clearances (CL_efflux = 10–3,000 mL/min) across a range of GFRs (5–120 mL/min). The sensitivity analyses using proportional model and the comparison between the two models are shown in the Figure S2 . (c, d) The simulations of CL_r of para‐amino‐hippuric (PAH) and memantine in red curves, respectively, using adaptive model, at multiple stages of CKD, and comparison to the observed data (Table S2 ) shown in black open circles with calculated absolute folderror (AFE)_A shown in the insets. The simulation results for PAH and memantine using proportional model are shown in Figure S3 .