A Continuous Intestinal Absorption Model to Predict Drug Enterohepatic Recirculation in Healthy Humans: Nalbuphine as a Model Substrate

Abstract

Nalbuphine (NAL) is a κ-agonist/μ-antagonist opioid being developed as an oral extended formulation (ER) for the treatment of chronic cough in idiopathic pulmonary fibrosis and itch in prurigo nodularis. NAL is extensively glucuronidated and likely undergoes enterohepatic recirculation (EHR). The purpose of this work is to develop pharmacokinetic models for NAL absorption and enterohepatic recirculation (EHR). Clinical pharmacokinetic (PK) data sets in healthy subjects from three trials that included IV, oral solution, and ER tablets in fed and fasted state and two published trials were used to parametrize a novel partial differential equation (PDE)-based model, termed "PDE-EHR" model. Experimental inputs included in vitro dissolution and permeability data. The model incorporates a continuous intestinal absorption framework, explicit liver and gall bladder compartments, and compartments for systemic drug disposition. The model was fully PDE-based with well-stirred compartments achieved by rapid diffusion. The PDE-EHR model accurately reproduces NAL concentration-time profiles for all clinical data sets. NAL disposition simulations required inclusion of both parent and glucuronide recirculation. Inclusion of intestinal P-glycoprotein efflux in the simulations suggests that NAL is not expected to be a victim or perpetrator of P-glycoprotein-mediated drug interactions. The PDE-EHR model is a novel tool to predict EHR and food/formulation effects on drug PK. The results strongly suggest that even intravenous dosing studies be conducted in fasted subjects when EHR is suspected. The modeling effort is expected to aid in improved prediction of dosing regimens and drug disposition in patient populations.

Keywords: enterohepatic recirculation; nalbuphine; partial differential equations; pharmacokinetic models.

Figure 1.

Schematic of the PDE-EHR model. (A) Intestine is modeled as a physiological continuous compartment based on the convection-diffusion-reaction equation. The intestine is a 7 m continuous tube (plus 1 m with velocity = 0) with radii $r_1$ and $r_2$ for the small intestine and colon, respectively. Cross-sectional view: concentric tubes depict the lumen (drug concentration, C1), apical membrane (C2), enterocyte cytosol (C3), and intracellular lipid (C4). The two-dimensional depiction of the concentric tubes is modeled as a five-compartment model with drug concentrations C1–C4 and input into liver via $\text{fg}∕{\text{CL}}_{\mathrm{i},1}∕2$; fg: fraction of drug dose escaping gut metabolism. (B) Upon dosing into the stomach, the parent drug moves along the length of the intestine and is absorbed into the liver compartment. The liver compartment is connected reversibly via hepatic blood flow to central compartment A, where IV dosing as well as plasma sampling occurs. The central compartment A is reversibly connected to peripheral compartments B and C via first-order rate constants. Parent drugs in the liver can be glucuronidated. Both parent and glucuronide can distribute from the liver to compartments A–C and can be secreted into the gall bladder. The gall bladder secretes the parent and glucuronide into the duodenum. The parent can be recycled via absorption into the liver (red arrows). The glucuronide can be hydrolyzed by β-glucuronidase (GUS) expressed in the lower intestine to parent drug, which results in recycling of parent via glucuronidation-deglucuronidation (blue arrows). Parent concentrations in the intestinal lumen (C1 in Figure 1) are predicted upon dosing (I), upon recycling from the gall bladder (II), and after several hours via deglucuronidation (III) (see related simulations in Figure 5). Parent and glucuronide are eliminated from the system via a combination of presystemic loss and hepatic plus nonhepatic elimination.

Figure 2.

Physiological functions describing intestinal physiology, input functions from the stomach, and gall bladder emptying. Functions are shown for (A) intestinal velocity, $\text{vel}(x)$, (B) intestinal effective diffusion, $\text{dif}(x)$, (C) intestinal cross-sectional area, $a_1(x)$, (D) lumenal surface area, $sa(x)$, (E) microvilli expansion factor, $\text{mf}(x)$, (F) intestinal pH, $\text{pH}(x)$, (G) intestinal GUS expression function, $\text{clgus}(x)$, (H) input function from fasted stomach, (I) input function from fed stomach, (J) gall bladder emptying distance function, $\text{clgo}(x)$, and (K) post-prandial gall bladder output, $\text{clgo}2(t)$.

Figure 3.

Schematic for the PDE-EHR model. Compartments (except stomach) have a length of $x=8\mathrm{m}$. Bidirectional diffusion with thicker arrows denoting fast diffusion: green arrows; velocity terms (either a physiological, $\text{vel}(x)$ for the intestinal lumen compartments, or an artificial): blue arrows; intercompartmental clearances (modeled along the length): gray arrows; secretion from the gall bladder into the duodenum lumen, and deglucuronidated parent (via GUS) colonic absorption: orange arrows. Compartmental concentrations are defined in eqs 22-34 in the Experimental Section.

Figure 4.

Predictions of $C-t$ profiles upon a solution dose with and without enterohepatic recirculation. (A) Observed $C-t$ data set (blue circles) and predicted $C-t$ profile (PO 45 mg NAL solution dose, Study 1) without recirculation (magenta), with only parent recirculation (green), and with recirculation of both parent and glucuronide (green). (B–D) Predicted intestinal lumen parent concentration-distance-time profile $\mathrm{C}1(x,t)$ of NAL (B) without any parent or glucuronide recirculation, (C) with parent recirculation only, and (D) with both parent and glucuronide recirculation.

Figure 5.

Prediction of $C-t$ profiles for IV/PO crossover studies with PO solution dosing to fasted subjects. IV data for (A) Study 1, (B) Aitkenhead et al., and (C) Lo et al. Mean IV data (filled circles), compartmental model-predicted profile (solid line). (D) PO data for Study 1, (E) Aitkenhead et al., and (F) Lo et al. Mean PO observed data ± SD (shaded band). Model-predicted $C-t$ profile (solid black line). Standard errors for PO predictions are listed.

Figure 6.

Prediction of $C-t$ profiles for fasted versus fed studies upon solution or ER tablet dosing, Study 2. Mean observed data are depicted by blue circles with the ± SD depicted by the shaded band. Model-predicted $C-t$ profiles are depicted by the solid black line. IV data from Study 1 were used for parametrization. Standard errors for each prediction are listed. (A) 60 mg fasted solution, (B) 60 mg fed solution, (C) 120 mg fasted ER tablet, and (D) 120 mg fed ER tablet.

Figure 7.

Prediction of $C-t$ profiles for PO ER tablet dosing studies, Study 3. Mean observed data are depicted by blue circles with ± SD depicted by the shaded band. Model-predicted $C-t$ profile is depicted by the solid black line. IV data from Study 1 were used for parametrization. Standard errors for each prediction are listed. (A) 30 mg, (B) 60 mg, (C) 120 mg, and (D) 180 mg.

Figure 8.

Predicting impact of intestinal P-gp on absorption of NAL. Mean observed data for Study 3 180 mg dose are depicted by blue circles with ± SD depicted by the shaded band. 0.5–2.5× P-gp activity was modeled as described under Methods. (A) Model-predicted $C-t$ profiles are depicted by solid lines as follows: black, no P-gp; green, −0.5× P-gp; blue, −1× P-gp; and purple, 2.5× P-gp. (B) Predicted AUCs for each profile and the % AUC relative to no P-gp.