A quantitative systems pharmacology approach, incorporating a novel liver model, for predicting pharmacokinetic drug-drug interactions

Abstract

All pharmaceutical companies are required to assess pharmacokinetic drug-drug interactions (DDIs) of new chemical entities (NCEs) and mathematical prediction helps to select the best NCE candidate with regard to adverse effects resulting from a DDI before any costly clinical studies. Most current models assume that the liver is a homogeneous organ where the majority of the metabolism occurs. However, the circulatory system of the liver has a complex hierarchical geometry which distributes xenobiotics throughout the organ. Nevertheless, the lobule (liver unit), located at the end of each branch, is composed of many sinusoids where the blood flow can vary and therefore creates heterogeneity (e.g. drug concentration, enzyme level). A liver model was constructed by describing the geometry of a lobule, where the blood velocity increases toward the central vein, and by modeling the exchange mechanisms between the blood and hepatocytes. Moreover, the three major DDI mechanisms of metabolic enzymes; competitive inhibition, mechanism based inhibition and induction, were accounted for with an undefined number of drugs and/or enzymes. The liver model was incorporated into a physiological-based pharmacokinetic (PBPK) model and simulations produced, that in turn were compared to ten clinical results. The liver model generated a hierarchy of 5 sinusoidal levels and estimated a blood volume of 283 mL and a cell density of 193 × 106 cells/g in the liver. The overall PBPK model predicted the pharmacokinetics of midazolam and the magnitude of the clinical DDI with perpetrator drug(s) including spatial and temporal enzyme levels changes. The model presented herein may reduce costs and the use of laboratory animals and give the opportunity to explore different clinical scenarios, which reduce the risk of adverse events, prior to costly human clinical studies.

Fig 1. Lobule geometry and modelling.

(A) The lobule cross section as represented displays an apparent elementary symmetry essential for its physiology primarily given by the blood vessels and the blood flow (Credit to Dr. Roger C. Wagner, University of Delaware). (B) This symmetry is used when lobule modeling or representation are involved. In general, a lobule is represented by a hexagon composed of hepatocyte plates. These plates are hierarchically organized to optimize exchanges. (C) To model the blood flow (and subsequent exchanges between the liver tissues and the blood), an algorithm was designed to automatically generate the length and radius of the sinusoids. The latter is used to estimate the changes in velocity within a sinusoid portion by assuming a constant blood flow and a constant velocity over the cross section.

Fig 2. The seven compartmental model.

Red and blue arrows represent blood flows (Q_i where i represents: T for total blood flow, ha hepatic artery blood flow, pv portal vein blood flow, L for the liver blood flow, G for the gut blood flow, K for the kidneys blood flow and RB for the blood flow going to the rest of the body). The black arrows represent absorption (k_a: absorption constant rate) or excretion (CL_R: Renal Clearance).

Fig 3. Enzymatic reactions taken into account in the liver model.

Reversible inhibition: A drug binds to an enzyme which may result in its metabolism (but not necessarily) resulting in the temporary blockade or inhibition of the enzyme. Here only competitive inhibition will be studied, which assumes that each enzyme can interact with one drug at a time. Mechanism Based Inhibition (MBI): A drug inactivates an enzyme through direct interaction resulting in an inhibited metabolism of any drug metabolized by these enzymes. Induction: A drug induces the expression of one or more enzymes resulting in an induced metabolism of any drug metabolized by these enzymes. Note that the notations in this figure regarding the kinetic rate constants are used in the text.

Fig 4. The gut-compartmental model.

The gut compartment is composed of two sub-compartments; the gut wall and the portal vein sub-compartments. After an oral administration of a given drug, a fraction F_a is absorbed from the intestine to the gut wall with an absorption rate constant k_a. Once the drug is in the gut wall, it may be metabolized and will cross the cell membrane (passively or actively) at a flow Q_g, depending on drug permeability and villous blood flow (see S3 Appendix), to join the blood circulatory system. Once the drug is in the blood, it goes to the liver through the portal vein.

Fig 5. Properties of 5 sinusoid levels from the lobule model.

(A) The radius of the sinusoids is expressed as a function of the distance to the periphery of the lobule. For a given level, the radius is decreasing as the sinusoids are converging toward the center of the lobule. Once the sinusoids reach their minimum size they merge together which increases the radius size in a stepwise manner. (B) The flow of the sinusoids is expressed as a function of the distance to the periphery of the lobule. For a given level, the flow is constant, but double when two sinusoids merge. (C) The velocity of the sinusoids is expressed as a function of the distance to the periphery of the lobule. For a given level, the velocity is increasing as the sinusoid radius is decreasing. Once the sinusoids reach their minimum size they merge which decreases the blood velocity suddenly.

Fig 6. Simulated PK of the perpetrator (blue) and victim (orange) drugs.

The simulation were run using the clinical dose regimens from Table 2: (A) Azithromycin (B) Cimetidine (C) Ethinyl Estradiol (D) Rifampin.

Fig 7. Simulated enzyme levels as a function of time.

The total enzyne level (free enzyne + enzyme-substrate complex) is represented as a fold change compared to the initial level. The color gradient indicates the positions within the lobule from blue (Entrance of the lobule) to red (Exit of the lobule): (A) Azithromycin (MBI inducer) (B) Cimetidine (Reversible inhibitor: No effect on enzyme level) (C) Ethinyl Estradiol (MBI inhibitor and inducer: It seems that in this case the effect cancels each other out) (D) Rifampin (Inducer).

Fig 8. Simulated PK profile for midazolam after an oral dose of 15 mg and comparison to clinical data.

(⋆) Fee et al. 1987 [20] (•) Zimmermann et al. 1996 [19].

Fig 9. Simulated PK profiles for midazolam with a placebo (blue) or a perpetrator (orange) and comparison to clinical data.

The dots represent the clinical observations: (A) Azithromycin [19] (B) Cimetidine [20] (C) Ethinyl Estradiol [23] (D) Rifampin [28].

Fig 10. Observed AUC_ratio versus predicted AUC_ratio.

The solid line represents the line of unity, the dashed lines are the 2-fold errors and the dotted lines the 5-fold errors.