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 (Qi 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 (ka: absorption constant rate) or excretion (CLR: Renal Clearance).
Table 1.
Lobule parameters.
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 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 Fa is absorbed from the intestine to the gut wall with an absorption rate constant ka. Once the drug is in the gut wall, it may be metabolized and will cross the cell membrane (passively or actively) at a flow Qg, 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.
Table 2.
Summary of 10 in vivo clinical studies used in comparison to the simulations.
Table 3.
Metabolism parameters of the drugs.
Table 4.
Fraction unbound and blood-to-plasma ratio of the drugs.
Table 5.
Tissue-to-plasma partition coefficients of the drugs.
Table 6.
Interaction parameters of the drugs.
Table 7.
Fraction absorbed, absorption constant rate, Qg and permeability of drug chemicals.
Table 8.
Sinusoids length for each level.
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.
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 AUCratio versus predicted AUCratio.
The solid line represents the line of unity, the dashed lines are the 2-fold errors and the dotted lines the 5-fold errors.
Table 9.
DDI prediction for the 10 clinical studies.