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Predictions of Metabolic Drug-Drug Interactions Using Physiologically Based Modelling

Two Cytochrome P450 3A4 Substrates Coadministered with Ketoconazole or Verapamil

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Abstract

Background and Objective: Nowadays, evaluation of potential risk of metabolic drug-drug interactions (mDDIs) is of high importance within the pharmaceutical industry, in order to improve safety and reduce the attrition rate of new drugs. Accurate and early prediction of mDDIs has become essential for drug research and development, and in vitro experiments designed to evaluate potential mDDIs are systematically included in the drug development plan prior to clinical assessment. The aim of this study was to illustrate the value and limitations of the classical and new approaches available to predict risks of DDIs in the research and development processes.

Methods: The interaction of cytochrome P450 (CYP) 3A4 inhibitors (ketoconazole and verapamil) with midazolam was predicted using the inhibitor concentration/inhibition constant ([I]/Ki) approach, the static approach with added variability (Simcyp®), and whole-body physiologically based pharmacokinetic (WB-PBPK) modelling (acslXtreme®). Then an in-house reference drug was used to challenge the different approaches based on the midazolam experience. Predicted values (pharmacokinetic parameters, the area under the plasma concentration-time curve [AUC] ratio and plasma concentrations) were compared with observed values obtained after intravenous and oral administration in order to assess the accuracy of the prediction methods.

Results: With the [I]/Ki approach, the interaction risk was always overpredicted for the midazolam substrate, regardless of its route of administration and the coadministered inhibitor. However, the predictions were always satisfactory (within 2-fold) for the reference drug. For the Simcyp® calculations, two of the three interaction results for midazolam were overpredicted, both when midazolam was given orally, whereas the prediction obtained when midazolam was administered intravenously was satisfactory. For the reference drug, all predictions could be considered satisfactory. For the WB-PBPK approach, all predictions were satisfactory, regardless of the substrate, route of administration, dose and coadministered inhibitor.

Conclusions: DDI risk predictions are performed throughout the research and development processes and are now fully integrated into decision-making processes. The regulatory approach is useful to provide alerts, even at a very early stage of drug development. The ‘steady state’ approach in Simcyp® improves the prediction by using physiological knowledge and mechanistic assumptions. The DDI predictions are very useful, as they provide a range of AUC ratios that include individuals at the extremes of the population, in addition to the ‘average tendency’. Finally, the WB-PBPK approach improves the predictions by simulating the concentration-time profiles and calculating the related pharmacokinetic parameters, taking into account the time of administration of each drug — but it requires a good understanding of the absorption, distribution, metabolism and excretion properties of the compound.

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Table I
Table A-I
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Fig. A-2
Table II
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Notes

  1. It is interesting to point out that Simcyp® also allows the use of WB-PBPK models including the interindividual variability on several parameters (PK profiles option), but this feature was not evaluated in the present work. Moreover, the present version of Simcyp® (9.0) is supposed to calculate more accurately the risk of MBI by including a different way of [I] calculation.

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Acknowledgements

The authors would like to thank all members of the PBPK working group within Servier for the useful discussions they had about this work.

No sources of funding were used to assist in the preparation of this study. The authors have no conflicts of interest that are directly relevant to the content of this study.

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Correspondence to François Bouzom.

Appendices

Appendix A

Methods for the Dynamic WB-PBPK Approach

The in-house PBPK models were built using the acslXtreme® modelling environment.[45] They were composed of the following tissues: blood, liver, kidneys, adipose, RVT and PVT. They also included, as the gut model, a CAT model located between the blood and the liver compartment (figure A-1). Oral doses were administered in the gut model and intravenous doses were administered in the blood compartment. This generic model was used for all compounds, taking into account the input parameters specific to each of them.

The Blood Compartment

The arterial and venous blood was considered as one single blood compartment (equation A-1):

$${{{\rm{dA}}} \over {{\rm{dt}}}} = \sum\limits_{{\rm{i}} = 1}^{\rm{n}} {{{\rm{Q}}_{\rm{i}}} \times {{\rm{C}}_{\rm{i}}} - {{\rm{Q}}_{{\rm{tot}}}} \times {\rm{A}}/{\rm{V}}} + {{\rm{R}}_{{\rm{adm}}}} - {{\rm{R}}_{{\rm{ex}}}}$$
((Eq. A-1))

where A is the amount in the blood compartment; V is the volume of the blood compartment; Qi and Ci are the blood flow and concentration of the peripheral compartment i, respectively; Qtot is the total cardiac blood flow; Radm is the rate of intravenous input (infusion or bolus); and Rex is the rate of elimination of the compound from the blood compartment (for ketoconazole), equal to the in vivo blood clearance multiplied by the blood concentration.

The Peripheral Organs (Liver, Kidneys, Adipose, Richly Vascularized Tissue, Poorly Vascularized Tissue)

The equations for these organs follow the classical flow-limited model (equations A-2, A-3 and A-4), the theoretical basis of which has been detailed elsewhere:[60]

$${{{\rm{dA}}} \over {{\rm{dt}}}} = ({\rm{Q}} \times {{\rm{C}}_{\rm{a}}} - {\rm{Q}} \times {{\rm{C}}_{{\rm{tb}}}}) - {{\rm{R}}_{{\rm{ex}}}}$$
((Eq. A-2))
$${{\rm{C}}_{{\rm{tb}}}} = {\rm{C}}/{{\rm{K}}_{\rm{p}}}$$
((Eq. A-3))
$${\rm{C}} = {\rm{A}}/{\rm{V}}$$
((Eq. A-4))

where A is the tissue quantity; C is the tissue concentration; Ctb is the tissue blood concentration; Ca is the arterial blood concentration; Q is the tissue blood flow; V is the tissue volume; Kp is the tissue to blood partition coefficient; and Rex is the elimination rate (in the liver and kidneys only).

The physiological parameters (volumes [V] and blood flows [Q]) of these organs are summarized in tables A-I and A-II Volumes are expressed as fractions of total body volume (Vtot = 70 L) and the blood flows as fractions of Qtot (Qtot = 6 L/min). Vtot is derived from bodyweight (BW), assuming a body density of 1, whereas Qtot is scaled from BW, using the classical allometric scaling (equation A-5):

$${{\rm{Q}}_{{\rm{tot}}}} = {{\rm{Q}}_{{\rm{car}}}} \bullet {\rm{B}}{{\rm{W}}^{3/4}}$$
((Eq. A-5))

where Qcar = 15 L/h/kg.[5,63]

Table A-II
figure Tab6

Physiological and drug parameters of the whole-body physiologically based pharmacokinetic (WB-PBPK) models, with their respective variability within the acslXtreme® software

The Kp values were calculated from mechanistic equations[64,65] for midazolam and ketoconazole, for which rat in vitro values were used [corrected by the factor fu,plasma(human)/fu,plasma(rat)]. The Kp values are listed in table A-I.

The elimination processes occur only in the liver and in the kidneys, and are applied on the Ctb. In the liver, the metabolism rate (i.e. Rex) is coded as follows (equation A-6):

$${{\rm{R}}_{{\rm{ex}}}} = {{{\rm{C}}{{\rm{L}}_{{\mathop{\rm int}} }}} \over {{{\rm{f}}_{{\rm{u}},{\rm{mic}}}}}} \times {\rm{Acc}} \times {{\rm{C}}_{{\rm{tb}}}} \times {{\rm{f}}_{{\rm{u}},{\rm{blood}}}}$$
((Eq. A-6))

or (equation A-7):

$${{\rm{R}}_{{\rm{ex}}}} = {{\rm{V}}_{\max ,{\rm{liver}}}} \bullet {{{\rm{Acc}} \bullet {{\rm{C}}_{{\rm{tb}}}} \bullet {{\rm{f}}_{{\rm{u}},{\rm{blood}}}}} \over {{\rm{Km}} \bullet {{\rm{f}}_{{\rm{u}},{\rm{mic}}}} + {{\rm{C}}_{{\rm{tb}}}} \bullet {{\rm{f}}_{{\rm{u}},{\rm{blood}}}}}}$$
((Eq. A-7))

where CLint is the intrinsic clearance for the liver; fu,mic is the HLM free fraction; fu,blood is the unbound fraction in the blood; Vmax,liver is the maximum turnover rate of the liver; Km (the Michaelis-Menten constant) is the affinity of the drug for the metabolizing enzyme; and Acc is a factor representing the potential drug accumulation in the liver. For verapamil, the total elimination rate (Rex) corresponded to the sum of the different elimination pathways of the three main metabolites [table I] (equation A-8):

$${{\rm{R}}_{{\rm{ex}}}} = {{\rm{R}}_{{\rm{met}}1}} + {{\rm{R}}_{{\rm{met}}2}} + {{\rm{R}}_{{\rm{met}}3}}$$
((Eq. A-8))

where Rmet1 is the norverapamil formation rate; Rmet2 is the D-617 formation rate; and Rmet3 is the D-703 formation rate.

Then, to take into account the formation of norverapamil in the liver, the change of norverapamil quantity with time was defined as follows (equation A-9):

$${{{\rm{dA}}} \over {{\rm{dt}}}} = ({\rm{Q}} \times {{\rm{C}}_{\rm{a}}} - {\rm{Q}} \times {{\rm{C}}_{{\rm{tb}}}}) - {{\rm{R}}_{{\rm{ex,met1}}}} + {{\rm{R}}_{{\rm{met}}1}}$$
((Eq. A-9))

where Rex,met1 is the norverapamil elimination rate.

In the kidneys, the Rex is equal to the in vivo CLR multiplied by the blood concentration.

DDI Equations in the Liver

When the coadministered drug leads to competitive inhibition, the metabolism rate of the substrate is modified as follows (equation A-10):

$${{\rm{R}}_{{\rm{ex}}}} = {{\rm{V}}_{\max ,{\rm{liver}}}} \bullet {{{\rm{Acc}} \bullet {{\rm{C}}_{{\rm{tb}}}} \bullet {{\rm{f}}_{{\rm{u}},{\rm{blood}}}}} \over {{\rm{Km}} \bullet {{\rm{f}}_{{\rm{u}},{\rm{mic}}}}(1 + {\rm{Ac}}{{\rm{c}}_{\rm{I}}} \bullet [{{\rm{I}}_{\rm{u}}}]/{{\rm{K}}_{\rm{i}}}) + {\rm{Acc}} \bullet {{\rm{C}}_{{\rm{tb}}}} \bullet {{\rm{f}}_{{\rm{u}},{\rm{blood}}}}}}$$
((Eq. A-10))

where [Iu] is the unbound concentration of the inhibitor available for enzyme inhibition in vivo; and AccI is the accumulation factor of the inhibitor in the liver.

When the coadministered drug leads to mechanism-based inhibition, the metabolism rate of the substrate is modified by substituting Vmax,liver in equation A-7 for (equation A-11):

$${{\rm{V}}_{\max ,{\rm{MBI}},{\rm{liver}}}} = {{\rm{V}}_{\max ,{\rm{liver}}}} \times {{{{\rm{k}}_{\deg }}} \over {{{\rm{k}}_{\deg }} + {{{\rm{Ac}}{{\rm{c}}_{\rm{I}}} \bullet {{\rm{I}}_{\rm{u}}} \times {{\rm{k}}_{{\rm{inact}}}}} \over {{\rm{Ac}}{{\rm{c}}_{\rm{I}}} \bullet {{\rm{I}}_{\rm{u}}} + {{\rm{K}}_{\rm{i}}} \times {{\rm{f}}_{{\rm{u}},{\rm{mic}},{\rm{I}}}}}}}}$$
((Eq. A-11))

where kdeg is 0.000825 min−1 for CYP3A4.[37]

When verapamil and norverapamil are present in the system, their metabolism rates correspond to those specified for MBI, since they inhibit their own metabolism as well as that of the substrate.

The Gut Model

This model was adapted from the model of Ploeger et al.,[66] which is a transit and absorption model based on the same principles as the well-known CAT model.[67] The gastrointestinal tract is divided into six sections: the stomach, duodenum, jejunum, ileum, caecum and colon (figure A-2). Each section is composed of three ‘layers’: one represents the lumen (the volume is determined from the length and the radius of the considered section), an epithelium compartment (possibly including metabolism and transporter efflux) and a mucosa subcompartment (considered as a well-stirred organ; see equations A-2, A-3 and A-4). The dissolved compound can transit from one section to the next only in the lumen layer, according to transit half-lives (summarized in table A-I). It can be absorbed in all sections (except in the stomach), proportionally to the surface area of the section and the effective permeability (Peff). The value of the Peff (common in all sections) was calculated from an initial value determined from the apparent permeability on Caco-2.[68] The compound goes through the epithelium with the same input and output rates (i.e. the same surface and the same Peff are used on the apical and basolateral sides). Once the compound has crossed the epithelium, it distributes in the mucosa layer according to equation A-4. A compartment representing the portal vein collects blood flows coming from the six sections, and goes directly to the liver.

As the substrates are metabolized by CYP3A4, the gut metabolism was included in the model. The elimination process was coded as in the liver (see above), taking into account the relative abundance of CYP3A4 in each section of the gut.[69] When the substrates were coadministered with the inhibitors, the gut metabolism was fixed at 0, considering that it was totally inhibited.

Monte-Carlo Simulations

acslXtreme® was used to simulate virtual populations of healthy subjects with bodyweight ranges consistent with those in the in vivo studies. The doses administered corresponded to those administered in the selected in vivo studies.

Using Monte-Carlo analysis, 200 virtual subjects were simulated for each substrate administration with and without the inhibitor. The parameters of the virtual subjects were sampled from prior normal distributions of selected parameters (table A-II). These parameters were selected as the most sensitive from previous sensitivity analyses. The variability associated with each parameter was set from the literature (e.g. a coefficient of variation [CV] of 70% associated with CYP3A4 abundance/activity)[40] or arbitrary (e.g. a CV of 30% associated with the B/P ratio, fu,blood, etc.). The same 200 subjects were selected with and without inhibitor coadministration.

The following pharmacokinetic parameters were calculated from the individual plasma concentration profiles: the CL (for intravenous administration), AUC, Cmax and t½. These parameters were summarized by their mean values associated with the standard deviations, as well as their 90% prediction intervals (i.e. the difference between the 5th percentile and the 95th percentile).

Finally, the individual virtual AUCi/AUC ratios were summarized by their median values and their 90% prediction intervals, corresponding to the overall picture of the acslXtreme® virtual population.

Appendix B

Inhibitor Models and Results

The equations used in the WB-PBPK models and physiological and drug parameters for ketoconazole, verapamil and norverapamil are described in Appendix A.

The pharmacokinetic profiles of ketoconazole and verapamil after oral administration (figures B-1 and B-2) were considered satisfactory.

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Perdaems, N., Blasco, H., Vinson, C. et al. Predictions of Metabolic Drug-Drug Interactions Using Physiologically Based Modelling. Clin Pharmacokinet 49, 239–258 (2010). https://doi.org/10.2165/11318130-000000000-00000

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