Clinical Trials And Translational Medicine CommentariesPHRMA CPCDC initiative on predictive models of human pharmacokinetics, part 5: Prediction of plasma concentration–time profiles in human by using the physiologically‐based pharmacokinetic modeling approach
Section snippets
INTRODUCTION
There is a need for better predictions of human pharmacokinetics (PK) in early drug development, and a clear description of the predictability of the different approaches. A Pharmaceutical Research and Manufacturers of America (PhRMA) initiative previously evaluated interspecies allometry and related methodologies to predict individual ADME properties of drugs, for which the outcome is presented in companion manuscripts.1., 2., 3. Another initiative was also taken.4 However, it is not
Overall Work Flow
The method consisted of verifying the ability of the PBPK model to reproduce the shape of the plasma concentration–time curve observed in human under intravenous (i.v.) and oral (p.o.) conditions for the PhRMA dataset of drugs. Combination of absorption models with disposition models was tested with a PBPK approach for human.21 The overall strategy used for this analysis of PBPK modeling is depicted in Figure 1. Five different methodologies for predicting human distribution PK were implemented
THE PRESENTATION OF PREDICTION METHODS
This work consisted of the application of an “independent” or “in‐house” PBPK model developed based on published equations.21 The base PBPK‐model framework constructed in this study is briefly describes below, and for comparability reasons all equations of this framework and its corresponding input parameters are presented in detail in Appendix.
Base PBPK‐Model Framework for Human
A single PBPK‐modeling framework has been evaluated. This is based on a recent publication that presented a standard PBPK framework, which integrates prediction models of absorption, distribution, and metabolic CL.21 The performance of this published PBPK framework can be tested and also various methods for estimating compound‐specific parameters be incorporated. It will also offer a baseline performance against which commercial software solutions can be compared in the future and any “added
Absorption Modeling Within the PBPK Model
Oral administration is by far the most common route of drug administration. Therefore, it is of particular interest to predict p.o. absorption/bioavailability (F%) in humans from experimental in vivo and in vitro biopharmaceutical properties. The rate of drug absorption (Rabs) after a p.o. dose is incorporated in the gut compartment and is predicted using the ACAT model (in vitro) and simple single‐compartment absorption (in vivo).
In Vitro‐Based Modeling of Absorption
Oral absorption is determined by complex mechanisms that are governed by physiology, biochemical, and physicochemical processes. The main determinants considered in the nine‐compartment absorption model, describing the gastrointestinal tract in the PBPK model are shown in Figure 4.10,21 The first compartment is the stomach, the last compartment is the colon, and the seven remaining compartments represent the small intestine (SI). For the ACAT model Rabs is the sum of absorption rates from the
In Vivo‐Based Modeling of Absorption
Single‐compartment absorption, described by first‐order input kinetics are defined by the fraction absorbed (Fabs) and absorption rate constant (ka). When in vivo‐absorption data were used, the gut differential equations applied (see Eqs. 20 and 21 in Appendix).
Single‐compartment absorption, described by first‐order input kinetics, is defined by the fraction absorbed (Fabs) and absorption rate constant (ka). Human estimates of Fabs and ka were taken as the average observed in vivo in
CL Modeling Within the PBPK Model
A previous comprehensive analysis conducted by PhRMA analysing the predictive performance of different plasma CL methodologies was used as a basis for the selection of CL methods used in the analysis.3 In this study, predicted human CL was modeled using two conceptually different methods, namely, the IVIVE (in vitro‐based) and the unbound fraction corrected intercept allometry (FCIM) (in vivo‐based). These two methods are presented in detail below.
In Vitro‐Based Modeling of CL
The hepatic elimination is determined from human microsomal intrinsic CL (CLint), which in turn is determined in vitro.29 A companion study found that of the IVIVE methods studied, the method that incorporated binding to plasma proteins and microsomes was the most accurate method for predicting CL in human.3 Using this approach, the in vitro intrinsic CL (CLint,in vitro) is scaled to the in vivo situation (CLint,in vivo) based on physiological scaling factors and binding parameters (fup and fu
In Vivo‐Based Modeling of CL
The in vivo prediction of human CL used the allometric fu correlation intercept method (FCIM) method reported by Tang and Mayersohn,31 based on a detailed analysis in a companion paper.3 The equation for this method is provided in Appendix (Eq. 27). Furthermore, the FCIM method was used for comparability reason with a companion study on the Css‐MRT,5 which is also based on FCIM.
Distribution Modeling Within the PBPK Model
The parameters characterizing the extent of tissue distribution in a PBPK model are referred to as the tissue:plasma partition coefficients (Kp), which can be used to derive volume of distribution at steady state (Vss).22,24 Kp can be estimated using in vitro‐ or in vivo‐based algorithms.11,22., 23., 24., 25., 26. Despite the success of these methods at predicting the overall human Vss,2 assessing the prediction accuracy for individual tissue Kp values in human remains impossible because of the
In Vitro‐Based Modeling of Distribution
The main principle is that physicochemical and binding data determined in vitro predict Kp values in human.
The Tissue Composition Method
The mechanistic models for tissue distribution refer to TC‐based equations developed for calculating Kps of lean and adipose tissues.22., 23., 24. The principle of these equations is that a Kp is described from the relationship determined between physiological data (neutral and charged lipids, plasma proteins and lipoproteins, and water) and compound‐specific determinants of distribution like lipophilicity (log octanol:water partition coefficient for the unionized form (log P)), ionization (pK
In Vivo‐Based Modeling of Distribution
The main principle is that Kp values of human tissues can be predicted from rat Vss determined in vivo.
The Jansson Correlation Method
Jansson's method is based on the observation that there is a correlation between the Kp values for various tissues in the rat. Specifically, muscle partitioning is predictive of partitioning in the other tissues.26 The method produces predictions of Kps by varying muscle partitioning (and consequently the Kp in other tissues) until the predicted volume of distribution in the rat matches the observed value. In the current PBPK model, a simple Newton solver was implemented that uses an initial
The Arundel Method
The Arundel method for predicting Kp values uses measured Vss in the rat.11,25 The main principle of the Arundel model is based on the empirical finding that there is a relationship between Vss and the time constant of distribution of a drug (reciprocal of the rate constant) in particular groups of tissues in the rat. The Kp of lean tissues can be derived from this using the volume and blood flow of the tissue group, assuming the kinetics are perfusion‐rate limited. The only parameter that
DATASETS
A diverse and blinded dataset of 108 compounds from 12 member companies of PhRMA were used in this evaluation as detailed in a companion paper.1 Considering the criteria of the present modeling approach, p.o. kinetic data were collected in human for a total of 95 drugs, whereas i.v. kinetic data were available in human for 18 drugs (Tables 1 and 2). It is clear that different prediction methods require differing amounts of input data. All methods require predicted or observed human CL. The ACAT
PRESENTATION OF THE PBPK MODEL SIMULATION SCENARIOS
Given the number of combinations of distribution, CL and/or absorption methods in the PBPK model, and the corresponding drug datasets studied for each of those scenarios, three flow charts of simulation scenarios are presented to guide the reader in Figures 5 (i.v. datasets), 6 (p.o. datasets), and 7 (for the common drugs in the i.v. and p.o. datasets). The contents of these figures are detailed below.
Intravenous Kinetics
Simulation of i.v. kinetics was made according to the chart of simulation scenarios in Figure 5. The simulation of i.v. kinetics in human was performed in two steps. First step: The first step consisted of predicting the disposition kinetics in human by combining the observed CL and the various prediction methods of Kps to identify which of these distribution models is the most effective at simulating plasma concentration–time profiles. Therefore, six simulations for each drug were generated,
Oral Kinetics
Simulation of p.o. kinetics was made according to the chart of simulation scenarios in Figure 6 and7. In general, effectively simulating the p.o. kinetics of a drug is more challenging than i.v. because of the additional parameters needed to describe absorption. This aspect was verified also in two steps.
First step:
We investigated the prediction of p.o. kinetics in human by combining disposition and absorption models in the PBPK framework. In this case, an in vitro‐based approach for predicting disposition and absorption was compared to an in vivo‐based approach (Figure 6).
Second step:
An important assessment is the comparison between predicted i.v. and p.o. kinetics for the common drugs in the i.v. and p.o. datasets (Figure 7). Given the dataset challenges, there are only 18 drugs for which the i.v. and p.o. kinetics were available in human. Therefore, the combination of the observed CL with an in vivo‐based distribution model for Kp prediction (JA) in the PBPK model was used to estimate drug disposition in human for these 18 common drugs. This was also made for the p.o.
IMPLEMENTATION OF PBPK SCRIPTS
To maximize the use of the data, each method was run for a given compound providing that the required input for that method was available. In other words, missing information for a compound was used to decide which predictive methods to run. In this case, a “switch” selected which model to use for each run (Figure 2). To process analyses and simulations in a batch format, all the modeling and simulation operations (fitting of the i.v. and p.o. datasets in the preclinical species, PBPK
PREDICTED HUMAN PK PROPERTIES
The human PK parameters to be simulated with the PBPK scenarios after i.v. and/or p.o. dose involve the following:
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Plasma concentration–time profiles at the lowest dose tested in the single ascending doses studies in fasted healthy volunteers.
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Secondary global PK parameters and descriptors derived from the simulated and observed plasma concentration–time profiles, including, AUC, mean residence time (MRT), terminal T1/2, plasma Cmax and at the first (Cfirst) and last (Clast) time point, time when
PHARMACOKINETIC ANALYSES
The i.v. and p.o. plasma concentration–time profiles in vivo (normalized to dose) for each preclinical species were used to simultaneously fit an appropriate compartment model (one or two compartment) to derive key PK parameters (Vss, CL, F%, ka, and microconstants). An F‐test (α = 0.05) was applied to the sum of weighted residuals for each model to decide which was the most appropriate. Noncompartmental analyses (NCA) were performed to estimate the PK parameters at the given dose while
STATISTICAL ANALYSES AND ASSESSEMENT OF PREDICTIVITY
The steps involved in this assessment are listed in a sequential manner in a companion paper1 and was used also for the current in‐house PBPK approach. Furthermore, the rules for the quality assessment are the same as those applied to the empirical allometric Css‐MRT in a companion manuscript.5 Comparative assessment of the predicted and observed data in human was made at two different levels. First, the observed versus predicted PK parameters of each drug were compared. Second, the curve shape
RESULTS
Detailed results are presented in Tables 3 and 4 for the prediction of human PK parameters of plasma concentration–time profiles as well as in Figures 5, 6, and 7 for the resulting overall degree of accuracy of each simulation scenario studied.
ASSESSMENT OF TISSUE DISTRIBUTION MODELS AGAINST THE PHRMA I.V. DATASET FOR HUMAN
Six distribution Kp models were evaluated within the PBPK framework (, , , Arundel, ArundelExtended, and JA). PBPK model simulations of the plasma concentration–time profile in human using the observed CL were run for each of the six distribution models, and compared to observed profiles in Figure 5. Among the distribution models investigated here, the models that use in vivo data were superior to those relying purely on in vitro data. The best performing in vitro‐based model (
Simulation of Plasma Concentration–Time Profiles for I.V. Kinetics
Using the predicted CL (instead of observed CL) and Kps in the PBPK model, the full plasma concentration–time profile in human were simulated and compared to observed data (Figure 5). No significant gain in accuracy was noted by using observed CL compared to using predicted CL, demonstrated by no improvement in the level of accuracy particularly in low‐to‐low/medium zone. This indicates that CL is relatively well predicted for most drugs in the i.v. dataset using at least one method studied
Prediction of Human PK Parameters of Plasma concentration–time Profiles for I.V. Kinetics
Between 50% and 71% of predictions of the primary human PK parameters for i.v. dosing (AUC0‐t,i.v., Cfirst,i.v., T1/2,i.v., and MRTi.v.) were predicted within a twofold error (Table 3). The percentage within threefold was between 57% and 93%. AUC0‐t,i.v. was the parameter most accurately predicted, followed by Cfirst,i.v. followed by MRTi.v. followed by T1/2,i.v.. This was confirmed by looking at the CCC values, a global measure of accuracy, which was higher for AUC0‐t,i.v. (0.92–0.93) compared
Comparison Between In Vitro and In Vivo‐Based Pbpk Models for I.V. Kinetics
Comparing simulations produced by a complete in vitro approach ( with CL predicted by IVIVE) to a complete in vivo approach (JA with CL predicted by FCIM) shows that both approaches achieve very similar levels of accuracy, with respect to the prediction of the PK parameters and their effectiveness at simulating plasma concentration–time profile shapes (Figure 5 and Table 3). This is in line with the prediction of the individual ADME parameters (e.g., Vss, CL) in the companion papers where,
Simulation of Plasma Concentration–Time Profiles for P.O. Kinetics
Different scenarios for combining in vitro and in vivo approaches for predicting absorption, distribution, and CL were applied to simulate the plasma concentration–time profile in human after p.o. administration (Figure 6). Compared to the simulation of i.v. kinetics, the p.o. simulations achieved less accuracy. Only up to 23% of the predictions made in human obtained a medium–high degree of accuracy for p.o. PK compared to 69% for the i.v. PK. The additional model parameters necessary to
Prediction of Human PK Parameters of Plasma Concentration–Time Profiles for P.O. Kinetics
The decrease in prediction performance from i.v. to p.o. kinetics is reflected by less accurate prediction particularly for AUC0‐t and Cmax (Table 4). However, for the other parameters, namely T1/2 and MRT, the degree of accuracy is similar between i.v. and p.o. simulations (Table 3 vs. Table 4), and this is indicated by almost equivalent statistical measures (percent twofold error, percent threefold error, AFE, AAFE, RMSE, CCC). Looking at the statistical results for the prediction of AUC0‐t
Comparison Between In Vitro and In Vivo‐based PBPK Models for P.O. Kinetics
Once again, using in vitro‐based approaches (Vss, , CL, IVIVE, ACAT model) as input parameters to the PBPK model resulted in similar levels of accuracy as the in vivo‐based approaches (Vss, JA, CL, FCIM, average ka, and Fabs) for p.o. simulations (Table 4 and Figure 6).
A closer examination of the prediction of p.o. absorption is performed by comparing the prediction of absorption using the approaches based on in vivo ( and and in vitro (ACAT model with measured or estimated Sol
DISCUSSION
A significant amount of work has already been performed by PhRMA to collect a blinded dataset as well as conduct analyses to predict PK properties of ADME.1., 2., 3. However, to predict the overall PK of a compound, the ADME properties must be integrated into a PBPK model to simulate plasma concentration–time profiles. Integrating predictions of ADME properties generated from the initial phase of this study provided a natural extension and application of the initial work. This study has
CONCLUSION
In conclusion, this present study is the first time to our knowledge that such an extensive evaluation of the most common PBPK models published in the literature has been completed for drugs. The analyses conclude that PBPK models are more effective at simulating after i.v. dosing compared to the p.o. route, which is in accordance with two companion studies.3,5 This is to be expected given the complex kinetic processes associated with the p.o. route. Our investigations suggest that for this
Acknowledgements
The authors kindly acknowledge Natalie Bolea, Michael Garvin, and Vail Fucci at PhRMA), Les Z. Benet at UCSF, Gregg Ludeen at Lilly, as well as Ken Korzekwa for their assistance and support.
APPENDIX
This section contains the equations of the PBPK model investigated, and four tables for the corresponding physiological input parameters.
BASE PBPK MODEL FRAMEWORK
The differential equations for noneliminating tissues take the form (A: amount, Q: blood‐flow rate, Qc: cardiac output, C: concentration, V: volume, Kp: tissue:plasma ratio, B:P: blood to plasma concentration ratio, VB: venous blood leaving the tissue):
NONELIMINATING TISSUE
ELIMINATING TISSUE
For the liver, the equation is as follows:
The intrinsic CL (CLint) with respect to unbound compound is derived from the predicted human hepatic CL referring to blood kinetics (CLblood) (i.e., the predicted plasma CL corrected with the measured B:P) by rearranging the well‐stirred model to obtain:
Differential Equations of the Acat Model
The differential equations of the nine compartment of the ACAT model are presented below, wherein C refers to the drug concentration; NI, the nonionized fraction in the lumen; Diff, the diffusion velocity; B:P, blood‐to‐plasma ratio; Kp the plasma‐tissue partition coefficient; Q, the blood flow to tissue; KS, the gastric emptying rate constant; KT, the intestinal transit rate constant; KD, the dissolution constant; and A, the amount of drug. The subscripts refer to stomach (stom), lumen (lum),
Emptying (KS) and Transit Rate (KT)
The gastric emptying rate constant (KS) and the small intestine transit rate constant (KT) are set to 0.1 and 0.035 min−1, respectively.21
Lumen Volume (Vlum)
The total lumen volume was calculated according to the following equation: Vlum,tot = πLR2, where R (=1.75 cm) is the mean radius lumen and L (= 680 cm), the total small intestine length. As the small intestine is divided in seven compartments (n = 7); the lumen volume and membrane volume of each compartment were obtained by dividing the
Dissolution Constant (KD)
Once the drug is swallowed, the tablet starts dissolving at a dissolution rate KD driven by the difference between the drug solubility (Sol) and the concentration of the dissolved drug (Ci). For any given gastrointestinal compartment i (i = 1–8), KD was calculated as follows: KD = 3D (Sol − Ci) /(ρrT), where D is the diffusion coefficient of the drug (default value = 10−4 cm2/min), ρ is the effective drug particle radius (default value = 5 µm if no value is provided), r is the drug particle
Solubility (Sol)
The drug solubility (Sol) used in the ACAT model is estimated from the experimentally determined solubility in the intestinal fluid (Solfassif), which can also be estimated from the measured water solubility (Solwater). The drug solubility Solfassif (expressed in mg/L) can be calculated from Mithani equation versus bile salt concentration27:where SR is the molar solubility ratio of a drug expressed as log SR = 0.75log P + 2.27, where log P is the n‐octanol:buffer
Drug Diffusion Velocity Through the Gut Membrane (Diff)
The fraction of unionized drug in each of the intestinal compartments was calculated using Henderson–Hasselbach equations based on drug pKa and intestinal lumen pH. The apparent permeability of drug through intestinal cells, measured from apical to basolateral (Pappab) and from basolateral to apical side (Pappba), was scaled up by the intestinal exchange surface area (ESA) to estimate the apparent diffusion velocity (Diff) of the drug through the intestinal membrane of any compartment, such as:
in Vivo‐based Modeling of Absorption
When in vivo‐absorption data were used, the gut differential equations applied were:are then calculated using the predicted blood CL in human assuming again that CL is solely hepatic.where the value of F and Fabs was estimated in each preclinical species and for each drug for which the IV and PO plasma concentration‐time profiles were available in vivo, whereas the human CLblood is estimated from the predicted plasma CL and measured
In Vivo‐based Modeling of Cl
In the method section, it is demonstrated that CLin vivo can be calculated from CLint,in vivo, which has been estimated from CLint,in vitro and binding parameters. Using this approach, the in vitro intrinsic CL is scaled to the in vivo situation3 using Eq. 23:where PBSF is the physiologically based scaling factor and fup and fuinc are the unbound fraction in plasma and incubation medium, respectively. PBSF was set equal to 822 mg protein/kg body weight
Estimation of Drug Lipophilicity
In all prediction methods of distribution (Kp, Vss) investigated in the present study, the drug lipophilicity (log P) is an important input parameter. Here lipophilicity may refer to drug distribution in n‐octanol or vegetable oil as demonstrated below.22,24
Octanol:buffer Ratio
Po:w refers to the octanol:buffer ratio of the unionized form determined in vitro for each basic drug, Do:w refers to the octanol:buffer ratio of the total concentrations for a given pH (unionized and ionized). Do:w was
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This work was undertaken by the Pharmaceutical Research and Manufacturers of America (PhRMA), 950 F StNW,Washington,DC 20004; Clinical and Preclinical Development Committee (CPCDC); Predictive Models of Human Pharmacokinetics Limited Duration Key Issue Team (LDKIT), previously known as a working group under the Pharmaceutical Innovation Steering Committee (PISC).