Model-Based Analysis of Biopharmaceutic Experiments To Improve Mechanistic Oral Absorption Modeling: An Integrated in Vitro in Vivo Extrapolation Perspective Using Ketoconazole as a Model Drug

: Mechanistic modeling of in vitro data generated from metabolic enzyme systems (viz., liver microsomes, hepatocytes, rCYP enzymes, etc.) facilitates in vitro − in vivo extrapolation ( IVIV_E ) of metabolic clearance which plays a key role in the successful prediction of clearance in vivo within physiologically-based pharmacokinetic (PBPK) modeling. A similar concept can be applied to solubility and dissolution experiments whereby mechanistic modeling can be used to estimate intrinsic parameters required for mechanistic oral absorption simulation in vivo . However, this approach has not widely been applied within an integrated work ﬂ ow. We present a stepwise modeling approach where relevant biopharmaceutics parameters for ketoconazole (KTZ) are determined and/or con ﬁ rmed from the modeling of in vitro experiments before being directly used within a PBPK model. Modeling was applied to various in vitro experiments, namely: (a) aqueous solubility pro ﬁ les to determine intrinsic solubility, salt limiting solubility factors and to verify p K a ; (b) biorelevant solubility measurements to estimate bile-micelle partition coe ﬃ cients; (c) fasted state simulated gastric ﬂ uid (FaSSGF) dissolution for formulation disintegration pro ﬁ ling; and (d) transfer experiments to estimate supersaturation and precipitation parameters. These parameters were then used within a PBPK model to predict the dissolved and total (i.e., including the precipitated fraction) concentrations of KTZ in the duodenum of a virtual population and compared against observed clinical data. The developed model well characterized the intraluminal dissolution, supersaturation, and precipitation behavior of KTZ. The mean simulated AUC 0 − t of the total and dissolved concentrations of KTZ were comparable to (within 2-fold of) the corresponding observed pro ﬁ le. Moreover, the developed PBPK model of KTZ successfully described the impact of supersaturation and precipitation on the systemic plasma concentration pro ﬁ les of KTZ for 200, 300, and 400 mg doses. These results demonstrate that IVIV_E applied to biopharmaceutical experiments can be used to understand and build con ﬁ dence in the quality of the input parameters and mechanistic models used for mechanistic oral absorption simulations in vivo , thereby improving the prediction performance of PBPK models. Moreover, this approach can inform the selection and design of in vitro experiments, potentially eliminating redundant experiments and thus helping to reduce the cost and time of drug product development.


■ INTRODUCTION
−4 This interest is markedly reflected in the increased number of research publications on this topic 5 and their applications in regulatory submissions and recently approved drug labels, 6 regulatory guidance, 7,8 and concept papers. 9−21 PBPK models facilitate the integration of two classes of information: (1) "System Data", consisting of physiological, biological, and genetic characteristics of the species studied, and (2) "API Data", consisting of the relevant physicochemical and disposition attributes of the compound and/or its dosage Special Issue: Industry-Academic Collaboration in Oral Biopharmaceutics: The European IMI OrBiTo Project form. 22In addition to reliable physiological data, the predictive performance of PBPK modeling depends strongly on drugspecific parameters. 3Physiological/system-related parameters are typically curated, verified, and provided within databases as part of some commercial PBPK platforms; it is usually up to users to obtain the required drug-specific parameters.Some drug-specific parameters are obtained from complex in vitro studies which typically rely on mechanistic model-based analysis of in vitro experimental results.−26 Similar concepts can be applied to solubility and dissolution experiments in the form of mechanistic analysis of such assays to confirm and/or estimate intrinsic parameters required for mechanistic oral absorption simulations in vivo.However, this approach has not widely been applied within an integrated workflow.
The Advanced Dissolution, Absorption, and Metabolism (ADAM) model is a population-based mechanistic absorption modeling framework available within the Simcyp populationbased PBPK simulator (Figure 1). 16,27Generally, there are two ways to handle particle dissolution rates in vivo (Figure 2).First, the dissolution rates can be measured in "biorelevant" in vitro experiments (dissolution rate profile) and without adjustment directly used within the PBPK model or they can be modeled  mechanistically using a theoretical approach such as a diffusion layer model (DLM).In the latter case, drug solubility (both in bulk solution and within the particle surface microenvironment), particle size, bile-micelle partition, and a number of other particle-related parameters are considered explicitly.Once established and having gained confidence in the mechanistic model and its parameters (established by accurate prediction of experimental in vitro dissolution profiles) these can then be combined with physiological system parameters describing the gut luminal environment including pH, bile salt concentration, fluid volumes, and transit times to estimate the dissolution rate from drug particles within the various regions of the gastrointestinal (GI) tract.Thus, using a mechanistic model, such as the DLM, enables the simulator to account for regional and between-subject differences in the physiological parameters related to pH, bile salt concentration, and fluid volume dynamics in a mechanistic manner.Overall, this approach facilitates mechanistic translation of in vitro experiments to in vivo and enables the investigation of other factors such as food or even disease status impact on the absorption processes where the appropriate physiological data and mechanistic models are available.
The direct use of in vitro dissolution profiles as input to a PBPK model is available as noted above, but, without breaking down the in vitro information into its underlying mechanistic components, such an approach prohibits the incorporation of the known variability of physiological parameters into in vivo dissolution rate simulations which, particularly for BCS class II and IV drugs, may result in significant between-subject variability of dissolution rate unless attenuated through formulation strategies.Of course where in vivo variability of dissolution is known in advance not to be significant in terms of PK/PD outcomes, simpler approaches may be sufficient.Typically, in vitro dissolution assays are performed in conventionalUSP I (basket apparatus), II (paddle apparatus), III (reciprocating cylinder apparatus), or IV (flow through) apparatus and can in some circumstances quite closely simulate in vivo luminal conditions of the small intestine or stomach at least for a representative ("average") individual.However, more generally, in vitro dissolution conditions are static and hence can only partially represent a particular location within the GI tract and perhaps then only over a short time frame due to time-dependent changes in in vivo fluid volumes (particularly in the proximal small intestine), absorption of dissolved drug, absorption of bile salt micelles in the distal small intestine, and other factors.Furthermore, these in vitro dissolution tests are not generally designed to account for the inherent betweensubject physiological variability of luminal pH, luminal fluid volume, buffer capacity, bile salt concentration etc., to which the drug/dosage form is exposed during GI transit.Other differences between in vitro and in vivo conditions include, for example, the hydrodynamics (stirring rates, fluid flow patterns, etc.) and the lack of an absorptive component in vitro.It is important to emphasize that not all drugs, drug products, or doses of a given drug are likely to be sensitive to all of the aforementioned parameters.BCS class I drugs tend to be least sensitive to these factors and thus, in general, will not benefit from mechanistic modeling of dissolution.However, given that a high proportion of new drugs are BCS II or IV, there is a clear benefit to the use of mechanistic models to better characterize in vivo behavior where there is sensitivity to physiological conditions.
As a result of the factors discussed above, for many drug products, the direct use of in vitro dissolution profiles to estimate in vivo dissolution rates in PBPK models may not be appropriate.It is, therefore, desirable to confirm and/or estimate the required parameters of the mechanistic equations through modeling of in vitro experiments and then apply these models and parameters to in vivo simulations where the system parameters differ in general to those of the in vitro system, an approach we refer to as in vitro−in vivo extrapolation (IVIV_E) of dissolution and solubility.Such biopharmaceutic IVIV_E techniques rely on mechanistic understanding, appropriate experiments, and the modeling of in vitro dissolution profiles.
During luminal transit, the drug may undergo disintegration, dissolution, luminal degradation, supersaturation, precipitation, and redissolution.It is, however, not practical to mimic and therefore characterize all these complex processes in a single in vitro experiment.An alternative approach is to perform multiple, simpler independent experiments, each assessing relevant biopharmaceutical parameters of the drug product as required.These can then be combined in a mechanistic framework as discussed above.
Modeling of in vitro dissolution within the same mechanistic framework as that used for in vivo simulations provides three important benefits: (1) It allows assessment of the validity of the mechanistic dissolution model (the DLM in this case), and its assumptions, against a controlled and well-defined in vitro dissolution environment.This is otherwise difficult to assess in the complex in vivo luminal environment where dissolution is not directly measured.(2) It allows assessment of the quality and relevance of model input parameters such as solubility, particle size, disintegration rate, etc. (3) It can help to identify incorrect parameters or assumptions of the model.In such circumstances the user may choose to remeasure certain parameters (perhaps after additional sensitivity analysis) and/or estimate them using parameter estimation tools.A systematic IVIV_E approach may therefore help to build confidence in the quality of the input parameters and mechanistic models (and their associated assumptions) before doing in vivo simulations with PBPK models, with the aim to improve predictive performance (Figure 2).−30 To assess the performance of IVIV_E and provide a proof of concept, we herein present a stepwise in vitro data modeling approach for ketoconazole (KTZ), a weakly basic drug known to precipitate in vivo, and its impact of in vivo predictions from a PBPK model.The performance of the proposed approach was assessed by comparing the predicted dissolved and total (precipitated and dissolved drug) concentration of KTZ (300 mg) in the duodenum with those reported from clinical studies.Predicted and reported plasma concentration time profiles were also compared.

■ MATERIALS AND METHODS
Materials.KTZ aqueous and biorelevant solubility data, the dissolution of Nizoral (ketoconazole) tablets in the USP-II apparatus, and its supersaturation/precipitation behavior using transfer experiments were determined at Goethe University (Ruff et al. 31 ).Human in vivo duodenal luminal KTZ (300 mg) concentrations were reported by Psachoulias et al. 42 Stepwise IVIV_E Approach.Figure 3 graphically illustrates the stepwise IVIV_E modeling approach undertaken in this study.First, intrinsic aqueous solubility (S 0 , the solubility of unionized drug) and its salt limiting solubility factors (SFs; maximum solubility governed by the solubility product K sp ) were characterized using the measured pH−solubility profile of KTZ.The consistency of the experimental pH−solubility profile with pK a , S 0 , and the SF were also confirmed at this stage.Next, having fixed the aqueous phase parameters, the bile micelle:water partition coefficients (K m:w ) for the ionized and un-ionized monomers were estimated through modeling of biorelevant solubility, i.e., in FaSSIF (fasted state simulated small intestinal fluid) and FeSSIF (fed state simulated small intestinal fluid).Solubility measurements at different pH and bile salt concentrations, obtained from the literature, were also used as an external validation of the estimated parameters.The formulation disintegration profile was established from the dissolution profile in FaSSGF at pH 1.6 in the USP II apparatus.KTZ is highly soluble at pH 1.6, and the dissolution profile is assumed to be disintegration controlled rather than controlled by dissolution rate of the API.Once the robustness of the mechanistic particle dissolution model parameters was confirmed in FaSSIF dissolution medium at pH 6.5 for an IR formulation, the transfer experiment data were modeled to determine the first-order precipitation rate constant for the drug product studied.Finally, all these parameters, determined using in vitro experiments, were incorporated into the KTZ PBPK model.This approach facilitates combining the drug and formulation data with the relevant in vivo physiology rather than that of the in vitro experiments to simulate in vivo behavior.Each step is explained in detail below.
Modeling Aqueous Solubility Data.Equation 1 describes the overall structure of the solubility model used which is a composite function of aqueous phase solubility, governed by the Henderson−Hasselbalch equation for electrolytes and a bile micelle partition model accounting for micelle-mediated solubility of the API.The maximum aqueous phase solubility of ionized form of drug is also governed by the salt limiting solubility which is defined using the solubility factors (SFs).The mechanistic separation of the components of solubility enables calculation of free fraction and therefore the driving concentrations for permeation and precipitation models.It also enables individualized effective diffusion coefficients to be calculated for use in diffusion layer models of dissolution 16 when simulating populations with PBPK models.
In eq 1, [BS] is the concentration of bile salt (sodium taurocholate:lecithin molar ratio 4:1); S 0 is the aqueous intrinsic solubility; S ionized refers to the aqueous phase solubility of the ionized form of the drug at a given pH (total aqueous phase solubility = S 0 + S ionized ); S(BS) Tot is the combined total solubility (aqueous at given pH and micelle mediated solubility at a stated [BS]); C H2O is the concentration of water (55.56 mM); and K m:w,un-ionized/ionized are the bile micelle:water partition coefficients for neutral (or ionized) molecular species, respectively.
The equilibrium solubility of the unformulated (pure) KTZ in blank aqueous buffersHCl/NaCl and maleate buffer used in the preparation of biorelevant media, pH 2.0 FaSSGF-V2 and pH 6.5 FaSSIF-V2, respectively, was determined using HPLC (Table 1).These aqueous solubility measurements are devoid of bile micelle-mediated solubility effects and hence were used for intrinsic solubility and SF verification within the solubility model.Moreover, the solubility measurements in aqueous phosphate buffer 32 and Tris/maleate buffer 33 were used for the external validation once the solubility parameters were established.
Modeling Bile Micelle-Mediated Solubility.A key parameter for defining micelle-mediated solubility is the micellar partition coefficient (K m:w ), for which separate values can be defined for the neutral and charged forms of the drug.Initial estimates of K m:w values can be obtained from a linear regression equation based upon log P o:w of the compound developed by Glomme et al. 34 where a = 0.74 and b = 2.29 for sodium taurocholate/lecithin (4:1 ratio) mixtures and m diff is a "rule-of thumb" correction factor for ionized drug partition; the default m diff values (which serve as initial estimates) for mono-and dications are 1 and 2 respectively. 35t this stage, S 0 and SF (eq 1), which were previously confirmed using aqueous only solubility measurements, were fixed and only the two K m:w values were estimated using biorelevant solubility modeling (Figure 3).Hence biorelevant media FaSSGF-V2 and FaSSIF-V2 solubility measurements were explicitly used for the estimation of the micelle:water partition coefficients for KTZ.
Such a model facilitates translating the in vitro determined micelle-mediated solubility parameters to in vivo allowing incorporation of the regional luminal pH and bile salt concentration in fasted and fed states and their interindividual variability within the PBPK framework.
Modeling Formulation Disintegration.During formulation disintegration it may be that disintegration is rate determining for the dissolution process and thus in general should be accounted for. 36While disintegration for IR formulations may be sufficiently rapid as to be not significant in terms of clinical PK profiles, it may be of great importance to separate disintegration from API particle dissolution when assessing or parametrizing mechanistic models from in vitro dissolution experiments.Two of the doses modeled herein (discussed below) are IR dosage forms.KTZ has high solubility at the low gastric pH typical of the fasted state, and, therefore, formulation disintegration may be dissolution rate limiting; the solubility of KTZ in FaSSGF-V2 is very high (>10 mg/mL).Hence, we used the dissolution profile of Nizoral tablets from a FaSSGF-V2 medium in a USP 2 paddle apparatus to estimate a first-order disintegration rate constant using eq 3.
where % F disint is the percentage disintegrated at time t, F max(%) is the maximum disintegration which was assumed to be 100% in this case, K d1 is the first-order disintegration rate constant (h −1 ), and t lag is the lag time.This simple exponential function captured the in vitro dissolution profile in FaSSGF-V2 very well (AFE = 0.99).
Modeling Precipitation Kinetics.Experimental assessment of supersaturation and precipitation properties of drug products relevant to their in vivo behavior involves consideration of a multitude of factors, including rate and extent of drug solubilization in the gastric (donor) compartment, transfer rate, composition and volume of the simulated fluids, pH, bile salt concentration, bound and unbound micelle fraction, hydrodynamics (e.g., paddle RPM), ionization, permeation, and effect of formulation excipients. 31 number of dynamic in vitro models for studying intestinal precipitation have been developed with varying degrees of complexity. 37Kostewicz et al. originally presented a transfer model in which a two compartment USP dissolution method is used corresponding to the stomach and first part of the small intestine, respectively; 38 subsequently, the original experimental setup underwent considerable improvements. 31A wide range of physiologically relevant experimental parameters such as gastric emptying rate, hydrodynamics, GI pH, fluid volume, and bile salt concentration were taken into consideration before narrowing these down to the conditions of the current transfer experiment setup.
As a low pK a weak base, KTZ may dissolve completely at fasted gastric pH but precipitate upon transit to the higher pH intestinal environment where it has much lower equilibrium solubility.Specifically, for this experiment the Nizoral tablet (200 mg) was placed in a 250 mL simulated gastric fluid (pH 2.0 FaSSGF-V2) compartment (donor phase), which was pumped into the 350 mL simulated intestinal fluid (pH 6.5  The modeling of the in vitro experiment outcomes was carried out using the Transfer Module of the SIVA toolkit (Figure 4).There are reports of transfer experiments with varying donor and acceptor fluid volumes, paddle speeds (hydrodynamics), media composition, transfer rates, and also the number of compartments. 37Recently, a transfer system with three compartments, representing the stomach, duodenum, and jejunum, was used to model the impact of disintegration on IR formulations of BCS I compounds. 39he flexible options within the SIVA module thus not only help to model these varying experimental setups under one platform but, in principle, can help scientists to design experiments.A database of library files defining the composition of widely used media (FaSSIF, FeSSIF, and simpler buffer systems) is provided which can be added to as required; in this study medium files were established representing donor (pH 2.0 FaSSGF) and acceptor (pH 6.5 FaSSIF-V2) media.
The pH and bile salt concentration within the donor compartment medium were assumed to remain static throughout the experiment (evaporation of the medium is considered to be negligible), and, as with the acceptor compartment, the medium is assumed to be well-stirred.The acceptor compartment pH was measured at the start (pH 6.50) and at the end of the complete transfer (pH 5.86) and then predicted at each sampling point dynamically using linear interpolation.The surfactant (in this case bile salt) concentration in the acceptor phase was recalculated at each time point during the simulations based on the volume of the donor phase transferred and the volume of the acceptor phase.Thus, thermodynamic solubility mediated by pH and [BS] were recalculated dynamically.However, measured pH and bile salt/ surfactant concentrations at regular, shorter sampling intervals would be useful in the future.
The average dissolved concentration profile obtained from the replicate transfer experiments (n = 3) was then fitted using  built-in parameter estimation (PE) tools to estimate the precipitation parameters of an empirical first-order model, namely, the critical supersaturation ratio (CSR), precipitation rate constant (PRC), and (an optional) secondary PRC (sPRC).The CSR specifies the maximum extent of supersaturation of a drug in solution and is the ratio of the critical supersaturation concentration (CSC, sometimes referred to as the Kinetic "Solubility") to the equilibrium solubility at a given pH and [BS] (region A, Figure 5).Precipitation can only start once the CSC is reached: this is one way in which the model is able to accommodate a lag time between the onset of supersaturated conditions and the onset of precipitation.The rate of precipitation is governed by the PRC (regions B and C, Figure 5).Where a single PRC is insufficient to capture the concentration time profile, the sPRC can be activated (region B only; i.e., when the dissolved concentration reaches or exceeds the CSC).Once the concentration drops below the CSC again, the PRC (alone) is applied until the concentration reaches the equilibrium solubility (region D).This model is not intended to capture the underlying processes determining the shape of the concentration time profile.In particular, there may be a variety of mechanisms determining the observed concentrations within region B including nucleation, a metastable liquid−liquid phase separation (LLPS), 40 and transfer of dissolved drug from the donor to the receptor compartment (and also out of the compartment were a 3 compartment system to be used).
Where the plateau region (B) concentration remains stable for an extended period, the sPRC may be activated and assigned a very low value effectively providing an additional lag time prior to precipitation.More mechanistic models could be developed (parametrized) to better capture these processes, but these would require additional experimental measurements to be made in the in vitro studies such as, for example, identification and characterization of LLPS, knowledge of amorphous solubility, detection of the onset of particle growth, monitoring of particle size distributions over time, etc., which were not available for this study.The KTZ intrinsic solubility (S 0 ), bile micelle partition coefficients (K m:w values), and tablet disintegration parameters estimated in the previous modeling steps were fixed at this stage.Particle size distribution (PSD) for the IR dosage forms is not available in the public domain.Hence PSD was assumed to be monodispersed and particle radius was manually fitted to 12 μm based on modeling of multiple in vitro dissolution profiles.The drug parameters not readily available experimentally were calculated using built-in models within the Simcyp Simulator (viz., monomer diffusion coefficients) as reported in Table 2.The particle density (ρ) was assigned a software default value within the model (ρ = 1.2 g/mL); sensitivity analysis was performed for this parameter, and within typical ranges encountered with API (1.0 to 1.3 g/mL) ρ does not have a significant impact on predicted profiles.
Modeling of Particle Dissolution.As described in the previous section, the dissolution of Nizoral tablets (200 mg) was tested in simulated gastric fluid where the solubility of KTZ was very high and disintegration of the drug dosage form was assumed to be rate limiting for dissolution.In order to assess the model and its parameters for handling fine particle dissolution (required for the in vivo simulations) the tablet dissolution data published by Galia et al. 41 was analyzed.The dissolution of Nizoral tablets in a medium simulating the small intestinal content in the fasted state (pH 6.5 FaSSIF) was used; the experiments were performed in the USP II paddle apparatus at 100 rpm with 500 mL of medium (Table 3).
The estimated parameters from previous experiments were used in the diffusion layer model (eq 4), and the model simulations were compared with extracted literature data.
where N is the number of particles (in a given particle size bin for polydispersed formulations), S is empirical scalar (default value 1), D eff is the effective diffusion coefficient, a(t) is particle radius at time t, h eff (t) is the effective diffusion layer thickness at time t, S surface (t) is the concentration of drug at the particle surface at time t, and C bulk (t) is the concentration of the drug in the bulk solution at time t.Integration of the Estimated Model Parameters within PBPK Framework.To evaluate the proposed IVIV_E approach, the model parameters evaluated and/or estimated in the various in vitro experiments (Table 1) (viz., solubility, disintegration/dissolution, and supersaturation/precipitation values) were integrated into a human population PBPK model.The model was used to simulate plasma concentration profiles in healthy Caucasian individuals, and the predicted dissolved and total duodenal concentrations were compared to those reported for 12 subjects studied in the clinic (Psachoulias et al. 42 ).The simulations are repeated with 10 different sets of 12 individuals in order to assess the impact of interindividual variability (sample size) on the interpretation of the outcomes.All simulations were performed using the Simcyp Population Based Simulator (Version 15 Release 1, Simcyp Ltd., Sheffield, U.K.).The simulator separates information based on the system (i.e., human body) from those of the drug and the study design parameters (e.g., dose, subject number, duration of study, fasted/fed state, etc.).The "System Data", in the form of population libraries built from extensive analyses of demographic, anatomic, genetic, and tissue-specific characteristics of a population, was used as a basis to generate virtual healthy subjects.The virtual trials were built to mimic as closely as possible the clinical study design (Psachoulias et al. 42 ) in terms of dose, study duration, proportion of males and females, age range, fluid intake with administered dose, and clinical sampling times (Table 4).
The model performance was evaluated by comparing the area under the total and dissolved duodenal concentration time profiles (AUC 0−t ), precipitated fraction, and overall shape of the duodenal profiles of the observation and prediction.The precipitated fraction in the simulated aspirate, π lumen , was estimated by eq 5 per Psachoulias et al. 42 The mean precipitated fraction was estimated using the average precipitated fractions up to 30 min post administration (n = 120) and then calculating the overall mean of these averages.
where C is the concentration of the dissolved drug and C t is the total amount of drug (dissolved and precipitated) per unit fluid volume.
Model Performance for the Prediction of Plasma Concentration−Time Profiles.Psachoulias et al. 42 evaluated the precipitation behavior of KTZ in GI luminal fluid samples; however, the clinical study did not involve assessing the systemic exposure of the drug in the same volunteers; dual duodenal and plasma sampling has been reported in recent study protocols such as with posaconazole, 43 which provides additional simultaneous reference concentrations for assessing PBPK model performance.Therefore, in order to further validate the model, additional human clinical studies (immediate release oral doses ranging from 200 to 400 mg) were identified from the published literature, simulated with the appropriate trial design, and compared via plasma concentration time profiles (Table 4).Parameters determined through the use of the stepwise, mechanistic modeling of in vitro pharmaceutical experiments along with physiochemical, protein and blood binding, permeability, and metabolism parameters of KTZ, collated from the literature, were integrated within the PBPK model (Table 2).However, with the limited information on the formulations used in these studies (dating from the period 1982−1986) and inconsistent disintegration results reported in vitro, 41,44−48 disintegration was assumed to be negligible in these additional simulation trials.As with the simulations of the study of Psachoulias et al., 42 ten independent virtual trials, each with the number of subjects used in the associated clinical study, were simulated in each case in order to make an assessment of the representativeness of a single trial in relation to interindividual variability.The predictive performance of the model was then assessed by comparing the predicted to the observed PK profiles reported in the literature studies. 49−51

■ RESULTS
Aqueous and Biorelevant Solubility Modeling.The aqueous solubility modeling confirmed the intrinsic solubility of KTZ as 0.0034 mg/mL while the SF was estimated to be 3404.The estimated aqueous solubility parameters were successfully used to predict the KTZ solubility in aqueous phosphate and Tris/Maleate buffer which were not used at the fitting stage (Figure 6A).Observed vs model predicted values were as follows: 0.012 mg/mL vs 0.0144 mg/mL in Tris/maleate pH 6.0 buffer, 0.00394 mg/mL vs 0.00384 mg/mL in phosphate pH 7.4 buffer, and 0.026 mg/mL vs 0.0036 mg/mL in Tris/ maleate pH 7.8 buffer.
The aqueous phase solubility parameters having been established, the bile-micelle partition coefficients were assessed using biorelevant solubility measured in FaSSGF-V2 (pH 3.24; pH 3.49), FaSSIF, and FeSSIF media.Bile-micelle partition coefficients predicted from the built-in log P o:w model were not sufficiently predictive when used in eq 1 to predict total solubility and were, therefore, estimated (Figure 6B); fitted log K m:w values were 4.838 and 4.124 for neutral and ionized monomers, respectively.The external predictability of the model was also confirmed using the solubility of the KTZ in mixture of the buffers: FaSSGF-V2 + FaSSIF-V2 (250 mL + 350 mL) with final pH of 5.77 and bile salt concentration of 1.75 mM and FaSSGF-V2 + FaSSIF-V2 (250 mL + 500 mL) with final pH of 5.96 and bile salt concentration of 2.026 mM.
Disintegration Model Parametrization.The diffusion layer model (DLM) alone could not correctly predict the dissolution of the tablet in the FaSSGF-V2 medium without accounting for the disintegration process (Figure 7).The results clearly underline the importance of accounting for disintegration which, while sometimes not significant in terms of PK outcomes in vivo, can significantly bias assessment of the DLM against in vitro experimental results.Fitting the release profile of the drug in the medium using a first-order disintegration function gave an F max of 100%, K d1 of 0.079 h −1 , and t lag of zero.These parameters were then used to characterize the disintegration of KTZ tablet in the donor compartment of the subsequent transfer experiment.
External Validation for the Assessment of the Particle Dissolution Model.To further assess the model performance we also evaluated its ability to predict in vitro FaSSIF dissolution data of 200 mg Nizoral tablets reported by Galia et al.; Figure 8 graphically illustrates the simulated and experimental profiles which are in good agreement (AFE = 1.01).The dissolution of the Nizoral tablet is solubility limited in vitro, and only 6.01% of the drug dissolved in the medium, which corresponds to an apparent KTZ solubility of ∼0.024 mg/mL in FaSSIF.This value is very close to the reported FaSSIF solubility of unformulated KTZ, viz., ∼ 0.022 ± 0.001 mg/mL.Hence, it seems reasonable to assume that formulation excipients did not have a significant impact on drug solubility in this study.Therefore, the API solubility parameters established previously are expected to be relevant for modeling the dissolution of the API particles in Nizoral IR tablets.
In Vitro Model Performance: DLM and Precipitation Model.The concentration profile of the dissolved KTZ in the acceptor phase of the transfer experiment was modeled using a first-order precipitation model (Figure 8).The observed and the predicted profiles were also compared against the theoretical concentration profiles predicted considering the concentration of dissolved KTZ transferred into the acceptor phase, the transfer rate, and thereby the dilution effect, but assuming "no precipitation".The maximum KTZ concentration reached and the corresponding equilibrium solubility of KTZ in the diluted acceptor phase medium (FaSSGF-V2:FaSSIF-V2, 250:350) were used to calculate CSR (7.7) and PRC (1.8 h −1 ) 31 and were a direct input into the SIVA model.The SIVA Toolkit was then used to estimate the sPRC (1.64 h −1 ) for KTZ.A fifth-order Runge−Kutta method was used to solve the ordinary differential equations with an integration error tolerance of 0.001.
The PBPK Model Performance.The KTZ parameters, assessed and, where required, estimated through modeling of in vitro experimental data, were incorporated into the PBPK model, which was used to predict the duodenal fluid concentration profiles in 120 individuals (10 trials with 12 volunteers as described above).The simulated values compared favorably to the clinical values (Figures 9A and 9B).The mean predicted AUC of the total duodenal (513.76 μg h mL −1 ) and dissolved duodenal concentration (421.90 μg h mL −1 ) profiles  of KTZ were comparable to the corresponding observed profile values of 520.42 μg h mL −1 and 434.68 μg h mL −1 , respectively.The overall shapes of the duodenal profiles observed and predicted were also similar.The mean precipitated fraction (π), calculated as a grand average at 30 min post administration, was found to be 0.15 compared to the in vivo value of 0.16 reported by Psachoulias et al. 42 Prediction of Systemic Plasma Concentration Profiles.Psachoulias et al. evaluated the precipitation attributes of KTZ in GI luminal fluid samples at 300 mg dose; however, their clinical study protocol did not measure the systemic exposure in parallel from same volunteers.The in vitro transfer experiments were conducted at 200 mg dose and compared with the luminal profile data 42 at 300 mg dose.Therefore, in order to further verify the suitability of the model, additional human clinical studies (oral doses ranging from 200 to 400 mg) were identified from the published literature and simulated with the appropriate trial design (Table 4).
The model reproduced the effect of supersaturation and precipitation on systemic exposure of the 200 mg IR tablet formulations very well (Table 5).The % prediction errors (% PE) for C max and AUC 0−t against corresponding observed clinical values were less than 25% across all tested studies.The ability of the model to predict the PK of a 400 mg IR tablet dose of KTZ (after Daneshmend et al. 64 ) using corresponding clearance values was also studied and found comparable to the clinical profiles (Figure 10).As the simulations were able to predict the observed PK data well for multiple dosage strengths, it suggests that an increase in dose "may" not have significant effect on the precipitation kinetics, probably, due to the lower precipitation and high permeation (predicted jejunal P eff = 3.76 × 10 −4 cm/s) of this API.Of course, there is an identifiability issue here which may warrant more in vitro and in vivo studies to establish the dose related changes in precipitation kinetics parameters.Additionally, it also can be noted that Psachoulias et al. 42 estimated the precipitated fractions at two different dose levels, 100 mg and 300 mg, which brackets the simulated dose of 200 mg in our study.The maximum precipitated fractions at 30 min were 0.11 ± 0.15% and 0.16 ± 0.26%, respectively, but with SD associated with the values' small study size (n = 12), the difference between both values is statistically insignificant.While there is consistent negative trend in % PE of kinetic parameters of KTZ across all the clinical studies, the error is relatively small (<25%) considering the known population variability of KTZ PK.It is important to note that the PBPK models were not optimized against the clinical studies described herein.Model predictions can of course be improved by optimizing (fitting) parameters to accurately match the in vivo clinical data where available.However, the main purpose of this study is to demonstrate, with examples, the use of stepwise bottom-up biopharmaceutic IVIV_E modeling approach, so no further optimization of the models was undertaken.
Dose proportionality studies (Huang et al. 51 ) suggest that CL/F decreases as dose is increased and hence the appropriate clearance values, obtained from an in-house established and validated compound database available within the Simcyp inhibitor library, were used to simulate the higher doses.Whether this nonlinearity is via a capacity-limited hepatic uptake/metabolic mechanism or is due to a change in the tissue distribution pattern of KTZ due to changes in tissue or plasma protein binding (or both or other mechanisms) at higher doses than 400 mg remains to be fully investigated. 51Hence, caution is recommended when extrapolating the developed model to simulate higher doses.

■ DISCUSSION
For immediate release formulations of orally dosed drugs there are several approaches implemented within PBPK models for determining or specifying in vivo dissolution rate.One approach is to directly use an in vitro dissolution profile (or profiles) as input to the simulations.This approach is most reasonable where dissolution rate is not sensitive to variability in physiological conditions (pH, bile salt concentrations, fluid volumes, etc.) in the gastrointestinal tract, which is most likely to be the case for BCS I drugs (highly soluble, highly permeable).However, for low solubility drugs (BCS II/IV) this is much less likely to be true unless an appropriate formulation strategy is applied.It is of interest to provide tools to be able to anticipate in vivo dissolution rate both in an average subject and in a population of individuals where there may be significant between-subject variability in PK linked wholly or partly to interindividual variability of dissolution rate and associated factors such as solubility, buffer capacity, fluid volumes, etc.In addition to interindividual variability there are regional differences in physiological parameters to which dissolution rate may be sensitive; exposure time of the drug product to a given regional environment is linked to gastric emptying rate and (regional) intestinal residence times which themselves exhibit significant interindividual variability (and interoccasion variability).The term "variability" refers to regional differences as well as between-subject differences in each of the 9 gut regions.
Thus, for a drug (product) sensitive to such considerations, a single dissolution profile measured in vitro under a single set of conditions cannot be representative of the range of conditions expected in vivo.One could of course generate an in vitro dissolution profile for the stomach, one or more regions of the small intestine, and the colon (if applicable), but these will have no link to intersubject variability.One approach to this problem is to perform the in vitro test under mean conditions and at the extremes expected in vivo.However, this method does not give   64 an indication of the likelihood of outcomes in a given set of individuals drawn from a population distribution.An alternative approach is to use mechanistic models of dissolution (and solubility) which can pick up the impact of variations in physiological parameters and propagate these PK outcomes across a range of individuals.The ADAM model uses an amended Wang and Flanagan equation (eq 4) to predict particle dissolution that allows incorporation of physiological variability in luminal pH, luminal fluid volume, residence time, bile salt concentration, etc., to which the drug/dosage form is exposed during GI transit.With the particle motion model (not used in this study but now available in Simcyp) h eff is linked to particle size, fluid velocity, fluid density, and D eff .Alternative methods such as the Z-factor 52 approach lump many of the parameters of eq 4 into a single parameter (Z) which always has to be estimated from the available dissolution data.As a result the Z-factor has no link (sensitivity) to the variability of physiological parameters, or, put another way, the model cannot extrapolate to different conditions.
It is possible with a series of in vitro experiments in appropriate media to estimate Z for each region, or several regions, of the GI tract and apply these values to in vivo simulations.However, this approach, while probably satisfactory for a representative (average individual), still does not address between-subject variability of gut physiological parameters which, particularly for BCS II and IV drugs, may result in significant variability in absorption rate and thence overall PK.In eq 4, S (the DLM scalar) is a multiplier which, if required, can be estimated through fitting, but for the reasons given we have retained the other mechanistic aspects of the diffusion model.An estimated S (or Z-factor) is of course a lumped parameter, and, while one might consider it to be a shape factor or a scalar to represent reduced surface area where particles aggregate, it may account for any mechanistic aspect not captured correctly by the model.Hence, the use of DLM scalar is not encouraged for biopharmaceutic IVIV_E purposes unless its necessity can be related to a mechanism missing from the model or where there is great confidence in the required parameters (PSD, D eff , etc.) and therefore no obvious reason to assign lack of model predictive performance to one or several of these parameters.
The performance, assumptions, and parametrization (e.g., particle size information) of such models can be assessed through first modeling in vitro experiments where conditions are known (or controlled) prior to applying such models within in vivo simulations with PBPK models.In principle this approach may mean that in vitro dissolution conditions do not have to be an exact match to in vivo conditions since the models are able to account for pH differences or hydrodynamic differences etc.However, this remains to be demonstrated and probably requires improved characterization of in vivo conditions particularly in relation to hydrodynamics, for example.
−55 Overall, the stepwise approach presented herein provides a mechanistic framework for handling in vitro solubility, disintegration, dissolution, and precipitation experiments, permitting the confirmation and/or estimation of drug-specific parameters (viz., salt limited solubility factors, bile micelle partition coefficients, supersaturation, and precipitation related values) required to simulate the in vivo behavior of the API.Performance assessment of these models directly within PBPK frameworks and their ability to accurately simulate intestinal drug dissolution/precipitation can be confounded by a multitude of factors affecting the drug absorption process.Consequently, assessment of mechanistic absorption models, and herein the accompanying IVIV_E strategy, using plasma concentration profiles and derived PK parameters as the comparators is challenging. 30The proposed approach can be used to assess the model performance for various in vitro experiments including the USP 2 and USP IV dissolution and transfer experiments and if required improve its prediction performance by measuring or estimating unknown or uncertain parameters.Although this process may be hindered by issues of parameter identifiability, this can in some instances be ameliorated through simultaneous fit across multiple different experiments.
In terms of the handling of supersaturation and precipitation, the described approach is semimechanistic, essentially mapping the characteristics of a concentration−time profile measured in the receiver (duodenal) compartment of an in vitro system to in vivo.Nonetheless, the use of a critical supersaturation concentration below which precipitation does not occur (unless precipitation has already begun) means that the variability in dissolved API concentration between individuals and in different regions of the GIT is considered.The variability built into the models in terms of gastric emptying times, duodenal (or other segment) transit time, fluid volumes, gut wall permeation rate, and other factors is accounted for when simulating the time-dependent concentration of API in the luminal fluids.The use of first-order rate constants to characterize precipitation rate has the disadvantage that the mass deposition (particle growth) rate is not sensitive to particle size and other factors such as hydrodynamics.On the other hand, use of a more mechanistic model of particle growth requires knowledge, or prediction, of the numbers and sizes of particles present, which is usually not experimentally available.Classical nucleation theory (CNT) is in principle able to predict nucleation rate but has some major limitations. 56,57hese include the assumptions of the capillary approximation and homogeneous nucleation together with the inherent inability to deal with the LLPS phenomenon which occurs when the amorphous solubility is exceeded. 58Erdemir et al. 57 have described in detail the limitations of CNT and have emphasized the need for further research; the nucleation of solids from solution does not proceed via the classical pathway, but instead follows more complex routes. 57Overall there are few reports of successful modeling of nucleation and precipitation within a PBPK framework 59−62 and there is not a standardized approach available in terms of either the in vitro experiments required or a suitable mechanistic framework for the in silico modeling.
Predictive models based purely on mechanistic rationales are certainly of great interest in a "bottom-up" IVIV_E approach.These advanced models, however, have an advantage over "empirical" models, provided that the required parameters are experimentally available or can be estimated using mechanistic frameworks such the SIVA toolkit.In terms of the clinical studies, against which to evaluate and potentially refine in vitro and in silico strategies, the increasing availability of drug concentrations measured in both gastrointestinal fluids and plasma is of great benefit 42,43 and certainly provides an opportunity to compare these empirical vs mechanistic approaches and their probable applications in PBPK modeling studies.
To a great extent, drug product development is still an empirical process and is often based on trial and error and can be highly dependent on the experience of the formulation scientist, with little input from predictive in vitro and in silico modeling tools. 63The proposed approach can help formulation scientists to simulate and better understand the effect of critical parameters on drug behavior.A systematic modeling approach may enable selection of the most informative in vitro experiments and help identify the optimum biorelevant conditions for the drug product, ultimately accelerating product development in a systematic way.Such an approach can also help formulation scientists to assess the impact of drug product characteristics such as particle size, drug precipitation parameters, etc. on pharmacokinetic properties, generally unavailable in the early product development stages.Moreover, this approach streamlines the designing of informative in vitro experiments while omitting redundant methods, potentially reducing the cost and time of product development.At the same time it is acknowledged that further developments are required in terms of mechanistic understanding and modeling of the impact of excipient effects upon solubility, dissolution, and supersaturation and precipitation properties.The tools described form the basis for such developments.
The approach described herein has performed reasonably well at simulating the in vivo concentrations in luminal fluids and for a separate set of studies the clinical plasma profiles with a range of different doses.The results of this study demonstrate that the proposed stepwise IVIV_E approach can help build confidence in the quality of the input parameters and assumptions of the mechanistic models used for in vivo simulations, with the ultimate aim to improve prediction performance of PBPK modeling tools.However, this integrated IVIV_E, a "bottom-up" approach within PBPK framework, is still in its infancy, and further studies are needed to improve the confidence in the methodology.

Figure 1 .
Figure 1.Schematic representation of the Advanced Dissolution, Absorption, and Metabolism (ADAM) model within the Simcyp population based simulator.

Figure 3 .
Figure 3.An integrated sequential in vitro modeling workflow followed within this research work.
FaSSIF-V2) compartment (acceptor phase) at a first-order rate constant of 0.123 min −1 .31The paddle rotation speed in both of the compartments was 100 rpm.The final pH, bile salt concentration, and volume in the acceptor phase vessel varied with the actual volume of donor phase transferred, and hence values were monitored at intervals during the experiment.These dynamic changes in model parameters (fluid volume, pH, and bile salt concentration) over time were accounted for as part of the mechanistic modeling of the transfer experiment results.Drug supersaturation and precipitation behavior in the acceptor compartment was modeled by analysis of the concentration versus time profile in the intestinal compartment, measured by a validated HPLC method.

Figure 4 .
Figure 4. Details of transfer experiment module built into SIVA.

Figure 5 .
Figure 5. Schematic representation of first-order precipitation model built within the ADAM model.

Figure 8 .
Figure 8. pH 6.5 FaSSIF dissolution data modeling using a mechanistic diffusion layer model (DLM) within the ADAM model.

Figure 9 .
Figure 9. (A) Mean predicted and observed duodenal dissolved ketoconazole concentrations (data for all 120 simulated virtual subjects also plotted for the reference).(B) Mean predicted and observed duodenal total ketoconazole concentrations (data for all 120 simulated virtual subjects also plotted for the reference).

Figure 10 .
Figure 10.Simulated versus observed mean plasma concentration−time profiles of KTZ after single oral dose of 200 mg and 400 mg of KTZ.Ten virtual trials were simulated based on trial design and age/sex after Daneshmend et al.64

Table 1 .
Aqueous and Biorelevant Solubility of KTZ a a Stated media pH values were not target pH values but were measured after the 24 h solubility experiment.Solubility is measured using pure (unformulated) API at 37 °C.

Table 2 .
Summary of Input Parameter Values Used for Ketoconazole Formulation Simulations in the Simcyp Simulator a ChEMBL Database (https://www.ebi.ac.uk/chembl/compound/inspect/CHEMBL75).KTZ enzyme inhibition (CYP2C8, CYP2C9, CYP3A4, and CYP3A5) parameters are also available as part of the Simcyp compound file, but this study does not consider DDIs, so the associated values have not been reported here.See also main text.b First-order precipitation model parameters: critical supersaturation ratio (CSR); precipitation rate constant (PRC) and secondary precipitation rate constant (sPRC).

Table 3 .
Summary of the Experimental Conditions Followed in in Vitro Dissolution Studies

Table 4 .
Clinical Trial Design Parameters Used in the Simulation Studies

Table 5 .
Observed and Predicted Drug Exposure PK Parameters for 200 mg IR Tablet Formulations of Ketoconazole Mean of individual volunteer PK parameters.b PK parameter values obtained from mean drug concentration vs time profile.c % PE = (predicted mean − observed mean)/(observed mean) × 100. a