Development of a Unified Dissolution and Precipitation Model and Its

Article pubs.acs.org/molecularpharmaceutics

Development of a Unified Dissolution and Precipitation Model and Its Use for the Prediction of Oral Drug Absorption Paulina Jakubiak, Björn Wagner, Hans Peter Grimm, Jeannine Petrig-Schaffland, Franz Schuler, and Rubén Alvarez-Sánchez* Roche Pharmaceutical Research and Early Development, Roche Innovation Center Basel, Basel, Switzerland S Supporting Information *

ABSTRACT: Drug absorption is a complex process involving dissolution and precipitation, along with other kinetic processes. The purpose of this work was to (1) establish an in vitro methodology to study dissolution and precipitation in early stages of drug development where low compound consumption and high throughput are necessary, (2) develop a mathematical model for a mechanistic explanation of generated in vitro dissolution and precipitation data, and (3) extrapolate in vitro data to in vivo situations using physiologically based models to predict oral drug absorption. Small-scale pH-shift studies were performed in biorelevant media to monitor the precipitation of a set of poorly soluble weak bases. After developing a dissolution−precipitation model from this data, it was integrated into a simplified, physiologically based absorption model to predict clinical pharmacokinetic profiles. The model helped explain the consequences of supersaturation behavior of compounds. The predicted human pharmacokinetic profiles closely aligned with the observed clinical data. In summary, we describe a novel approach combining experimental dissolution/precipitation methodology with a mechanistic model for the prediction of human drug absorption kinetics. The approach unifies the dissolution and precipitation theories and enables accurate predictions of in vivo oral absorption by means of physiologically based modeling. KEYWORDS: solubility, FaSSIF, FeSSIF, BCS, dissolution, precipitation, supersaturation, oral absorption, biorelevant media, simulated intestinal fluids, weak bases, in vitro−in vivo correlation, physiologically based pharmacokinetic modeling, formulation testing

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solubility is expected to be high.5,6 Ultimately, the in vitro data generated in solubility/dissolution experiments can be integrated in mathematical physiologically based pharmacokinetic models (PBPK) with the aim to quantitatively predict oral drug absorption.7 Following this paradigm it is possible to integrate other underlying processes such as drug permeation, transport, or metabolism as well as physiological differences across species or individuals.8 The quantitative understanding of drug dissolution has progressed substantially since the first dissolution model was published by Noyes and Whitney9 and refined by Nernst10 and Brunner.11 These advances have been thoroughly reviewed in the context of pharmaceutical research from both a historical12 and a mechanistic perspective.2 Intestinal precipitation of drugs is a process that has been investigated to a lesser extent and has yet to be adequately described. Precipitation upon entry into the intestine is a phenomenon mainly relevant for weak bases which can fully ionize in the stomach at low pH but are only partially ionized once they pass into the intestine at higher pH. Thus, the

INTRODUCTION Oral drug absorption results from the interplay of concurrent processes involving dissolution, partitioning into bile salt micelles, cellular permeation, and intestinal drug transport and metabolism. Besides physiological parameters such as gastrointestinal transit rates, luminal pH, effective intestinal surface area, and bile salt and phospholipid concentrations, the extent of drug absorption is strongly dependent on compound properties such as ionization, permeability, crystallinity, and solubility-related processes. For the latter, low solubility, slow dissolution rate, and rapid precipitation are all integral to drug research and development1 and can be the cause of costly and unsuccessful clinical trials. To streamline experimental efforts and minimize in vivo preclinical and clinical studies, in vitro test systems have been developed to characterize solubility and dissolution.2 Biorelevant media such as fasted (FaSSIF) and fed (FeSSIF) state simulated intestinal fluids have been used to account for certain physiological conditions.3 These media contain ingredients such as taurocholate and lecithin, which mimic human intestinal fluid and have been proven more relevant for prediction of drug absorption than simple, aqueous buffers.4 For this reason, performing solubility/dissolution assessments in biorelevant media is recommended for those compounds where the difference between aqueous and biorelevant © 2015 American Chemical Society

Received: Revised: Accepted: Published: 586

October 26, 2015 December 1, 2015 December 16, 2015 December 16, 2015 DOI: 10.1021/acs.molpharmaceut.5b00808 Mol. Pharmaceutics 2016, 13, 586−598

Article

Molecular Pharmaceutics

instrument (Sirius Analytical Instruments Ltd., Forest Row, U.K.) that allows real-time monitoring of the dissolved compound concentration by UV spectroscopy. Initially, the molar extinction coefficients and ionization constants of the investigated compounds were determined in blank buffer and FaSSIF media by UV-metric titration. The compounds were added to the experiment vials as 5 mM DMSO stock solutions and titrated between pH 2 and pH 12 in 1.5 mL of 0.15 M aqueous KCl or FaSSIF. The precipitation studies were performed in two consecutive phases at different pH (pH 2 and pH 6.5), simulating the conditions in gastric and fasted-state upper small intestinal environment, respectively. In brief, the compound of interest was first added as an acidic buffer or DMSO stock solution into the testing vial at different starting concentrations. Additional phosphate buffer at pH 2 was dispensed to reach the final volume of 2.6 mL. After 10 min of stirring, a 29-fold concentrated stock solution of FaSSIF medium and 0.5 M KOH were automatically added to ensure a final bile acid and phospholipid concentration and pH in agreement with the reported FaSSIF specifications.3 Similarly, the dissolution experiments in aqueous buffer pH 6.0 and in FaSSIF pH 6.5 were performed starting from 0.1 to 0.5 mg of powder and dispensing 2.7 mL of the respective medium to the vial. The medium was stirred at room temperature at a constant rate of 2000 rpm, and the UV spectra were recorded every 30 s over the duration of the experiment. Results from the standard calibration and sample measurements were processed using the Sirius T3 refinement software, resulting in concentration−time profiles for each experiment. Development of the Unified Dissolution−Precipitation Model. The kinetics of the compound dissolved (Ad) and solid (As) over time (t) is the result of three processes: dissolution, particle growth, and nucleation rates (eq 1).

passage to the intestine can lead to precipitation of the drug at a rate and to an extent that are highly dependent on the pH conditions in both the stomach and the intestine. This mechanism is known to be the cause of pharmacokinetic drug−drug interactions of weak bases with gastric pHmodulating agents such as proton pump inhibitors.13 Several in vitro models have been developed to recapitulate the highly dynamic gastric emptying process and the generation of supersaturated conditions. Gao et al.14 and Mathias et al.15 reported on a two-step pH-shift test under biorelevant conditions to investigate the effect of the pH transition on solubility of drugs and to identify correlations to clinical pharmacokinetic data. A well recognized paradigm is the transfer model introduced by Kostewicz et al.,16 which employs two connected vessels simulating the gastric and intestinal phases, respectively. Other reported models with increased complexity, aimed at capturing different physiological features by means of additional compartments and dynamic flows, have proven useful to understand the in vivo PK data.17−19 Besides the experimental challenges typically associated with precipitation experiments using traditional methods, another limit to progress in understanding of drug precipitation is the complexity of the involved microscopic mechanisms, namely, nucleation and particle growth. This complexity is reflected in crystallization theory,20,21 which, despite significant work,22−25 still remains challenging for a straightforward application in pharmaceutical research. Recent technical developments using real-time UV spectroscopy have allowed access to in vitro dissolution and precipitation data in a practical way. These small-scale methodologies use limited amounts of starting material and a dynamic control of pH and buffer composition, making them ideal to broadly explore the influence of biorelevant conditions on the dissolution and precipitation behavior of candidates at early drug-development stages.26−28 These miniaturized approaches have led to work demonstrating the in vivo relevance of the dissolution and precipitation processes.15,29,30 With the goal of achieving a quantitative prediction of oral drug absorption by means of in vitro testing combined with modeling approaches, we developed an experimental and mathematical framework to account for the concentration changes in cases when both precipitation and dissolution occur. The model was evaluated using in vitro dissolution and precipitation data generated for a set of poorly soluble weak bases. Ultimately, the proposed dissolution−precipitation model was incorporated into a simplified physiological absorption model and used to predict clinical plasma concentrations.

dA d dA =− s dt dt = dissolution − particle growth − nucleation

(1)

Such a system can be described in classical kinetic terms as a combination of different molecular elementary steps as shown in Figure 1. Under the assumption of a monodisperse solid with

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EXPERIMENTAL SECTION Chemicals. Dipyridamole, sodium phosphate monobasic monohydrate, sodium hydroxide, and sodium chloride were purchased from Sigma-Aldrich (St. Louis, MO). Bifonazole was purchased from Syntex (Buenos Aires, Argentina). Erlotinib HCl, aripiprazole, RO-A, and RO-B were synthesized at Roche. Titrisol concentrates of hydrochloric acid and potassium hydroxide were purchased from Merck Millipore (Darmstadt, Germany). FaSSIF was prepared starting from the instant SIF powder (Biorelevant.com, Croydon, U.K.) according to the protocol published by Kloefer et al.31 All other chemicals were of high purity or reagent grade. Dissolution and Precipitation Tests. The dissolution− precipitation experiments were performed on the Sirius T3

Figure 1. A schematic drawing to illustrate the elementary molecular steps involved in the proposed dissolution−precipitation model accounting for the interconversion of solid and dissolved compound. 587

DOI: 10.1021/acs.molpharmaceut.5b00808 Mol. Pharmaceutics 2016, 13, 586−598

Article

Molecular Pharmaceutics no change in particle size over time, the dissolution rate can be considered directly proportional to the amount of solid and expressed as dissolution rate = kdiss·A s

In cases where nucleation can be neglected (i.e., dissolution experiments as explained in the Supporting Information), eq 7 can be further simplified to eq 8, where only two parameters (Csol, implicit within SR, and kdiss) derived from classical dissolution experiments would be sufficient to characterize the system:

(2)

In this expression, kdiss represents the dissolution rate constant, a parameter that integrates particle and medium properties such as particle size, diffusivity, and diffusion layer thickness. Precipitation, in turn, is a more complex process involving two main molecular events: particle growth and particle nucleation. For a particle to grow, a discrete dissolved molecule needs to aggregate onto an already existing particle. Thus, the growth process will be directly proportional to both the amount of solid material (As) and the concentration of dissolved material (C). With kgrowth denoting the reaction rate of the solid particles with dissolved molecules and assuming monodispersity, the growth process is represented by particle growth rate = kgrowth·A s ·C

A ·(1 − SR) dC = kdiss· s dt V

Simplified Physiologically Based Model. Simulations of the intestinal absorption process were performed using a simplified physiologically based absorption model. The model structure consisted of two main compartments, stomach and small intestine, defined by the following differential equations accounting for the amount of compound present in the stomach (Astomach, assumed to be completely dissolved), the concentration of dissolved drug in the intestine (Cgut), and the amount of undissolved drug in intestine (As):

(3)

dA stomach = − emptyingstomach dt

The nucleation process refers to the spontaneous generation of an aggregate out of the dissolved compound. At a microscopic level, the nucleation can be thought of as a result of the simultaneous encounter of two or more molecules of solute (or of very small aggregates). Thus, nucleation can be expressed in kinetic terms as a polymolecular event: nucleation rate = k nuc·C α·V

Vgut·

emptyinggut/stomach = −k tr,gut/stomach·Agut/stomach

(10)

(11)

(12)

Dissolution and precipitation are formulated in analogy to eq 7: dissolution− precipitation ⎛ Cgut ⎞ = kdiss·A s ·⎜1 − ⎟ − Vgut·k nuc·Cgut α Csol ⎠ ⎝

(13)

The permeation involves the permeability-surface product for an idealized cylindrical intestine where Peff is the human jejunal effective permeability, r is the average intestinal radius, and Vgut is the intestinal fluid volume: 2 permeation = Peff · ·Vgut·Cgut r

At equilibrium in saturating conditions, the nucleation term becomes negligible (as shown post hoc in the Supporting Information). The equilibrium is then given by the balance of the particle growth and dissolution rates and is precisely the condition defining the solubility. From the model described above and after neglecting the nucleation rate, the solubility Csol is derived as

(14)

Peff was calculated in ADMET predictor version 7.2 (Simulation Plus, Lancaster, CA). The physiological parameters were derived from the Advanced CAT model available in GastroPlus version 9.0 (Simulation Plus, Lancaster, CA) for the human fasted physiology. In particular, r was calculated as the average intestinal radius for the small bowel (1.1 cm), Vgut was the sum of the intestinal fluid in the same tract (531 mL), and ktr,stomach and ktr,gut were also derived from the transit time estimates for the stomach (0.25 h) or the sum for the different small intestine segments (3.22 h). In cases where incomplete gastric dissolution was modeled (elevated gastric pH study), dissolution profiles in aqueous buffer at the relevant pH were generated and the data was used to estimate the gastric kdiss and Csol parameters. In such cases, eq 9 was converted into 2 differential equations accounting for

(6)

Equation 6 and the definition of supersaturation ratio (SR = C/Csol) can be incorporated into eq 5 to give eq 7: A ·(1 − SR) dC = kdiss· s − k nuc·C α dt V

= emptyingstomach − emptyinggut + dissolution

Emptying from stomach and gut is assumed to follow firstorder kinetics with emptying rate constants ktr,stomach and ktr,gut, respectively.

(5)

kdiss kgrowth

dt

dA s = −emptyinggut − dissolution + precipitation dt

(4)

dA dC = − s = kdiss· A s − kgrowth· A s · C − V · k nuc·C α dt dt

Csol =

dCgut

(9)

− precipitation − permeation

In this expression knuc is the nucleation rate constant, indicative of the degree of likelihood of aggregate formation upon collision of a certain number of discrete molecules of solute, α is the molecularity index, representing the average number of molecules involved in the formation of an embryonic nucleating particle, and V is the compartment volume in which the reactions take place. In the absence of pre-existing particles, nucleation is an essential process for precipitation to begin. Note that this process does not need to be numerically large in order to start precipitation, since tiny amounts of solid formed in this way will be amplified exponentially by the particle growth process outlined above. Bringing eqs 2−4 into eq 1 and substituting C = Ad/V, we obtain eq 5, describing the time profile of dissolved and solid material: V·

(8)

(7) 588


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Molecular Pharmaceutics Table 1. Physicochemical Properties of the Compounds Investigated compound

MW (g/mol)

aripiprazole bifonazole dipyridamole erlotinib (HCl) RO-A RO-B (HCl) a

pKa c

448.4 310.4 504.6 429.9 291.3 388.8

7.95 6.12c 6.12c 5.47c 3.36;c 5.36c 3.74;c 6.15c

LogD7.4a

LogPb

PSA (Å2)b

Peff (10−4 cm/s)b

blood to plasma concn ratiob

4.0 ND 3.8 2.9 3.5 4.7

5.2 4.9 3.0 3.1 3.8 3.9

44.8 17.8 145.0 74.7 30.7 77.0

3.12 7.40 0.45 2.72 7.15 5.41

1.00 0.85 0.98 0.71 0.71 0.73

Method as described in Wagner et al.51 bCalculated in ADMET predictor version 7.2. cBasic pKa value, determined by UV-metric titration.

fitted to a two-compartment disposition model coupled to a first-order absorption compartment. To obtain the right systemic parameters, the dose included in the fitting was corrected by the oral bioavailability. The absorption rate constant of the resulting PK model was subsequently replaced by the input function of the physiologically based absorption model to simulate the corresponding PK profiles. The normal gastric pH group was modeled applying the parameters derived from the in vitro pH-shift precipitation study. The gastric compartment of the elevated gastric pH group was modeled using dissolution data in buffer at pH 6. As for the intestine, given the fact that the dissolution− precipitation model parameters identified from the pH-shift tests average the dissolution of particles of different sizes starting from the very smallest nucleation particles, we anticipated a difference of kdiss and Csol values between particles starting from solid and particles generated from a supersaturated milieu. To account for these differences, dissolution data in FaSSIF pH 6.5 were used to model the intestinal compartment of the elevated gastric pH group (data and parameters shown in the Supporting Information).

dissolved and undissolved compound, similarly as for the intestinal compartment. The fraction of compound absorbed (Fabs) can be defined as Fabs =

2·Peff ·Vgut A abs · = D r·D

∫0

∞

Cgut·dt

(15)

where Aabs is the amount absorbed and D is the administered dose. As precipitated compound cannot be absorbed, the fraction of compound precipitated (Fppt) for the studies assuming full gastric dissolution can be defined as the amount of solid collected after passage through the intestine: Fppt =

∫0

∞

k tr,gut·A s ·dt

(16)

Modeling Methodology. The dissolution−precipitation modeling of the in vitro data and the physiologically based absorption modeling were performed using Berkeley Madonna software version 8.3.18. The model parameters were estimated by using the curve-fitting procedure in the software. The integration step size was fixed at 0.001 min, and the Rosenbrock “stiff” method was used as the integration method in all the models tested. The precipitation−dissolution profiles generated at different concentrations were fitted simultaneously to provide a single set of parameters describing the complete data set for a single compound in the corresponding buffer. The codes developed for main models used in this work are listed in the Supporting Information. Calculation of Human Fraction Absorbed. Fraction absorbed values were estimated for the drugs where sufficient pharmacokinetic data existed. Oral bioavailability (F) was first estimated either from existing intravenous and oral PK data32,33 or from oral data assuming equal body weight normalized volume of distribution (Vss) between human and rat.34 In the latter case, Vss/F was estimated by noncompartmental analysis of the clinical oral PK study and Vss was assumed to be the same as reported for the rat.35 Assuming that all systemic clearance was hepatic, the plasma clearance (CL) was used to calculate the fraction escaping the hepatic first-pass (Fh = 1 − (CL/R)/Qh), where Qh, the hepatic blood flow, was considered to be 96 L/h (GastroPlus version 9.0) and the blood to plasma ratio (R) was predicted using ADMET predictor. In the case where intravenous data was not available, this term was estimated from oral data (CL/F) using the previously estimated bioavailability. Finally, the fraction absorbed (Fabs) was estimated from the oral bioavailability (F) and the fraction escaping the hepatic first-pass assuming that no intestinal first-pass occurred (Fabs = F/Fh). Pharmacokinetic Modeling of Elevated Gastric pH Studies for Erlotinib. Pharmacokinetic data for erlotinib in elevated gastric pH conditions were obtained from a published study.36 The PK profile of the normal gastric pH group was

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RESULTS pH-Shift Dissolution and Precipitation Tests. To study the intestinal precipitation of drugs, a set of weak bases was selected based on pilot in vitro studies showing their ability to precipitate without significant generation of light scattering. The compound set and main physicochemical properties are listed in Table 1. The studies were performed in a pH-shift setting from pH 2 to 6.5, mimicking the gastrointestinal conditions. Figure 2 illustrates some characteristic concentration−time profiles for two different compounds. The full data set is included as Supporting Information (Figure S2). The resulting profiles exhibited common characteristics: (1) the observed precipitation rates were consistently faster at higher supersaturation levels, (2) a latency time was frequently observed before precipitation started to occur, and (3) most tests led to a final concentration corresponding to the equilibrium solubility with few exceptions observed for conditions where the degree of supersaturation was very low. In those cases, the concentration remained constantly above the equilibrium solubility for the time of the study. Although this supersaturation state could be maintained for a very long time, additional experiments showed that, upon storage over weeks or addition of silica particles, the equilibrium solubility was also reached for these samples (data not shown). The precipitation profiles in FaSSIF and aqueous buffer were different, but the curves showed identical patterns, suggesting a precipitation behavior governed by the same processes and only differing in rate constants in both media. Modeling of in Vitro Profiles. The precipitation data generated for the compound set was modeled using eq 7, and 589


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Figure 2. Precipitation profiles from in vitro pH-shift tests (pH 6.5 phase, continuous UV recording). Dipyridamole in blank buffer (A) and FaSSIF (B); erlotinib in blank buffer (C) and FaSSIF (D). Lines represent the different concentrations tested.

Table 2. Identified Model Parameters from Eq 7 Obtained by Fitting pH-Shift Data in Aqueous Buffer and in FaSSIF at pH 6.5 compound aripiprazole bifonazole dipyridamole erlotinib (HCl) RO-A RO-B (HCl)

medium buffer FaSSIF buffer FaSSIF buffer FaSSIF buffer FaSSIF buffer FaSSIF buffer FaSSIF

knuc (1/min·μMα−1)

kdiss (1/min) 1.85 1.64 1.15 7.23 7.40 5.60 1.76 3.30 5.30 1.10 2.52 1.98

× × × × × × × × × × × ×

−2

9.12 3.82 3.97 6.36 7.52 6.57 7.54 3.26 2.09 8.45 5.45 6.91

10 10−1 10−2 10−2 10−2 10−2 10−1 10−1 10−2 10−1 10−3 10−2

the model parameters identified for the different compounds and conditions are listed in Table 2. As shown in Figure 3 for some examples and in Figure S3 for the complete compound set, the model described very well the experimental data, recapitulating the main observed features, namely, concentration-dependent precipitation rates, latency times, and sustained supersaturation at low concentrations. The identified model parameters varied across investigated compounds and dissolution media. Analysis of the resulting parameter estimates for the different conditions and compounds led to the conclusion that the particles dissolve faster in FaSSIF compared to aqueous buffer, with the exception of dipyridamole. The nucleation term of eq 7 showed a higher contribution and a lower molecularity in blank buffer compared to FaSSIF. This observation suggests that the initial nucleation particles in FaSSIF are either less frequently formed or more unstable possibly due to the presence of micelles. Precipitation Induction Studies. To further strengthen the understanding of the proposed model and to substantiate

× × × × × × × × × × × ×

−35

10 10−61 10−14 10−82 10−17 10−32 10−14 10−15 10−21 10−83 10−3 10−23

α

Csol (μM)

17.0 22.1 10.0 30.1 7.9 12.4 6.0 6.0 8.0 33.8 1.0 8.3

24 165 2 65 28 100 13 60 26 51 1 40

the hypothesis that the precipitation rate does not depend solely on the supersaturation ratio, additional experiments were conducted where the supersaturation of dipyridamole was induced by pH-shift and the precipitation kinetics was followed after addition of increasing solid amounts. As seen in Figure 4, for experiments showing identical degree of supersaturation, the rate of precipitation was dose-dependently accelerated by addition of a solid. The figure also shows how the dissolution− precipitation model could explain this data. This data set underlines the need to take into account not only the concentration of compound in solution but also the amount of solid when studying the precipitation kinetics. Extension of the Model Applicability Using Published Transfer Model Data. The ability of the model to explain other, more complex in vitro settings was addressed by modeling the data published by Kostewicz in the transfer model.16 The proposed model was a simple adaptation of the combined dissolution−precipitation model accounting for the specific experimental conditions, in particular, transfer rates, 590


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Figure 3. Experimental data and dissolution−precipitation model fits described by eq 7. Dipyridamole in blank buffer (A) and FaSSIF (B); erlotinib in blank buffer (C); erlotinib in FaSSIF (D). Solid lines represent the experimental data, and red dashed lines represent the model fits. Remaining data set disclosed in Supporting Information.

drug concentration rises in the intestine, the precipitation process is sharply triggered, resulting in a fast transition to the solid state and a decrease of the dissolved concentration down to the equilibrium solubility, at which point the absorption rate decreases. In contrast to erlotinib, the predicted intestinal concentrations of dipyridamole and aripiprazole at clinical doses were shown as insufficient to promote the formation of significant amounts of precipitate. Absorption Model Sensitivity Analysis. We performed a sensitivity analysis where the fraction absorbed was simulated at varying administered doses. The outcome of this analysis, depicted in Figure 9, shows how the precipitation behavior and properties of different drugs require different doses before precipitation compromises the fraction absorbed, and how this effect would relate to the total amount of drug absorbed. In the cases considered, it was observed that increasing doses would lead to an increase in the fraction precipitated and a concomitant decline in the fraction absorbed. However, the total amount absorbed was greater as doses increased. As different gut fluid volumes have been reported in literature, we also conducted a sensitivity analysis to ascertain how changes in the intestinal fluid volume would impact the outcome of the predictions. As seen in Figure 9 for dipyridamole and erlotinib, a decrease in the volume of

vessel volume changes as result of the transfer process, and initial dipyridamole concentration (model disclosed as Supporting Information). We kept the exact set of parameters identified in our pH-shift studies in FaSSIF and directly overlaid the predicted curves with the extracted literature data (Figure 5). Despite the implicit assumption made that the FaSSIF dilution effect during the transfer process does not alter the buffer composition, the model accurately explained the reported data. Assessment of the in Vivo Relevance of the Proposed Model To Predict Fraction Absorbed. In order to evaluate the in vivo relevance and applicability of the dissolution− precipitation model we developed a schematic physiologically based absorption model depicted in Figure 6 and described in the Experimental Section. When used to simulate the absorption of drugs with available clinical PK data, i.e., dipyridamole, erlotinib, and aripiprazole, the model allowed for a good prediction of the fraction absorbed (Figure 7). It also provided insights into the coexistence of precipitated and dissolved material within the small intestine at clinical doses. As shown in Figure 8, a clinical 150 mg dose of erlotinib was sufficient to induce precipitation. In such a scenario, erlotinib enters the intestinal compartment in a fully dissolved state, resulting in a rapid increase of the compound absorbed. As the 591


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Figure 6. Structure of the physiologically based model used for the prediction of in vivo absorption. The model is described by eqs 9, 10, and 11 and parametrized with physiological values derived from the human fasted ACAT model from Gastroplus as indicated in the Experimental Section. Figure 4. Concentration versus time profile in pH-shift induced supersaturated conditions for dipyridamole in FaSSIF. The black lines show the precipitation profiles without the addition of the undissolved powder at two different supersaturation levels. The green and blue lines show the precipitation profiles after spiking the samples with different amounts of solid material. The legend indicates the amounts of the added material for the respective experiment.

effect results from the lower volume, which leads to a higher extent of supersaturation and thus accelerates the precipitation process. Assessment of the in Vivo Relevance of the Proposed Model To Predict PK Profiles. The model was further used to simulate available clinical data for erlotinib and dipyridamole. The systemic PK parameters were independently fitted (Table 3), and the combined absorption−systemic model was used to simulate a set of clinical studies, involving in the case of

intestinal fluids leads to a decrease in the fraction absorbed concomitant to an increase in the fraction precipitated. This

Figure 5. In vitro dissolution data of dipyridamole in FaSSIF reported by Kostewicz et al.16 modeled with the proposed dissolution−precipitation model. The dots represent the published experimental results at different flow rates: 0.5 mL/min (A), 2 mL/min (B), 4 mL/min (C), and 9 mL/min (D). The solid lines describe the simulation output based on data presented in Table 2. 592


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state of the art dissolution platform28 with testing conditions similar to those described elsewhere.14,15 This miniaturized experimental setting is well-suited to profile drug candidates in early stages as it offers the significant advantages of low compound consumption, automation, and technical flexibility to address a variety of mechanistic questions, frequently arising in research programs. In addition, the system allows for realtime monitoring of the compound concentration, eliminating any need for the off-line analysis and providing straightforward and rich data outputs. The main technical limitations while studying the supersaturating concentrations were the saturation of the UV signal at high concentrations, light scattering due to the formation of the precipitate, or very fast precipitation rates leading to immediate equilibrium solubility concentrations. These technical issues limited the precipitation testing to a reduced set of compounds. The experiments were run under nonsink conditions and, thus, do not capture the permeation process. Even if the system allows for this additional level of convolution by employing an organic phase on top of the aqueous compartment,37 we opted for a simple experimental setting to obtain data exclusively driven by precipitation and dissolution processes. The resulting precipitation profiles generated for a set of weak bases showed a well-defined set of phases: (1) a supersaturation latency phase during which the compound stayed in solution at a constant, supersaturated concentration, (2) a precipitation phase, where the compound disappeared from solution at different rates dependent on the initial supersaturation state, and (3) an equilibration phase, where the concentration of compound in solution attained the corresponding equilibrium solubility (Figure 1). The congruence of this process across the studied compounds encouraged us to model this phenomenon with the goal of achieving a quantitative understanding that would ultimately allow the description of these processes in more complex situations. We approached this modeling effort from a purely mechanistic viewpoint by rationalizing which key molecular events drive the interconversion of solid particles and dissolved molecules. To describe the observations, three different events were considered: (1) dissolution of solid particles, mainly dependent on the amount of solid, (2) particle growth, dependent on both amount of solid and concentration

Figure 7. Observed and predicted values for the fraction absorbed in vivo using the simplified absorption model. Observed fraction absorbed values were derived as explained in the Experimental Section.

erlotinib alteration of the gastric pH.36 As shown in Figure 10, the model accurately described the absorption phase of the plasma profiles, while differentiating the PK profile of the groups with elevated and normal gastric pH for erlotinib. Similarly, dipyridamole PK was modeled and showed a good agreement with the reported PK profile.34

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DISCUSSION Good understanding of a drug candidate’s biopharmaceutical properties and how these attributes define the in vivo performance is crucial to successful drug development and remains at the core of a quality-by-design strategy. When explored early enough, this information can help in (1) understanding and explaining the absorption profile observed in animal PK studies as a first step to understanding human outcome, (2) increasing the confidence when extrapolating from low dose PK studies to first high dose safety studies, (3) increasing the accuracy in first human PK predictions, (4) identifying and characterizing potential clinical issues such as food effects, gastric pH effects, or insufficient maximal absorbable dose, and (5) supporting the selection of the appropriate formulation vehicle or salt forms. To bring biopharmaceutical characterization to early stages of drug research, we have developed in vitro methodologies to assess dissolution and precipitation processes. We combined a

Figure 8. Simulated intestinal amount of different compound pools as a function of time. Dipyridamole at the dose of 75 mg (A) and erlotinib at the dose of 150 mg (B). Solid lines represent the amount dissolved, dashed lines represent the amount undissolved, and the dotted lines indicate the amount of absorbed drug. 593


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Figure 9. Sensitivity analysis showing the influence of the administered dose and intestinal fluid volume (Vgut) on the fraction absorbed, fraction precipitated, and amount absorbed. The red squares represent the amount absorbed, the blue triangles show the fraction absorbed, and the black circles indicate the fraction precipitated for different doses or intestinal fluid volumes for dipyridamole (A and D), erlotinib (B and E), and aripiprazole (C and F).

from other previous attempts to quantify precipitation7,28,38−40 is that particle growth is considered to be a second-order kinetic process and thus it depends not only on the compound concentration but also on the amount of solid particles. This consideration allowed for a good description of the precipitation phases where it can clearly be noticed that the rates of precipitation do not follow first-order kinetics. This influence of the amount of both dissolved and undissolved pools is evident in the precipitation studies performed for dipyridamole where the precipitation rates were found to be different at the same supersaturation levels for different amounts of spiked solid material (Figure 4). When extrapolating to an in vivo setting, this observation underlines the importance of quantifying the amount of undissolved compound transferred from the stomach into the intestine as the solid particles may act as a precipitation catalyst. A common way to describe intestinal precipitation is by applying a first-order precipitation model. In such a model the rate of precipitation depends on the difference between the dissolved drug concentration and the solubility limit. Although the first-order model can be useful to describe certain in vivo

Table 3. Systemic PK Parameters for Erlotinib and Dipyridamole Used for the Simulation of the PK Dataa systemic PK param −1

k10 (min ) k12 (min−1) k21 (min−1) Vcb (mL) F (%) Fh (%)

dipyridamole −2

2.82 × 10 5.97 × 10−2 1.33 × 10−3 2371 45 94

erlotinib 1.48 × 10−3 3.25 × 10−3 2.17 × 10−3 63283 59 95

a

Fitting for erlotinib was performed on the control group showing normal gastric pH. Dose was corrected by the estimated oral bioavailability. bVc = volume of the central compartment.

of solute, and (3) particle nucleation, a sporadic polymolecular event that leads to the formation of a solid particle out of discrete molecules and that depends on the concentration of dissolved material. The proposed model (eq 7) managed to describe the experimental precipitation data accurately, recapitulating the different phases and profile shapes for a wide set of experimental conditions and all compounds investigated. One key feature that distinguishes this model 594


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Figure 10. Experimental and simulated plasma concentration−time profiles for erlotinib and dipyridamole. (A) Erlotinib administered as a single oral dose of 150 mg to healthy volunteers cotreated with or without the proton pump inhibitor omeprazole (40 mg). The triangles and squares represent the reported data36 for the normal and for the elevated gastric pH group, respectively. (B) The dots represent the results from a clinical study of a single oral dose of 75 mg dipyridamole to healthy volunteers.34 The solid lines represent the simulations applying the proposed model.

conditions, it shows certain limitations when describing the in vitro data: (1) It fails to capture the delayed onset of precipitation observed in vitro, which can be of physiological relevance in some instances where the compound does not precipitate at slightly supersaturated conditions. (2) The model does not consider the existing amount of solid that can catalyze the precipitation process and have great influence in vivo in cases where incomplete dissolution has occurred in the stomach. (3) Different precipitation times need to be proposed for different experimental conditions (concentrations or transfer rates). Ultimately, an arbitrary selection of the rate constant needs to be done for in vivo extrapolation, limiting the prospective application of the model. (4) Given its linear nature, the first-order model does not seem a priori suitable for explaining nonlinear precipitation effects, important to describe the dose dependency. These points are further illustrated in the Supporting Information. In contrast, the proposed dissolution−precipitation model, based on a purely mechanistic rationale, allows a complete description of the in vitro data under a variety of experimental settings such as dissolution and dose-dependent precipitation as well as situations when the precipitation is induced by the undissolved compound. All these conditions can be captured using a single set of parameters defined for a specific drug in a specific buffer system. To check the scope of applicability of the model, we explored its ability to explain data from another reported in vitro model: the transfer model. This setting developed by Kostewicz et al.16 stands as a well-established tool for the study of compound precipitation in intestinal conditions.38,39 As shown in Figure 5, our model provided an accurate description of the published data. The transfer model was previously modeled by Sugano24 by means of the classical nucleation theory and later by Arnold et al.25 using a kinetic model. In the latter model, the growth term was found to be higher than first-order, however, the term was considered to be dependent only on the dissolved material, omitting the influence of the amount of undissolved compound. Their model provided an excellent fit of the in vitro data generated in the transfer model. However, the fit involved six different parameters and four different sets of equations to be applied at the different phases of the

experiment. Furthermore, the set of parameters was specific for each experiment at a specific transfer rate. The model proposed here describes all experimental phases using two differential equations involving four parameters. Furthermore, the model is able to explain the data generated in other settings such as the transfer model at any postulated transfer rate (Figure 5). Its mechanistic nature and simplicity make it attractive to describe concentration time profiles for dissolution and precipitation experiments. Even though our model succeeds in explaining the in vitro data, it includes in its formulation some assumptions and simplifications. Particularly, the system is assumed to be monodisperse and particle growth and dissolution do not influence the particle surface to mass ratio. In reality, the three different microscopic events are composed of a large set of elementary events, determined by the heterogeneity of the particle population. Each elementary event would be defined by a parameter set and would influence the process to an extent proportional to the abundance of such particle population. As an example, the dissolution rate constant kdiss is understandably different for a large API particle where the particle surface to mass ratio is low compared to a nucleation particle where the surface/mass ratio is large. We found that these model simplifications are a necessary step to provide a comprehensible conceptual framework that minimizes the number of model parameters and brings computational needs to a manageable level, while still accurately describing the data. Having reached a strong predictability for the in vitro supersaturation kinetics for a set of weak bases, we then studied how the involved processes would integrate in a more complex physiological setting. To achieve this, we developed a simplified physiologically based absorption model inspired by the work previously developed by Nicolaides et al.41 and Takano et al.30 (Figure 6). These schematic, compartmental-based absorption models can be considered simplified versions of more elaborated and comprehensive models available as commercial software solutions and have shown their practicality in the prediction of different drugs.7,38,39 The integration of the combined dissolution−precipitation model in the physiologically based absorption model allowed for a very convincing prediction of the fraction absorbed for the three drugs 595


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required to translate them into in vivo relevant parameters. Similar to other work,14,30 the approach presented here relies instead on reducing the complexity of the test system to an extent where the processes of interest can be directly measured, together with its integration within a robust modeling framework able to capture the in vivo complexities. We believe that this approach can help in streamlining experimental efforts and allow a straightforward extrapolation of the data to various in vivo conditions. Such a paradigm can address absorption issues and support a rational and efficient biopharmaceutical strategy.

investigated (Figure 7). The model also suggested that, at clinical doses, dipyridamole and aripiprazole remained fully in solution, whereas erlotinib formed a precipitate within the intestine. This observation holds true for dipyridamole, where studies performed on intestinal aspirates suggested no or very limited amount of solid formed.42 Fraction absorbed represents a suitable, but not unique, indicator to assess the validity of a prediction model and can be directly related to an AUC term. Ultimately, a suitable absorption model should also be able to capture the absorption kinetics related to the plasma Cmax. To address this latter aspect, we coupled our simplified absorption model to a twocompartment PK model and tested it against clinical data for dipyridamole and erlotinib. Model and data provided a good explanation of relative bioavailability differences in conditions of elevated gastric pH compared to normal conditions for erlotinib and managed to describe well the absorption part of dipyridamole plasma profile (Figure 10). It is expected that as the dose increases, the intestinal concentration of the compound rises and, at a certain point, the resulting supersaturating conditions can lead to a fast and critical precipitation event. To address this scenario we performed a sensitivity analysis where the fraction absorbed was simulated at varying administered doses (Figure 9). This type of sensitivity analysis can be very useful when anticipating absorption limits in clinical studies. On one hand, it defines the anticipated degree of dose linearity and dose scalability, useful to guide ascending dose studies. It can also help in designing alternative dosing schedules in cases where precipitation might become limiting to the amount absorbed or may increase the variability in exposure. The simplified absorption model was parametrized by extracting values from the more comprehensive ACAT human fasted state model available in the commercial software GastroPlus, which has proven successful in predicting the intestinal absorption of many drugs. Nevertheless, being aware of different reports for physiological values, in particular for the volume of intestinal fluids,43−45,39 we analyzed the influence of the intestinal fluid volume on fraction absorbed (Figure 9). This sensitivity analysis confirmed the strong impact of this parameter on the modeling outcome and highlighted the importance of the choice of the appropriate physiological parameter set when including the proposed dissolution− precipitation model into PBPK models. Prediction of oral absorption continues to be an important focus in the pharmaceutical industry. It is expected that, as understanding of this process progresses, this can directly contribute to reducing the attrition rate and simplifying clinical development by extending the application of BCS biowaivers, reducing the need for extensive bioequivalence studies.46 One strategy to bridge the in vitro testing to the in vivo conditions has been to increase the degree of complexity of the different experimental systems to capture different features of the gastrointestinal physiology. As a result, different methodologies have been proposed including transfer methods,16,47,48 sink conditions simulating drug permeation49,50 or full GI tract models.19 The different models can often explain the in vivo data; however their degree of complexity makes them experimentally demanding and limits the scope of conditions that can be explored. They may be suitable for stages where API availability is not a constraint and substantial experimental resources can be spent on a single molecule. Also, their readouts are often qualitative and further modeling work is

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CONCLUSIONS This work summarizes the combination of a simple, low consumption, automated dissolution−precipitation test with a mechanistically derived mathematical model accounting for the different microscopic events occurring in a precipitating solution. The proposed model unifies the dissolution and precipitation theories and elucidates the concentration−time profiles of compounds subjected to complex supersaturation conditions. The model was integrated into a simplified physiologically based absorption model and could predict the fraction absorbed along with pharmacokinetic profile of a set of drugs under different physiological conditions. Such an approach can be integrated into existing PBPK tools and support the prediction of the absorption of molecules exhibiting complex behaviors, such as weak bases. This strategy brings us closer to achieving the goal of increasing the probability of technical success of drug candidates.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.molpharmaceut.5b00808. Nucleation rate studies, precipitation and dissolution profiles, modeling of precipitation profiles, and Berkeley Madonna model codes (PDF)

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AUTHOR INFORMATION

Corresponding Author

*F. Hoffmann-La Roche Ltd, Grenzacherstrasse 124, 4070 Basel, Switzerland. Phone: +41 61 688 1941. Fax: +41 61 688 29 08. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We wish to express our sincere thanks to many colleagues, among them Birgit Schröder, Sabine Pita, and Michael Gertz (Roche) as well as Rebeca Ruiz (Sirius Analytical) for their technical assistance. We highly appreciate the support and discussions within the Roche Biopharmaceutics Working Group and all the valuable comments and manuscript revisions provided by Sara Belli (Roche), Koji Shiraki, and Noriyuki Takata (Chugai Pharmaceutical) as well as Jon Kyle Bodnar. We would especially like to acknowledge Neil Parrott (Roche) and Viera Lukacova (Simulations Plus) for their encouragement and the very stimulating discussions. 596


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ABBREVIATIONS USED API, active pharmaceutical ingredient; AUC, area under the curve; BCS, Biopharmaceutics Classification System; Cmax, maximal plasma concentration; FaSSIF, fasted state simulated intestinal fluid; FeSSIF, fed state simulated intestinal fluid; LogD, octanol/water distribution coefficient at a defined pH; PBPK modeling, physiologically based pharmacokinetic modeling; PK, pharmacokinetics; pKa, ionization constant

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Development of a Unified Dissolution and Precipitation Model and Its

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