Evolution of Supersaturation of Amorphous Pharmaceuticals: The

Article pubs.acs.org/molecularpharmaceutics

Evolution of Supersaturation of Amorphous Pharmaceuticals: The Effect of Rate of Supersaturation Generation Dajun D. Sun and Ping I. Lee* Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, Toronto, Ontario M5S 3M2, Canada ABSTRACT: The combination of a rapidly dissolving and supersaturating “spring” with a precipitation retarding “parachute” has often been pursued as an effective formulation strategy for amorphous solid dispersions (ASDs) to enhance the rate and extent of oral absorption. However, the interplay between these two rate processes in achieving and maintaining supersaturation remains inadequately understood, and the effect of rate of supersaturation buildup on the overall time evolution of supersaturation during the dissolution of amorphous solids has not been explored. The objective of this study is to investigate the effect of supersaturation generation rate on the resulting kinetic solubility profiles of amorphous pharmaceuticals and to delineate the evolution of supersaturation from a mechanistic viewpoint. Experimental concentration− time curves under varying rates of supersaturation generation and recrystallization for model drugs, indomethacin (IND), naproxen (NAP) and piroxicam (PIR), were generated from infusing dissolved drug (e.g., in ethanol) into the dissolution medium and compared with that predicted from a comprehensive mechanistic model based on the classical nucleation theory taking into account both the particle growth and ripening processes. In the absence of any dissolved polymer to inhibit drug precipitation, both our experimental and predicted results show that the maximum achievable supersaturation (i.e., kinetic solubility) of the amorphous solids increases, the time to reach maximum decreases, and the rate of concentration decline in the de-supersaturation phase increases, with increasing rate of supersaturation generation (i.e., dissolution rate). Our mechanistic model also predicts the existence of an optimal supersaturation rate which maximizes the area under the curve (AUC) of the kinetic solubility concentration−time profile, which agrees well with experimental data. In the presence of a dissolved polymer from ASD dissolution, these observed trends also hold true except the de-supersaturation phase is more extended due to the crystallization inhibition effect. Since the observed kinetic solubility of nonequilibrium amorphous solids depends on the rate of supersaturation generation, our results also highlight the underlying difficulty in determining a reproducible solubility advantage for amorphous solids. KEYWORDS: supersaturation rate, kinetic solubility, crystallization, amorphous solid dispersion, poorly water-soluble drug

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INTRODUCTION One major challenge in drug development has been the growing number of poorly water-soluble discovery candidates being generated, which often lead to suboptimal bioavailability thereby requiring enabling formulation approaches to enhance their rate of dissolution and oral bioavailability.1,2 Among various known approaches, incorporating a poorly watersoluble compound in a suitable polymeric carrier to form an amorphous solid dispersion (ASD) has become an increasingly important strategy in the solubility and bioavailability enhancement for oral delivery of poorly water-soluble compounds, and various approaches for the preparation, characterization and stabilization of ASDs for oral drug delivery have been reviewed comprehensively.3−9 Poorly soluble drugs in their stabilized amorphous form in an ASD can generate a transient but highly supersaturated solution concentration (i.e., kinetic solubility) significantly greater than the equilibrium saturation concentration of their crystalline counterparts. Since drug supersaturation increases the driving force for oral absorption, © 2013 American Chemical Society

maintaining an elevated and sustained level of drug supersaturation is critical to improving the bioavailability of poorly water-soluble drugs. The causality between increased kinetic solubility from ASDs and improved oral bioavailability has been demonstrated in many in vivo studies.10−15 Nevertheless, one inherent challenge that often compromises the extent of solubility enhancement in ASDs is the recrystallization of metastable supersaturated drug solution originated from the dissolution of amorphous drugs under nonsink finite-volume conditions as commonly encountered in the GI tract. Although several previous studies have calculated theoretical solubility advantages of amorphous pharmaceuticals based on thermodynamic considerations and compared them with experimentally measured kinetic solubilities,16−19 discrepancies between the Received: Revised: Accepted: Published: 4330

July 27, 2013 September 10, 2013 September 23, 2013 September 25, 2013 dx.doi.org/10.1021/mp400439q | Mol. Pharmaceutics 2013, 10, 4330−4346

Molecular Pharmaceutics

Article

lization. A similar observation showing more sustained supersaturation resulting from a more gradual drug release under nonsink dissolution conditions has also been reported recently for drug release from ordered mesoporous silica materials in the absence of any crystallization inhibitor.27 These seemingly counterintuitive examples suggest that the rate of supersaturation generation may play an important role in determining the level of transient solubility enhancement, thereby affecting the overall kinetic solubility profiles in a dissolution medium free of any crystallization inhibitor. It is well-known that the driving force for the nucleation and crystallization processes in a supersaturated solution depends on the degree of supersaturation; however, the effect of rate of supersaturation buildup on the overall time evolution of supersaturation during ASD dissolution is not recognized and has not been explored. Although the effect of rate of supersaturation generation has been investigated to a limited extent in industrial crystallization processes where the focus is on the control of metastable zone width and the resulting crystal particle size distribution, crystal quality and potential polymorphic forms,28−33 these results are not directly applicable to the ASD dissolution processes considered here where the emphasis is on sustaining the supersaturation level. In addition, available analyses of the effects of rate and schedule of supersaturation generation on the kinetics of industrial crystallization processes are mostly based on empirical correlations with fitted parameters or time constants similar to that in the “spring and parachute” amorphous dissolution model discussed above; as such they provide no fundamental and mechanistic insights.34−37 Therefore, the objective of this study is to investigate for the first time the effect of supersaturation rate (generated from infusing solvent dissolved drugs at different rates into a miscible antisolvent, i.e. dissolution medium) on the resulting kinetic solubility profiles of amorphous systems under nonsink dissolution conditions. We delineate the evolution of supersaturation from a mechanistic viewpoint based on the classical nucleation theory taking into account both the particle growth and ripening processes. The obtained dependency of attainable maximum supersaturation on the rate of supersaturation generation should provide insights on strategies to maximize the area under the concentration−time curve in order to optimize bioavailability, and also to shed light on the difficulty in attempting to estimate and measure the true “solubility advantage” of amorphous solids. Experimental concentration− time curves with varying rates of supersaturation generation and recrystallization using indomethacin (IND), naproxen (NAP) and piroxicam (PIR) as model poorly water-soluble drugs were generated and compared with the predicted and simulated behavior where applicable. The mechanistic understanding gained here is expected to aid the design of ASD oral dosage forms to create optimal sustained supersaturation of poorly water-soluble drugs.

predicted and observed solubility advantages remain significant and there is still insufficient mechanistic understanding as to the relationship between the observed kinetic solubility profiles and the underlying nucleation and crystallization events. The design of conventional ASD-based oral dosage forms for poorly water-soluble drugs typically focuses on increasing the dissolution rates, elevating the degree of supersaturation and extending its duration following the dissolution of various ASD systems. It is a common practice to employ soluble polymers such as polyvinylpyrrolidone (PVP), hydroxypropylmethylcellulose (HPMC), hydroxypropylmethylcellulose acetate succinate (HPMCAS) and so on as carriers in conventional ASDs to inhibit drug precipitation from the supersaturated state. Typically, the dissolution of ASDs based on water-soluble polymers is very rapid, resulting in an initial surge of drug concentration in the dissolution medium followed by a decline in drug concentration due to the nucleation and crystallization events triggered by the rapid buildup of drug supersaturation. Depending on the ability of the dissolved polymer to inhibit drug precipitation from the supersaturated state, such a decline in drug concentration can be retarded to different degrees. In general, the more gradual the decline in drug concentration, the better its effectiveness in inhibiting drug precipitation and in maintaining drug supersaturation.17,18 In this regard, amphiphilic HPMCAS has been identified to be the most effective in achieving and maintaining drug supersaturation among several available water-soluble polymers commonly employed in ASDbased oral drug products.20,21 Typical dissolution profiles of ASDs showing rapid initial buildup of drug supersaturation and subsequent retardation of precipitation have been qualitatively characterized as a “spring and parachute” approach.22,23 This combination of a rapidly dissolving and supersaturating “spring” with a precipitation retarding “parachute” has been pursued as an effective formulation strategy to enhance the rate and extent of oral absorption. Although such “spring and parachute” dissolution data have been fitted to empirical rate equations to estimate the time constants for the “spring” and “parachute” portions of the dissolution profiles,24 the interplay between these two rate processes in achieving and maintaining supersaturation remains inadequately understood. On the other hand, in demonstrating the feasibility of generating ASDs based on insoluble cross-linked poly(2hydroxyethyl methacrylate) (PHEMA) hydrogel beads, we recently compared the solubility improvement of the more gradually released indomethacin from this hydrogel-based ASD system with that from the rapidly dissolving ASDs based on soluble PVP and HPMCAS under nonsink dissolution conditions.25,26 Our results reveal that a sustained level of supersaturation is achieved, but with an apparent absence of a “spring” and “parachute” behavior in the dissolution from ASDs based on cross-linked PHEMA hydrogel beads as compared with that based on water-soluble polymers, despite the lack of any dissolved polymer in the former case to retard drug precipitation from the resulting supersaturated solution (note: cross-linked PHEMA is insoluble in water). In fact, ASDs based on PHEMA hydrogels exhibit a sustained solubility enhancement later surpassing that based on soluble polymer carriers as the drug concentration in the latter case declines due to more rapid de-supersaturation.26 This has been attributed to the gradual, diffusion-controlled drug release from the PHEMA matrix which provides a feedback-controlled mechanism thus preventing a sudden surge of supersaturation in the dissolution medium thereby avoiding rapid drug nucleation and crystal-

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THEORY To delineate the effect of rate of supersaturation generation on the resulting concentration−time curves, we consider the physical processes when a poorly water-soluble drug dissolved in a small amount of water-miscible solvent is added at a constant rate into a continuously mixing aqueous dissolution bath for a length of time t1. Figure 1 depicts the progression of such an infusion process which includes the following three stages: (1) the start of infusion of dissolved drug in solvent 4331

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where the nucleation rate constant Jc, the capillary length ω, the molar volume υ and the constant β are defined as

Figure 1. Schematic depiction of the nucleation and crystallization events due to supersaturation generation of slowly infused poorly water-soluble drugs in a continuously stirred USP II dissolution vessel.

before the appearance of any detectible nuclei; (2) the buildup of supersaturation and subsequent initiation of nucleation and crystallization events as a result of continuous addition of dissolved drug; (3) the continuation of the growth and ripening processes after the completion of drug infusion. An isothermal, primary (unseeded) nucleation mechanism is assumed to take place in this system. Crystal breakage, agglomeration and interaction are considered negligible since the crystal concentration in a typical dissolution batch is small and consequently the distance between the crystals is significantly larger than the crystal size. A mathematical simulation of this system can be formulated by modifying the comprehensive mechanistic model of Chacron and L’Heureux38 originally drived for a more complex phenomenon of periodic precipitation (e.g., no contribution from chemical reaction in the present case). Based on mass balance considerations, the rate of change of drug concentration in the above system can be expressed by a governing differential equation: dC =R−u dt

4π 3υ

∫0

t

∫0

where rn denotes the critical particle size when nuclei start to form [i.e., rn = r(t,t′=t)]. On the right-hand side of the equation, the first term corresponds to the instantaneous nucleation process and the second term represents the growth of particles nucleated in the past (at t′). The nucleation rate and critical particle size can be calculated according to Dee:40

ω ln(s)

(6)

C CS

(7)

(8)

where G is the particle growth rate constant and Ceq(r) the concentration in equilibrium with a precipitate particle of radius r. The relationship between Ceq(r) and r is described by the Gibbs−Thomson relation:

dr J(t ′) r (t , t ′) dt ′ dt (3)

rn = ωg (s) =

MW ρ

⎡ N0C − Ceq(r ) ⎤ dr ⎥ = G⎢ ⎢⎣ ⎥⎦ dt CS

2

2 ⎧ exp(− [βg (s)]2 ), s ≥ 1⎫ ⎪J s ⎪ c ⎨ ⎬ J = Jc F(s) = ⎪ ⎪ 0, s < 1 ⎩ ⎭

υ=

where D is the diffusion coefficient, C the bulk concentration, CS the equilibrium solubility, N0 Avogadro’s number, T the temperature, kB Boltzmann’s constant, σ the surface tension (assumed to be independent of particle radius), d a typical molecular size (taken to be twice the molecular diameter of the precipitating molecule), MW the molecular weight and ρ the crystal density. Equation 4 suggests that nucleation only occurs when the concentration is above saturation and the nucleation kinetics significantly depends on the degree of supersaturation. At a very low supersaturation level, when the nucleation rate is too low to be measured, a lag time (or induction time) usually appears before the formation of any detectable nuclei. On the other hand, nucleation becomes spontaneous when the concentration reaches a “critical supersaturation”41 or the upper limit of a “metastable zone width”.35,36 In either case, nucleation is an ongoing kinetic process when the solution concentration is above the saturation solubility. Furthermore, to include the postnucleation events, the approach of LeVan and Ross is adopted to take into account crystal growth and ripening dynamics.38,42 In this case, the particle growth rate is described by an interface-controlled process:

(2)

t

2υσ N0kBT

s=

where υ is the molar volume of precipitate, J(t′) is the nucleation rate and r(t,t′) is the radius of precipitated particles at time t, given that it was nucleated at time t′. The molar precipitation rate is therefore df 4π 4π = J(t ) rn 3(t ) + u= υ dt 3υ

ω=

and the dimensionless supersaturation s is defined as

(1)

J(t ′) r 3(t , t ′) dt ′

4πDω 2CS2 d

⎛ 4πσω 2 ⎞1/2 β=⎜ ⎟ ⎝ 3kBT ⎠

where t is time, C the molar concentration of dissolved drug, R the rate of drug input and u the drug precipitation rate. Starting from the classical nucleation theory39 and assuming that spherical drug particles with a time-dependent radius r are precipitated at a nucleation rate J, the molar concentration of precipitate f is then calculated by38,40 f=

Jc =

⎡ ωΨ(r ) ⎤ Ceq(r ) = CS exp⎢ ⎥ ⎣ r ⎦

(9)

with Ψ(r ) ≅

r 2 + δr r 2 + 3δr +

δ2 q

where the dimensionless function Ψ(r) represents the particle radius-dependent interfacial tension simplified from a thermodynamically based expression of Koenig (with a maximum relative error of 0.8%),43 with q = 0.304359 and δ, a parameter

(4) (5) 4332



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Table 1. Physicochemical Properties of Model Poorly Water-Soluble Drugs Used in This Study

We therefore obtain the following generalized set of five coupled nonlinear differential equations that can be solved numerically for the evolution of supersaturation s(t):

(of the order of capillary length ω) characterizing the thickness of the Gibbs surface. Based on the approach of Chacron and L’Heureux,38 the integrodifferential equation 3 can be transformed into a set of coupled differential equations by defining the average surface of the precipitate particle per unit volume Σ as Σ = 4π

∫0

t

J(t , t ′) r 2 (t , t ′) dt ′

α ⎧ R * − (s − e Ψ / r *)Σ − g 3F , t < ⎪ ⎪ 3 ds =⎨ dt * ⎪ −(s − e Ψ / r *)Σ − α g 3F , t ≥ t ⎪ 1 ⎩ 3

(10)

the average radius of the particles per unit volume Φ as Φ=

t

∫0

J(t , t ′) r(t , t ′) dt ′

(11)

and the average particle number density N as N=

∫0

t

J(t , t ′) dt ′

(12)

We further define the following dimensionless variables (*): Gt ω

t* =

4πJc ω N0 N0ω Σ υCS

Φ* =

4πN0ω 2 Φ υCS

N* =

4πN0ω3 N υCS

ωR CSG

(14b)

dΦ* = αgF + (s − e Ψ / r *)N * dt *

(14c)

dN * = αF dt *

(14d)

dr * = s − eΨ/r* dt *

(14e)

s (t 2 ) = s ′

(15)

where s′ is the measured concentration at time t2 which represents the time when the dissolution measurement ends. The kinetic solubility profile s(t) so obtained describes the time evolution of supersaturation as affected by the rate of supersaturation generation and the interplay between the dissolution and precipitation processes during the dissolution of an amorphous solid.

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EXPERIMENTAL SECTION Materials. Indomethacin (IND), naproxen (NAP) and piroxicam (PIR) were purchased from Sigma-Aldrich Canada and used without further purification. Polyvinylpyrrolidone (PVP K-90) was kindly provided by ISP Technologies Inc. All other chemicals were reagent grade obtained commercially and used as received. Measurement of Kinetic Solubility Profiles. IND, NAP and PIR were selected as model poorly water-soluble drugs because of their coverage of a range of low aqueous solubility and the relatively higher solubility in water-miscible organic

r * = ωr R* =

dΣ* = αg 2F + 2(s − e Ψ / r *)Φ* dt *

s(0) = 0

GυCS

Σ* =

(14a)

Subject to boundary conditions corresponding to experimental end points:

4

α=

⎫ t1⎪ ⎪ ⎬ ⎪ ⎪ ⎭

(13)

The dimensionless rate of supersaturation generation R* may have different time-dependent functional forms based on the specific amorphous system being considered. For the present investigation where supersaturation is generated through a constant-rate infusion of drug solution, R* is a constant, characteristic of the infusion rate being studied. 4333



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solvents (Table 144−46). To provide a convenient way to vary the supersaturation of these model drugs, concentrated drug solutions were prepared in a small volume of water-miscible organic solvent to achieve a concentration of 2 mg/mL in ethanol for IND, 5 mg/mL in ethanol for NAP and 10 mg/mL in acetone for PIR. The addition of a small volume of a concentrated drug solution in a water-miscible organic solvent (e.g., methanol) to generate a supersaturated solution in an aqueous medium is an accepted practice in studying the dissolution of amorphous pharmaceuticals.17,18 For the preparation of amorphous solid dispersions (ASDs) of IND in a polymer carrier, IND and PVP (1:9 by wt) were completely dissolved in an appropriate amount of ethanol. The drug/polymer solution was then poured into a Teflon dish and the solvent removed under vacuum at 50 °C for 24 h. The thin cast film was collected and ground with mortar and pestle in a small amount of liquid nitrogen to avoid heat-induced crystallization. The resulting powder with particle size under 90 μm was collected using a minisieve. The IND loading in PVP was confirmed by fully dissolving a known amount of resulting ASD powder in 250 mL of ethanol and determining the drug concentration spectrophotometrically on a Cary 50 UV−vis spectrophotometer (Varian, ON, Canada) at 320 nm. To evaluate the recrystallization process of these model drugs in solution as a function of supersaturation rate, a nonsink condition was maintained during dissolution in order to facilitate the supersaturation buildup and to track the associated nucleation and crystallization events. A dimensionless sink index (SI) defined as SI = CsV/(dose) previously introduced by us was utilized here to quantify the degree of deviation from sink condition in a dissolution experiment, where Cs is the equilibrium solubility of crystalline drug, V the volume of dissolution medium and “dose” the total amount of drug in the sample.26 A dissolution system that is close to a perfect sink condition translates to a large SI value (e.g., SI > 10). The dissolution experiments in the present study were conducted under nonsink condition by either infusing a total of 10 mL of the concentrated drug solution at different rates from a glass syringe using a Fusion 100 syringe pump (Chemyx Inc., Stafford, TX) or manually adding a total of 200 mg of INDPVP (1:9 wt %) ASD powder, in divided quantities at evenly spaced time intervals, into 250 mL of distilled water as dissolution medium in a USP II dissolution apparatus. The infusion experiment was designed to provide mechanistic insight in the intrinsic relationship between supersaturation rate and the resulting kinetic solubility profiles in the absence of any dissolved polymer, whereas the ASD powder addition experiment was intended to examine kinetic solubility profiles of ASD based solid dosage forms as a function of supersaturation rate in the presence of dissolved polymer. To ensure a similar solution environment as the infusion experiment, the dissolution of crystalline drug was carried out in dissolution medium containing 250 mL of distilled water and 10 mL of watermiscible organic solvents (ethanol for IND and NAP; acetone for PIR). The total amount of drug infused or added in each experiment was maintained at ∼20 mg of IND, 50 mg of NAP and 100 mg of PIR which translates to 76.9 μg/mL IND (or 80 μg/mL for IND-PVP ASD), 192.3 μg/mL NAP and 384.6 μg/ mL PIR if completely dissolved in the dissolution medium, equivalent to approximately SIIND = 0.10, SIIND‑PVP = 0.096, SINAP = 0.30 and SIPIR = 0.069. The dissolution testing was conducted on a Vankel 7000 dissolution apparatus (InterScience Inc., ON, Canada) at 37 °C ± 0.5 °C using a paddle

speed of 150 rpm. A second-derivative UV spectroscopic method was employed to measure drug concentrations in order to eliminate any potential scattering interference created by newly formed particles in the supersaturated solution.47,48 At each predetermined time interval, an approximately 3 mL aliquot of dissolution medium was removed from the dissolution vessel and the UV scan from 200 to 600 nm was obtained on a Cary 50 UV−vis spectrophotometer at a scan rate of 600 nm/min and average data acquisition time of 0.1 s. The drug concentration was spectrophotometrically determined from the second-derivative spectra at 295, 295 and 320 nm for IND, NAP and PIR, respectively. The removed aliquot was immediately returned to the dissolution medium after each measurement to maintain a constant total volume of dissolution medium. Triplicate measurements were run, and average values with standard deviations are presented for all dissolution results. X-ray Diffraction (XRD). In order to determine the polymorphic form of precipitated IND in the supersaturated solution, samples of precipitated IND from the dissolution testing were collected on filter paper and air-dried under ambient conditions. Reference samples of γ- and α-polymorphs and amorphous IND were prepared based on previously published methods.49,50 The physical states of collected samples were analyzed on a Philips XRD system (Phillips, ON, Canada) equipped with PW 1830 HT generator, PW 1050 goniometer and PW 3710 control electronics and X’pert software system. The experimental parameters included 1° of divergence slit and 0.1 mm receiving slit for the incident beam with a scan rate of 2° per min over a 2θ range of 5−35°. Differential Scanning Calorimetry (DSC). A TA Instruments 2010 DSC (Delaware, USA) was used to confirm the polymorphic melting transition of IND precipitated from the supersaturated solution. The system was calibrated with indium. Approximately 5−10 mg of collected sample prepared as described above was weighed into an aluminum pan on a Mettler Toledo precision scale and cold-sealed. The reference pan was left empty and sealed in the same way. The sample and reference were heated from ambient temperature to 200 °C at a rate of 5 °C per minute. Scanning Electron Microscopy. Precipitated crystalline drug samples collected at the end of dissolution testing were filtered and dried under ambient conditions for 3 days. The collected solids were examined by scanning electron microscopy (SEM). Prepared samples were imaged at ambient temperature at 15 kV on a JEOL JSM-6610-LV SEM equipped with an Oxford/SDD EDS detector and an IXRF 500 digital pulse processor (Jeol USA Inc., Peabody, MA). Particle Size Distribution. The particle size distribution data were obtained on a laser scattering particle size analyzer (Beckman-Coulter LS 13 320, Brea, CA) with a universal liquid module. In order to cope with the volume limitation of circulating fluid in this module system (125 mL), the infusion rate of drug solution, volume of infused drug solution and volume of dissolution medium in the above-mentioned study of kinetic solubility profiles were reduced in half for the present sample preparation in order to maintain the same rate of supersaturation generation by keeping the same infusion rate to dissolution medium volume ratio. Typically, 5 mL of 2 mg/mL IND solution in ethanol was infused at a rate ranging from 0.05 to 1 mL/min into a 250 mL beaker containing 125 mL of distilled H2O, stirred with a magnetic bar at approximate 150 rpm at ambient temperature. The entire 125 mL dissolution 4334



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medium containing precipitated particles was transferred into the particle size analyzer after 4 h for the determination of particle size distribution. In this case, the rate of supersaturation generation at 1 mL/min infusion rate in the present particle size distribution study is equivalent to that of the 2 mL/min infusion rate in the study of kinetic solubility profiles. Simulation of Modeling Equations. Drug concentration profiles were simulated by numerically solving eqs 14a, 14b, 14c, 14d and 14e with appropriate values of constants for IND and boundary conditions from eq 15 using COMSOL Multiphysics (version 3.5a) software on a desktop Dell PC (Intel Core i7 CPU 2.67 GHz processor and 12 GB RAM) with a mesh size of t* = 0.01. No spurious oscillations or numerical diffusion occurred.

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RESULTS AND DISCUSSION Effect of Rate of Supersaturation Generation on the Kinetic Solubility Profiles. To investigate the effect of rate of supersaturation generation, kinetic solubility profiles of poorly water-soluble drugs were generated by infusing a small volume of concentrated drug solution prepared in a water-miscible solvent at various constant infusion rates while keeping the total amount of drug infused constant. The drug concentration in the dissolution medium at any given time point was determined with the second-derivative UV spectroscopy method. Secondderivative UV spectroscopy was employed to minimize the light scattering interference from any particulate matter formed during the precipitation process (more on the justification of this to be discussed later with the particle size results). Representative absorbance and the corresponding second derivative spectra of IND, NAP and PIR are shown in Figure 2. The second-derivative absorbance spectra exhibit maxima for IND, NAP and PIR at 295, 295 and 320 nm, respectively, yielding linear standard curves with correlation coefficients of R2 = 0.9828, 0.9950 and 0.9964 up to concentrations of 80.5, 185.3 and 314.2 μg/mL, respectively (data not shown). Experimental kinetic solubility profiles of IND, NAP and PIR are presented in Figure 3 as a function of supersaturation rate generated with various drug infusion rates (0.03 to 2 mL/min) and compared with that of the corresponding crystalline drugs. It is seen that, for all three model drugs, a maximum kinetic solubility ranging from 2- to 10-fold that of the equilibrium solubility of the crystalline counterpart is reached before the completion of the infusion. Figure 3 further shows that the faster the rate of drug infusion (or the rate of supersaturation generation), the higher the maximum kinetic solubility, the shorter the time to reach maximum solubility and the faster the rate of de-supersaturation in the resulting kinetic dissolution profile. In addition, when the rate of drug supersaturation generation is decreased (i.e., a lower infusion rate), the maximum kinetic solubility diminishes and the maximum concentration peak widens, reflecting a slower rate of desupersaturation before approaching either a quasi-steady state of elevated kinetic solubility in the case of IND (Figure 3A; more on this aspect to be discussed later) or an equilibrium solubility of crystalline drug in the case of NAP (Figure 3B) and PIR (Figure 3C), beyond 5 to 6 h of dissolution period. Next, it will be shown that the above-described trends in the observed kinetic solubility profiles as a function of supersaturation rate can be predicted from the proposed comprehensive mechanistic model taking into account the role of supersaturation in both the nucleation and crystallization processes as well as the associated competitive particle

Figure 2. Representative ultraviolet (UV) absorbance spectra and the corresponding second derivative spectra for (A) IND, (B) NAP and (C) PIR. Inset: Representative second-derivative UV spectra at various drug concentrations.

growth and ripening effects, using IND as an example. To this end, relevant empirical parameters for the model drug reported in the literature were adopted for the numerical simulation of eqs 14a, 14b, 14c, 14d, 14e and 15 in order to avoid parametric adjustment through curve fitting. For the model drug IND, the equilibrium solubility of IND 7.72 μg/mL was measured from the dissolution experiment, and reported values of crystal density 1.38 g/cm3,51 molecular diameter 8.5 Å,52 diffusion coefficient 1.9 × 10−5 cm2/s53 and crystallization rate coefficient 7.8 × 10−9 cm/s47 were used. The interfacial 4335



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solubility profiles. Figures 4A−4E compare the experimental and calculated IND kinetic solubility profiles as a function of each individual rate of supersaturation (via a specific drug infusion rate). In order to illustrate the accuracy of our dynamic model prediction, the coefficient of determination, R2 value, was statistically determined for each set of data at a given infusion rate, which ranges from 0.8124 to 0.9556 (see Figures 4A−4E). The accuracy of model prediction appears to be reasonably good with R2 being higher for the midrange drug solution infusion rates (0.1 and 0.5 mL/min, Figure 4B,C) than those from the highest (2 mL/min, Figure 4A) and the lowest two (0.03 and 0.05 mL/min, Figure 4D,E) infusion rates. Although there are some discrepancies in Figure 4A−E with the onset of precipitation occurring somewhat earlier than predicted, the critical trend between the supersaturation rate and the maximum achievable supersaturation agrees well between the experimental data and model prediction. Considering the fact that the present mechanistic model simulation is based solely on physical parameters reported in the literature without employing any curve fitting, the abovementioned discrepancies are therefore not surprising and the model predictions can be considered as quite good. It is worth noting that the general trend of the predicted kinetic solubility profiles of IND as a function of supersaturation rates generated from various drug infusion rates as summarized in Figure 5 agrees well with that of the experimental data in Figure 3A. It is clear that, under a constant total amount of drug infused, the maximum achievable supersaturation (i.e., kinetic solubility) of the amorphous solids increases, the time to reach the maximum decreases and the rate of concentration decline in the desupersaturation phase increases, with increasing rate of supersaturation generation (i.e., dissolution rate). This phenomenon can be realized by the fact that a high degree of supersaturation achieved through rapid dissolution will lead to a high nucleation rate, and the crystallization of such a high number of nuclei leads to a rapid depletion of dissolved drug therefore resulting in an earlier but higher maximum kinetic solubility followed by a sharp decline in drug concentration. Conversely, a slower dissolution rate avoids a sudden surge of supersaturation resulting in slower nucleation and crystallization events and therefore a later-appearing but lower maximum kinetic solubility followed by a more gradual decline in drug concentration. In other words, in the absence of any dissolved polymer to inhibit drug precipitation from the supersaturated state, both our experimental and predicted results confirm that the faster rise of the kinetic solubility profile of an amorphous drug will inevitably lead to an earlier but higher maximum kinetic solubility and a sharper drop in the de-supersaturation phase, and vice versa. Furthermore, results of Figures 4A−4E confirm that, for IND, a predicted maximum kinetic solubility is reached before the completion of drug infusion (indicated by arrows) in agreement with the experimental data (see Figure 3A). A similar trend for NAP and PIR is also observed experimentally (see Figure 3B and Figure 3C). For the purpose of designing an effective amorphous system for oral dosage forms, both the maximum attainable kinetic solubility and the ability to maintain supersaturation for a longer duration are essential for achieving solubility and bioavailability improvement. For this purpose, the area under the curve (AUC) of the in vitro kinetic solubility concentration−time profiles therefore can be used to correlate the corresponding trend in bioavailability enhancement for in vivo studies.20,27 It should be emphasized here that experiments

Figure 3. Experimental kinetic solubility profiles of (A) IND, (B) NAP and (C) PIR as a function of supersaturation rate generated with various drug solution infusion rates (0.03 to 2 mL/min), compared with that of the crystalline drugs. Total amount of drug infused or introduced for each run: 20 mg for IND (SI = 0.10), 50 mg for NAP (SI = 0.30) and 100 mg for PIR (SI = 0.069). Arrows with corresponding colors indicate the time at which the infusion has ended.

tension between IND and water was estimated to be 26.8 dyn/ cm from the contact angle data and the surface free energy estimation reported by Zografi and Tam.54 This allows for a realistic test of the validity of model predictions and provides a mechanistic interpretation of the resulting IND kinetic 4336



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Figure 4. Kinetic solubility profiles of IND as a function of supersaturation rate generated with various drug solution infusion rates: (A) 2, (B) 0.5, (C) 0.1, (D) 0.05 and (E) 0.03 mL/min; a comparison between experimental data and COMSOL simulation of eqs 14a, 14b, 14c, 14d and 14e with boundary condition of eq 15. The total amount of IND infused for each run is 20 mg (SI = 0.10). Arrows indicate the time at which the infusion has ended.

reported thus far were conducted in the absence of any dissolved polymer to inhibit drug precipitation from the supersaturated state for the purpose of gaining a better mechanistic understanding of the evolution of supersaturation. Both our experimental and predicted results show that the maximum kinetic solubility increases monotonically with the rate of supersaturation generation in the IND solution infusion rate range of 0.03 to 2 mL/min (Figure 6A), however the highest AUC occurs at an intermediate infusion rate of 0.1 mL/ min (Figure 6B) under a constant total amount of drug infused.

In other words, in the absence of any dissolved polymer to inhibit drug precipitation from the supersaturated state, we have shown for the first time that the proposed mechanistic model predicts the existence of an optimal supersaturation rate which maximizes the AUC of the kinetic solubility concentration−time profile, and confirmed this finding experimentally. In this case, a smaller rate of supersaturation generation (or infusion rate) leads to a reduced AUC due to the lower maximum kinetic solubility achieved, whereas a higher supersaturation rate beyond the optimal also leads to a reduced 4337



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slow), while keeping the total amount of infused IND constant under each infusion schedule. As shown in the results of Figure 7, the “fast−slow” schedule of a combination of fast and slow

Figure 5. Predicted kinetic solubility profiles of IND as a function of supersaturation rate generated with various drug solution infusion rates based on COMSOL simulation. Total amount of IND infused in each run is 20 mg. Figure 7. Kinetic solubility profiles produced from three different rate schedules of IND infusion: 0.05 mL/min for 200 min (slow), 0.5 mL/ min for 20 min (fast) and 0.5 mL/min for 10 min plus 0.05 mL/min for 100 min (fast−slow). Total amount of IND infused: 20 mg (SI = 0.10). Arrows without label with corresponding colors indicate the time at which the infusion has ended. For the “fast−slow” combination of infusion rates, T1 indicates 10 min, at which the first infusion segment of 0.5 mL/min has ended, and T2 indicates 110 min, at which the second infusion segment of 0.05 mL/min has ended. Inset: Effect of IND infusion rate schedule on the AUC of the resulting kinetic solubility profile. Statistically significant differences are observed (* indicates p < 0.05).

AUC because, beyond the optimal rate of supersaturation generation, the anticipated gain in AUC due to increased maximum kinetic solubility is overcompensated by the sharper decline in drug concentration due to the faster nucleation and crystallization events in the de-supersaturation phase. This agreement between our predicted and experimental results supports the notion that a faster supersaturation generation rate does not always translate to a higher AUC of the kinetic solubility profile, rather an optimal AUC exists at an intermediate supersaturation rate. This also correlates well with recent reports in bioavailability enhancement showing that the fastest dissolution of a supersaturating formulation is insufficient for an optimal in vivo performance, rather a more gradual in vitro release results in an optimal in vivo performance (i.e., in vivo AUC).27,55 To further elucidate the effect of supersaturation rate on the AUC of the resulting concentration−time profiles, we compared kinetic solubility profiles and their resulting AUC over a 6 h dissolution period under three different IND infusion rate schedules: 0.5 mL/min for 20 min (fast), 0.05 mL/min for 200 min (slow) and a combination of 0.5 mL/min for the first 10 min and 0.05 mL/min for the subsequent 100 min (fast−

infusion rates produces the highest AUC (inset of Figure 7) over the 6 h dissolution period. In this case, a faster drug infusion at the beginning of the dissolution phase helps to quickly elevate the kinetic solubility and the subsequent slower drug infusion results in a lower maximum kinetic solubility, and a more gradual decline of drug concentration due to slower nucleation and crystallization events as elaborated earlier, thus helping to sustain supersaturation. This latter phenomenon appears to play a key role in the recently reported solubility advantage of ASD drug release from an insoluble cross-linked

Figure 6. Effect of supersaturation rate generated with various IND infusion rates on (A) maximum kinetic solubility and (B) area under the curve (AUC) of the kinetic solubility profile; a comparison between experimental and predicted (theoretical) results with data for crystalline IND included for reference. Total amount of IND infused or introduced: 20 mg. Statistically significant differences are observed (* indicates p < 0.05). 4338



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in supersaturated solutions,57,58 the decline in drug concentration in the de-supersaturation phase associated with INDPVP ASD appears to be much slower than in the absence of any dissolved polymer (comparing Figure 8 with Figure 3A). Furthermore, a slower IND-PVP ASD addition rate appears to maintain a higher kinetic solubility in the desupersaturating phase which is sustained for a longer period of time during the initial 8 h of dissolution, after which the kinetic solubility profiles eventually merge into a quasi-steady state of elevated kinetic solubility at 24 h (Figure 8). This finding confirms our earlier report that a more gradual drug release avoids a sudden surge of supersaturation thus circumventing a more rapid decline in drug concentration in the de-supersaturation phase as a result of diminished nucleation and crystallization events.26 This is further supported by the results of Six et al.14 which show that Sporanox, an ASD formulation of itraconazole in polymeric carrier HPMC having a slower in vitro dissolution rate than ASDs prepared in Eudragit E100 and Eudragit E100/ PVPVA64, actually produces a better oral bioavailability enhancement for itraconazole. These trends are consistent with our findings discussed earlier that an optimal AUC of the in vitro concentration−time profile exists at an intermediate supersaturation rate (or a modest in vitro dissolution rate) which results in an optimal in vivo performance (i.e., in vivo AUC or bioavailability). In other words, fast dissolution of a supersaturating formulation does not always translate to an optimal in vivo performance. “Kinetic” Solubility Advantage of Amorphous Solids. All the above-mentioned lines of evidence suggest that the maximum achievable supersaturation of amorphous solids depends on the competing kinetic processes of dissolution (or supersaturation buildup) and precipitation (or nucleation and crystallization). Since a supersaturated solution is thermodynamically in a nonequilibrium state, its transformation toward equilibrium is kinetically driven via a time-dependent process. In this case, the relationship between the achievable maximum supersaturation and the rate of supersaturation generation in the observed kinetic solubility profiles has been predicted for the first time by our comprehensive mechanistic model taking into account the role of supersaturation in both the nucleation and crystallization processes as well as the associated competitive particle growth and ripening effects as demonstrated earlier. Thus, the true solubility advantage of amorphous solids cannot be accurately determined by only considering the classical nucleation theory alone or simply estimating values of the Gibbs free energy differences between the amorphous and crystalline states. Physically, as a system moves very rapidly from an equilibrium saturated state to a nonequilibrium supersaturated state during supersaturation generation, the newly formed supersaturated phase may not have sufficient time to form a separate solid phase. In other words, the faster the system moves away from equilibrium (i.e., the higher the rate of supersaturation generation), the higher the maximum supersaturation will be reached, as already demonstrated in Figures 3−8. Therefore, at least in principle, the “true” solubility advantage of an amorphous solid may be better determined if the manifested maximum concentration in the overall kinetic solubility profile during dissolution of an amorphous solid can be extrapolated to an infinite dissolution rate. Accordingly, the relationship between the maximum concentration (Cmax) attainable in the kinetic solubility profile and the corresponding rate of supersaturation generation from

hydrogel carrier compared to that from water-soluble polymers, in which a less rapid drug release from the hydrogel carrier helps to maintain and prolong supersaturation by gradually compensating the decline of drug concentration due to nucleation and crystallization events via a diffusion-controlled feedback mechanism.26 This trend is also consistent with a recently reported study showing that a modest dissolution rate of itraconazole from a solid dispersion achieved by a combination of fast and slowly dissolving polymers reaches a sustained supersaturation without precipitation, whereas the dissolution of the same amount of itraconazole from the fast dissolving polymer causes precipitation from the supersaturated drug solution after 2 h.56 Amorphous Solid Dispersions in Polymeric Carriers. In the design of ASD oral dosage forms for poorly watersoluble drugs, water-soluble polymeric carriers are often employed to retard the nucleation and crystallization processes both in the solid state and during dissolution. To illustrate the combined effect of rate of supersaturation generation and the presence of a polymeric carrier, the kinetic solubility profiles of IND-PVP ASD (10 wt % drug) were generated by administering repeatedly a fixed amount (20 mg) of ASD powder into the dissolution medium at evenly spaced time intervals up to a total amount of 200 mg of ASD added. The highest rate of supersaturation generation was achieved by the addition of the entire 200 mg of IND-PVP ASD at time zero, denoted as “all at 0 min”. There may be potential differences in the resulting rate of supersaturation generation between the IND solution infusion experiment and the addition of INDPVP ASD powder due to the effect of polymer dissolution and particle size of ASD, but the general trend of kinetic solubility profiles as a function of different addition rates of solid INDPVP ASD as shown in Figure 8 still resembles that generated by infusing IND solution at different infusion rates (see Figure 3A): a faster rate of addition (or supersaturation generation) leads to a higher maximum kinetic solubility and a sharper decline in drug concentration in the de-supersaturation phase. However, since dissolved PVP is known to retard crystallization

Figure 8. Kinetic solubility profiles of IND-PVP ASD (10 wt % loading) manually administered into the dissolution medium at different rate schedules as indicated in the legend; total amount of ASD added: 200 mg (SI = 0.096). For example, “all at 0 min” indicates the addition of the entire 200 mg of IND-PVP ASD at time zero and “20 mg/2 min for 20 min” indicates the addition of 20 mg of INDPVP ASD every 2 min for 20 min. 4339



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likely reasons for such discrepancy can be readily understood. Experimentally, the apparent solubility of an amorphous solid is usually determined by the highest attainable peak concentration Cmax in a kinetic solubility profile under a nonsink dissolution condition. With the mechanistic understanding developed in this study that the achievable Cmax of a kinetic solubility profile depends on the rate of supersaturation generation, it is virtually impossible to ascertain the same rate of supersaturation generation produced in studies conducted by different research groups, hence the great degree of variability in reported solubility advantages on the same drug.19,60−63 Although one can attempt to generate a hypothetical solubility for amorphous solids when the dissolution rate approaches infinity, the results described above suggest that the extrapolated solubility reduces to a concentration approximately equivalent to having all added amorphous drug completely dissolved in the solution phase. In previous reports, all thermodynamic predictions of the solubility enhancement ratio between an amorphous glass and its crystalline counterparts rely on the fundamental assumption that the amorphous form can be treated as a pseudoequilibrium state and the difference in their Gibbs free energy is responsible for determining the theoretical solubility advantage. This free energy difference has been initially assumed to be equivalent to the molar free energy change of the crystal-to-amorphous transformation, estimated by the melting temperature and enthalpy of fusion difference between the two physical forms.60,61 This theoretical consideration has been the basis for the thermodynamic prediction of solubility enhancement ratios between the amorphous and crystalline forms of poorly water-soluble drugs. Additional rigorous modifications including the consideration of configurational heat capacity, water sorption during dissolution and different degrees of drug ionization in amorphous and crystalline forms have provided further improvements in producing a closer agreement with the measured data.16,19,61−65 Nevertheless, amorphous glassy solid is in a nonequilibrium state at which the disordered molecular structure does not require the breaking of crystal lattice upon dissolution. The solubility of a supercooled and liquid-like amorphous material in aqueous solution is analogous to that of two miscible liquids: each component dissolves completely in the other regardless of the proportions in which two liquids are mixed. Since the observed kinetic solubility of nonequilibrium amorphous solids depends on the rate of supersaturation generation as demonstrated in this study, our results further highlight the underlying difficulty in determining a reproducible solubility advantage for amorphous solids. Crystallization Kinetics and Particle Size Distributions. The recrystallization process of a poorly water-soluble drug from supersaturated solution is essentially the same as that in a well characterized industrial semibatch crystallizer where the crystallization kinetics generally depends on the rate of supersaturation generation. To better illustrate this point, the concentration−time profiles from the infusion experiments of Figure 3 can be converted to those of Figure 10 characterizing the crystallization kinetics under different drug solution infusion rates (or rate of supersaturation generation) for the three model drugs, IND, NAP and PIR. This is accomplished by plotting the difference between the theoretical infusion concentration profile without crystallization and the observed kinetic solubility profile of Figure 3. As shown in Figure 10, the induction period of nucleation becomes shorter and the crystallization rate gets faster (a larger slope in the linear

the infusion experiment can be delineated by building a linear correlation between the measured Cmax and the inverse of infusion rate raised to an empirically determined exponent of α (Figure 9), analogous to the so-called Wilson’s plot.59 It can be

Figure 9. The maximum supersaturation concentration (Cmax) measured during the infusion experiment as a function of the inverse of infusion rate raised to an exponent α. The values of α for linearizing such plots are determined to be 0.3493, 0.3649, 0.2794 and 0.2813, and the Cmax values extrapolated to infinite infusion rates are 74.6, 79.3, 185.9 and 367.2 μg/mL for IND (experiment), IND (COMSOL simulation), NAP (experiment) and PIR (experiment), respectively. Total amount of drug infused or introduced for each run: ∼20 mg for IND, 50 mg for NAP and 100 mg for PIR. Inset: Cmax as a function of infusion rates of IND solution.

seen from Figure 9 when the infusion rate of drug solution approaches infinity (or the inverse infusion rate approaches zero), the extrapolated maximum concentration (Cmax,ext) approaches the hypothetical concentrations (Call) at which all drug content in the infused drug solution is fully dissolved in the dissolution medium. For example, the extrapolated values of Cmax,ext of 74.6, 185.9 and 367.2 μg/mL (Figure 9) are very similar to the calculated Call values of 76.9, 192.3 and 384.6 μg/ mL for IND, NAP and PIR, respectively. Here, the total amount of drug infused in each run was maintained constant, but a different total amount was employed for different drugs to account for their solubility differences. In this case, the closeness of Cmax,ext and Call values suggests that the effect of drug precipitation during this infinitesimally small infusion period (i.e., near infinite rate of supersaturation generation) is quite negligible. Furthermore, using IND as an example and numerically solving eqs 14a, 14b, 14c, 14d and 14e at an extremely high IND solution infusion rate (e.g., 15 mL/min), a Cmax of 77.1 μg/mL is predicted from the calculated kinetic solubility profile (see inset of Figure 9). This Cmax predicted at very fast IND infusion agrees very well (within 0.3%) with the theoretical Call at which all drug content in the infused drug solution is fully dissolved in the dissolution medium. In addition, the Cmax versus IND infusion rate plot in the inset of Figure 9 shows that the agreement between the current model simulations and experimental Cmax data is quite good. In previous attempts of estimating the solubility advantage of amorphous solids, there usually exists a large discrepancy between the measured values and the ones predicted from various estimations of Gibbs free energy difference.19,60−63 Based on the data and kinetic analysis presented above, the 4340



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Figure 10. Crystallization kinetics of (A) IND, (B) NAP and (C) PIR as a function of supersaturation rate generated with various drug solution infusion rates (0.03 to 2 mL/min) converted from kinetic solubility data described in Figure 3. Total amount of drug infused or introduced for each run: 20 mg for IND, 50 mg for NAP and 100 mg for PIR.

portion of the crystallization profile) as the drug solution infusion rate (or rate of supersaturation generation) increases. The total amount of drug crystallized from different supersaturated solutions eventually approaches a constant value characteristic of each drug. To investigate the difference between the observed quasisteady state drug concentration in the de-supersaturation phase of the IND kinetic solubility profile and the equilibrium solubility of its crystalline counterparts as described in Figure 3A, precipitated solids from the IND infusion experiments of Figure 3A and from the IND-PVP ASD addition experiments of Figure 8 were collected and air-dried at room temperature for XRD and thermal analysis. The XRD spectra of Figure 11 suggest that the precipitated IND solids from both the IND infusion (from sample of the highest infusion rate of 2 mL/ min) and the addition of IND-PVP ASD (from sample of the fastest addition rate; “all at 0 min”) are mostly the metastable α-polymorph, having characteristic peaks at 2θ of 8.4°, 14.4° and 22.0°. Since the solubility differences of IND polymorphs have been well documented,50 the elevated solubility of precipitated α-IND solids versus the lower solubility of the more stable crystalline γ-IND is manifested in the steady state portion of the kinetic solubility profiles generated from the infusion experiment of Figure 3A. Based on the DSC thermograms of Figure 12 where γ-IND shows a melting point at 162.8 °C and α-IND at 155.0 °C, IND solids precipitated in the dissolution medium infused with IND

Figure 11. Comparison of XRD spectra of (a) γ-IND, (b) α-IND, (c) IND precipitated from IND solution infusion experiment (2 mL/min from Figure 3A) and (d) IND precipitated from ASD IND-PVP addition experiment (rate schedule “all at 0 min” from Figure 8).

solution at both low and high infusion rates (0.03 and 2 mL/ min) appear to be completely the α-polymorph as a result of 4341



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supersaturation generation29 as well as the rate of crystal formation.66 Although the elevated solubility of precipitated αIND solids as compared to the lower solubility of the crystalline γ-IND is manifested in the kinetic solubility profiles from the infusion experiment (Figure 3A), the quasi-steady state drug concentrations in the de-supersaturation phase of NAP and PIR appear to be indistinguishable from the equilibrium solubility of their crystalline counterparts (Figure 3B,C). This may not be surprising since literature data reveal that all four polymorphs of NAP have similar equilibrium solubility67 and the polymorph I of PIR purchased from Sigma-Aldrich has similar equilibrium solubility as the most unstable polymorph II, among a total of three discovered polymorphs of PIR.68 The SEM images of these precipitated solids from kinetic solubility experiments are shown in Figure 13. It can be seen that IND solids precipitated from the IND solution infusion experiment exhibit a crystal habit of acicular (needle-like) tapered morphology (Figure 13A,B), as compared to the less pronounced fibrous structure produced from the dissolution of administered IND-PVP ASD powder (Figure 13C,D). The needle-like morphology agrees well with the previously reported SEM image of α-IND which was also confirmed by the XRD.69 The crystal habit of precipitated drug solids appears to be platy pinacoid sheets for NAP (Figure 13E,F) and isometric cubes for PIR (Figure 13G,H). In general, a faster rate of supersaturation generation (e.g., from faster infusion or addition rate) often leads to poorer crystal quality as a result of rapid and uncontrolled nucleation and crystal growth;70 this seems to be evident in Figure 13 between samples of slow and fast infusion rates. In addition, our experimental data show that a slower rate of supersaturation generation produces a wider particle size distribution and a larger average particle size (Figure 14). A similar trend of time-dependent growth of IND particle size under various rates of supersaturation generation can also be predicted from computer simulation based on the comprehensive mechanistic model presented earlier (see Figure 15). This agrees well with many previously studied crystallization processes where the correlation between the rate of supersaturation generation and the crystal size

Figure 12. Comparison of DSC thermograms of (a) γ-IND, (b) αIND, (c) amorphous IND, (d) IND precipitated from IND solution infusion experiment (2 mL/min from Figure 3A), (e) IND precipitated from IND solution infusion experiment (0.03 mL/min from Figure 3A), (f) IND precipitated from ASD IND-PVP addition experiment (rate schedule “all at 0 min” from Figure 8) and (g) IND precipitated from ASD IND-PVP addition experiment (rate schedule “20 mg/20 min for 200 min” from Figure 8).

the rapid crystallization process during the sharp decline of drug concentration in the de-supersaturation phase (Figure 3A and Figure 12d,e). However, IND solids precipitated in the dissolution medium administered with solid IND-PVP ASD powder at different addition rates are mainly α-polymorph mixed with a small amount of γ-polymorph (Figure 12f,g). The slight difference in the XRD and DSC results regarding the presence of γ-polymorph (Figure 11d vs Figure 12f) may be attributed to the better sensitivity of DSC in differentiating small quantities of crystalline polymorphs. Since dissolved PVP is known to retard crystallization in supersaturated solutions,57 the delayed and slowed recrystallization process may allow the system to form a more thermodynamically stable γ-polymorph as it is known that the type of polymorphs precipitated from supersaturated solution can be affected by the rate of

Figure 13. SEM images of (A) IND precipitated from IND solution infusion experiment (2 mL/min from Figure 3A), (B) IND precipitated from IND solution infusion experiment (0.1 mL/min from Figure 3A), (C) IND precipitated from ASD IND-PVP addition experiment (rate schedule “all at 0 min” from Figure 8), (D) IND precipitated from ASD IND-PVP addition experiment (rate schedule “20 mg/20 min for 200 min” from Figure 8), (E) NAP precipitated from NAP solution infusion experiment (2 mL/min from Figure 3B), (F) NAP precipitated from NAP solution infusion experiment (0.1 mL/min from Figure 3B), (G) PIR precipitated from PIR solution infusion experiment (2 mL/min from Figure 3C) and (H) PIR precipitated from PIR solution infusion experiment (0.1 mL/min from Figure 3C). 4342



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Figure 16. Conceptual concentration−time profile during dissolution and precipitation of amorphous sparingly soluble drugs.

Figure 14. Particle size distributions of precipitated IND from the infusion experiment (described under the subtopic of “particle size distribution” in the Experimental Section) under different IND solution infusion rates.

in a period of time) is a positive value when the degree of supersaturation is greater than unity (eq 4) and the primary nucleation spontaneously occurs via a homogeneous nucleation mechanism in the absence of crystalline seeds. In other words, when the drug concentration is higher than the equilibrium solubility, nucleation is a continuous kinetic process in which the rate significantly depends on the degree of supersaturation. At a low supersaturation level, nucleation rate is too slow to produce any noticeable depreciation of dissolved drug concentration in the dissolution medium. On the other hand, as the rate of supersaturation generation increases (or for a larger linear slope in phase 1), a higher degree of supersaturation is reached earlier in phase 1, resulting in an increase of the nucleation rate and an earlier onset of phase 2. At a higher nucleation rate, it is expected to generate a higher particle number density of crystalline particles and a smaller average particle size. This is supported by the observation that the average particle size produced at faster drug infusion rates is smaller than that at slower infusion rates (Figures 14 and 15). As soon as the nuclei are formed, a portion of them grow under local supersaturation conditions. At the same time, smaller particles may gradually dissolve via the Ostwald ripening mechanism creating supersaturation and thus becoming a source of drug for the growth of surviving nuclei. As a result, crystallization will only take place when a population of stable, surviving nuclei establishes itself. Subsequent consumption of dissolved drug in supersaturated solution results in the growth of the stable nuclei. In phase 2, while the drug dissolution continues to build up supersaturation, the measured drug concentration starts to deviate from the theoretical limit of complete dissolution of added amorphous drug (red dotted line) as a result of further crystal growth from established nuclei in highly supersaturated solution. Subsequently, a local maximum in the concentration− time profile (kinetic solubility) occurs in phase 2 below the critical supersaturation as a result of comparable rates of dissolution (supersaturation) and crystallization (de-supersaturation). Here, the “critical supersaturation”, to use terminology from the field of crystal engineering, represents a limiting state of supersaturation above which spontaneous and uncontrolled crystallization occurs. After reaching the maximum supersaturation, crystallization rate begins to dominate the latter part of phase 2, triggering the onset of a rapid decline of drug concentration in the de-supersaturation phase.

Figure 15. Simulated time-dependent growth of IND particle size under various rates of supersaturation generation based on eq 14e.

distribution has been elucidated.71,72 Moreover, the multimicrometer size range of our particle size data (Figures 14 and 15) suggests that the second-derivative UV method employed in the present study for the measurements of drug concentration in the presence of precipitated particles should not encounter the issue of spectroscopic interference previously observed in drug solutions containing precipitated particles in the nanometer size range.18,73 Evolution of Concentration−Time Profiles Due to Dissolution and Recrystallization Processes. Based on the present results, it is clear that the evolution of supersaturation during the dissolution of amorphous pharmaceuticals is governed by competing processes involving dissolution and precipitation, and Figure 16 depicts a conceptual concentration−time profile of such a system. For the sake of simplicity, the drug dissolution will be assumed to follow a linear profile as produced by the present drug infusion experiment; nevertheless, the analysis presented here can be readily extended to other drug dissolution profiles. In Figure 16, phase 1 corresponds to the gradual buildup of supersaturation in a precipitate-free solution leading to the formation of small embryos and nuclei (i.e., nucleation). According to the classical nucleation theory, nucleation rate (number of particles formed 4343



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for each individual drug. Based on the present results, the rate of supersaturation generation plays a key role in determining the overall shape of the resulting kinetic solubility profiles, which is a manifestation of the competing dissolution and crystallization processes. The critical finding of this study that the maximum peak concentration of a kinetic solubility profile depends on the rate of supersaturation generation has revealed the likely underlying cause of the large variability in the reported solubility advantage values. This is because these are routinely determined from the highest attainable peak concentration in a kinetic solubility profile, but it is virtually impossible to ascertain the same rate of supersaturation generation in these different studies. Although the present comprehensive mechanistic model for the prediction of kinetic solubility profiles considers only a linear dissolution profile from the drug infusion, this analysis can be readily extended to other nonlinear drug dissolution profiles from polymers, and as such it should be of great utility for comparing solubility improvement of ASD systems of poorly water-soluble drugs involving various polymeric carriers.

When drug dissolution stops (onset of phase 3), the remaining concentration−time curve is governed solely by the crystal growth kinetics of existing and continuously formed nuclei. Several theories have been proposed to describe the mechanism and rate of crystal growth, and the kinetics of crystal growth from supersaturated solutions has been covered in comprehensive reviews.74,75 In general, two main processes occur sequentially during the growth of crystals from solution: the mass transfer of growth unit via bulk diffusion and the incorporation of growth units into the crystal lattice through surface integration. Lastly, after the crystal growth exhausts most of the dissolved solute from the surrounding solution, the equilibrium solubility of the most stable crystalline form, or of a metastable polymorph that is sometimes higher than that of the most thermodynamically stable polymorphic form, would be reached. The concentration range between the critical supersaturation and the equilibrium solubility of the most stable crystalline form (or sometimes the equilibrium solubility of a metastable polymorph) is known as the metastable zone width. This metastable zone width as a function of supersaturation rate provides a working concentration range for creating supersaturated solutions of poorly water-soluble drugs. The rate of supersaturation generation thus plays a key role in determining the overall shape of the resulting kinetic solubility profiles, which is a manifestation of the competing dissolution and crystallization processes as illustrated in earlier sections.

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AUTHOR INFORMATION

Corresponding Author

*Leslie Dan Faculty of Pharmacy, University of Toronto, 144 College Street, Toronto, Ontario M5S 3M2, Canada. Tel: +1416-946-0606. Fax: +1-416-978-8511. E-mail: ping.lee@ utoronto.ca.

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CONCLUSIONS The effect of rate of supersaturation generation of poorly watersoluble drugs on the resulting kinetic solubility profiles of amorphous systems under nonsink dissolution conditions has been examined in detail both theoretically and experimentally. In the absence of any dissolved polymer to inhibit drug precipitation from the supersaturated state, both our experimental and predicted results confirm that the faster rise of the kinetic solubility profile of an amorphous drug will inevitably lead to an earlier but higher maximum kinetic solubility and a sharper drop in the de-supersaturation phase, and vice versa. The relationship between the achievable maximum supersaturation and the rate of supersaturation generation in the observed kinetic solubility profiles has been described for the first time by our comprehensive mechanistic model taking into account the role of supersaturation in both the nucleation and crystallization processes as well as the associated competitive particle growth and ripening effects. Our mechanistic model also predicts the existence of an optimal supersaturation rate which maximizes the area under the curve (AUC) of the kinetic solubility concentration−time profile, which agrees well with experimental data. Therefore, the effect of rate of supersaturation generation should be carefully considered in designing an optimal oral dosage form of ASD in order to achieve an appropriate level of sustained solubility enhancement for poorly water-soluble drugs such that the AUC of the kinetic solubility concentration−time profile and ultimately the bioavailability can be optimized. We have also shown that the crystallization kinetics under different rates of supersaturation generation for the three model drugs IND, NAP and PIR can be evaluated from the concentration−time profiles of the kinetic solubility experiments. Based on the XRD and SEM analyses of the precipitated crystalline drugs, it is clear that the types of polymorphs (if they exist) precipitated from supersaturated solutions will depend on the rate of supersaturation generation as well as on the rate of crystal formation

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC). D.D.S. was also supported by a University of Toronto Fellowship Award.

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REFERENCES

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