Evolution of Supersaturation of Amorphous Pharmaceuticals

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Evolution of supersaturation of amorphous pharmaceuticals: Nonlinear rate of supersaturation generation regulated by matrix diffusion Dajun D. Sun, and Ping I. Lee Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/mp500711c • Publication Date (Web): 16 Mar 2015 Downloaded from http://pubs.acs.org on March 21, 2015

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Molecular Pharmaceutics

Evolution of supersaturation of amorphous pharmaceuticals: Nonlinear rate of supersaturation generation regulated by matrix diffusion

Dajun D. Sun1,2 and Ping I. Lee1,3 Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, Toronto, Ontario M5S 3M2, Canada

1. Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, Toronto, Ontario M5S 3M2, Canada 2. Present address: Food and Drug Administration, 10903 New Hampshire Avenue, Silver Spring, MD 20993, USA 3. To whom correspondence should be addressed. Mailing address: Leslie Dan Faculty of Pharmacy, University of Toronto, 144 College Street, Toronto, Ontario M5S 3M2, Canada. Tel: +1-416-9460606 Fax: +1-416-978-8511 E-mail: [email protected] ACS Paragon Plus Environment


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Abstract The importance of rate of supersaturation generation on the kinetic solubility profiles of amorphous systems has recently been shown by us; however, the previous focus was limited to constant rates of supersaturation generation. The objective of the current study is to further examine the effect of nonlinear rate profiles of supersaturation generation in amorphous systems, including (1) instantaneous or infinite rate (i.e., initial degree of supersaturation), (2) first-order rate (e.g., from dissolution of amorphous drug particles), and (3) matrix diffusion regulated rate (e.g., drug release from amorphous solid dispersions (ASDs) based on crosslinked poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogels), on the kinetic solubility profiles of a model poorly soluble drug indomethacin (IND) under nonsink dissolution conditions. The previously established mechanistic model taking into consideration both the crystal growth and ripening processes was extended to predict the evolution of supersaturation resulting from nonlinear rates of supersaturation generation. Our results confirm that excessively high initial supersaturation or a rapid supersaturation generation leads to a surge in maximum supersaturation followed by a rapid decrease in drug concentration owing to supersaturation-induced precipitation; however, an exceedingly low degree of supersaturation or a slow rate of supersaturation generation does not sufficiently raise the supersaturation level, resulting in a lower but broader maximum kinetic solubility profile. Our experimental data suggest that an optimal AUC of the kinetic solubility profiles exists at an intermediate initial supersaturation level for the amorphous systems studied here, agreeing well with the predicted trend. Our model predictions also support our experimental findings that IND ASD in crosslinked PHEMA exhibits a unique kinetic solubility profile because the resulting supersaturation level is governed by a matrix diffusion regulated mechanism as oppose to that resulted from a high level of initial supersaturation or a rapid dissolution of amorphous solids. This more gradual drug release from IND-PHEMA ASD leads to a more gradual buildup of a sustained supersaturation even without the presence of any dissolved polymer to inhibit the drug precipitation, which avoids the rapid surge of supersaturation above a critical value as normally associated with high initial degrees of 2 ACS Paragon Plus Environment


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supersaturation or rapid dissolution of amorphous IND solids, thus avoiding the onset of fast uncontrolled precipitation. This characteristic feature makes crosslinked insoluble PHEMA an attractive carrier for amorphous pharmaceuticals.

Key words: supersaturation rate, kinetic solubility, crystallization, amorphous solid dispersion, poorly water-soluble drug, crosslinked hydrogels


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Introduction The technology of forming amorphous solid dispersions (ASDs) of a poorly soluble drug in a suitable polymeric carrier has gained increasing popularity as a viable formulation strategy for improving the kinetic solubility and oral bioavailability of drugs with poor aqueous solubility1-3. In this case, the inherently higher kinetic solubility of amorphous drugs, due to their higher internal free energy than that of their crystalline counterparts, provides an increased driving force for oral absorption. However, amorphous drugs incorporated in soluble polymeric carriers have a tendency to generate a transient but exceedingly supersaturated drug solution under nonsink dissolution conditions, which inevitably leads to the onset of recrystallization manifested by a sharp decline in the overall supersaturation over time4-7. The occurrence of such supersaturation-induced recrystallization in the dissolution medium reduces the effectiveness of ASD systems in achieving dissolution and oral bioavailability enhancement. We have previously explored the dissolution behavior of a solid molecular dispersion system incorporating a poorly water-soluble model drug indomethacin (IND) in water-insoluble crosslinked poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogel beads and compared it with that of conventional ASDs in water-soluble polymeric carriers8. Our previous findings demonstrate that the sustained drug supersaturation observed during the gradual release of IND from PHEMA beads-based ASDs is a direct result of a matrix diffusion regulated mechanism under nonsink dissolution conditions, which prevents the drug supersaturation from exceeding its critical value in the bulk medium. As a consequence, a sharp decline in drug supersaturation triggered by the accompanying nucleation and crystallization processes as generally observed in conventional ASDs based on water-soluble polymeric carriers is avoided. This sustained level of supersaturation is maintained by the IND-PHEMA ASD system despite the absence of any dissolved excipient (i.e., crosslinked PHEMA is insoluble) to inhibit the nucleation and crystallization events. Other studies have also observed drug supersaturation sustaining over a prolonged period of time as a result of slow fenofibrate release from ordered mesoporous silica9 and 4 ACS Paragon Plus Environment


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retarded griseofulvin release from swelling clay minerals10 (note: both the mesoporous silica and the swelling clay minerals are insoluble) under nonsink dissolution conditions. These independent studies together have provided strong evidence that the kinetic solubility profiles of amorphous pharmaceuticals is significantly influenced by the rate of supersaturation generation. Recently, our group showed that the rate of supersaturation generation critically affects the kinetic solubility of amorphous drugs determined under nonsink dissolution conditions, and characterized the kinetic solubility profiles quantitatively by delineating the interrelationship between the kinetics of dissolution and precipitation from a mechanic viewpoint11. The time evolution of supersaturation as a function of linear rate of supersaturation generation for indomethacin, naproxen and piroxicam was determined by infusing drug solutions in water-miscible organic solvents into the bulk medium. A mechanistic model based on classical nucleation theory considering both crystal growth and ripening was developed to predict the overall trends of the resulting kinetic solubility profiles. Both experimental data and theoretical prediction illustrate that a faster generation of supersaturation will result in a shorter Tmax (i.e., time to reach the maximum concentration), a higher Cmax (i.e., maximum supersaturation in the kinetic solubility profiles), and a more rapid decline in drug concentration after reaching Cmax. Conversely, a slower rate of supersaturation generation leads to a lower kinetic solubility followed by a slower decrease in drug concentration. For the sake of simplicity, this semiquantitative analysis was initially established to demonstrate the dependency of maximum supersaturation achievable and the overall supersaturation concentration-time profile as a function of the supersaturation generation rate based on infusion experiments having simple constant rates of drug input (i.e., a constant rate of supersaturation generation from a constant rate of addition of dissolved drug). However, the release of amorphous drugs from a variety of carriers is rarely at a constant rate and is often governed by a diffusion regulated mechanism under nonsink dissolution conditions (e.g., nonlinear drug release from ASDs based on hydrogels). Therefore, the previously established theoretical framework will be further extended here to characterize kinetic solubility profiles of amorphous drugs 5 ACS Paragon Plus Environment

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resulting from various nonlinear rates of supersaturation generation (e.g., from nonlinear drug release profiles, including those from IND-PHEMA ASDs under finite-volume or nonsink diffusion conditions). In this case, previous modeling equations for linear rates of supersaturation generation will be modified to predict the overall kinetic solubility profiles under nonlinear rates of supersaturation generation associated with diffusion regulated release of amorphous drugs from swollen hydrogel beads under nonsink dissolution conditions. Many oral controlled release delivery systems based on crosslinked hydrophilic polymers have been extensively characterized12, 13. A variety of mathematical models of general validity have been proposed to describe the release of poorly water-soluble crystalline drugs dispersed in carriers14-19. Nevertheless, the diffusion regulated release of amorphous drugs from insoluble polymeric carriers into a finite-volume dissolution medium has not been fully investigated. For example, such ASD systems under nonsink dissolution conditions can still generate a sufficiently high drug supersaturation which eventually leads to nucleation and crystallization in the finite-volume dissolution medium. Thus, for ASD systems based on PHEMA hydrogels, the proposed model needs to take into account both the diffusion regulated amorphous drug release from the hydrogel matrix and supersaturation-induced drug precipitation in the external finite-volume dissolution medium. The present work aims at extending our previously established mechanistic model to delineate the interplay between the diffusion regulated supersaturation buildup from a hydrogel ASD and the drug precipitation event in the external medium at the molecular level so as to predict the macroscopic kinetic solubility profiles. Here, we will also employ experimental and predicted results to compare the dissolution behavior of pure amorphous IND particles with that of amorphous IND ASD in crosslinked PHEMA, thereby demonstrating the advantage of the matrix diffusion regulated mechanism in generating and sustaining drug supersaturation from ASDs based on crosslinked hydrogels.



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Theory Overview of the theoretical framework. We have recently shown that the rate of supersaturation generation and the rate of recrystallization are important factors that dictate the observed kinetic concentration-time profiles during the dissolution of amorphous pharmaceuticals11. From a mass balance perspective, the rate of concentration change of dissolved drug molecules in a closed dissolution system can be expressed by the following differential equation:

=−

Equation 1

where t is time, C the concentration of dissolved drug in the dissolution medium, R the rate of drug input, and u the rate of drug precipitation. For the sake of clarity and completeness, we will present here the main features of the comprehensive mechanistic model proposed by Sun and Lee11 and generalize it to include various nonlinear rate profiles of supersaturation generation. Based on the classical nucleation theory and the assumption that all spherical drug particles grow independently of each other, a molar precipitation rate u taking into account both the instantaneous nucleation and the growth of particles nucleated in the past (at t’) can be expressed as: =

+

, ′ ′

Equation 2

where υ is the molar volume of precipitate, J(t’) the nucleation rate, r(t,t’) the radius of precipitated particles at time t given that it was nucleated at time t’ and rn the critical particle size when nuclei start to form. The nucleation rate J and critical particle size rn can then be calculated by20: = =

! −"#$ % , ≥ 1 * 0, < 1

Equation 3

,

= +$ = -. 0

Equation 4

where the dimensionless supersaturation s, the nucleation rate constant , the capillary length ω, the molar volume 1 and the constant # are defined as

=

Equation 5

2


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and 445+ 67 = += 1=

219 :;

?@

A

C, D

# = B E

FG

H

IJ

Equation 6

where D is the drug diffusion coefficient in the dissolution medium, C the bulk concentration, Cs the equilibrium solubility, N0 the Avogadro’s number, T the temperature, kB the Boltzmann’s constant, σ the surface tension and d a typical molecular size, MW the molecular weight, and ρ the crystal density. The particle grow rate is an interface-controlled process described by the following rate equation21, 22:

=KL

MN OPQ

R

2

Equation 7

where G is the particle growth rate constant and Ceq(r) the concentration in equilibrium with a precipitate particle of radius r. The Gibbs-Thomson relation provides an expression for Ceq(r) which includes the radius-dependent surface tension via a dimensionless parameter Ψ: 6ST = 67 exp L Ψ ≅

D [\

D [ \[

,X

R Equation 8

]D Q

where q = 0.304359 (simplified from a thermodynamically based expression with a maximum relative error of 0.8%) and δ the thickness of the Gibbs surface23. We then introduce the average surface of the precipitate particle per unit volume Σ, the average radius of the particles per unit volume Φ, and the average particle number density N as follows:

Σ = 44 , ′ , ′

Φ = , ′ , ′′ 8 ACS Paragon Plus Environment


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: = , ′′

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Equation 9

A list of dimensionless variables (*) are then defined as follows: ∗ =

a

b=

cd , e MN

,

a2

Σ∗ =

MN , 2

Σ

Φ∗ =

MN ,D

Φ

N∗ =

MN ,g

N

2

2

r ∗ = ωr

Equation 10

Based on the approach of Chacron and L’Heureux21, Equation 1 and the integro-differential Equation 2 can be transformed into a set of coupled differential equations by taking the time-derivative of Σ, Φ and N in Equation 9. The following generalized set of five nondimensionalized differential equations are therefore obtained and can be solved numerically for the evolution of supersaturation, s(t): XJ ∗ HΣ

0

= ∗ − B −

k∗

= b$ + 2 B −

l∗

= b$ + B −

M ∗

= b

∗

=−

∗ ∗

∗

∗

∗

j

− $

Equation 11

XJ ∗ H Φ∗

Equation 12

XJ ∗ H :∗

Equation 13 Equation 14

XJ ∗

Equation 15

Subject to initial conditions and experimental end point: 0 = m 0 = n 0 = : 0 = 0 = 0 " = ′

Equation 16

where ′ is the measured concentration at time t” which represents the time when the dissolution measurement ends. The kinetic solubility profile obtained here describes the time evolution of 9 ACS Paragon Plus Environment

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supersaturation as affected by the rate of supersaturation generation through the interplay between the dissolution and precipitation processes during the dissolution of an amorphous pharmaceutical system. The dimensionless R* in Equation 11 describing the rate of supersaturation generation may have various time-dependent functional forms depending on the dissolution profile of the specific amorphous pharmaceutical system. We have previously studied a simple scenario at which supersaturation is generated through a constant-rate infusion of dissolved drug (i.e., a linear dissolution rate with a constant R*)11. For the purpose of this study, the following dissolution profiles of amorphous drugs will be employed here to cover a range of different rate profiles of supersaturation: (1) instantaneous or infinite rate (i.e., initial degree of supersaturation), (2) first-order rate (e.g., from dissolution of amorphous drug particles) and (3) matrix diffusion regulated rate (e.g., drug release from amorphous ASDs based on crosslinked PHEMA hydrogels).

Effect of initial degree of supersaturation (instantaneous generation of supersaturation). To examine the effect of initial degree of supersaturation on the kinetic solubility profiles, we consider the physical process involved when a small amount of water-miscible solvent containing a given amount of a poorly water-soluble drug (i.e., dissolved drug) is added all at once into an aqueous dissolution medium. This instantaneously added drug solution generates a prescribed degree of initial supersaturation. A mathematical simulation of this system can be formulated by modifying the current set of coupled nonlinear differential equations for the evolution of supersaturation. In this case, the infusion rate R* of drug input in Equation 11 can be eliminated as there is no drug input after time zero, and the initial degree of supersaturation can be replaced by a constant supersaturation, sinitial. Equation 11 then becomes: 0

∗

= 0 − B −

XJ ∗ HΣ

j

− $

Equation 17

Subject to the initial condition and experimental end point: 0 = pppqr 10 ACS Paragon Plus Environment


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" = ′

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Equation 18

First-order supersaturation generation - dissolution of amorphous drug particles. The evolution of supersaturation from the dissolution of solid particles of amorphous pharmaceuticals such as pure amorphous drugs or ASD based on water-soluble polymers can be delineated from the present mechanistic model. Here, we consider the physical process when amorphous drugs or soluble ASD particles of different particle sizes are added to the dissolution medium under nonsink and well-stirred conditions. The dimensionless rate of supersaturation generation R* in Equation 11 can be described by an appropriate time-dependent function characteristic of the amorphous system being considered. In this case, the dissolution of amorphous solids is assumed to be rapid and therefore unaffected by any subsequent recrystallization in the dissolution medium, which can be approximated by a general empirical first-order equation: C = Ct u1 − eOvt w

Equation 19

where C is drug concentration at time t, Ct the drug concentration if all the drug is dissolved, and k the rate constant for the drug dissolution (note: it is understood that k is a lumped parameter which encompasses the effect of different particle sizes and their distribution). The dissolution rate or the rate of drug input can be determined by taking the first derivative:

= 0,

= 0,

| |}

=0

> 0, = , 6 = !6 or > 0, = ,

= 5′

Equation 25

=

I |

Equation 26

|

|

Equation 27

|}

where Co is the initial drug loading in the hydrogel based ASD, p the partition coefficient between the hydrogel phase and the dissolution medium, V the volume of dissolution medium and A the surface area of the hydrogel bead. Combining Equations 26 and 27, the boundary condition at the surface of the hydrogel bead (t > 0, x = a) becomes: |

|} = B

5′

|

H |

Equation 28

In Equations 23-28, the drug concentration C in the hydrogel bead is a function of both time t and radial position variable x, but the bulk concentration of the external medium Cb or the drug supersaturation s (i.e., Cb/Cs) is a function of time only. The exact solution to the partial differential equation, Equation 23, with similar initial and boundary conditions was originally obtained by Carman and Haul24 for analyzing a diffusion-controlled sorption process from a constant and limited volume of a well-stirred fluid. Mathematically, this is similar to an equivalent problem in heat conduction between a solid and a finite volume of well-stirred fluid25. The major difference between the release of amorphous drugs from PHEMA hydrogels considered here and that described by Carman and Haul’s solution is the additional account of the precipitation process triggered by the drug supersaturation buildup in the external medium generated by drug release from the present hydrogel based ASD. Therefore, Equation 11 is modified into the following equation to account for the rate of supersaturation generation in the external finite-volume medium: 0

∗

=

/2 ∗

− B −

XJ ∗ HΣ

j

− $

Equation 29

It should be noted that the diffusion equation based on Fick’s second law, Equation 23 with initial and boundary conditions Equations 24, 25 and 28, describes the drug concentration changes within the hydrogel bead, whereas the set of coupled differential equations based on the classical nucleation theory 14 ACS Paragon Plus Environment


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taking into account both the particle growth and ripening processes (Equations 29, 12-15 with initial conditions Equation 16) describe the drug concentration changes in the external finite-volume medium. These two sets of differential equations linked by the external bulk concentration term Cb in both sets of equations will be numerically solved together using the COMSOL Multiphysics® software.


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Experimental Section Materials. γ-polymorph of indomethacin (γ-IND) was purchased from Sigma-Aldrich Canada and used without further purification. PHEMA hydrogel beads were synthesized by a free radical initiated polymerization process based on previously reported protocols26. Preparation of amorphous IND and ASD IND-PHEMA. Pure amorphous IND was prepared by completely melting crystalline γ-IND at approximately 10 degree above its melting temperature (161 o

C) on a small piece of aluminum foil using a hot plate and holding for approximately 2 min. The

melted drug was subsequently quenched in liquid nitrogen. The solidified sample was then lightly grounded with a mortar and pestle in a small amount of liquid nitrogen to avoid heat-induced crystallization. The resulting powder was sieved into various particle size ranges using a mini-sieve (10) was carried out. Dissolution testing of solid-state amorphous IND of various particle sizes was performed on a USP II dissolution apparatus using 900 mL 3% SDS in distilled H2O as dissolution medium maintained at 37oC ± 0.5 oC and at a paddle speed of 150 rpm. At each predetermined time interval, 3 mL aliquot was removed and replaced with 3 mL fresh dissolution


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medium. The removed aliquot was then passed through a Millex 0.22-µm syringe filter. Drug concentration in the aliquot was determined spectrophotometrically at 320 nm for IND. Simulation of modeling equations. Drug concentration profiles were simulated by numerically solving coupled differential equations with appropriate values of constants for IND and boundary conditions using the 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. All physical constants for IND used in the present numerical simulation can be found in our previous study11.



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Results and Discussion Effect of initial degree of supersaturation. IND kinetic solubility profiles empirically obtained at different degrees of initial supersaturation between sinitial =1.3 and 10.9 (note: supersaturation s = C/Cs), which correspond to initial IND concentrations between 10.1 and 84.3 µg/mL, are shown in Figure 2. When the IND initial concentration exceeds approximately 30 µg/mL, a prominent desupersaturation phase appears as evident by the rapid depreciation of drug concentration with time during dissolution. The kinetic solubility profiles and crystallization kinetics of IND are evidently dependent on the initial degree of supersaturation. In this case, the IND crystallization rate is much faster when the de-supersaturation phase is initiated at a high initial degree of supersaturation as compared with that at a low initial supersaturation. This trend is not surprising as the nucleation rate directly depends on the degree of supersaturation according to the classical nucleation theory (Equation 3). Thus, a high degree of initial supersaturation inevitably leads to a rapid nucleation rate followed by the crystal growth. When the IND initial supersaturation is lower than a critical value of approximately 30 µg/mL, the nucleation and crystallization rates are evidently rather slow as indicated by the absence of an apparent decline in drug concentration over 8 h (sinitial =1.3, 2.6 and 3.9 in Figure 2). Although the drug solution is considered supersaturated in these cases (i.e., higher than the equilibrium solubility of the most thermodynamically stable γ-IND crystal), the crystallization process is apparently quite slow during this observation period due to a diminished driving force for nucleation and crystallization as reflected in the relatively constant level of drug concentration over 8 h.


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Figure 2: Kinetic solubility profiles of IND at various initial degrees of supersaturation between sinitial =1.3 and sinitial =10.9 which translate to drug concentrations between 10.1 and 84.3 µg/mL.

The abovementioned trends in observed kinetic solubility profiles as a function of the initial degrees of supersaturation can be predicted from the proposed mechanistic model using empirical parameters related to the IND crystallization kinetics as described in the previous study11. It should be noted that these parameter values employed in the numerical simulation were adopted from relevant empirical data reported in the literature without any parametric optimization through curve fitting in order to provide mechanistic insights into the resulting kinetic solubility profiles of ASD systems. Numerically solving Equations 17 and 12-15 with the initial conditions of Equation 18 generates different kinetic solubility profiles based on the initial degrees of supersaturation. The general trend of IND supersaturation profiles predicted from the mechanistic model (shown in Figure 3) is quite similar to that observed from the experimental data (see Figure 2). A high degree of initial supersaturation leads to a rapid nucleation rate, and therefore a high number of nuclei form in the supersaturated solution that lead to a fast rate of de-supersaturation due to crystallization. Conversely, a lower degree of initial supersaturation avoids a sudden surge of supersaturation that manifests in a more gradual decline in drug concentration in the de20 ACS Paragon Plus Environment


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supersaturation phase. During the time period of the dissolution study, it appears that below an initial supersaturation of sinitial=3.9, the kinetic solubility profiles exhibit a much widened peak (appearing like a quasi-steady state of elevated kinetic solubility) with a very slow de-supersaturation phase which eventually approaches the solubility of the metastable α-IND polymorph (IND concentration around 23.3 µg/mL or s’ =3; Figure 2). This is consistent with our previous findings11 that the precipitated IND from both the IND solution infusion and the dissolution of IND-PVP ASD are mostly the metastable αIND polymorph. It is expected that, given sufficient time, this metastable α-IND polymorph will eventually undergo solvent-mediated transformation to the thermodynamically stable γ-IND polymorph (solubility 7.72 µg/mL). From the perspective of mathematical modeling and simulation, the numerical solution does not converge if the initial degree of supersaturation is set to be lower than s’.

Figure 3: COMSOL simulation of kinetic solubility profiles solving Equations 17 and 12-15 with initial conditions of Equation 18 at various initial degrees of supersaturation, sinitial.


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Supersaturation provides the driving force for crystal nucleation and growth and the kinetics of the overall crystallization process depends on the degree of supersaturation30-33. The relationship between indomethacin crystallization kinetics and the degree of supersaturation has been previously investigated27. The degree of supersaturation generated by supersaturating drug delivery systems in in vitro studies also depends on the drug loading, matrix composition and preparation method34. Since the degree of supersaturation is a ratio between measured concentration and the equilibrium solubility (Equation 5), increasing the solubility reduces the degree of supersaturation and slows the associated nucleation and crystallization events. Therefore, it is important to be aware that the degree of supersaturation will depend on the choice and composition of excipients. For example, some excipients act as surfactants to increase the solubilizing capacity of drugs thereby decreasing the degree of supersaturation and changing the precipitation kinetics. In other words, these factors can alter the equilibrium solubility of the drug and their dissolution behavior, thus affecting the degree of supersaturation and precipitation kinetics as a consequence35, 36. For the purpose of designing an optimal ASD system for oral dosage forms, both the maximum attainable solubility in the kinetic solubility profiles and the ability to maintain supersaturation for a prolonged duration are essential for achieving enhanced solubility and bioavailability. Both the experimental data and simulation results of this section show that the highest measured drug concentrations during the progression of the kinetic solubility profiles after a bolus dose are the earliest measurements or the initial degrees of supersaturation (Figures 2 & 3). Therefore, it is expected that Cmax (the maximum concentration measured along the kinetic solubility profile) increases as the initial degree of supersaturation increases (Figure 4A). The Cmax of the experimentally measured kinetic solubility profile from the highest initial degree of supersaturation (sinitial =10.9 or IND concentration of 84.3 µg/mL) deviates from that of the simulation results because rapid nucleation and crystallization processes at such a high supersaturation level may have taken place prior to the first time point of concentration measurement. Furthermore, the area-under-the-curve (AUC) of in vitro kinetic solubility 22 ACS Paragon Plus Environment


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concentration-time profiles can be used to correlate the corresponding trend in bioavailability enhancement for in vivo studies. Although the Cmax is increasing with the initial supersaturation level (Figure 4A), there seems to exist an optimal initial supersaturation level that maximizes the AUC of the kinetic solubility concentration-time profile (Figure 4B). This complements our previous finding of an optimal supersaturation rate which maximized the AUC of the kinetic solubility concentration-time profile11. At a very high degree of initial supersaturation, although Cmax is also high, the overall AUC would be compromised by a corresponding sharp decline in drug concentration due to precipitation. On the other hand, at a very low initial supersaturation, the overall AUC would be dominated by the effect of a low Cmax. Although it is commonly known that the nucleation rate in a supersaturated solution increases as the degree of supersaturation increases, we have shown here that an optimal initial degree of supersaturation that balances the solubility enhancement with the reduction in nucleation rate is in principle achievable and would therefore be desirable in designing an effective supersaturating drug delivery system. From a conventional viewpoint of designing ASD systems based on soluble carriers, the initial production of a highly supersaturated system may seem to be important for absorption enhancement. Nevertheless, for slowly permeating drugs in the GI tract, the required time for the stabilization of supersaturation needs to be sufficiently long in order to achieve adequate oral absorption37. Therefore, dissolution from an ASD system with an optimal initial degree of supersaturation and a more prolonged maintenance of such supersaturation should be more advantageous in improving oral absorption as compared with that having a high initial degree of supersaturation while triggering rapid nucleation and crystallization events.


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Figure 4: (A) Maximum concentrations (Cmax), and (B) area-under-the-curve (AUC) from in vitro kinetic solubility profiles and simulation results as a function of initial degree of supersaturation.

Dissolution of amorphous IND from the solid state. The dissolution of amorphous IND solid particles of various particle size ranges (

Evolution of Supersaturation of Amorphous Pharmaceuticals

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