Characterizing the Impact of Hydroxypropylmethyl Cellulose on the

Article pubs.acs.org/crystal

Characterizing the Impact of Hydroxypropylmethyl Cellulose on the Growth and Nucleation Kinetics of Felodipine from Supersaturated Solutions David E. Alonzo,†,‡ Shweta Raina,† Deliang Zhou,§ Yi Gao,‡ Geoff G. Z. Zhang,*,‡ and Lynne S. Taylor*,† †

Department of Industrial and Physical Pharmacy, College of Pharmacy, Purdue University, West Lafayette, Indiana 47907, United States ‡ Global Pharmaceutical Research and Development, Abbott Laboratories, Abbott Park, Illinois 60064, United States § Global Pharmaceutical Operations, Abbott Laboratories, North Chicago, Illinois 60064, United States ABSTRACT: The use of amorphous drugs to generate supersaturated solutions that have the potential to enhance oral drug delivery is currently an area of intense interest. From an in vivo performance standpoint, inhibiting crystallization from these supersaturated systems is extremely important. In this study the ability of a polymer, hydroxypropylmethyl cellulose (HPMC), to inhibit nucleation and crystal growth of felodipine from supersaturated solutions was investigated. Nucleation and bulk crystal growth rates, in the absence and presence of seed crystals, were estimated from de-supersaturation curves. It was found that the presence of ppm levels of predissolved HPMC could inhibit both nucleation and growth of felodipine crystals. Empirical and mechanistic models were used to quantify the magnitude of inhibition. Crystal growth shifted toward an integration-controlled mechanism in the presence of HPMC where the overall impact on the growth rate was found to be strongly dependent on the extent of supersaturation. As predicted by theory, the polymer became less effective as a growth inhibitor with increases in supersaturation. The nucleation rate at similar supersaturations was significantly reduced in the presence of HPMC. A direct comparison of the impact of HPMC on nucleation and growth demonstrated that delaying nucleation was much more crucial to the stabilization of a supersaturated solution than hindering crystal growth.

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INTRODUCTION Crystallization of organic molecules from supersaturated solutions is an important phenomenon in many different fields of research in addition to being a commercially valuable process. It is highly desirable to have the capacity to intentionally manipulate a crystallization process in order to increase product quality as well as process efficiency. This requires a fundamental understanding of the thermodynamic and kinetic factors that govern crystallization. Among the most important of these factors are nucleation and crystal growth, both of which have a significant impact on the physicochemical and structural properties of crystals formed from solution and are often extensively characterized.1 For example, it is well documented that modification of growth by changing the crystallization solvent can alter the habit of a crystal as clearly demonstrated in the case of aspirin.2,3 The habit of a given crystal directly affects macroscopic properties such as flow, which can vary dramatically for different formations (i.e., acicular vs tabular). One important area of research interest is in the ability of dissolved additives or impurities to inhibit or facilitate crystallization.4,5 These impurities can come in many forms including small molecule analogues, proteins, and polymers.6−8 In the pharmaceutical industry, the use of © 2012 American Chemical Society

polymers as crystallization inhibitors to enhance drug delivery has been of interest for decades.9−13 Inhibition of crystallization from supersaturated aqueous solutions is an important area of research in drug delivery for several reasons. Crystalline active pharmaceutical ingredients (APIs) are often poorly soluble in aqueous media as a consequence of some combination of hydrophobicity and crystal lattice energy.14 This is an issue in drug delivery because oral dosage forms (specifically tablets and capsules) are the most convenient way to administer pharmaceuticals with a high level of patient compliance.15 Before an orally dosed API can access the bloodstream and reach its intended site of action, there are two major steps that have to take place. The API must first dissolve in the aqueous based lumen of the gastrointestinal (GI) tract and then pass through the wall of the intestine. If the equilibrium solubility of a crystalline API is very low, the dissolution rate and/or solubility may be a limiting factor in the ability of the API to permeate the wall of the intestine and reach a therapeutically effective plasma concentration. Therefore, formulations that generate supersaturated solutions or Received: December 1, 2011 Revised: January 25, 2012 Published: January 26, 2012 1538

dx.doi.org/10.1021/cg201590j | Cryst. Growth Des. 2012, 12, 1538−1547

Crystal Growth & Design

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is equal to the natural log of the growth rate constant. Equation 3 is the formula used for these plots in this work:

increased dissolution rates are of interest to circumvent this challenge. Examples of these dosage forms include salts, nanosuspensions, and lipid solutions.16−18 Another common method for increasing exposure is to render an insoluble API amorphous. This strategy often results in an enhanced dissolution rate and the generation of a supersaturated solution, both of which provide an opportunity for increased oral exposure over the less soluble crystalline form.19−21 However, there are several stability concerns with amorphous solids as well as other supersaturating drug delivery systems that need to be addressed prior to successful implementation of these formulations. One of the most important concerns with these systems is crystallization from the supersaturated solution. Preventing crystallization and maintaining a supersaturated solution is essential to effectively using supersaturating drug delivery systems to increase the oral exposure. There has been a significant amount of research conducted in the area of identifying polymers that stabilize supersaturated solutions of active pharmaceutical ingredients. However, much less effort has been put into quantifying the relative impact of these polymers on nucleation and growth rates.14 The purpose of the current study was to investigate the ability of hydroxypropylmethyl cellulose (HPMC) to inhibit crystallization of felodipine, an API utilized in the treatment of hypertension, from supersaturated solutions. Herein, the relative growth and nucleation rates of felodipine in the presence and absence of predissolved HPMC are presented. The impact of HPMC on nucleation of felodipine was characterized by measuring de-supersaturation rates in the absence of seed crystals, while the impact on growth was measured in the presence of seed crystals. Theoretical models were used to quantify the impact of HPMC on the nucleation and growth of felodipine from solution, and these are described in detail in the following section.

ln R G = ln kG+g ln S

These relationships provide insight into the rate and mechanism of growth while allowing for a quantitative comparison of the growth order and rate constant of a given compound in the presence and absence of inhibitors. The empirical equations shown above allow for a fast and relatively easy approach for characterizing the growth behavior of crystallizing systems. The use of more fundamental models can help characterize the impact of inhibitors on the crystal growth process from a mechanistic standpoint. One model proposed for quantifying the ability of impurities to inhibit crystallization from supersaturated solutions was developed by Kubota and Mullin.25−27 This model is described below, with some modifications to make it more applicable to the systems investigated in this study. For a complete summary and review, see Kubota.28 The Kubota−Mullin model is based on fundamental parameters important to crystal growth. The proportionalities shown in eq 4, where the numerator is the growth rate in the presence of an impurity and the denominator is the rate of growth in the absence of the impurity, relate growth rates from different length scales. Kubota and Mullin define V as the rate of growth of a single step on a crystal face and G as the rate of growth of the face containing a step V. This proportionality was assumed by Kubota and Mullin as face growth rates are more accessible than step growth rates. However, overall mass growth rates are even easier to obtain experimentally through bulk measurements such as the rate of de-supersaturation or changes in particle size distribution. Given these considerations, herein it is assumed that the proportionality between V and G also extends to Rg, the overall mass growth rate, as suggested by Garside et al.29 Thus, in this study, overall mass growth rates were utilized. In the interest of clarity, it should be noted that G (from Kubota−Mullin) is defined as vhkl by Garside.

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THEORETICAL CONSIDERATIONS Crystal Growth. Crystal growth rates can be characterized by several empirical and fundamental relationships.22 These relationships are often based on the degree of supersaturation of a system, which can be defined as a supersaturation ratio (S) S=

C Ceq

V G R ∝ ∝ V0 G0 R0

(4)

Two approximations need to be made when utilizing the proportionalities in eq 4. The first is that the ratio of the seed density to the total surface area is the same in the presence and absence of an inhibitor. The seed density would be the same in either case since the same amount of seeds were used in each de-supersaturation experiment. The surface area would not be measurably different, even though the growth rates would be, because the model compound (felodipine) used in this study has a very low solubility (∼0.5 μg/mL at 25 °C) in the crystallization media. The highest supersaturation ratio investigated was 10 (5 μg/mL). As a result there were not enough felodipine molecules present in the supersaturated solution to impact particle size to an appreciable extent, and therefore surface area can be assumed to remain constant. The second assumption is that the relative surface area of the individual faces is the same in the presence and absence of the inhibitors throughout the experiments. While we acknowledge this as a potential source of error, it is likely to be small based on the same argument given for the overall surface area. Assuming these proportionalities are appropriate for the systems investigated in this study, the overall impact of

(1)

where C is the solution concentration and Ceq is the equilibrium solubility. Equation 2 describes an empirical relationship between the overall rate of growth (Rg) of a crystal and the supersaturation ratio (S), where the growth rate constant is kG and g is the overall order.23 R G = k GS g

(3)

(2)

For the overall order (g), a value of 1 indicates diffusion controlled growth, whereas a value of 2 indicates integration controlled growth.24 More specifically, a g value of 1 means that diffusion of the crystallizing molecules to the incorporation site on the crystal surface is the rate limiting step. In contrast, when g is 2 the incorporation of the crystallizing molecule into the lattice is the rate limiting step. Values for g are commonly measured to be between 1 and 2.22 In order to estimate the rate constant and growth order, the natural log of growth rate vs the natural log of the relative supersaturation can be graphed, where the slope is equal to the growth order and the y-intercept 1539



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The distance between adsorbed impurity molecules will determine the radius of the growing 2D nucleus, where closer spacing of these impurity molecules leads to smaller 2D radii and therefore a slower growth rate. In the case where the spacing of the additive is equal to 2ρc , growth will be completely arrested. Since the closest distance between adsorbed additives is determined by L, L will also determine the maximum effectiveness of an impurity at a given level of supersaturation. Considering that the critical radius for a 2D nucleus is determined by the degree of supersaturation, it follows that as supersaturation increases the critical radius for growth will decrease. This in turn will reduce the maximum impact that an additive will have on crystal growth assuming L is not dependent on supersaturation as well. While this model has been shown to approximate the behavior of inorganic systems, to the best of our knowledge it has not been used to date to characterize the influence of polymers on the crystal growth rate of organic pharmaceutical systems. Nucleation. One common way to quantify nucleation is by measuring the induction time, which is defined as the time required for stable nuclei to form and grow to a detectable size.31 In general, if the growth rate and induction time are known, then the nucleation rate can be estimated. In our case, the objective is to understand the impact of HPMC on the nucleation rate. Hence, if the seedless induction times and the seeded growth rates in the presence and absence of HPMC under identical experimental conditions are known, the following two eqs 9 and 10 can be used to estimate the relative nucleation rate in the presence and absence of the inhibitor:32

HPMC on the growth of felodipine crystals can be quantified by eq 5: R = 1 − αθeq R0

(5)

where R/R0 is the mass growth rate in the presence of the polymer divided by the rate in the absence of HPMC, α is the impurity effectiveness factor, and θeq is the surface coverage (assuming Langmuir type adsorption of the impurity) given by

θeq =

Kx 1 + Kx

(6)

where K is the adsorption equilibrium constant and x is the mole fraction concentration, and

α=

γa kT (ln S)L

(7)

where γ is the surface excess energy, a is the surface area occupied by one crystallizing molecule, k is the Boltzmann constant, T is the temperature, S is the supersaturation ratio, and L is the separation of sites available for impurity adsorption. In the treatment by Kubota and Mullin, ln S was approximated by the relative supersaturation (σ), defined as S − 1, which was appropriate for the low supersaturations investigated. However, in the current study, the supersaturations used were not low enough to apply this approximation, and therefore the supersaturation ratio was used. The relationships given by eq 7 have important implications. First, the effectiveness of the impurity, in our case HPMC, at inhibiting crystal growth is expected to be inversely proportional to the supersaturation ratio. In other words, regardless of the inherent ability of a given impurity to inhibit crystal growth, as supersaturation increases, the impact on crystal growth should decrease. Second, the effectiveness factor is inversely proportional to the separation of sites available for impurity adsorption (L). The shorter this distance is, the greater the ability of the impurity to inhibit crystal growth. The fundamental basis for the relationship between separation of impurity adsorption sites and impact on growth is highlighted in eq 8 and is based on the pinning mechanism described by Cabrera and Vermilyea.30 V∞ is the step growth rate where the two-dimensional (2D) radius (or curvature) of the growth step is infinite (i.e., no curvature to the growing face) and Vρ is the growth rate of a 2D nucleus with a radius ρ, where the subscript c indicates the critical radius for a 2D nucleus.7

ts,0 R = R0 ts

(9)

where ts,0 is the seeded growth induction time in the absence of the inhibitor divided by that in the presence of the inhibitor (ts), which can be calculated from R/R0 obtained directly from de-supersaturation curves. These values can then be used in eq 10 to obtain the nucleation rate ratio: ⎛ t ⎞3⎛ t u,0 ⎞4 J =⎜ s ⎟ ⎜ ⎟ J0 ⎜⎝ ts,0 ⎟⎠ ⎝ t u ⎠

(10)

(8)

where J is the nucleation rate in the presence of the inhibitor and J0 is the rate in the absence of the inhibitor, tu,0 is the unseeded induction time in the absence of polymer and tu is the induction time in the presence of the inhibitor. These equations were used to estimate of the relative impact of HPMC on the nucleation rate of felodipine from a supersaturated solution.

This equation implies that as the actual radius of the growing step gets closer to the critical radius for a 2D nucleus, the rate of growth of the step will decrease toward zero. At the critical radius, increases in size due to growth are accompanied by increases in total free energy and become unfavorable. This is a consequence of the fact that the surface component of the total energy upon further growth is larger in magnitude than the energy reduction yielded by new bond formation. This scenario is directly analogous to three-dimensional (3D) homogeneous nucleation.22 Note that this should not be confused with an increase in surface free energy upon adsorption of the polymer molecules, as this is not thermodynamically correct.

Felodipine was provided by AstraZeneca, Södertälje, Sweden. The polymer used in this study as a crystallization inhibitor was hydroxypropylmethyl cellulose (HPMC) Pharmacoat grade 606 (Shin-Etsu Chemical Co., Ltd., Tokyo, Japan). The crystallization medium used in all of the following experiments was 50 mM pH 6.8 phosphate buffer, where the presence or absence of predissolved HPMC is indicated for each experiment in the Results and Discussion section. Felodipine seeds were created by grinding with a mortar and pestle and sieved to a size below 106 μm. The particle size and surface area were measured by laser diffraction as described below. Particle Size Analysis by Laser Diffraction. Particle size was measured using a Malvern Mastersizer laser diffractometer (Worceste-

Vρ

ρ =1− c ρ V∞

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shire, UK) with a Hydro 2000 μP accessory. A concentrated suspension of felodipine seeds was created in a pH 6.8 phosphate buffer solution containing HPMC at a 0.1% w/v concentration. 0.1% HPMC solution was initially added to the Mastersizer sample chamber. The concentrated suspension of felodipine seeds was then transferred into the sample chamber until the Mastersizer software indicated the signal being detected was sufficiently high. Stirring was set to 2500 rpm, sonication was used at 50% max power, and the measurements were performed at room temperature. Particle size distribution was measured 5, 10, and 15 min after addition to the sample chamber. Surface area calculations made with the Mastersizer software were averaged for the three time points and taken as the surface area of the seed crystals used in subsequent experiments. Ultraviolet (UV) Spectroscopy. De-supersaturation profiles were measured using an Ocean Optics 6 channel fiber optic system (Dunedin, FL 34698 USA) under isothermal conditions (25 °C). Wavelength scans were performed every 2 s for all experiments, and in the interest of clarity some of the data points were omitted from the graphs presented in the Results and Discussion section. The wavelength range from 270 to 440 nm was used for performing concentration estimates. A partial least-squares (PLS) calibration was built with SIMCA P+ V.12 software (Umetrics Inc., Umea Sweden). The resultant model had one principal component, a R2 value of 0.999, and a cross validation coefficient, Q2, of 0.999. Second derivatives of the spectra were taken for the calibration as well as the sample data in order to mitigate particle scattering effects. Briefly, second derivatives remove the linear (horizontal and sloped) baseline shifts seen in UV sprectra that are taken in the presence of particles that scatter light, which is the case in this study.33 Calibration solutions were prepared in methanol. In order to generate supersaturated solutions felodipine predissolved in methanol was added to the pH 6.8 buffer. Data collection commenced immediately upon addition of the methanolic solution of felodipine. Approximately 2.5 mg of felodipine seed crystals were added to 18 mL of pH 6.8 buffer and allowed to equilibrate for 40 min at 25 °C prior to addition of the solubilized felodipine. The equilibrium solubility of felodipine was approximately 0.5 μg/mL.34 Adsorption Isotherms. Surface tension measurements were performed using a Krüss K12 tensiometer. Briefly, calibration solutions of pure HPMC ranging from 0.2 to 5 μg/mL were carefully prepared and poured into sample cells. The surface tension was then measured 16−24 h after the initial pour. The measurement was considered stable when the standard deviation in surface tension of 10 consecutive readings was less than 0.1 mN m. For the isotherm measurements, the felodipine seeds described above were added to solutions containing various HPMC concentrations and allowed to equilibrate for 16 to 24 h. Surface tension was then measured similarly to the calibration samples. Seed crystals were also added to pure buffer solutions, and the surface tension of these samples was used to correct the total tension measured in the presence of both HPMC and felodipine. The actual equilibrium polymer concentrations in the growth rate experiments could not be measured with the surface tension method. Therefore, these values had to be estimated by interpolating a plot of the initial polymer concentration vs final polymer concentration obtained from the adsorption isotherm data. Growth Rate and Nucleation Induction Time Experiments. Overall mass growth rates and nucleation induction times were estimated from desupersaturation experiments. Desupersaturation was the most practical means of estimating the crystal growth rates and induction times of felodipine in solution as a result of low equilibrium solubility. Felodipine was predissolved in methanol and then transferred into the crystallization medium in the presence or absence of seed crystals. These experiments were conducted in the presence and absence of predissolved HPMC at various concentrations. It has been demonstrated elsewhere that an HPMC solution concentration of 1 mg/mL does not have an impact on the equilibrium solubility of felodipine, a concentration 3 orders of magnitude higher than what was used in the current study.35 The slope of the concentration vs time data over the initial 5 min of the experiment was taken as the initial desupersaturation/crystal growth rate for the seeded experiments. Both the Kubota−Mullin as well as the empirical model described in the

theoretical section were used to quantitatively characterize the behavior of felodipine in the presence and absence of HPMC. All experiments in the absence of predissolved HPMC were performed in triplicate. In the experiments where HPMC was predissolved in the buffer, samples at supersaturation ratios of 5 and 10 were performed in triplicate. Samples in the presence of HPMC at other supersaturations were single measurements. Polymer concentrations quoted in Figures 4 and 5 are the equilibrium solution concentration after adsorption to the seed crystals and are referred to as equilibrium concentration. All other polymer concentrations described herein are the solution concentrations prior to seed addition and are referred to as initial concentration. Equations 9 and 10 were used to estimate the nucleation kinetics from the unseeded induction time measurements combined with the seeded growth data in the presence and absence of HPMC. It should be noted that felodipine nanoparticles absorb light similar to felodipine molecules dissolved in solution and interfere with concentration estimates.33 However, it was found that these nanoparticles yield a UV spectrum where the felodipine peak at 361 nm has a significant red shift. The spectra from this study were analyzed and no red shift was observed.

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RESULTS AND DISCUSSION De-supersaturation Curves. Plots of solution concentration as a function of time, at supersaturation ratios of 5 (S of 5) and 10 (S of 10), are shown in Figure 1 and 2a−c for

Figure 1. Desupersaturation of seeded felodipine solutions (initial S of 5) in the absence of HPMC (■) and in the presence of 0.2 (red solid circles, ●), 0.5 (blue solid triangles, ▲), 1 (□), and 3.5 (○) μg/mL HPMC. Error bars represent 1 standard deviation (n = 3).

felodipine in the presence and absence of dissolved HPMC. Seed crystals were added to the solutions prior to supersaturation, and the observed de-supersaturation profiles were considered to be directly proportional to the overall growth rate of felodipine. Initial polymer solution concentrations ranged from 0.2 to 3.5 μg/mL. Data points are shown every 15 s for 5 min and were used to estimate the initial growth rates. For an S of 5, Figure 1 shows a measurable reduction in the rate of desupersaturation in the presence of HPMC at all concentrations investigated. From this it can be surmised that the presence of predissolved HPMC, even at very low solution concentrations, will hinder the growth of felodipine crystals from a supersaturated solution. Figure 2a−c shows de-supersaturation profiles for seeded experiments at an initial S of 10. Figure 2a shows two profiles, one in the absence of HPMC and one in the presence of 0.2 1541



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μg/mL HPMC (initial). In contrast to the results from Figure 1, a solution concentration of 0.2 μg/mL HPMC did not have an impact on the initial growth rate when compared to the same medium at a supersaturation ratio of 5. When the initial solution concentration of HPMC was increased to 0.5 μg/mL (Figure 2b), there was a reduction in the average growth rate. It should be noted that the error was quite large at 0.5 μg/mL HPMC. Figure 2c contains the de-supersaturation profiles at initial polymer concentrations of 1, 1.5, and 3.5 μg/mL. In all the cases there is a significant reduction in the rate of desupersaturation in the presence of predissolved HPMC. An additional set of experiments was performed where desupersaturation was measured for 60 min (data shown for S of 10 and 1 mg/mL HPMC in Figure 10) at several supersaturation ratios, including 5 and 10. In all cases, the felodipine solution concentration had dropped below 2.5 μg/ mL (or lower) in less than 45 min, after which the concentration began to stabilize at values above the equilibrium solubility (0.5 μg/mL). The de-supersaturation results from the growth rate experiments can be qualitatively summarized as follows: First, very low amounts of dissolved polymer have the ability to impact the growth rate of crystalline seeds of felodipine. Second, at an S of 5, HPMC at all concentrations investigated was able to inhibit growth. This was not the case at an S of 10, which indicates a supersaturation dependence on the ability of HPMC to impact growth and is consistent with theory. Growth Rate Analysis: Kubota-Mullin Model. Figure 3 contains a plot of the overall mass growth rate as a function of

Figure 3. Growth rate of felodipine as a function of S in the absence of HPMC (■) and in the presence of 0.2 (red solid circles, ●), 1 (blue solid triangles, ▲), and 3.5 (□) μg/mL HPMC. Error bars represent 1 standard deviation (n = 3).

supersaturation ratio estimated from the slope of the desupersaturation profiles. In almost every system investigated, a reduction in growth rate was observed in the presence of predissolved HPMC. The growth rate measured in 0.2 μg/mL HPMC at an S of 6 (indicated by the arrow) appears to be a random outlier and has been removed from the data set for all subsequent analysis. In the presence of HPMC at 0.2 μg/mL (initial), higher S (8, 10 and 12) yielded the same or higher growth rates when compared to those in the absence of HPMC.

Figure 2. (a) Desupersaturation of seeded felodipine solutions (initial S of 10) in the absence of HPMC (■) and in the presence of 0.2 (red solid circles, ●) μg/mL HPMC. (b) Desupersaturation of seeded felodipine solutions (initial S of 10) in the absence of HPMC (■) and in the presence of 0.5 (red solid circles, ●) μg/mL HPMC. (c) Desupersaturation of seeded felodipine solutions (initial S of 10) in the absence of HPMC (■) and in the presence of 1 (red solid circles, ●), 1.5 (blue solid triangles, ▲) and 3.5 (□) μg/mL HPMC. Error bars represent 1 standard deviation (n = 3). 1542



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concentrations similar in magnitude to those of maximum growth inhibition shown in Figure 5 suggesting that the surface coverage estimates are reasonable.

As would be expected from classical crystallization theory, the rate of seed growth increased as a function of supersaturation in the presence or absence of the polymer. The fact that the rate of growth increases as a function of supersaturation regardless of the presence or absence of polymer indicates that there is an inherent limit to how much growth inhibition can be provided by HPMC for felodipine at a given S. In order to properly utilize the Kubota−Mullin model in combination with the growth rate ratios shown in Figure 3, an estimation of the amount of HPMC covering the surface of the seeds had to be performed. This allows for the growth inhibition to be normalized with respect to the amount of HPMC covering the surface of the seed crystals. Figure 4 shows

Figure 5. Measured growth rate ratio (■) of felodipine (S of 8) as a function of polymer concentration and predicted growth rate ratios for an unmodified (red dashed line, ---) and modified (black solid line. ) theta at an α of 0.45.

Figure 5 contains a plot of the measured growth rate ratio (S of 8) and two predictions using eq 5 as a function of equilibrium polymer concentration. The dashed line and solid line represent unmodified and modified theta values, respectively. The isotherm in Figure 4 predicted by eq 11 shows almost no adsorption at low polymer concentrations. As a result R/R0 modeled from eq 5 shows a plateau at 1 until the concentration becomes large enough to have a numerical impact on the αθ term in eq 5. When the model is artificially adjusted down (solid line fit) by removing the horizontal portion of the curve, it can be seen that the shape resembles the profile of the data quite well. This adjustment is necessary due to the limitations of the model discussed above and was also made when estimating alpha at other supersaturations. Along with the calculated theta values, an alpha value of 0.4 was used with eq 5 which provided a good fit of the predicted growth ratio with the measured data. An alpha value of 0.4 indicates there will be an initial reduction in growth rate with increasing inhibitor concentration followed by a plateau, above a zero growth rate, at complete coverage. To put this into perspective, an alpha value of 1 predicts a growth rate of 0 at complete surface coverage, and a value above 1 means that growth will be completely inhibited prior to full surface coverage. In contrast, an alpha value near 0 means there will be no reduction in growth at any concentration. Table 1 contains the alpha

Figure 4. Measured adsorption isotherm (■) of HPMC on felodipine crystals and theta estimate from eq 11 (line).

the actual concentration of HPMC adsorbed to the seeds, normalized to the surface area of the seeds. The average surface area was calculated to be 0.804 ± 0.3 m2/g and was based on the particle size distribution measured by a Malvern Mastersizer laser diffractometer. The surface weighted mean particle size was 7.78 μm. The data were fit to a modified version of the Langmuir isotherm using eq 1136

θeq =

Kx n 1 + Kx n

(11)

where K and n are constants that were estimated using a fitting function in the Origin graphing software program, where a preset model (LangmuirEXT1) of the form seen in eq 11 yielded 58.1 and 6.9 for K and n, respectively. The adjusted R2 value was found to be 0.79, which provided a better fit of the measured isotherm data than eq 6. It should be noted that at low equilibrium polymer concentrations the model begins to breakdown by suggesting no adsorption, which is in direct conflict with the measured data. In order to address this, there are several assumptions made in the Langmuir model that need to be considered. First, in order for the Langmuir isotherm to apply to a given system the adsorbing surface needs to be homogeneous.37 The surface of the seed crystals in these experiments is likely to be quite heterogeneous. Furthermore, since HPMC is a polymer, it will not rigorously comply with this model as the size of the polymer is not close to the size of the solvent (i.e., water). However, complete monolayer layer coverage as predicted by the isotherm is shown to occur at equilibrium solution

Table 1. Alpha Estimates at Various Supersaturations

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supersaturation ratio

alpha estimate

3 5 8 10 12

0.7 0.5 0.4 0.6 0.2



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estimates for supersaturation ratios of 3, 5, 8, 10, and 12. The observed trend has important implications that were touched on earlier and will be put into further perspective here. As S was increased from 3 to 12 (Table 1), the alpha parameter decreased from 0.7 to 0.2 indicating a reduction in the ability of HPMC to inhibit growth at the higher supersaturation. For an S of 5, 8, and 10 (table) an intermediate alpha parameter somewhere between 0.4 and 0.6 was estimated. These observations would be predicted a priori by eq 7 suggesting that the behavior of the systems investigated herein can be approximated by the Kubota−Mullin model. Hence, our most important experimental finding, namely, that that the polymer has a much smaller impact on growth rate inhibition as the supersaturation increases, is supported by theoretical predictions. Furthermore, these results suggest that the spacing between adsorbed HPMC molecules on felodipine crystals is relatively far apart limiting the impact on crystal growth at the supersaturations investigated. In order to confirm that growth inhibition plateaus at very low initial polymer concentrations (∼1 μg/mL), additional experiments were performed in solutions where the initial HPMC concentration was increased to 50 μg/mL and 100 μg/ mL (data not shown). At an S of 5, the growth rate ratios were 0.45 and 0.61 for both concentrations. For an S of 10 the growth rate ratios were 0.45 and 0.50 at initial polymer concentrations of 50 and 100 μg/mL, respectively. These values were in reasonable agreement with R/R0 plateaus at an S of 5 (0.65) and 10 (0.55) from the alpha estimates (highest initial HPMC concentration was 3.5 μg/mL). This confirms that at very low polymer concentrations, there is an observable impact on the rate of growth. As the polymer concentration is increased, its effect on the growth rate of felodipine rapidly reaches a plateau. This observation lends support to the proposed adsorption mechanism of inhibition, since the adsorption isotherm in Figure 4 indicates a maximum coverage at around 1 μg/mL and this level of polymer corresponds to the plateau region in terms of extent of growth rate inhibition. In order to support the above interpretation an empirical analysis was also conducted on the growth rate data and is discussed in the following section. Growth Rate Analysis: Empirical Model. An empirical analysis of the ability of HPMC to reduce the growth rate of felodipine was conducted by plotting the natural log of the growth rate vs the natural log of the supersaturation ratio. Crystal growth orders of these data were extracted from the slope values of linear regression analysis (R2 values were 0.94 or better for all data sets). Representative plots can be seen in Figure 6 for two systems; one in the absence of polymer and one in the presence of HPMC at an initial solution concentration of 1 μg/mL. Figure 6 clearly illustrates the diminishing effectiveness of the polymer as a growth rate inhibitor with increasing supersaturation. Similar plots were obtained at other polymer concentrations. Values for both g and kG at all polymer concentrations investigated are shown in Figures 7 and 8. Figure 7 is a bar plot of the growth order in the presence and absence of predissolved HPMC. Error bars represent the standard deviation of the slope (i.e., growth order). It can be seen that there is an increase in the average order of growth from 1.5 to approximately 2 when HPMC is present in the solution at any concentration. If the growth order in Figure 7 is averaged for all of the polymer concentrations, the result is 1.97 ± 0.12. Assuming the rate limiting step in the growth is the same in all cases, this can be

Figure 6. Natural log of the growth rate in the absence of HPMC (■) and the presence of 1 μg/mL (red solid circles, ●) HPMC as a function of the natural log of the supersaturation ratio.

Figure 7. Growth order of felodipine crystals as a function of polymer concentration.

taken as the growth order in the presence of HPMC. This suggests a shift in the growth mechanism in the presence of HPMC toward integration controlled from a combination of integration and diffusion controlled in the absence of HPMC. This result was consistent with the Kubota−Mullin model for inhibition where a reduction in growth rate can be directly linked to a reduction in ρ, leading to an unfavorable change in total free energy upon crystal growth.7 This unfavorable change in total free energy would ultimately be linked to the rate at which felodipine molecules would be incorporated into the growing crystal and would not have an obvious impact on diffusion of felodipine molecules to an incorporation site. If an overall growth order of 2 is assumed for all of the experiments in the presence of HPMC and 1.5 for the experiments in the absence of HPMC, eq 3 can be used to calculate the growth rate constant kG at the individual supersaturation ratios investigated. The growth rate constant is expected to be a function of temperature, crystal/solution 1544



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was generated in the absence of seed crystals and in the presence or absence of dissolved HPMC at a concentration of 1 μg/mL. The initial time points (horizontal data) as well as the linear portion of the de-supersaturation regions were fit by linear regression. The equations from each fit were set equal to each other, and the induction time was taken as the intersection of these two lines. In the absence of polymer, the induction time was determined to be 15.3 min and in the presence of HPMC the induction time was estimated at 136.5 min. These two numbers were used as inputs for the second term of eq 10. The inputs for the first term in eq 10 were calculated from eq 9 using the seeded growth rate data. The ratio of the growth rate in the presence of HPMC divided by that in the absence of the HPMC was used to estimate ts,0/ts. This value is plotted in Figure 3 and is 0.607 at an S of 10, where the inverse is 1.643 and is used for the input for the first term in eq 10. J/J0 was then estimated to be 7.05 × 10−4 indicating a substantial (more than a thousand fold) reduction in the nucleation rate in the presence of the inhibitor. The objective of this study was to quantify the impact of HPMC on the growth and nucleation of felodipine from supersaturated solutions. Although it was observed that very low HPMC solution concentrations could effectively hinder crystal growth of felodipine, similar concentrations of HPMC significantly reduced nucleation such that elevated levels of supersaturation could be maintained for extended periods of time. If the seeded de-supersaturation data at an S of 10 and 1 μg/mL HPMC (60 min extended experiment) is graphed with the unseeded 1 μg/mL HPMC data from Figure 9, it becomes quite clear from Figure 10 that inhibiting nucleation has a far

Figure 8. Natural log of the growth rate constant of felodipine crystals as a function of polymer concentration.

velocities, and impurities according to Garside.29 Consequently it is not expected to vary with supersaturation. As expected, results from the calculated kG values did not show a dependence on supersaturation, only on HPMC concentration. Figure 8 is a bar graph of the natural log of the average kG calculated at the supersaturations investigated. Error bars represent 1 standard deviation of the intercept. These data show that there is a substantial drop in the rate constant at all polymer concentrations indicating a significant reduction in growth rate in the presence of the predissolved HPMC. The trend with increasing polymer concentration qualitatively agrees with the analysis from the Kubota−Mullin model, where the impact of increasing polymer concentration plateaus very rapidly with increasing polymer concentration. Nucleation. Figure 9 shows a plot of the concentration vs time where a supersaturated solution of felodipine (S of 10)

Figure 10. Unseeded (■) and seeded (red solid circles, ●) desupersaturation of felodipine (S of 10) in the presence of 1 μg/ mL HPMC.

more significant impact on maintaining supersaturation than inhibiting growth does. At a concentration of 1 μg/mL, the ability of HPMC to inhibit crystal growth of felodipine at an S of 10 is at a maximum (Figure 8). However, the overall ability of HPMC to maintain supersaturation via growth inhibition at 1 μg/mL is still quite poor, especially when compared to its ability to inhibit nucleation. Implications. As noted in the Introduction, there are several formulation strategies used to increase API bioavail-

Figure 9. Unseeded desupersaturation of felodipine (S of 10) in the absence of HPMC (■) and in the presence of 1 (red solid circles, ●) μg/mL HPMC. Error bars represent 1 standard deviation (n = 3). 1545



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Notes

ability via supersaturation. The supersaturation ratios used in this study were based on the theoretical and measured solubility advantage of amorphous felodipine (S of ∼10),38 an appropriate benchmark given the current level of industrial interest in amorphous pharmaceuticals for bioavailability enhancement. When using these strategies, it is important that supersaturation is maintained for a biologically relevant time frame in the GI tract in order to maximize the impact on absorption. Consequently, it is of interest to understand the mechanism by which crystallization inhibitors stabilize these supersaturated solutions. It can be concluded for the felodipine−HPMC system that inhibiting nucleation would be critical when using formulations that result in supersaturation upon oral administration. Although HPMC did have a measurable impact on crystal growth rate, the magnitude of de-supersaturation whether in the presence or absence of HPMC was similar over the course of the experiments in this study. Therefore, preventing the formation of crystals altogether would be the only effective method for stabilizing felodipine with HPMC. This in turn would make characterization of the nucleation behavior of felodipine in the presence and absence of HPMC a key component of formulation development. While preventing nucleation altogether would be the best strategy for stabilization in most cases, it may not always be possible, and extensive inhibition of crystal growth might be necessary to maintain supersaturation. One practical example of this situation would be in the use of amorphous pharmaceuticals to increase in vivo exposure as noted in the Introduction. In the case of felodipine, it would be extremely important to ensure that residual crystallinity in an amorphous formulation was minimized. The presence of residual (seed) crystals in an amorphous formulation could have a large impact on the degree of supersaturation maintained, even in the presence of an inhibitor like HPMC. Knowing the mechanism by which these inhibitors work for a given API would be extremely helpful when choosing which excipients to include in a formulation.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We would like to acknowledge PhRMA foundation for financial support for David E. Alonzo, as well as research funding from Abbott Laboratories. Dr. James D. Litster and Ms. Kaoutar Aboucherif are thanked for helpful discussions.

■

■

CONCLUSIONS HPMC was shown to be effective at reducing both the nucleation and the growth rates of felodipine crystals from supersaturated solutions. The rate of both processes was measurably reduced at relatively low solution concentrations of HPMC. However, the relative impact of the polymer on nucleation (factor of 1000) was much more pronounced than the impact on growth rate (factor of 2) with respect to maintenance of supersaturation. As a result, ensuring that nucleation does not take place is the key factor in maintaining supersaturated solutions of felodipine for a biologically relevant time frame. These considerations are extremely important when dealing with supersaturating drug delivery systems and should be given priority when making formulation decisions.

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AUTHOR INFORMATION

Corresponding Author

*(L.S.T.) Address: Department of Industrial and Physical Pharmacy, College of Pharmacy, Purdue University, 575 Stadium Mall Drive, West Lafayette, Indiana 47907, USA. Tel: +1-765-496-6614; fax: +1-765-494-6545; e-mail: lstaylor@ purdue.edu. (G.Z.) Global Pharm. Res. and Development, Abbott Laboratories, 100 Abbott Park Road, Abbott Park, Illinois 60064, USA. 1546



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