International Journal of Pharmaceutics 468 (2014) 64–74

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An improved method for the characterization of supersaturation and precipitation of poorly soluble drugs using pulsatile microdialysis (PMD) Kosha B. Shah a , Piyush G. Patel a , Akm Khairuzzaman b , Robert A. Bellantone a,c, * a Division of Pharmaceutical Sciences, Arnold & Marie Schwartz College of Pharmacy and Health Sciences, Long Island University, 75 Dekalb Avenue, Brooklyn, NY 11201, United States b United States of Food and Drug Administration, 10903 New Hampshire Avenue, Silver Spring, MD 20993, United States c Physical Pharmaceutica LLC, 38 Oak Avenue, Tuckahoe, NY 10707, United States

A R T I C L E I N F O

A B S T R A C T

Article history: Received 8 November 2013 Received in revised form 12 February 2014 Accepted 3 April 2014 Available online 05 April 2014

In current pharmaceutical drug discovery, most candidates are poorly soluble in water, which can result in poor bioavailability. To overcome this problem, formulations that create supersaturation of the drug are a well-studied alternative. Characterizing the dissolution from these systems is challenging because conventional methods, such as sampling with a syringe then filtering with a 0.2–0.45 mm filter before an HPLC assay, can overestimate the concentration of dissolved drug by allowing nuclei or small precipitated particles to pass, which then dissolve in the HPLC mobile phase. Nuclei and small particles can also cause overestimation of the dissolved concentration when using optical methods. Such overestimations can lead to failure of in vivo prediction of drug bioavailability from supersaturated systems. This paper reports a novel method to determine the free dissolved drug concentration in a dissolution medium using pulsatile microdialysis (PMD). Ibuprofen was used as a model drug for determining precipitation and supersaturation. Supersaturation was induced chemically by changing pH, and also by dissolution/ release from an in-house formulation. The adaptation of a previously developed PMD model is summarized, and experimental results comparing dissolved concentrations determined using PMD and direct sampling by syringe and filtering are presented. ã 2014 Elsevier B.V. All rights reserved.

Keyword: Supersaturation Precipitation Poorly soluble Pulsatile microdialysis PMD Dissolution

1. Introduction Many drugs on the market and in development are poorly soluble in water (Lipinski et al., 2001; Ozaki et al., 2012), which results in low bioavailability when administered orally (Brouwers et al., 2009) because poorly soluble drugs produce low dissolved concentrations in GI fluids. One approach to increase absorption rates is to formulate drugs to produce supersaturated solutions, using technologies such as solid dispersions and nanoparticles (Vaughn et al., 2006). Supersaturation in GI fluids increases passive absorption rates because it provides higher dissolved drug concentrations on the donor side of the membranes (Brewster et al., 2008; Gao and Shi, 2012; Bevernage et al., 2013).

* Corresponding author at: Division of Pharmaceutical Sciences, Arnold & Marie Schwartz College of Pharmacy and Health Sciences, Long Island University, 75 Dekalb Avenue, Brooklyn, NY 11201, United States. Tel.: +1 718 780 4154; fax: +1 718 780 4586. E-mail addresses: [email protected], [email protected] (R.A. Bellantone). http://dx.doi.org/10.1016/j.ijpharm.2014.04.012 0378-5173/ ã 2014 Elsevier B.V. All rights reserved.

A major problem associated with this approach is that supersaturated solutions are not stable, so nuclei and precipitated particles can also be present along with the higher dissolved drug concentration (Nkansah et al., 2013). This is important for drugs that are absorbed by passive diffusion across the GI membranes because only the dissolved drug is absorbed in vivo (Macheras et al., 2013). Here, the term “dissolved” refers to molecules that are individually dispersed in the medium and free (i.e., not complexed, contained in structures such as micelles, etc.). Since the dissolved drug is the absorbable form in vivo for most drugs, it is of interest in drug development to know the dissolved concentration and kinetics of precipitation (Augustijns and Brewster, 2012; Stillhart et al., 2013). Various methods have been employed to study precipitation from supersaturated solutions (Bagchi et al., 2012; di Cagno and Luppit, 2013; Patel and Anderson, 2013; Stillhart et al., 2013). However, these methods can introduce errors in determining the dissolved concentration of drug in supersaturated systems. For instance, when performing a dissolution experiment, the amount of dissolved drug is determined by taking direct samples of the dissolution

K.B. Shah et al. / International Journal of Pharmaceutics 468 (2014) 64–74

medium, filtering the sample using a 0.1–0.45 mm filter, then assaying for the drug content (Schmelzer and Schmelzer, 1999; Bevernage et al., 2013). If present, nuclei and small precipitates can pass through these filters in vitro and subsequently dissolve in an HPLC mobile phase, thus leading to overestimation of the amount actually dissolved in the dissolution medium. Small particles might also lead to errors in determining the dissolved drug concentration using optical concentration characterization methods (Petrusevska et al., 1999). Ultracentrifugation can be used to separate particles from the solution, but the rate and effectiveness of the separation depends on the particle size and difference in density between the particle and the liquid medium in which it is suspended (Hiemenz and Rajagopalan, 1997). Nuclei and precipitating particles at early times are very small, so the time required for separation would be long. In addition, for some drugs the true density of the drug is close to one, reducing the effectiveness of ultracentrifugation for separating out particles. Finally, additional precipitation can occur during the ultracentrifugation. Errors in the dissolved concentration determinations in vitro can lead to problems with predictions of in vivo performance and in vitro/in vivo correlations (IVIVC). Thus, it is of interest to have a method that is more discriminatory in terms of determining the actual dissolved concentration, especially in systems that are multi-phasic on a microscopic scale (Bellantone, 2012). This paper reports a new method to characterize the dissolved concentration and precipitation of a drug in supersaturated systems. The method uses the pulsatile microdialysis method (PMD), which is well suited for determining the dissolved drug concentration in systems that change with time and/or microscopically multiphasic. This paper presents the experimental method and mathematical model for data analysis, and reports results of using PMD to study supersaturated solutions of the poorly soluble model drug, ibuprofen. 2. Description of PMD and the experimental setup PMD is a recently developed variation of microdialysis (Kabir et al., 2005; Bellantone, 2012). The method employs a microdialysis probe consisting of a short length of porous regenerated cellulose membrane tubing that acts as a dialysis membrane, which is referred to as the probe window (or window). Impermeable tubing is connected to each end of the probe window, with one end connected to a programmable syringe pump and serving as an inlet, and on the other serving as an outlet. Fig. 1 shows a diagram of a PMD probe. The probe windows used in this work were of length L
5–10 cm, inner radius a
0.01 cm, window volume VW
2–5 mL, and window wall thicknesses of
0.001 cm. For the probe windows, the surface-to-volume ratio is
200 cm1. The probe window is immersed in an external liquid medium, and a liquid, referred to as the dialysate, is pumped through the probe. While the dialysate is in the probe window, dissolved drug molecules exchange between it and the external medium by

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passively diffusing through the liquid filled pores of the window. The concentration of drug in the PMD sample is related to the dissolved concentration in the external medium. In this work, the external medium corresponds to the supersaturated medium and act as a diffusion donor. The dialysate contains no drug when it enters the probe, and acts as the receiver to collect the molecules from the donor, and the dissolved concentration of drug in the external medium will be determined from the concentration in the PMD sample. The PMD sampling process consists of three steps: (1) the dialysate is pumped into the probe at a rapid flow rate Q; (2) The pumping is stopped and the dialysate is allowed to remain stationary in the probe for a specified resting time tR; (3) The dialysate is flushed out at the same flow rate as in step (1) until a specified volume VS is collected for assay. The volume of dialysate collected in step (3) is chosen to be large enough to ensure that all or most of the dialysate that had rested in the probe window is collected. Each of these samples is referred to as a pulse, and in practice the total PMD sample may contain a single pulse or a combination of two or more pulses taken in rapid succession. While at rest, part of the dialysate that is eventually collected rests in the probe window and part rests in the impermeable inlet and outlet tubing. Thus, a PMD sample volume of VS can be thought of as containing two portions. The portion that rests while in the probe window is referred to as the pulsed portion, and has a volume equal to the window volume VW. The remainder of the sample is referred to as the continuous portion, with volume VS  VW. The time spent in the probe window by any portion of the sample is referred to as its exposure time, because the dialysate is only “exposed” to the external medium and accumulate dissolved drug molecules while it is in the window. The distinction between the pulsed and continuous portions is important because the pulsed portion has a longer exposure time than the continuous portion, and thus has more time to accumulate drug molecules. The exposure time for each element of the continuous portion equals its transit time through the probe window tQ, while the exposure time for each element of the pulsed portion tP is the sum of the time spent resting in the probe window and its transit time through the probe window. These are given by tQ ¼

VW and tP ¼ tR þ tQ Q

(1)

When all of the drug is dissolved, the total drug concentration in the external medium CD equals the dissolved concentration CD,f. However, in the presence of nuclei, particles, complexes, etc., CD includes contributions from dissolved and un-dissolved forms of the drug and CD > CD,f. Typically, CD is known from the experimental setup and CD,f must be determined. PMD offers several features which make it well suited for the purpose of this study. (1) The probe window acts as a dialysis membrane, so that particles are filtered and only individual drug molecules pass into

Fig. 1. A schematic diagram of a microdialysis probe.

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the dialysate. (2) For the probe windows, the walls are very thin and the inner radii are very small, so short times are needed to collect PMD samples. Thus, filtered samples can be taken as frequently as every 15–30 s. (3) By controlling the exposure time and the dialysate medium, the concentration of drug in the dialysate can be kept below the saturation level in that medium. As a result, the PMD samples reflect CD,f in the external medium. For supersaturated solutions undergoing precipitation, PMD sample can be collected often enough to characterize even rapid precipitation. In addition, by using short enough resting times, supersaturation can be avoided in the dialysate. Thus, once the dialysate exits the probe window and is collected, no further precipitation occurs in the collected sample. Thus, the method is well suited to characterize the external dissolved concentration and its changes in time. 3. The PMD mathematical model and equations used for data analysis The experimental implantation of PMD is done so most of the mass taken up by the sample occurs while the dialysate is at rest within the probe window. This allows modeling the drug uptake by passive diffusion equations, and equations have been developed for data analysis. PMD has been described mathematically by solving equations arising from diffusion theory in cylindrical coordinates (Kabir et al., 2005; Bellantone, 2012), but the main points are given here for convenience. The concentration of drug in a PMD sample CS is the mass of drug sample divided by the sample volume VS. It is convenient to define the fractional recovery FR, which relates the concentration in the sample to the dissolved concentration in the donor as CS C D;f

FR ¼

(2)

As the dissolved and total concentrations of drug in the donor medium are not always equal, it is also convenient to introduce the term fD, which is the fraction of total drug concentration in the donor that is in dissolved form. It is also convenient to define the apparent fractional recovery F App R , which relates the PMD concentration to the total concentration in the donor. These are given by C D;f CD

fD ¼

¼ F App R

(3)

CS ¼ f DFR CD

(4)

For the case in which CD,f can be assumed constant while a PMD sample is collected, the concentration of drug in the sample is given as (Bellantone, 2012) " ( #  )  1 X   VW VS  VW 1 dn exp g n tP þ F RQ (5) CS ¼ f D CD VS VS n¼1 so F App R

" ( #  )  1 X   VW VS  VW ¼ fD 1 dn exp g n tP þ F RQ VS VS n¼1

(6)

The term FRQ characterizes the contribution of dilution of the pulsed portion by the continuous portion in the total sample. The parameters dn and g n arise from the solution to Fick’s second law in cylindrical coordinates and are given as

gn ¼

b2n D a2

¼

b2n g1 b21

2

dn ¼



4l

b2n b2n þ l2



(7)

l¼

aP D

(8)

P¼

App 1 V S dF R aX j ¼ dn g n AW f D dtP tP !0 2 n¼1

(9)

where a is the inner radius of the probe window, P is the permeability of the probe window with respect to the drug, D is the diffusion coefficient of the drug in the dialysate, and AW ¼ 2paL is the area  of the probe   window. The parameters bn are the roots of bn J 1 bn  lJ0 bn ¼ 0. It can be shown that P1 n¼1 dn ¼ 1; d1 > d2 . . . > 0; 0 < g 1 < g 2 . . ., and the infinite series in Eqs. (5), (6) and (9) converge. For chosen probe window geometry, sample volume and exposure time, Eqs. (7)–(9) along with l, fD, g1 and FRQ provide a full description of all the terms in Eq. (6). In a PMD experiment, the same flow rate, probe, temperature and dialysate are used. Thus, Q, VW, a and D do not change. In practice, the value of CD,f is determined from Eq. (2), using the value of FR determined from the probe calibration. However, it is possible for the properties of the probe to change during an experiment due to coating of the surface, precipitation in the pores, etc., which can change the permeability of the window wall. As a result, the value of FR can potentially change during an experiment. Because of this, a check is done before and after each experiment. PMD is performed in which tP and the total donor concentration CD are known from the setup, so values of fD, g1, FRQ and l can be obtained from fits of F App vs. tP data. Eqs. (6)–(9) show R that l and P are related in such a way that they must be determined simultaneously by iterative nonlinear regressions. Thus, the fitting of F App vs. tP data is done as follows: (1) iterate on R l, fD, g1 and FRQ to fit Eq. (6); (2) require that the permeability calculated with Eq. (9) equal the value calculated using Eq. (8) using the known value of D. 4. Materials and methods 4.1. Materials Ibuprofen was obtained from Letco Medicals (Decatur, AL). Syloid 244FP (Grace Corporation, NJ) was obtained from Grace Corporation. All of the solvents used were obtained from VWR (Bridgewater, NJ). Potassium phosphate monobasic was obtained from VWR (Bridgewater, NJ). The phosphate buffer system 25 mM (USP) contains potassium phosphate monobasic and NaOH at pH 7 and HCl at pH 2. Ibuprofen is a weak acid with pKa
4.5. In aqueous buffer at pH 2, its solubility is approximately 20 mg/mL at 23  C and 40 mg/mL at 37  C. Its solubility in pH 7.2 phosphate buffer is 6.5 mg/mL at 25  C. The exact solubility in 25 mM phosphate buffer at pH 7 (which was used in this study) was not determined, but it was experimentally verified that it exceeded 1 mg/mL at 23  C and 37  C, so it is at least twice the highest concentration used for any experiment in this study (500 mg/mL), and five times higher than any precipitation experiment (200 mg/mL). 4.2. PMD method PMD probes were constructed in our laboratory using a tubular dialysis membrane with a nominal inner radius of 100 mm and molecular weight cutoff of 18 kDa, made from reconstituted cellulose (Spectra/Por RC Hollow Fiber Bundles). Polyimide tubes with an outer radius of 83 mm (MicroLumen, Tampa, FL) were connected to both sides of the microdialysis probe and glued using instant cyanoacrylate glue. One of the segments was connected to a 15 cm Tygon tube that was connected to a syringe pump and used

K.B. Shah et al. / International Journal of Pharmaceutics 468 (2014) 64–74

as an inlet. The other segment served as the outlet for sampling. The length of the probe window was 5–10 cm. In a PMD experiment, the probe window was immersed in a temperature controlled liquid donor medium. PMD was controlled by a HARVARD Model PHD 2000 programmable syringe pump (Harvard Apparatus, Holliston, MA), which controlled parameters such as the flush rate, sample volume, resting time and the number of pulses that were combined to make the total PMD sample. The flush rate used to pump the dialysate was Q = 100 mL/min in all experiments. After pumping the specific amount of dialysate, the dialysate was stopped and allowed to remain stationary inside the probe for a pre-determined resting time required by the particular experiment. At the end of the resting time, the dialysate was flushed out at the same Q and collected for assay. The sample volume flushed out with each pulse VS was 11 mL in all experiments except the window volume calibration, for which VS was varied. Two consecutive pulses were combined to make the total PMD sample as follows: flush the dialysate through the probe, stop the flow and allow the dialysate to rest for tR seconds, flush and collect a first pulse of volume VS, stop the flow and allow the dialysate to rest for tR seconds, then flush and a second pulse of VS. All samples were immediately analyzed by HPLC. In all cases, the dialysate consisted of 25 mM phosphate buffer at pH 7. 4.3. Direct sampling Direct sampling of the donor media was done by taking 0.5 mL of the medium with a syringe, then filtering with a 0.2 mm Teflon1 filter before assaying. Teflon filters were chosen to minimize nonspecific binding, and 0.2 mm was the smallest pore size for which they were available. 4.4. Window volume calibration Window volume calibrations were performed because optical microscopic methods are not accurate enough to support the data analysis using the equations described above. To determine VW, the probe window was immersed in a donor solution containing ibuprofen in a concentration below its solubility, so fD = 1 and F App ¼ F R . PMD was performed as described above with a constant R resting time tR of at least 300 s, and VS was varied from 10 to 100 mL. The resting time was long enough to allow the approximation of tP ! 1 in Eq. (6), which leads to  V W F R ¼ F RQ þ 1  F RQ VS

(10)

Plots of FR vs. 1/V  S were constructed, and the slope and intercept were taken as 1  F RQ V W and FRQ, respectively, so the window volume is given by VW = slope/(1  intercept). 4.5. F App vs. tP plots R In some experiments, plots of F App vs. tP data were constructed R before and after to assess the values of the probe properties. This was done by performing PMD in the 50–100 mL of an external medium containing a constant concentration of ibuprofen, using a probe with known VW, and using Q = 100 mL/min and VS = 11 mL. The dialysate consisted of 25 mM phosphate buffer at pH 7. Four or five resting times, ranging from
10 to 300 s, were used. For each resting time, two consecutive pulses were combined to form the total PMD sample of 22 mL, which was assayed by HPLC. Eq. (6) was fit to the F App vs. tP data, and values of l, fD, g1, FRQ and P were R determined. Comparisons of these parameters were done before and after experiments to determine if the probe properties, such as P, had changed during the experiment.

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4.6. Dynamic probe calibration To assess the relationship between the concentrations in the PMD sample and the donor when the donor concentration changes, dynamic probe calibration experiments were performed in which the donor concentration was reduced in a known manner, using a variation of a previously published method (Dai, 2010). Aqueous solutions of ibuprofen 500 mg/mL in 100 mL of pH 7 phosphate buffer were prepared. This concentration was below the solubility of the drug in the medium, so fD = 1. The dissolved ibuprofen concentration C D;f was reduced over time by continuously adding 25 mM phosphate buffer at pH 7 that was void of drug to the stirred donor at a flow rate q, while simultaneously withdrawing the mixed solution at the same rate continuous flow rate. This caused the ibuprofen concentration to decline in a first order manner given by C D;f ¼ C 0 expðktÞ k ¼

q V

(11)

In these experiments, the target flow rate was q = 35 mL/min, which would produce a target rate constant of k = 0.35 min1 and half-life of 2 min. Since the pumps varied slightly with changing temperatures, the values of q used in calculating C D;f were obtained experimentally at each temperature after setting the pump controls. In all cases, the initial concentration was below the solubility of ibuprofen at pH 7, so fD = 1 at all times. PMD was performed using a probe with VW = 3.0 mL, Q = 100 mL/min, tR = 9 s and VS = 11 mL. The dialysate consisted of 25 mM phosphate buffer at pH 7. Two consecutive pulses were combined to form the total PMD sample of 22 mL. The value of FR in the PMD sample was plotted at the time when the first pulse stopped (after the first 11 mL was collected), which was the midpoint of the time interval during which the total PMD sample was taken. Because the pumps took several seconds to come up to speed, the first sample was not included in the data analysis. After collection, samples were immediately analyzed by HPLC. The value of FR was taken as the slope of the experimental CS vs. the calculated value of CD corresponding to each experimental time. Calibrations were performed at 10, 20, 30 and 40  C, and interpolations of FR vs. T were done to determine FR at other temperatures. 4.7. Precipitation when supersaturation is induced by pH changes Ibuprofen solutions of various initial dissolved concentrations (50, 100, and 200 mg/mL) were prepared at different temperatures (10, 20 and 30  C) in 25 mM phosphate buffer at pH 7. Precipitation was induced by adding 1 N HCl to reduce the pH to 2. (Ibuprofen is a weak acid with a pKa of 4.5.) Based on preliminary observations, PMD was started before the HCl was added, then samples were taken approximately every minute seconds for the first 10 min after adding the HCl, then every five minutes. PMD was performed using a probe with VW = 3.0 mL, Q = 100 mL/min, tR = 9 s, and VS = 11 mL. The dialysate consisted of 25 mM phosphate buffer at pH 7. Two consecutive pulses were combined to form the total PMD sample of 22 mL, which was assayed by HPLC, and the dissolved concentration in the donor was calculated as CS/FR. The value of F App in the PMD sample was R plotted at the time when the first pulse stopped, which corresponded to the midpoint of the time interval during which the total PMD sample was taken. Before and after each experiment, PMD was performed using a range of resting times and plots of F App vs. tP were constructed to verify that the R probe properties had not changed. For comparison, direct sampling of the donor was also done every five minutes for the duration of the experiment.

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4.8. Precipitation when supersaturated is created by release from an in-house formulation

the probe pores. Thus, significant nonspecific binding would be expected to partially clog the pores, reducing the permeability.

Supersaturation was produced by dissolving/releasing ibuprofen from formulations prepared in-house into a stirred aqueous medium at pH 2, and the dissolved drug concentrations were determined using PMD and direct sampling. The in-house formulations were produced as follows. Ibuprofen was dissolved in ethanol to make a concentrated solution. Syloid-244FP was held under vacuum for 2–4 h, then immediately mixed into the concentrated ibuprofen solution, covered to prevent evaporation of the ethanol, and allowed to stand. The ibuprofen:Syloid:ethanol ratios were 1:1:10 (w/w/v). After standing for 4 h, the excess solution was decanted and the Syloid particles were immediately washed with several mL of ethanol to remove drug on the surface of the Syloid, then dried in a vacuum oven overnight. The drug loading was determined by extracting ibuprofen from 10 mg of formulation into 10 mL of ethanol (Malzert-Freon et al., 2010). Ibuprofen dissolution was performed in 100 mL of in aqueous buffer at pH 2 and 20  C, in which the ibuprofen solubility is approximately 20 mg/mL. The formulations were characterized by differential scanning calorimetry (DSC) using a TA Instrument Model Q200 (TA Instruments, New Castle, DE). Accurately weighed samples were placed in a crimped pan, then heated from 20 to 100  C at a rate of 5  C/min. The absence of a peak corresponding to that of pure ibuprofen was taken to mean that all or nearly all of the drug was contained in the Syloid pores. The goal of the washing procedure was to remove particulates from the Syloid particle surfaces, which was then verified for each batch by the DSC. Because of the washing procedure, the drug loading showed some variability between batches. To minimize loading differences, batch sizes did not exceed one gram. Various quantities of formulation were taken from the same batch to study the release of ibuprofen and supersaturation patterns of the drug. PMD was started before the formulation was added to the dissolution medium, then sampling was done every minute for the first 10 min, and every 2–5 min after that. PMD was performed using a probe with VW = 3.0 mL, Q = 100 mL/min, tR = 15 s, and VS = 11 mL. Two consecutive pulses were combined to form the total PMD sample of 22 mL, which was assayed by HPLC. The dialysate consisted of 25 mM phosphate buffer at pH 7. The dissolved concentration in the donor was calculated as CS/FR. The value of FR in the PMD sample was plotted at the time when the first pulse stopped (after the first 11 mL was collected), which corresponded to the midpoint of the time interval during which the total PMD sample was taken. Before and after each experiment, PMD was performed using a range of resting times and plots of F App vs. tP were constructed to verify that the probe properties had R not changed. For comparison, direct sampling of the donor was also done for the duration of the experiment.

4.10. Chemical assay Ibuprofen was analyzed by isocratic reversed-phase HPLC with UV detection. The HPLC system consisted of a Waters 2695 separation module and Water 486 ultraviolet detector (Waters, Milford, MA), and a mBondapak 3.9 mm  150 mm C18 10 mm column (Waters, Milford, MA). Output from the detector was processed on a personal computer using Empower-1 HPLC software (Waters, Milford, MA). The mobile phase consisted of methanol, 25 mM phosphate buffer (pH 2.5) and acetonitrile in a ratio of 38.5:38.5:23 by volume. The mobile phase flow rate was 1.5 mL/min and the detection wavelength was 214 nm. Samples were injected directly into the system using an auto sampler. The HPLC standard curve was linear with R2 = 0.999 for determination of ibuprofen concentration. The lower limit of quantitation (LOQ) was less than 0.1 mg/mL. All solvents were of HPLC grade. 5. Results and discussion 5.1. PMD system evaluation and probe calibration PMD experiments were performed to determine several properties. Results for a typical probe and calibration are shown below, using a donor solution of 20 mg/mL ibuprofen in pH 7 phosphate buffer at 23  C. In that system, the ibuprofen concentration is below its solubility, so fD = 1 and F App ¼ FR. R The window volume is a property of the probe that is required by Eq. (6). To evaluate VW, a series of PMD experiments was performed using the same resting time but varying VS. The resting time was 300 s, which was long enough for the exponential terms in Eq. (6) to become negligible and reduce to Eq. (10). (This is justified below.) Fig. 2 shows a plot of FR vs. 1/VS. The slope and intercept were approximately 2.38 mL and 0.010, respectively, giving VW = 2.40 mL. From this VW and using a flush rate of Q = 100 mL/min, the transit time tQ was approximately 1.5 s and the exposure time was taken as tP = tR + 1.5 s. Another set of PMD experiments was performed in which the resting time was varied but VS was held constant at 11 mL per pulse to evaluate the response of the PMD probe. The values of FR increased monotonically with increasing resting times and tP, and approached a plateau value at longer exposure times. A typical plot is shown in Fig. 3, which shows the average of three experiments in which the data were obtained using resting times ranging from 9 to 180 s and a donor ibuprofen concentration of 20 mg/mL in pH 7

4.9. Testing for nonspecific binding Solutions of ibuprofen (10 mg/mL and 20 mg/mL) were prepared at pH 2 and pH 7 in 25 mM phosphate buffer. 10 cm of the PMD probe material (regenerated cellulose) were immersed in quantities of solution upto 10 mL, then allowed to equilibrate 6 h. Samples of the solution were taken before and after, and compared to determine if there was nonspecific binding. As a corroborating procedure, the permeability of the probes were evaluated at the start and end of all precipitation experiments by constructing F App vs. tP plots, then determining R the probe permeability P as described in Section 4.5. This was done because nonspecific binding would be expected to reduce the probe permeability, as most of the surface area occurs in the wall of

Fig. 2. Window volume calibration curve from Eq. (10).

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concentration decline were constructed and were linear, with the slope representing the FR. The dynamic calibrations were performed at 10, 20, 30 and 40  C using 9 s resting times, and a plot of FR vs. T (Kelvin) was fit by the line given by FR = 0.00268 T  0.702 (R2 = 0.985), which was used to calculate the FR at any other temperature for that resting time. Fig. 4 shows an example plot of CS vs. CD using the data in Table 1. (The first two time points were excluded from the plot to allow the pumps to come up to speed.) 5.3. Supersaturation induced by pH change

Fig. 3. FR vs. tP for ibuprofen in an aqueous buffer. The diamonds represent experimental data, and the line represents fit of the data using Eq. (6) with VW = 2.4 mL.

buffer. The solid line represents a fit of Eq. (6) to the average of three experiments with fD = 1. The average of the three values of g 1 obtained separately from each experiment was 0.0208  0.0015 (RSD of 7.5%). Since g1 < g2 . . . , this justifies that a resting time of 300 s was long enough so all exponential terms in Eq. (6) were negligible, thus justifying the use of Eq. (10) to determine VW. As a check for consistency, the window volume obtained from Fig. 3 was used plateau value for FR calculated from the fit of Eq. (6) was compared with the value obtained from Eq. (10). Using parameters from the fits shown in Fig. 2 and a sample volume of VS = 11 mL per pulse, the plateau FR was calculated using the window volume obtained from Fig. 3 (VW = 2.3 mL) and the sample volume used to generate Fig. 2 (VS = 11 mL). The plateau values were in good agreement, with FR = 0.234 from Eq. (6) and FR = 0.238 from Eq. (10). The results shown in Fig. 3 were used to estimate the minimum quantifiable dissolved donor concentration (MQC D;f ). This parameter is important because the dissolved drug concentration in a dissolution medium will be determined using PMD, and the PMD sample concentration CS cannot be lower than the limit of quantitation (LOQ) of the HPLC assay. Eqs. (2)–(4) lead to MQC D;f ¼

LOQ FR

(12)

For the setups in this work and using ibuprofen as the drug, FR ranged from approximately 0.07 to 0.25, depending on the resting time. Taking the LOQ as 0.1 mg/mL, the calculated MQC D;f was approximately 1.5 mg/mL for ibuprofen when using a 9 s resting time, and lower for all other resting times used here. These MQC D;f values were low enough limits of quantitation were not an issue for any experiments in this study.

Ibuprofen solutions of 100 mg/mL and 200 mg/mL were prepared at both 23 and 37  C in phosphate buffer with initial pH of 7. PMD was started and at least two samples were collected, then sufficient HCl was quickly added to the stirred solution to reduce the pH to 2, at which the solubilities are approximately 20 mg/mL and 40 mg/mL at 20  C and 37  C, respectively. PMD sampling was continued, and direct sampling was also done. Based on preliminary data, PMD samples were taken every minute for the first 10 min, and then every five minutes after that. Typical data are shown in Fig. 5, which compares the concentrations obtained by the direct sampling with the dissolved concentrations obtained from the PMD data. In all cases, the dissolved concentrations determined using PMD were lower than the concentrations obtained by direct sampling in the first hour, and the differences were statistically significant for all times after 2 min (t-test, P < 0.05). However, the concentrations determined by each method became similar after 12 h in all cases, approaching the solubility of ibuprofen. The relative concentration differences between the methods shown in Fig. 5 were more distinct at 23  C than 37  C, which is qualitatively consistent the solubility differences at pH 2 occurring at the two temperatures. This is because, for a given dissolved concentration CD,f, the supersaturation ratio S ¼ C D;f =C 0 is larger at the lower temperature, which would be expected to lead to faster nucleation. At early times, when the particles are small, the PMD would provide more effective filtering than direct sampling, but as the particles grow the difference in filtering would be less, and after sufficient time becoming similar. The dissolved concentration data obtained by each method were also qualitatively different. In all cases, the dissolved concentrations determined using PMD showed a biphasic profile, with a phase of rapid decline from approximately 2 to 10 min, followed by another phase of slower decline. In addition, the

5.2. PMD dynamic probe calibration Since some experiments in this study involved donors in which rapid precipitation was occurring, PMD calibrations were also performed to determine the fractional recovery in solutions for which the dissolved drug concentration in the donor was changing rapidly in a known manner with time, which is referred to as a dynamic probe calibration. A first order decline in dissolved ibuprofen concentration was produced, in which the initial dissolved donor concentration was 500 mg/mL and the half-life was approximately two minutes. A pH of 7 was maintained, so the drug concentration was below the solubility and fD = 1 at all times. Plots of CS obtained using PMD vs. CD calculated from the known

Fig. 4. Dynamic probe calibration for ibuprofen in pH 7 buffer at 30  C. The data are taken from Table 1.

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Table 1 Dynamic probe calibration for ibuprofen in pH 7 phosphate buffer at 30  C. Time (s)

Calculated CD,f (mg/mL)

Experimental CS (mg/mL)

16 47 78 109 140 172 203 234 265 296 328 359 390 421 452 484 515

454.3 375.0 309.6 255.6 211.0 174.2 143.8 118.7 98.0 80.9 66.8 55.1 45.5 37.6 31.0 25.6 21.1

43.5 40.7 36.5 29.3 24.4 19.9 16.6 13.5 11.4 9.4 7.5 6.2 5.2 4.4 3.6 3.0 2.5

The dissolved donor concentration declined in a first order manner with a calculated half life of 109 s. In the PMD experiments, tR = 9 s.

dissolved concentrations obtained using PMD consistently followed biphasic log-linear declines. As discussed below, supersaturated solutions experience a decline in dissolved concentration by first going through a nucleation plus growth phase, followed by a   growth phase in which ln C D;f  C 0 or, equivalently, lnðS  1Þ, declines linearly with time. Plots of lnðS  1Þ vs. time constructed using the data shown in Fig. 5 over the first 2–10 min were linear (R2 > 0.98 in all cases), and again because linear over times greater than 10–15 min, but the magnitude of the slope was significantly smaller. Fig. 6 shows a plot of lnðS  1Þ vs. time for data obtained at 23  C using PMD, where C0 represents the solubility in pH 2

medium, with an initial dissolved concentration of 200 mg/mL. For initial dissolved concentrations of 200 and 100 mg/mL, the slopes over the first 8–10 min were 0.190 min1 and 0.153 min1 at 23  C, respectively, and 0.117 min1 and 0.039 min1 at 37  C, respectively. These results suggest that the rate of precipitation increases if the initial dissolved concentration of the ibuprofen is increased, or if its solubility is decreased (e.g., at lower temperature). Both of these are consistent with the notion that increasing the degree of supersaturation will increase the precipitation rate. The concentration data obtained by direct sampling were much less consistent. Except for the 200 mg/mL initial concentration at 23  C, the declines were not biphasic, and none closely followed a first order decline (data not shown). Also, as mentioned above, the concentrations obtained from direct sampling were higher than those determined from PMD data in all cases, but the two approached similar values at long enough times. This is consistent with the hypothesis that PMD data more accurately reflects the dissolved concentrations because PMD probes are more discriminating than 0.2 mm filters. Specifically, when nuclei are forming and growing, particles are initially small and can be filtered by PMD, but pass through more gross filters. However, as they increase in size over time, most become large enough to be excluded by the 0.2 mm filters as well as microdialysis probes. The biphasic behavior seen from the PMD data is not necessarily universally expected, but it was not surprising either. In preliminary experiments, it was seen that ibuprofen appeared to nucleate and precipitate rapidly when the pH was suddenly lowered, and the sampling times were chosen based on these data. Fig. 5 shows that the rate of decline of the dissolved concentration obtained from the PMD data drops significantly when the dissolved concentration approached 40 mg/mL for the systems at 23  C and 70–80 mg/mL at 37  C, which was approximately twice the solubility at each respective temperature. This is consistent with

Fig. 5. PMD vs. direct sampling for ibuprofen precipitation induced by sudden pH drop. The open squares represent the concentration obtained from direct sampling, and filled triangles represent CD,f determined using PMD. Initial concentrations were (A) 200 mg/mL at 23  C (B) 200 mg/mL at 37  C (C) for 100 mg/mL at 23  C and (D) 100 mg/mL at 37  C.

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where g is the excess surface energy of a forming nucleus, v is the volume of the molecule (ibuprofen in this case), kB is Boltzmann’s constant, and S is the supersaturation ratio. The growth phase has been modeled as variations of the Nernst–Brunner equation (Mullin, 2001), such as   dC D;f ¼ B C D;f  C 0 dt

(14)

where B depends on the total particle surface area and the diffusion coefficient of the drug in the medium. Eq. (14) can be approximately solved in the growth phase (over time intervals when the relative change the surface area of the particles is small) to give   (15) ln C D;f  C 0 ¼ Bt which can be rewritten in terms of the supersaturation ratio as lnðS  1Þ ¼ Bt  lnC 0 Fig. 6. Plot of ln (S1) vs. time from PMD data for ibuprofen at 23  C. The initial ibuprofen dissolved concentration was 200 mg/mL. The open squares represent the data obtained from direct sampling, and filled triangles represent data determined using PMD.

precipitation models (Cao, 2004), in which there is a dissolved concentration above which nucleation and particle growth occur, and below which nucleation becomes negligible and essentially only growth occurs. A well-known equation for nucleation is Tung et al., 2009) " # 16pg 3 v2 (13) ½nucleation rate ¼ Aexp 3 2 3ðkB T Þ ðlnSÞ

(16)

It has been reported for some systems that the nucleation rate sharply decreases when ln S becomes small (Mullin 2001). Mathematically, this can be seen in Eq. (13) when ln S < 1, which occurs when S < 2.7, and has been observed for lovastatin (Mahajan and Kirwan, 1996). With further decrease in the dissolved concentration below that level, the (ln S)2 term will cause the exponential term to drop off sharply, causing the nucleation plus growth stage to transition to growth phase only, resulting in a slower drop in dissolved concentration with time. For the systems illustrated in Fig. 5, it is not clear why the supersaturation ratio reached two at about the same time (8–12 min) for all of the systems, and may be coincidence from

Fig. 7. Comparison of dissolution profiles determined using PMD vs. conventional method on in-house formulation systems with different total donor concentration. The total ibuprofen per 100 mL of dissolution medium were (A) 15 mg; (B) 11 mg; (C) 8 mg; (D) 4.5 mg. The open squares represent the concentration obtained from direct sampling, and filled triangles represent CD,f determined using PMD.

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the experimental setup. Also, it is not clear if the initial decline lnðS  1Þ vs. time should be linear over the first 8–10 min, or if this is coincidental. A full study of the precipitation kinetics of ibuprofen and other drugs is currently being conducted, and will be the subject of a future report. 5.4. Supersaturation induced by rapid release from a formulation In-house formulation of ibuprofen in Syloid 244FP were made, and dissolution/release experiments were performed to evaluate the resulting supersaturation. In all cases, the dissolution medium was pH 2 aqueous buffer, and different amounts of formulation were taken from a single batch to vary the total drug being dissolved and the resulting supersaturation. Fig. 7 shows a typical set of results. Although there was batch-to-batch variability in the drug load, the results were consistent. The drug came out of the formulations quickly and produced supersaturation, but there were differences between the dissolved concentrations obtained using PMD and direct sampling. In all cases, release of the ibuprofen as determined by both methods was initially rapid and supersaturation was achieved, with spring and parachute patterns observed for all but the lowest drug amounts being dissolved. However, the dissolved concentrations obtained using PMD were always lower than those determined by direct sampling for the first 40 min, with the peak values determined by PMD typically being 25–50% lower than corresponding values from direct sampling. After 12 h, the dissolved concentrations determined from PMD and direct sampling converged, approaching the ibuprofen solubility. To check the probe permeability, PMD was performed before and after each dissolution with a series of resting times, and plots of F App vs. tP were constructed and fitted with Eq. (6). In all cases, no R significant changes in the permeability were observed. (Data not shown.) 5.5. General discussion Pulsatile microdialysis (PMD) is a procedure that can be used to determine the dissolved drug concentrations in a liquid medium. The model, equations and procedures described in the previous sections detail how the dissolved drug concentration in a donor medium can be determined from the fractional recovery FR. They also detail how the FR is determined for the given experimental setup. It is important to note that even if the experiments are performed using a different resting time or temperature, both of which would affect the concentration in the PMD sample CS, the FR calibration would account for these changes, so the the proper dissolved concentration C D;f in the donor would be calculated from the experimental CS. PMD was evaluated as a method for sampling dissolved concentrations of ibuprofen in microscopically and macroscopically heterogeneous systems. In this context, perhaps its most important application is as an alternative to direct sampling of supersaturated solutions using a syringe and filter. It was consistently seen that the dissolved concentrations in supersaturated solutions calculated from PMD data were lower than those obtained by direct sampling at relatively early times, but the two tended to converge after longer times. This behavior is reasonable based on simple filtration arguments, as dialysis membranes with small pores are more effective at excluding small particles than filters. Thus, smaller particles would be more effectively excluded from the dialysate at earlier times, while at later times the filtering done with direct samples would remove the particle that had grown to larger sizes. The pore size argument is generally accepted and supported by standard practices. For instance, protein binding experiments use dialysis

membranes instead of filters to separate proteins with bound drug from dissolved free drug. These results are difficult to corroborate by other methods. PMD is perhaps the only method that directly measures the dissolved drug in microscopically heterogeneous media in situ. Optical methods are not always applicable in situ because particles can cause light scattering. Focused beam reflectance measurements (FBRM) gives information about particle growth (Stillhart et al., 2013), but does not give accurate information about the dissolved drug concentration. Also, FBRM is most effective for particles above the micron scale, and thus is not suited for detecting effects of nuclei and small nano-scale particle. For comparison, experiments similar to those reported in Fig. 7 were performed in which dissolved concentrations found using PMD data were compared with direct sampling using a 0.2 mm filter, direct sampling using a 0.45 mm filter, and direct sampling using a 0.45 mm filter followed by ultracentrifugation for 3 min at 10,000 rpm (Eppendorf Model 5415R, Eppendorf North America, Hauppauge, NY). After the first two minutes and up to one hours (the last point taken), the concentrations found by direct sampling using 0.2 mm filters were lower than those by direct sampling using 0.45 mm filters plus centrifugation, which were lower than direct sampling with 0.45 mm filters. From those results, it was concluded that direct sampling with 0.2 mm filters provided the lowest concentrations among the direct sampling methods. In addition to pore size arguments, two other factors were be considered and eventually rules out as possible explanations for why the dissolved concentrations obtained from PMD data are less than those of direct sampling. These include nonspecific binding to the PMD probes and precipitation in the probes, both of which might reduce the concentration in the dialysate. It was found that nonspecific binding was not a significant factor, as evidenced by the soaking studies described in Section 4.9. A corroborating factor was the observation that the permeability of the probes did not change during the precipitation experiments. For dialysis membranes with molecular weight cutoffs of 18 kDa, the pore radius is generally estimated to be approximately 2 nm (for instance, http://www.spectrumlabs.com/filtration/PoreSize.html), and the reported radiusof diffusing ibuprofen molecules of 0.36–0.6 nm (Nghiem et al., 2006; Feng, 2008). Most of the surface area for the PMD probes is along the walls of the pores. Comparing the pore radii and molecular sizes, significant nonspecific binding along the pore walls would be expected to significantly reduce the porosity, which would in turn result in a reduced probe permeability. The absence of these changes supports that nonspecific binding is not a factor responsible for the lower dissolved concentrations found using PMD. Visual inspection of the probes after the experiments only revealed some loosely held particles on the probe surface that were easily removed with gentle rinsing after the experiments. Also, the dialysate consisted of 25 mM phosphate buffer at pH 7, in which the ibuprofen solubility is much higher than any concentration used in this study, which would prevent precipitation of the drug in the dialysate and likely discourage precipitation in the pores. Also, similar to the discussion in the previous paragraph, the lack of change of probe permeability after experiments suggests no precipitation of drug in the pores. Thus, precipitation on or in the probes is also not likely to account for the observed differences between PMD and direct sampling results. As a final factor to consider, although the dissolved concentrations obtained from PMD data were lower than those obtained using direct sampling, the ratios were not constant over time. In fact, for all cases studied, they converged by 12 h, consistent with the hypothesis that as particles grow, the two methods of filtering become similarly effective.

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One of the important features of the PMD method is that samples are taken rapidly. Unlike equilibrium dialysis, PMD samples are collected before equilibration occurs between the donor and dialysate. In addition, the probe radii are small and the surface-to-volume ratios are large, leading to relatively large changes in the dialysate concentration in short times. As a result, short sampling times (i.e., resting times from 10 to 300 s) can be used to collect filtered, assay ready samples using PMD. This leads to several important benefits. For instance, short sampling times allow rapid repeated sampling. Thus, PMD is suitable for systems that change quickly with respect to time. Another benefit of using short resting times is increased filtering efficiency. Molecular weight cutoff values are typically determined using equilibration experiments. However, even if a particle is small enough to pass through a pore, collisions with the walls would slow the rate of passage from the donor to the dialysate. The resting times used in PMD are very short by this standard—even if some particles cross the membrane, the amount of drug accumulated in the dialysate is dominated by individual molecules. Another benefit of not reaching equilibrium while sampling is that the PMD sample concentration changes with increasing resting times, which allows experiments to be done to construct plots of F App vs. tp, and fits of Eq. (6) to the data allow the probe wall R permeability P to be calculated. This is very important because it provides a means to detect changes in the probe window properties that might occur during an experiment. For instance, in supersaturated solutions, drug precipitation in the window pores might occur, which would have the physical effect of reducing the permeability. Thus, including l in the iterations to require it being consistent with P at any time is necessary to correctly determine the other parameters, including fD. Retrodialysis is another way to qualitatively determine whether probe properties change during an experiment, which is done by a different agent to the dialysate and tracking its loss to the external medium. However, this method does not provide sufficient information to allow a specific quantitative correction to the uptake rates of the in the donor by the dialysate. 6. Conclusions The pulsatile microdialysis (PMD) technique was used to characterize the supersaturation and precipitation behaviors of the poorly soluble drug ibuprofen. The motivation for developing this method was to assess the release profile of the drug and comparing those samples with the samples taken directly from the dissolution medium and then filtering with 0.2–0.45 mm filters. That would allow small particles to pass through the filter and overestimate the amount of drug in solution. PMD was chosen because it has been shown to be sensitive and accurate, and provides a means to collect filtered assayable samples in a matter of seconds. In addition, it was seen that PMD analyses gave dissolved concentration vs. time profiles that were significantly lower than those obtained by sampling and filtering. When supersaturation was induced by releasing ibuprofen from a formulation, the dissolved concentrations determined using PMD results were significantly lower than determined by direct sampling for at least the first hour, but the two values converged after long times. One of the anticipated applications for using PMD is in drug formulations that create supersaturation, such as nanoparticles or solid dispersions. For those systems, the dissolved concentration in the first hour or two is of interest, because that timeframe corresponds to the early absorption of drugs. In fact, knowledge of the actual dissolved concentration may be more important than the drug solubility when correlating in vitro dissolution with in

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vivo absorption. Thus, the results suggest that PMD might be useful in drug development for constructing in vitro in vivo correlation (IVIVC). References Augustijns, P., Brewster, M.E., 2012. Supersaturating drug delivery systems: fast is not necessarily good enough. Journal of Pharmaceutical Sciences 101, 7–9. Bagchi, S., Mukherjee, T., Plakogiannis, F.P., 2012. Re-evaluation of in vitro dissolution techniques for supersaturating drug delivery systems. Pharmaceutical Development and Technology 17, 477–482. Bellantone R.A., 2012. Method for use of Microdialysis. United States Patent #8,333,107. Bevernage, J., Brouwers, J., Brewster, M.E., Augustijns, P., 2013. Evaluation of gastrointestinal drug supersaturation and precipitation: strategies and issues. International Journal of Pharmaceutics 453, 25–35. Brewster, M.E., Vandecruys, R., Verreck, G., Peeters, J., 2008. Supersaturating drug delivery systems: effect of hydrophilic cyclodextrins and other excipients on the formation and stabilization of supersaturated drug solutions. Pharmazie 63, 217–220. Brouwers, J., Brewster, M.E., Augustijns, P., 2009. Supersaturating drug delivery systems: the answer to solubility-limited oral bioavailability? Journal of Pharmaceutical Sciences 98, 2549–2572. Cao, G., 2004. Nanostructures and Nanomaterials: Synthesis, Properties and Applications. Imperial College Press, London Chapter 3. Dai, W.G., 2010. In vitro methods to assess drug precipitation. International Journal of Pharmaceutics 393, 1–16. di Cagno, M., Luppit, B., 2013. Drug "supersaturation" states induced by polymeric micelles and liposomes: a mechanistic investigation into permeability enhancements. European Journal of Pharmaceutical Sciences 48, 775–780. Feng, H.A., 2008. In Vitro Determination of Drug Diffusion Coefficients in Viscous Media Using Pulsatile Microdialysis: Theory and Method Development. Doctoral Dissertation. Long Island University, Brooklyn, New York. Gao, P., Shi, Y., 2012. Characterization of supersaturatable formulations for improved absorption of poorly soluble drugs. AAPS Journal 14, 703–713. Hiemenz, P.C., Rajagopalan, R., 1997. Principles of Colloid and Surface Chemistry, third ed. Marcel-Dekker, New York Chapter 2. Kabir, M.A., Taft, D.R., Joseph, C.K., Bellantone, R.A., 2005. Measuring drug concentrations using pulsatile microdialysis: theory and method development in vitro. International Journal of Pharmaceutics 293, 171–182. Lipinski, C.A., Lombardo, J., Dominy, B.W., Feeney, P.J., 2001. Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Advanced Drug Delivery Reviews 46, 3–26. Macheras, P., Karalis, V., Valsami, G., 2013. Keeping a critical eye on the science and the regulation of oral drug absorption: a review. Journal of Pharmaceutical Sciences 102, 3018–3036. Mahajan, A.J., Kirwan, D.J., 1996. Micromixing effects in a two-impinging-het precipitator. AIChE Journal 42, 1801–1814. Malzert-Freon, A., Saint-Lorant, G., Hennequin, D., Gauduchon, P., Poulain, L., Rault, S., 2010. Influence of the introduction of a solubility enhancer on the formulation of lipidic nanoparticles with improved drug loading rates. European Journal of Pharmaceutics and Biopharmaceutics 75, 117–127. Mullin, J.W., 2001. Crystallization, fourth ed. Butterworth-Heinemann, Boston, pp. 5–6. Nghiem, L.D., Schafer, A.I., Elimelech, M., 2006. Role of electrostatic interactions in the retention of pharmaceutically active contaminants by a loose nanofiltration membrane. Journal of Membrane Science 286, 52–59. Nkansah, P., Antipas, A., Lu, Y., Varma, M., Rotter, C., Rago, B., El-Kattan, A., Taylor, G., Rubio, M., Litchfield, J., 2013. Development and evaluation of novel solid nanodispersion system for oral delivery of poorly water-soluble drugs. Journal of Controlled Release 169, 150–161. Ozaki, S., Minamisono, T., Yamashita, T., Kato, T., Kushida, I., 2012. Supersaturationnucleation behavior of poorly soluble drugs and its impact on the oral absorption of drugs in thermodynamically high-energy forms. Journal of Pharmaceutical Sciences 101, 214–222. Patel, D.D., Anderson, B.D., 2013. Maintenance of supersaturation II: indomethacin crystal growth kinetics versus degree of supersaturation. Journal of Pharmaceutical Sciences 102, 1544–1553. Petrusevska, M., Urleb, U., Peternel, L., 1999. Evaluation of a high-throughput screening method for the detection of the excipient-mediated precipitation inhibition of poorly soluble drugs. Assay and Drug Development Technologies 11, 117–129. Schmelzer, J.W., Schmelzer, J., 1999. Kinetics of nucleation at increasing supersaturation. Journal of Colloid and Interface Science 215, 345–355. Stillhart, C., Cavegn, M., Kuentz, M., 2013. Study of drug supersaturation for rational early formulation screening of surfactant/co-solvent drug delivery systems. Journal of Pharmacy and Pharmacology 65, 181–192. Tung, H.H., Paul, E.L., Midler, M., McCauley, J.A., 2009. Crystallization of Organic Compounds—An Industrial Perspective. Wiley, Hoboken, NJ Chapter 4. Vaughn, J.M., McConville, J.T., Crisp, M.T., Johnston, K.P., Williams, R.O., 2006. Supersaturation produces high bioavailability of amorphous danazol particles formed by evaporative precipitation into aqueous solution and spray freezing into liquid technologies. Drug Development and Industrial Pharmacy 32, 559– 567.

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Glossary

gn: defined by Eq. (7)

a: inner radius of the microdialysis probe window

L: length of the microdialysis probe window (= VW/pa2)

A: area of the probe window = 2paL

l: defined by Eq. (8)

bn: roots of bn J 1









bn  lJ0 bn ¼ 0

CD: total concentration in the donor medium CD,f: dissolved free concentration in the donor medium CS: average concentration in a collected dialysate sample

MQCD,f: minimum quantifiable dissolved free drug concentration in the donor when determined using PMD, defined by Eq. (12) P: permeability of the probe window wall PMD: pulsatile microdialysis Q: dialysis flow rate while pumped (mL/min)

D: diffusion coefficient of the drug in the dialysate tP: exposure time for the pulsed portion of the dialysate sample (tR + tQ)

dn: defined by Eq. (7) fD: defined by Eq. (3) FR: fractional recovery for a sample, defined by Eq. (2)

F App R : apparent fractional recovery, defined by Eq. (4) FRQ: idealized fractional recovery of the continuous portion of the PMD sample

tQ: transit time for the continuous portion of the dialysate sample = VW / Q tR: resting time for dialysate in the probe window VW: probe window volume = pa2L (same as the volume of dialysate allowed to rest) VS: volume of one dialysate sample from one pulse