PHARMACEUTICS, PREFORMULATION AND DRUG DELIVERY Release Mechanisms of a Sparingly Water-Soluble Drug from Controlled Porosity-Osmotic Pump Pellets Using Sulfobutylether-b-Cyclodextrin as Both a Solubilizing and Osmotic Agent SUTTHILUG SOTTHIVIRAT,1 JOHN L. HASLAM,2 PING I. LEE,3 VENKATRAMANA M. RAO,4 VALENTINO J. STELLA1 1
The Department of Pharmaceutical Chemistry, 2095 Constant Avenue, The University of Kansas, Lawrence, Kansas 66047
2
Higuchi Biosciences Center, Lawrence, Kansas 66047
3
Department of Pharmaceutical Sciences, Leslie Dan Faculty of Pharmacy, University of Toronto, 144 College Street, Toronto, Ontario, Canada M5S 3M2 4
Biopharmaceutics R&D, Bristol-Myers Squibb, New Brunswick, New Jersey 070761
Received 9 May 2008; revised 28 July 2008; accepted 7 August 2008 Published online 29 September 2008 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21567
ABSTRACT: The purpose of this work is to delineate the release mechanisms of a sparingly water-soluble drug, prednisolone (PDL), from a microporous or controlled porosity--osmotic pump pellet (CP--OPP) using sulfobutylether-b-cyclodextrin (CD) as both a solubilizing and osmotic agent. All factors, osmotic and diffusional, influencing drug release as described by the Theeuwes and Zentner equation were partially demonstrated in an earlier paper1 and are further quantitatively evaluated here to determine whether the equation may be applied to CP--OPPs. The PDL release rate from the CP--OPPs containing precomplexed PDL follows the zero-order kinetics for up to 30--40% of drug release during the first 1--2 h and subsequently nonzero order kinetics. The zero-order drug release phase reveals the main contribution is from osmotic pumping with a negligible diffusion component, resulting from the nearly constant driving forces in the system. The nonzero order drug release phase is associated with the dynamic changes in the system (e.g., declining osmotic driving force and greater diffusion component with time). In addition, the parameters related to membrane characteristics were determined, and the effect of viscosity was evaluated for the pellet system. The membranes coated on the CP--OPPs are less permeable to water or solutes than the membranes coated on the previously reported tablets. The viscosity due to the CD decreases as a function of CD concentration, which partly affects the observed drug release profiles. The viscosity effect of CD is significant and captured in a hydraulic permeability term. ß 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:1992--2000, 2009 Sutthilug Sotthivirat’s present address is Merck & Company, Inc., P.O. Box 4, West Point, Pennsylvania 19486. Correspondence to: Valentino J. Stella (Telephone: 785-8643755; Fax: 785-864-5736; E-mail:
[email protected]) Journal of Pharmaceutical Sciences, Vol. 98, 1992–2000 (2009) ß 2008 Wiley-Liss, Inc. and the American Pharmacists Association
1992
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1993
Keywords: investigation; mechanism; pellet; sulfobutylether-beta-cyclodextrin; controlled release; and prednisolone
INTRODUCTION Drug release from microporous or controlled porosity-osmotic pump tablets (CP--OPTs) using sulfobutylether-b-cyclodextrin (CD) as both a solubilizer and osmotic agent has been reported earlier.1--8 The use of CD in matrix tablets has also been described.9 Some of these papers have attempted to probe the mechanisms of the release process in these unit dose, dosage forms.2,6,7 Controlled porosity-osmotic pump tablets and pellets (CP--OPTs and CP--OPPs) are only possible when the drug under consideration is fairly soluble and by itself, or in the presence of an osmotic agent, provide sufficient internal osmotic pressure to help drive the release of the drug from these formulations. Sulfobutylether-b-cyclodextrin (CD) is highly anionic with, on average, seven negative charges and seven associated sodium ions. It is not only an effective solubilizing agent but when present with a sparingly soluble drug in the internal matrix of a CP--OPT or CP--OPP can also play the duel role of solubilizer and osmotic agent. A study describing the release of prednisolone (PDL), a sparingly water-soluble drug, from controlled porosity--osmotic pump pellets (CP--OPP) using CD has been recently published.1 Since a wet granulation technique was involved in pellet formation in that study, some CD-PDL complex formation did occur during the processing.10 In the drug release study some initial probing of the release mechanism/s was performed and briefly discussed.1 Presented here are further quantitative probes of the mechanism/s of PDL release from these CP--OPPs. Most mechanistic studies of drug or solute release from osmotic devices have attempted to describe its release using Eq. (1) from Theeuwes11 and Zentner et al.,12
the membrane, D is the drug diffusion coefficient across the membrane, and K is the partition coefficient of the drug between the aqueous medium and membrane. To achieve zero-order delivery, drug must be present in the core at its saturated solubility, and DP must remain approximately constant with time. In addition, in CP--OPPs where the drug can diffuse through aqueous-filled pores, the apparent or effective drug diffusion coefficient (Deff) should be used to better describe the system since it takes membrane porosity (e) and tortuosity (t) into account, as depicted in Eq. (2). " ð2Þ Deff ¼ D t A previous study has shown that this may need to be modified by taking into consideration the hydrostatic pressure assumption as discussed by Stella et al.,8 to account for the near zero-order release kinetics seen with tablet formulations. Unlike the earlier tablet studies,2,8 drug release from pellets does not follow a zero-order pattern for a long period of time.1 This leads to the investigation focused on not only the relative contributions from osmotic versus diffusional forces but also the viscosity effects with time.
EXPERIMENTAL Materials
where (dMt/dt) is the drug release rate, A, h, Lp and s are the membrane surface area, thickness, hydraulic permeability and reflection coefficient, respectively, S is the drug saturation solubility, DP is the difference in osmotic pressure across
Sulfobutylether-b-cyclodextrin (CD or Captisol) in its sodium salt form was a generous gift from CyDex, Inc. (Lenexa, KS). Materials were milled through a QuadroComil mill (Quadro, Inc., Millburn, NJ). Prednisolone (Sigma-Aldrich Co., St. Louis, MO), urea (Sigma-Aldrich Co.), microcrystalline cellulose or MCC (Avicel PH 101, FMC Corporation, Newark, DE), cellulose acetate butyrate (CAB 381-20, Eastman Chemical Company, Kingsport, TN), triethyl citrate (TEC; pharmaceutical grade, Morflex, Inc., Greensboro, NC), sucrose (crystal, NF, Spectrum Chemical Mfg. Corp., Gardena, CA), 2,6-TNS or 6-p-toluidinylnaphthalene-2-sulfonate (Acros Organics, Pittsburgh, PA), acetonitrile, acetone, and ethanol were used as received.
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dMt AS ADKS Lp sDP þ ¼ h h dt
ð1Þ
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Preparation of Pellets, their Coating and Drug Release Studies Both the preparation of the pellets and their coating have been described in detail in a previous paper.1 Briefly, the pellet core consisted of the drug/CD complex (5.5 g (2.75%) and 66.5 g (33.25%), respectively; 1:2 drug to CD mole ratio) and Avicel (128 g (64%)) using a wet granulation method. The pellets themselves were prepared using an extrusion-spheronization process followed by overnight drying at room temperature and coating using a UniGlatt fluidized-bed coater. The coating solution consists of CAB 381-20 (60.6% w/w, based on the total solids), TEC (plasticizer, 18.2% w/w), and sucrose (pore former, 21.2% w/w) in a mixed solvent of acetone, ethanol, and water (5:1:1, v/v/v). Also documented in that paper were details of the release studies and coating characterization. PDL release from the pellets was quantified by a UV-spectrophotometer at 250 nm connected to the dissolution apparatus as described earlier.1 All the release results presented in this paper used pellets where the CD/ PDL complex was preformed as discussed in an earlier paper.1 The calculations are based on approximate 146 CP--OPPs with an average diameter of 1.32 mm (average membrane thickness of 40 mm). Preparation of Membrane for Diffusion Cell Studies The same coating solution applied on CP--OPPs was used to prepare free membranes. The coating solution was sprayed using an airbrush (Paasche Airbrush Co., Harwood heights, IL) onto round Teflon sheets and dried with an air dryer at 40 (–2) C for 2 min, followed by additional 5 min drying to remove excess solvent. They were then peeled from the sheets and measured for dry film thickness using a caliper. The dry membranes were soaked in water to remove water-soluble compounds such as sucrose, and the hydrated film thickness was also measured prior to their use in diffusion cell studies. Membrane porosity was measured using a helium pycnomter (AccuPyc 1330, Micromeritics, Norcross, GA). The porosity was calculated from the difference in the true volume of the membrane before and after exposure to water.
cell and a receiver cell with sampling ports to allow sampling of solution. The capacity of each chamber is about 3.5 mL. Between the donor and receiver cells is a presoaked membrane sheet with a constant surface area of 0.5 cm2. The membrane sheet was sealed tight by a clamp. Water from a controlled temperature water bath was circulated around the diffusion cells to control the temperature at 37 C (–0.5 C). A magnetic stirrer drive unit was used with the diffusion cells to control the magnetic stirring at 600 rpm to prevent boundary effects.
Osmotic Volume Flux Determination Osmotic volume flux is defined as the flux of water through the membrane caused by the difference in osmotic pressure across the membrane when there are no hydrostatic pressure gradients in the system. The left chamber of Side-by-Side diffusion cells contained water while the right chamber contained a series of CD solutions (0.05--0.36 M). Hydrostatic pressure was maintained at constant by using horizontal capillaries (0.5 mm in diameter) of the same height for both chambers. The volume change in a water chamber was measured as a function of time. For each trial, at least six data points were collected. The product of hydraulic permeability and reflection coefficient (Lps) was determined from the slope of the linear regression line of the volume change versus the osmotic pressure gradient across the membrane while the surface area and the thickness of the membrane were known.
Hydraulic Permeability Determination
Side-by-Side diffusion cells (Crown Glass Company, Inc., Somerville, NJ) consist of a donor
The hydraulic permeability of a membrane is referred to as the flux of water through the membrane due to a hydrostatic pressure difference in the absence of a gradient of osmotic pressure across the membrane. Both chambers of Side-by-Side diffusion cells contained water to eliminate osmotic pressure differences. The left chamber had a horizontal capillary to measure the volume of change as a function of time when the head pressure was applied on the right chamber using a vertical glass tube containing water. For each determination, volume fluxes were measured at three different head pressures. The hydraulic permeability (Lp) was determined from the slope of the relationship of the volume
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Diffusion Cell Studies
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1995
change and hydrostatic pressure difference across the membrane.
RESULTS AND DISCUSSION Mechanistic Probing through Varying Osmolality The PDL release rate in water followed the approximate zero-order kinetics for up to 30--40% drug release during the first 1--2 h and nonzero order kinetics thereafter, as shown in Figure 1. The PDL release rate decreased as the osmolality of the dissolution medium (using urea) increased, indicating that osmotic pumping is part of the overall mechanisms. When the urea concentration increased from 30% w/v to 40% w/v, the PDL release rate did not change at all (Fig. 2). This is interpreted as the state where no osmotic gradient across the membrane exists. Therefore, the osmotic pumping contribution is suppressed, and the observed drug release rate is thereby only diffusion-controlled. The relative contributions from osmotic forces versus diffusion were also delineated during the initial zero-order drug release phase. The initial release rate of PDL (after correcting for lag times) was plotted against the osmotic pressure gradient across the membrane (Fig. 3). The main mechanism for drug released from CP--OPPs in water is shown to be osmotic pumping (76%) with the diffusion contribution of 24% of the total drug release
Figure 2. A plot of initial release rate of PDL (from CP--OPPs containing precomplexed PDL) as a function of external osmolality using the USP XXIV paddle apparatus in different urea solutions at 37 C, 50 rpm.
rate, and the percent contribution from osmotic pumping decreases with the initial osmotic gradient. It should also be noted that all these results are based on the following assumptions. Urea does not significantly interfere with the dissolution of precomplexed PDL, and the viscosity of urea at different concentrations has negligible effects on the release rate of precomplexed PDL.
Figure 1. PDL release profiles of CP--OPPs containing precomplexed PDL using the USP XXIV paddle apparatus in various osmolality in the release medium at 37 C, 50 rpm.
Figure 3. A plot of initial release rate of PDL (from CP--OPPs containing precomplexed PDL) as a function of osmotic pressure difference across the membrane using the USP XXIV paddle apparatus in various urea solutions at 37 C, 50 rpm.
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Estimation of Concentration, Diffusion Coefficient, and Viscosity Profiles Inside the CP--OPPs The concentration of CD in the pellet core during the zero-order drug release phase, could not be determined experimentally, but could be estimated to be about 0.36 M through the intersection where the osmotic pumping was totally suppressed (see Fig. 2), that is, the osmolality of approximately 5.3 Osm/kg inside the pellet corresponds to a CD concentration of 0.36 M. This value agrees with the value reported by Stella et al.8 for an earlier study from CP--OPTs.2 The concentration of CD dissolved in the initial release phase from their CP--OPTs (coated with ethyl cellulose (EC) and PEG 1450 as a pore former) was experimental determined to be 0.35 M.2,8 With the assumption of no significant change in the pellet volume during the release, the concentration profiles of CD could be established based on the approximate pellet volume at different water levels taken up by MCC.13 The estimated concentrations of CD, assuming all the CD is dissolved, could be >0.36 M (Fig. 4), suggesting that the constant concentration temporarily exists inside the pellets. This is possible since CD is very soluble in water, and there is no defined saturated solubility for amorphous CD. In addition, the relationship of the osmotic pressure, diffusion coefficient, and viscosity of CD as a function of time may be estab-
lished based on the CD concentration profiles to be discussed later, as shown in Figures 5--7. The constant CD concentration over this first 1--2 h also provides a constant osmotic pressure, viscosity and diffusivity, leading to the constant driving force for drug delivery out of the device, as illustrated in Figures 5--7.
Figure 4. Estimated concentration profiles of CD inside CP--OPPs containing precomplexed PDL (estimated based on the volume available for CD dissolution, volume of MCC, total pellet volume as well as the release profile of CD from CP--OPPs containing precomplexed PDL using the USP XXIV paddle apparatus in water at 37 C, 50 rpm).
Figure 6. Predicted diffusivity profiles of CD inside CP--OPPs containing precomplexed PDL as a function of time based on the estimated concentration profiles shown in Figure 4 and Eq. (8): DCD ¼ 4:83 106 e9:65CCD where DCD and CCD are the diffusion coefficient (cm2/s) and concentration (molarity, M), respectively.
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Figure 5. Predicted osmotic pressure profiles of CD inside CP--OPPs containing precomplexed PDL based on estimated concentration profiles shown in Figure 4 and Eq. (7): O ¼ 0.916((TDS þ 1)m)1.075 where O, TDS, m are the CD osmolality (Osm/kg), average total degree of substitution of sulfobutylether groups per CD molecule (TDS ¼ 6.5), CD concentration (molality), respectively.
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1997
Figure 7. Predicted viscosity profiles of CD inside CP--OPPs containing precomplexed PDL based on the estimated concentration profiles shown in Figure 4 and Eq. (9): hCD ¼ 0:69eðð7:59CCD Þ=ð11:49CCD ÞÞ where hCD and CCD are the viscosity (centipoises, cP) at concentration c and concentration (molarity, M) of CD, respectively.
After the first hour or so, the drug release rate tends to become slower with time because the CD concentration in the pellet dramatically decreases (Fig. 4). Consequently, the osmotic pressure and viscosity of the system both decrease and the diffusivity increases as a function of decreasing CD concentration (Fig. 8a and b), all of which lead to the observed nonzero order kinetics of drug release. These findings strongly suggest that the Theeuwes and Zentner equation (Eq. 1) may not be simply applied to the pellet system. The contribution of osmotic pumping versus diffusion is also expected to vary with time since the osmotic pumping should decrease due to the declining CD concentration with time, and the contribution from diffusion, therefore, becomes more significant with time.
Figure 8. Predicted osmotic pressure and viscosity of CD (a) and predicted diffusion coefficient of CD (b) as a function of its concentration inside CP--OPPs containing precomplexed PDL.
During the zero-order drug delivery, the product of Lp and s, which is known as the water permeability, was determined to be 1.51 107 cm2/(h atm) from the slope of the graph (Fig. 3). This value is significantly less than those reported for the CP--OPTs by about a factor of 50--100.2,12 For instance, Zentner et al.12 used cellulose acetate (CA) and sorbitol as a pore former for their CP--OPT, and the water permeability was 7.87
106 cm2/(h atm). Zannou2 reported that the water permeability of CD across the membrane consisting of ethyl cellulose (EC) and PEG 1450 as a pore former was 1.57 105 cm2/(h atm) for the CP--OPTs. In addition, the effective or apparent permeability of precomplexed PDL through the aqueous filled-pores was 1.85 109 cm2/s. This value is in the same order of magnitude as that reported in the literature for other pellets. For example, Ozturk et al. reported that the measured permeability of phenylpropanolamine HCl across the EC-based film (Aquacoat) coated on the pellet formulation was 3 109 cm2/s.14 In addition, the measured permeability of CD in the EC-based film was reported to be 1.86 108 cm2/s for the CP--OPTs.2
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Determination of Membrane Characteristics of CP--OPPs
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In summary, the water permeability and solute permeability values for the CP--OPPs are much less than the reported values for the CP--OPTs. This is not unreasonable because pellets with their higher surface to volume ratios than tablets require a membrane (CAB vs. CA) with lower permeability to water and solutes to obtain a desirable drug release rate. Based on the CD membrane diffusivity of 1.85 109 cm2/s as determined from the CP--OPPs taking into consideration that the partition coefficient of the precomplexed-PDL or approximately CD between the aqueous filled-pores and water (K) equals unity for microporous membrane14,15 and the predicted CD aqueous diffusivity of approximately 1.50 107 cm2/s2, the ratio of e/t for the membrane is estimated to be about 0.012 (Eq. 2). Since t usually has an upper limit of 10, the maximum value for e is, therefore, 0.12. The value of e appears to be lower than the experimental value (0.17) obtained with a helium pycnometer. This is due to the fact that measured porosity includes total voids for both dead-end and interconnected pores; however, only interconnected pores would be expected to be responsible for drug release. Effect of Osmotic and Hydrostatic Pressure on Water Volume Flux Eq. (3) describes the volumetric flow rate of water across a semipermeable membrane in a Side-bySide diffusion cell, where DP and DP are independent variables. When the hydrostatic pressure across the membrane is maintained constant (DP ¼ 0), only the osmotic term remains. dVt A ¼ Lp ðsDP DPÞ h dt
ð3Þ
where dVt/dt is the volumetric flow rate, and DP are the differences in hydrostatic pressure across the membrane, and the remaining parameters were previously defined in Eq. (1). The experimental results and discussions regarding the effect of osmotic and hydrostatic pressure on water transport across the membrane are as follows. The volumetric flow rate of water from the donor cell to receiver cell increased with the osmolality gradient between the two cells in a linear fashion up to 2 Osm/kg (equivalent to 0.2 M) (Fig. 9). Nevertheless, a negative deviation was observed at higher osmolalities. This is thought to be a consequence of the increased viscosity at high CD concentrations. The viscosity of a 0.35 M CD solution in water at JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 6, JUNE 2009
Figure 9. Volumetric flow rate of water as a function of osmotic pressure difference across the membrane at 37 C using Side-by-Side diffusion cells.
37 C is approximately 172 cP using a cup and bob Brookfield viscometer.16 Under the influence of osmotic pressure differences across the membrane without any hydrostatic pressure gradients, the product of Lp and s was determined from the linear regression line, as shown in Figure 9, to be 9.77 107 cm2/(h atm). On the other hand, under an applied hydrostatic pressure, Lp was (6.07 – 0.52) 104 cm2/(h atm) calculated from the slope of the linear relationship of the volumetric flow rate of water as a function of the hydrostatic pressure difference (Fig. 10). The value for s was, therefore, 0.0016 (–0.0001) according to Eq. (3), indicating that the membrane is not permeable to only water. This is because the micropores present in the membrane allow any solutes to pass through the pores when their size is not limited. One may expect that the reflection coefficient tends to decrease with the amount of added sucrose in the membrane. The membranes obtained from an air spraying method on Teflon sheets may not be identical to the membranes from the CP--OPPs. This reflects the differences in the values of membrane characteristics (Lp s) with the air-sprayed membrane giving a value six times higher than the CP--OPP membrane (data not shown here).
Influence of Viscosity on Overall Release Kinetics of CP--OPPs In the elementary osmotic pump tablet containing KCl, the KCl release rate is mainly governed by DOI 10.1002/jps
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1999
In this case, the viscosity effect of CD is implicitly included in the Lp term as indicated in Eq. (5). This may contribute to the nonlinearity observed in Figure 9 at high CD concentrations as above 2 Osm/kg (equivalent to 0.2 M), the viscosity increases significantly. In addition, an increase in boundary layer effect at higher CD concentrations could contribute to this observed nonlinearity. Based on the known membrane characteristics of CP--OPPs and s, the overall release profile of precomplexed PDL during the zero-order kinetics can be described using Eq. (6). Deff ;CD KCD A dMt A ðCCD Þ ð6Þ ¼ Lp ðsDPÞðCCD Þ þ h h dt Figure 10. Volumetric flow rate of water as a function of hydrostatic pressure at 37 C using Side-by-Side diffusion cells.
osmotic pumping with a negligible contribution from diffusion when the orifice size is properly customized.11,17 However, for our CP--OPPs, not only osmotic pumping but also diffusion components were identified to be important, and the relative contributions of both components change with time as previously discussed. In an enclosed system such as CP--OPPs, the moment an osmotic flow of water enters into the pellet core through the semipermeable membrane coating, a pressure gradient builds up across the membrane due to an increase in core volume from the osmotic water influx and the constraint from expansion by the membrane shell. Therefore, DP and DP are actually related and not independent quantities in CP--OPPs unlike the situation in Side-by-Side diffusion cells. According to Poiseuille’s law, the laminar flow of the solution through aqueous filled pores of a membrane, is related to the pressure gradient (DP) by the expression of Eq. (4) DP ¼
8lh dVt dVt ¼ kh n2 pR4 dt dt
ð4Þ
where h is the solution viscosity, l and R are the pore length and radius, n is the pore number, and k is a constant defined as (8l/(n2pR4)). Without any osmotic driving force in the system, Eq. (5) can be derived by combining Eqs. (3) and (4) in terms of dVt/dt. Lp
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A 1 ¼ h kh
ð5Þ
where all of parameters were previously defined in Eqs. (1) and (2) with the solute in Eq. (6) being precomplexed PDL, where the CD and PDL release profiles are comparable and related to the fixed ratio of CD to PDL in the precomplexed PDL. Deff,CD and KCD are the apparent or effective CD diffusion coefficient across the membrane as previously defined in Eq. (2) and the partition coefficient of CD between the aqueous medium and membrane, respectively. CCD is the concentration of CD, which remains approximately constant during the zero-order delivery. Eq. (6), therefore, not only describes the observed drug release zero-order kinetics during the first 1--2 h but also the drug release kinetics thereafter, except in the latter case, the osmotic pressure, diffusion coefficient and viscosity will change as a function of CD concentration. To fully utilize Eq. (6), one can determine the related parameters through Eqs. (7)--(9) previously described by Zannou2 and Zannou et al.18 once the time-dependent concentration of CD inside the CP--OPPs is known. OhOsm=kgi ¼ 0:916ððTDS þ 1ÞmÞ1:075
ð7Þ
DCD hcm2 =si ¼ 4:83 106 e9:65CCD
ð8Þ
hCD hcPi ¼ 0:69eðð7:59CCD Þ=ð11:49CCD ÞÞ
ð9Þ
where O, TDS, and m are the CD osmolality (Osm/kg), average total degree of substitution of SBE groups per CD molecule (e.g., TDS ¼ 6.5), and CD concentration (molality), respectively. DCD, CCD, and hCD are the diffusion coefficient (cm2/s), concentration (molarity, M), and viscosity (centioises, cP) of CD inside the pellet, respectively. It should be noted that O is osmolality (Osm/kg), while DP is osmotic pressure (atm). JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 6, JUNE 2009
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CONCLUSIONS The release mechanisms from the CP--OPPs containing precomplexed PDL were investigated to better interpret the mechanisms. The PDL or CD release rate follows zero-order kinetics for up to 30--40% of drug release during the first 1--2 h and nonzero order kinetics thereafter. Osmotic pumping appears to be the most important initial driving force but the diffusional component becomes more significant with time. The initial zero-order drug release is attributed to the constant driving forces mainly caused by the approximately constant concentration of CD with time. In contrast, the nonzero order drug release is associated with the combination of more significant diffusion with time as well as the change in concentration of CD resulting in changes in viscosity, diffusivity, and osmotic pressure in the pellet with time. The dynamic changes in the pellet core may be described by an equation analogous to that developed by Theewes and Zentner (Eq. 6) taking into consideration of the concentration dependence of osmotic pressure, viscosity and diffusivity.
ACKNOWLEDGMENTS This work was supported by a CyDex and Mossberg fellowship and the Kansas Technology Enterprise Corporation as part of its Center of Excellence program.
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