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Modeling of drug release from microemulsions: a peculiar case
Journal of Membrane Science 204 (2002) 401–412
Modeling of drug release from microemulsions: a peculiar case C. Sirotti a , N. Coceani b , I. Colombo c , R. Lapasin a , M. Grassi a,b,∗ a
Department of Chemical, Environmental and Raw Materials Engineering, DICAMP, Piazzale Europa 1, I-34127 Trieste, Italy b Eurand International S.p.A., via del Follatoio 12, I-34148 Trieste, Italy c Eurand International S.p.A., via Martin Luther King 13, I-20060 Pessano con Bornago, Milan, Italy Received 18 September 2001; received in revised form 18 February 2002; accepted 20 February 2002
Abstract This paper focuses on the experimental and theoretical study of drug release from microemulsions structured as a dispersion of oil droplets in water or vice versa. In particular, drug release kinetics is studied by means of permeation experiments where a synthetic thin (149 m) membrane separates the donor compartment, filled by the drug-loaded microemulsion, from the receiver one, filled by a drug-free aqueous-phase. Experimental trials evidences a peculiar release kinetics resembling that typical of permeation through a thick membrane where the permeated drug amount shows a not linear trend with time. This phenomenon is explained supposing the existence of an interaction between the drug and the surfactant micelles pervading the microemulsion aqueous-phase. This hypothesis is supported by independent experimental tests (critical micellar concentration measurements and release tests from a microemulsion containing small amounts of drug and surfactant) and by means of a mathematical model describing the whole permeation phenomenon. Nimesulide (anti-inflammatory action) is chosen as model drug for its industrial relevance while isopropyl myristate (oil-phase), benzyl alcohol (co-surfactant), Tween 80 (surfactant), compose our microemulsion (45.7% (w/w) water, 30.8% (w/w) surfactant, 11.75% (w/w) oil-phase and 11.75% (w/w) co-surfactant). The results of CMC measurements, release tests from low drug content microemulsion jointly with the good model data fitting ensure about the reliability of our hypothesis. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Drug release; Microemulsion; Mathematical modeling; Oil–water partitioning
1. Introduction Microemulsions are mixtures of oil in water (or vice versa) whose stability essentially comes from the very low interfacial tension due to the presence of the surfactant placed at the water–oil interface. Consequently, microemulsions become thermodynamically stable systems, which are able to form spontaneously without requiring any additional external energy. Very ∗ Corresponding author. Tel.: +39-40-67-63435; fax: +39-40-56-9823. E-mail address: [email protected] (M. Grassi).
often, the presence of a co-surfactant, usually an alcohol, is required to get an optimal formulation, also for the purpose of reducing the amount of surfactant. In this manner, the interfacial tension is generally lowered to less than 1 mN/m, and the formation of oil and/or water dispersed domains ranging from a few to 100 nm is allowed [1]. Accordingly, a huge water–oil interfacial area grows up, indicating that the entropy of mixing compensates the positive interfacial free energy associated to the domains formation. Although strictly depending on the specific components (surfactant, co-surfactant and oil), the energy balance can be heavily affected by temperature, so that a slight
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Nomenclature A A Ao At B C cm co co0 cr cso cst csw ct ct0 c2 cw cw0 D D Fow Fp Ftw Fwo Fwt hm kow kpd
fitting parameter (g/cm3 ) constant (cm3 ) oil–water interface area (cm) micelle–water interface area (cm) constant (g) constant (g2 /cm3 ) Nimesulide concentration in the membrane (g/cm3 ) Nimesulide concentration in the oil-phase (g/cm3 ) initial value of the Nimesulide concentration in the oil-phase (g/cm3 ) Nimesulide concentration in the receiver-phase (g/cm3 ) drug solubility in the oil-phase (g/cm3 ) drug solubility in the surfactantphase (g/cm3 ) time-dependent Nimesulide solubility in the aqueous-phase (g/cm3 ) Nimesulide concentration in the surfactant-phase (g/cm3 ) initial value of the Nimesulide concentration in the surfactant-phase (g/cm3 ) surfactant (Tween 80) bulk concentration (g/cm3 ) Nimesulide concentration in the aqueous-phase (g/cm3 ) initial value of the Nimesulide concentration in the aqueous-phase (g/cm3 ) drug diffusion coefficient inside the membrane (cm2 /s) constant (g3 /cm6 ) drug flux from oil to water-phase (g/cm2 s) drug flux through the membrane (g/cm2 s) drug flux from surfactant to waterphase (g/cm2 s) drug flux from water to oil-phase (g/cm2 s) drug flux from water to surfactant-phase (g/cm2 s) membrane thickness (cm) oil–water rate constant (cm4 /(g s)) partition constant between the microemulsion aqueous-phase and the membrane
kpr ktw kwo kwt M0
ro rt R Row Rwt s0 sf S t T Vd Vm Vo Vr Vt Vw X Greek α γ LV Γ21
partition constant between the receiver-phase and the membrane surfactant micelles–water rate constant (cm4 /(g s)) water–oil rate constant (cm4 /(mg s)) water–surfactant micelles rate constant (cm4 /(mg s)) total drug amount present in the microemulsion at the beginning of the permeation experiment (g) mean radius of the oil droplets (cm) mean radius of the surfactant micelles (cm) universal gas constant (J/mol ◦ K) kow /kwo kwt /ktw initial Nimesulide solubility in the aqueous-phase (g/cm3 ) final Nimesulide solubility in the aqueous-phase (g/cm3 ) membrane surface available for permeation (cm2 ) time (s) temperature (◦ C) donor phase volume (cm3 ) membrane volume (cm3 ) oil-phase volume (cm3 ) receiver-phase volume (cm3 ) surfactant-phase volume (cm3 ) aqueous-phase volume (cm3 ) abscissa (cm) letters parameter (1/s) (Eq. (23)) liquid–air surface tension (mN/m) surfactant molecules number per unit interface area (mol/cm2 )
difference, even lower than 1 ◦ C, can considerably alter the equilibrium concentration of components. Microemulsions can display several structures, such as oil droplets in water, water droplets in oil, random bicontinuous mixtures, ordered droplets, and lamellar mixtures with a wide range of phase equilibria among them and with excess oil and/or water-phases [1–3]. As the formation of a particular structure depends on
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the surfactant, co-surfactant and oil nature, the proper choice and dosage of these components become of primary importance. Depending on the final use of microemulsion, indeed, a particular structure can be specified and other structures have to be avoided. For instance, in the pharmaceutical field, a droplet dispersion (oil in water or water in oil) is normally desired [4,5], whereas, a bicontinuous structure could be of little use for an optimal control on drug delivery. What makes microemulsions fundamental in the pharmaceutical field, apart from their high stability and ease of preparation, is their ability to increase considerably the bioavailability of sparingly water-soluble drugs [6,7]. Indeed, a large amount of a lipophilic drug can be dissolved in the microemulsion oil droplets, so that drug solubility in the whole system is considerably enhanced. Drug diffusion from the oil droplets to the living tissues can take place by crossing the surrounding aqueous medium which essentially acts as a barrier to drug transport owing to the very low drug solubility in water. In this case, microemulsion is used to retard drug delivery [8] and the oil-phase works as a reservoir, but it may also happen that microemulsion speeds up the drug uptake by the living tissues as in the case of oil droplets phagocytosis led by particular biological structures [9]. Moreover, drug-loaded microemulsions are fundamental for delivery systems devoted to topical and transdermal administration [10–12], for solid nanoparticles preparation [13–15], and for loading process of a lipophilic drug into hydrophilic carriers [16], technologies that have a wide employment in the treatment of many diseases and that could have a considerable impact also in the gene delivery field [17]. This great variety of applications gave rise to numerous studies on the microemulsions properties such as the mechanism ruling the drug release [18–21]. Aim of this paper is the study of drug release from a microemulsion resorting to permeation experiments.
2. Modeling Although microemulsions can assume different topological structures [22], we focus our attention on dispersions of oil droplets in water or vice versa, as these should be the best structural conditions for microemulsion-based drug delivery systems. The
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Fig. 1. Schematic view of the phenomenon to be analyzed. The drug moves from the oil- and micellar-phases to the surrounding hydrophilic phase of the donor compartment and then crosses the interposed membrane to reach the receiver compartment.
analysis of drug release from O/W or W/O microemulsions is conceptually identical, and, then, henceforth we will refer to the case of drug release from an O/W system, which is more interesting for hosting sparingly water-soluble drugs. In the equilibrium state, drug can be distributed among three different phases: the dispersed phase, the continuous phase, and the surfactant micelles (see Fig. 1). The study of drug release from homogenous spherical particles can be discussed using two limiting models [5]: according to the former model, drug diffusion throughout the particle is the rate-determining step of the whole phenomenon, whereas, the latter one considers the interfacial barrier existing between each particle and its surroundings as the rate-determining step, being the drug concentration uniform inside the particle. Undoubtedly, the latter hypothesis fits better our real case because of the liquid state of the disperse phase. Starting from such assumptions and resorting to relevant mass balances, Yotsuyanagi et al. [23] modeled the
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mass transport into an oil–water emulsion in presence of an interfacial barrier between the emulsion and the aqueous-phase. Both fluxes (from oil into water and vice versa) were supposed to be linear functions of concentration. More recently, Guy et al. [24] solved the problem of drug release from an oil droplet phase into an outer aqueous environment not only assuming the same hypotheses of Yotsuyanagi but also considering that, at time zero, aqueous-phase is drug-free. This last condition clearly makes the model not suitable to mimic the real conditions occurring in microemulsions. Boddé and Joosten [25] matched approximately the inverse situation studied by Yotsuyanagi, i.e. drug release from a two-phase system to perfect sink, by starting from the same assumptions (mass balance coupled to linear expression for mass fluxes). Probably, Friedman and Benita [26] developed the most advanced model for drug release from emulsions by considering the existence of three phases: the continuous aqueous-phase, the oil droplets and the surfactant micelles. Also in this case, drug release from an O/W emulsion into an external environment through an interposed membrane is described by combining mass balances and linear dependences of mass fluxes on concentration. As we will explain later, all these approaches based on linear flux–concentration relationships cannot be reliably applied to sparingly water soluble (and/or oil soluble) drugs. As Washington and Evans pointed out [27], the measurement of the drug release from a colloidal system cannot be usually considered a trivial task [28]. Indeed, only two ways do exist for measuring drug release from microemulsions: membrane diffusion technique and in situ method [5]. Indeed, the latter method is disadvantageous since the microemulsion should be put in the release environment (usually an aqueous medium) and then diluted. In this manner, microemulsion will never maintain its original structure (the radius of oil droplets can change) and will surely evolve towards other unknown structural conditions due to its changed location in the phase diagram. As a consequence, this technique does not allow a theoretical analysis of drug release. Conversely, the membrane diffusion technique prevents from variations in the microemulsion structure and that is why a theoretical analysis of drug release is allowed, provided that the membrane effect is properly accounted for. This technique implies a permeation
experiment [29] in which the donor compartment is filled by the drug-loaded microemulsion while the receiver compartment is filled by an aqueous-phase containing a small amount of surfactant in order to resemble the microemulsion water-phase. In this way, we can assume that the drug solubility in the receiver fluid is not the rate-determining step of the whole permeation process. Obviously, we do not know exactly the surfactant and co-surfactant concentrations to be considered (it is virtually impossible to know the real composition of the microemulsion aqueous-phase) and in the light of the huge work developed by Gasco and co-workers [4,11,21], we choose the least amounts of surfactant and co-surfactant which can ensure a good drug solubility in the receiver environment, at least throughout the whole permeation experiment. When the drug-loaded microemulsion is prepared at least 24 h before the beginning of the permeation test, we can reasonably assume that the drug distribution among the three phases (oil, water, surfactant micelles) attains the thermodynamic equilibrium. Thus, the initial difference of drug concentration between the donor and the receiver compartments induce the drug diffusion through the interposed membrane. This process tends to lower the drug concentration in the microemulsion aqueous-phase and alter the drug partition equilibrium and then determines a consequent transfer of drug molecules from surfactant micelles and oil droplets to the surrounding aqueous-phase. As it will be demonstrated hereafter, the drug transfer from the micellar-phase may be combined with the disruption of some micelles and the consequent solubilization of surfactant molecules in the microemulsion aqueous-phase. This, in turn, is responsible for an increase of the drug solubility csw in the aqueous-phase that, for the sake of simplicity, can be conveniently modeled by the following equation: csw (t) = sf + (s0 − sf )(1 − e−at )
(1)
where s0 and sf are the initial and final solubilities, respectively, a an adjustable parameter and t is time. Even if micelle disruption leads to a decrease in the micellar-phase volume and a corresponding increase in the water-phase volume, these changes can be neglected, since, as later on demonstrated, a moderate csw variation, due to the breakup of few micelles, can explain the peculiar behavior we found. Accordingly,
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the drug transfer is governed by the following equations:
Fow = kow co (csw (t) − cw )
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(9)
Fwt = kwt cw (cst − ct )
(10)
(2)
Ftw = ktw ct (csw (t) − cw )
(11)
At At dct = Fwt − Ftw dt Vt Vt
(3)
Fp =
D (kpd cw − kpr cr ) hm
(12)
Vo dco Vt dct S dcw Fp =− − − dt Vw dt Vw dt Vw
(4)
Vr cr + Vo co + Vw cw + Vt ct + Vm cm = M0
(5)
Ao Ao dco = Fwo − Fow dt Vo Vo
where cm is given by: kpd cw + kpr cr cm = 2
(6)
S is the membrane surface available for permeation, Ao the oil–water interface area, Aw the micelle–water interface area; Vo , Vt , Vw , Vr , Vm are the oil-phase, the surfactant-phase, the water-phase, the receiver-phase and the membrane volumes, respectively; co , ct , cw , cr , cm are the drug concentrations in the oil-phase, the surfactant-phase, the aqueous-phase, the receiver-phase and the membrane, respectively; M0 represents the total drug amount present in the microemulsion at the beginning of the permeation experiment, while kpd and kpr are the partition constants between the microemulsion aqueous-phase and the membrane, and the receiver fluid and the membrane, respectively; Fwo , and Fow , represent the drug fluxes from the aqueous-phase to the oil-phase and vice versa, Fwt , Ftw the drug fluxes from the aqueous-phase to the surfactant-phases and vice versa, while Fp is the drug flux through the membrane. Ao and Aw are defined by Ao =
3Vo ; ro
At =
3Vt rt
(7)
where ro and rt are the mean radii of the oil droplets and the surfactant micelles, respectively. Eqs. (2)–(4) are the equations describing the kinetics of the drug concentration variation in every phase which depends upon the unbalance between the drug fluxes incoming and outcoming each phase, whereas Eq. (5) is the overall mass balance. Fwo , Fow , Fwt , Ftw and Fp can be expressed by the following equations: Fwo = kwo cw (cso − co )
(8)
where kwo is the water–oil rate constant, kow the oil–water rate constant, kwt the water–surfactant micelles rate constant, ktw surfactant micelles–water rate constant, while D is the drug diffusion coefficient inside the membrane (it is supposed independent of concentration) and hm is the membrane thickness. The non-linearity of the drug fluxes (Eqs. (8)–(11)) is required by the fact that, in more general terms, mass transfer between two liquid phases occurs if concentration (≈chemical potential) in the donor phase is greater than zero (trivial condition) and if the solubility threshold is not exceeded in the receiver-phase. One of the simplest ways for assessing both conditions is to consider the product of drug concentration in the donor phase and the difference between the solubility and the current concentration in the receiving phase as shown in Eqs. (8)–(11). Of course, non-linearity for flux expressions is not necessary when the drug is very soluble in both donor and receiver-phases, but it becomes important for poorly water soluble drug like Nimesulide. In a recent paper [30], we demonstrated that, also the simple kinetics of drug partition between two liquid phases (one of which characterized by low drug solubility) cannot be properly described without accounting for non-linearity. It is important to stress that up to now such an aspect was never taken into consideration, at least at our knowledge. The Fp definition implicitly requires the drug diffusion in the membrane to take place only in the x direction and the membrane to be thin (highly permeable to the diffusing drug). Accordingly, a linear concentration profile inside the membrane is assumed [31]. The system of Eqs. (2)–(5) is numerically solved by a five-order Runge–Kutta method, with adaptive stepsize [32]. The values of the initial drug concentration in the three phases (these values are required to perform the numerical solution) can be determined by means of the following equations: dco Ao Ao = Fwo − Fow = 0 dt Vo Vo
(13)
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dct At At Fwt − Ftw = 0 = dt Vt Vt
(14)
Vo co0 + Vw cw0 + Vt ct0 = M0
(15)
where c0 , cw0 and ct0 represent the initial values of co , cw and ct , respectively. These conditions directly descend from the hypothesis about the attainment of the drug partition equilibrium among the three phases at the beginning of the permeation experiment. Rearranging Eqs. (12)–(14) to express ct0 and cw0 as functions of co0 , we get a cubic expression in co0 : 3 2 + Bco0 Aco0 + Cco0 + D = 0
(16)
where the constants are defined as follows: A = Vo (Row − 1)(Rwt Row − 1)
(17)
B = Rwt Row (Vw Row csw + (Row − 1)(cst Vt − M0 ) + Vo cso ) + (Row − 1)(cso Vo + M0 ) − Vw Row csw − Vo cso
(18)
C = cso (Rwt Row (Vt cst − M0 ) + Vw Row csw + Vo cso − M0 (Row − 2))
(19)
2 −cso M0
(20)
D=
with R ow = k ow /kwo , and R wt = k wt /ktw . The only physically consistent root of Eq. (16) represents the starting value of co . Consequently, the initial values of cw and ct are given by cw0 =
Row csw co0 co0 (Row − 1) + cso
(21)
ct0 =
M0 − Vo co0 − Vw cw0 Vt
(22)
Obviously, the initial concentrations are functions of Row and Rwt .
3. Experimental The materials used for the preparation of the microemulsion are: isopropyl myristate (Fluka Chemika, Sigma–Aldrich, Italy) (11.75 wt.%), Tween 80 (polyoxyethylene 20 sorbitan monooleate; Fluka Chemika, Sigma–Aldrich, Italy) as surfactant (30.8 wt.%), benzyl alcohol (Fluka Chemika, Sigma–Aldrich, Italy)
as co-surfactant (11.75 wt.%), and distilled water (45.7 wt.%). Nimesulide (HELSINN, Pambio Noranco, CH; anti-inflammatory action) is chosen as model drug owing to its industrial relevance [33,34]. For the sake of simplicity, the co-surfactant is considered to belong to the oil-phase together with the equal amount of isopropyl myristate. Microemulsion is prepared in a thermostatic vessel by dissolving the drug (3590 g/cm3 in the final microemulsion formulation) in the oil-phase and then dispersing it in a water–surfactant–co-surfactant-phase by gentle stirring, in order to get the final composition. The mixture is left to rest overnight before checking its stability. The droplets size distribution of the oil-phase is determined by using a multiple scattering angle detector (Coulter N4 Plus, Instrumentation Laboratory, Italy). The scattering intensity data are obtained from a prefiltered microemulsion (<0.45 m) at 90◦ and analyzed with a digital correlator (photon correlation spectroscopy (PCS)) to calculate the mean droplet radius (r o = 27 nm). This value is confirmed by images of the microemulsion, obtained by using a transmission electron microscope Philips EM-208. Starting from the same TEM images the surfactant micelles can be assumed to be one-order of magnitude smaller than the oil droplets. The Nimesulide solubility in both the oil and surfactant-phases are measured by adding small drug amounts, under gentle stirring and controlled temperature, in a given solvent volume until the solution becomes permanently turbid. At 37 ◦ C, the solubility in isopropyl myristate–benzyl alcohol (1:1) is 18 mg/cm3 while its solubility in Tween 80 is 65 mg/cm3 . All the permeation experiments are performed at 37 ◦ C by resorting to the Franz cells apparatus, consisting of two (donor and receiver) compartments separated by an interposed silicone rubber membrane (SILASTIC, Dow Corning Corporation, Michigan) whose thickness is 0.0149 cm (Mitutoyo micrometer, Japan) and with a permeation surface S = 3.46 cm2 (we verified its negligible permeability to all the microemulsion components except for Nimesulide). The donor volume (V d = 4 cm3 ) contains the microemulsion loaded by Nimesulide, while the receiver compartment (V r = 22 cm3 ) is filled with a phosphate buffer (pH 7.4), which is initially drug-free and contains Tween 80 (1 wt.%) and benzyl alcohol (1.5 wt.%), in order avoid that the Nimesulide
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solubility in the receiver fluid could become the rate-determining step of the permeation. Inside the receiver and donor compartments homogeneity is ensured by a magnetic stirrer and a rotating impeller, respectively. The receiver solution is continuously sent, by means of a peristaltic pump, through an external circuit to the quartz cell of a double beams computer-aided on-line detector (UV spectrophotometer, Lambda 6/PECSS System, Perkin-Elmer Corporation, Norwalk, CT, wavelength 398 nm) so that the Nimesulide absorbance is measured in every 60 s for a period of 5 h. The conversion into concentration is performed through a calibration curve made up by preparing different reference solutions at different known concentrations (obviously inside the predictable experimental range) and determining the corresponding absorbance values. The droplets and micelles coalescence at the membrane interface is prevented by the intrinsic thermodynamic stability of microemulsions [6], as well as by the scarce affinity of the silicone rubber membrane with the external layer of the oil droplets and surfactant micelles, represented by the hydrophilic part of the surfactant. Moreover, the mixing conditions produced by the magnetic stirrer are unfavorable for the coalescence and the corresponding formation of a stagnant layer adjacent to the membrane. To ensure the reliability of the Nimesulide concentration detection, we verified that the spectrum of the receiver fluid at the end of the permeation experiment does correspond to a Nimesulide aqueous solution with 1% Tween 80 and 1.5% benzyl alcohol concentrations. This proves that no interference arose during permeation. In the attempt of characterizing the diffusive resistance offered by the membrane, the diffusion coefficient (D) of Nimesulide inside the membrane has been determined by means of an ad hoc independent permeation experiment. The donor volume is filled by a buffer surfactant–co-surfactant mixture (with the same composition of the receiver fluid used in the release tests from microemulsion) saturated by the drug and containing an excess of solid drug, while the receiver volume is filled with an identical drug-free aqueous-phase. In this manner, we can assume that the drug solubility in the microemulsion aqueous-phase coincides with that of the fluid filling both the donor and the receiver compartments. Moreover, the excess of solid drug guarantees the constancy of the drug
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concentration inside the donor liquid along the whole permeation time. The experimental permeation data are then compared with the following equation, suitable for describing drug permeation through a thin membrane [26,30]: cr =
kpd csw (1 − e−akpd t ); kpr
α=
SD Vr hm
(23)
where cr represents the Nimesulide concentration in the receiver fluid, while kpd and kpr (partition coefficients) are set equal to 1. The resulting diffusion coefficient value is D = 3.34 × 10−6 cm2 /s (it is assumed independent of concentration). The surface tension tests are performed by measuring the shape of a liquid drop hanging from a microsyringe with the tensiometer G10 (Krüss GmbH, Hamburg, D).
4. Results and discussion The time variation of Nimesulide concentration in the receiver during the release experiment is represented in Fig. 2. Interestingly, an unexpected behavior is observed since an induction period infers a sigmoidal trend, typical of drug permeation tests through thick membranes [35], to the release curve. Indeed, the drug concentration profile should be linear (or convex) over the whole time range considered in the
Fig. 2. Nimesulide concentration cr in the receiver-phase during the permeation experiment. Vertical bars indicate data S.E.
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light of the measured Nimesulide diffusion coefficient (D = 3.34×10−6 cm2 /s) and the membrane thickness (hm = 149 m, thin membrane). Such a trend could be attributable to electrostatic interactions between drug and membrane [36], but the small thickness of the membrane makes those interactions negligible anyway [37]. Consequently, attention should be focused on the micellar-phase to explain this anomalous behavior. Due to its lipophilic nature, a significant amount of drug could be reasonably assumed as solubilized inside the surfactant micelles (Nimesulide solubility in Tween 80 = 65 mg/cm3 , and in the oil-phase = 18 mg/cm3 ). We can also assume that the drug micelle–aqueous-phases exchange is much faster than that interesting the oil and aqueous-phases. Thus, the decrease in the aqueous-phase Nimesulide concentration cw , due to the drug flux across the membrane, firstly causes the Nimesulide transport from the micellar to the aqueous-phase and then also the internal equilibrium established between the surfactant (co-surfactant) and drug molecules within the micellar-phase is altered. Accordingly, if the critical micellar concentration (CMC) [6] is slowed down, some micelles can disrupt so that more surfactant molecules solubilize in the aqueous-phase. Such a phenomenon should lead to increasing Nimesulide solubility in the aqueous-phase. Due to the transient nature of the permeation phenomenon, a new thermodynamic equilibrium between micelles, drug and aqueous-phase is not established for a long time. In order to validate this hypothesis, permeation tests are performed from a microemulsion containing the minimum surfactant amount sufficient to get the microemulsion. So doing, we assume that the surfactant is placed only at the oil–water interface and no excess is available to form micellar structures (or, at least, the micelles concentration is negligible). Moreover, the microemulsion is loaded with a small amount of Nimesulide (1000 g/cm3 ) in order to minimize the drug–micelle interactions. Higher concentrations would probably result in unstable systems due to the low surfactant concentration. Fig. 3 reports the variation of the drug concentration in the receiver during a time period of 3 h. It is clearly evident that in this case the induction phenomenon in negligible. The differences between two release profiles in the initial
Fig. 3. Nimesulide concentration cr profile in the receiver-phase during the release from a microemulsion containing low amounts of drug and surfactant. Vertical bars indicate data S.E.
time interval can be illustrated more evidently by calculating the numerical derivatives of the concentration curves, and smoothing them with an exponential model. The results are reported in Fig. 4 in a normalized form (with reference to the 3 h value). In the case
Fig. 4. Fitting of the numeric derivates of the concentration curves (normalized on the 3 h values). A: release from a microemulsion containing high amounts of drug and surfactant (Fig. 2 data); B: release from microemulsion containing low amounts of drug and surfactant (Fig. 3 data).
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of low surfactant and Nimesulide contents, the slope variation vanishes after 6 min, while 1 h is needed for the microemulsion with high surfactant concentration to get a linear profile in the release curve. Such a time ratio (10) cannot be ascribed only to the different amounts of loaded drug (drug ratio equal to 3.6) so that we can conclude that surfactant micellar structures are responsible for the anomalous beginning of the drug release process. Additional experimental tests were performed to verify that the presence of Nimesulide affects the CMC of the water–Tween 80–benzyl alcohol system and, hence, to lead further confirmations to the our hypothesis about micelles disruption and consequent surfactant molecules solubilization in response to Nimesulide concentration variation. Liquid– vapor surface tension measurements were made on three systems (buffer–Tween 80, buffer + 2% benzyl alcohol–Tween 80, buffer + 2% benzyl alcohol + 14 g/cm3 Nimesulide–Tween 80) containing different amounts of surfactant. The buffer–Tween 80 system does not pose particular problems in the determination of the CMC value and it is considered as reference. On the contrary, the CMC determination is slightly more complex in the presence of benzyl alcohol (used as co-surfactant in our microemulsion) and Nimesulide. The starting point for the CMC measurement is the Gibbs equation [38]: 1 dγLV Γ21 = − (24) RT d ln c2 where c2 is the surfactant (Tween 80) bulk concentration, T the temperature, R the universal gas constant, Γ21 the excess of surfactant molecules number per unit interface area and γ LV is the surface tension [39]. In a binary system, Γ21 is constant below and above the CMC, with different values in the two concentration ranges. Accordingly, the CMC value can be approximately individuated at the intersection between the tangents to the γ LV versus ln c2 curve before and after the curve slope variation [40]. Similar changes in surface tension occur in multicomponent systems with increasing surfactant concentration, even if the phenomenology appears more complicated by binary interactions. Indeed, while for the buffer–Tween 80 system, the two tangents are easily located (see Fig. 5), in the system containing benzyl alcohol an initial increase in Tween 80 concentration does not generate a
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Fig. 5. Surface tension γ LV as a function of surfactant concentration c2 , for the three analyzed systems (W: water–Tween 80 (left ordinate axis), W + B: water–benzyl alcohol–Tween 80 (left ordinate axis), W + B + N: water–benzyl alcohol–Nimesulide–Tween 80 (right ordinate axis)).
decrease in surface tension because of the above mentioned Tween 80–benzyl alcohol binary interactions. Reasonably, the surfactant molecules are captured by benzyl alcohol until benzyl alcohol molecules are available and only afterwards the γ LV decrease with c2 takes place. The CMC position can be located in correspondence of the highest γ LV versus ln c2 slope variation [41–43]. The presence of a small amount of Nimesulide smoothes the γ LV versus ln c2 shape and lowers the γ LV value along the whole concentration field examined. The CMC values achieved for the analyzed systems are as follows: buffer–Tween 80 CMC = 276.2 g/cm3 , buffer + 2% benzyl alcohol–Tween 80 CMC = 150 g/cm3 , buffer + 2% benzyl alcohol + 14 g/cm3 Nimesulide–Tween 80 CMC = 87.7 g/cm3 . It is thus possible to observe how the presence of Nimesulide reduces the CMC of the system. This confirms the assumption of micelle breakup occurring during the drug transfer to the receiver when the drug concentration in the aqueous-phase decreases, CMC increases, so causing the solubilization of surfactant molecules previously arranged in micellar structures. On these bases, the proposed model is fitted on the experimental data assuming: V r = 22 cm3 ,
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Fig. 6. Comparison between the model best fitting (solid curve) and the permeation data (open circles). Vertical bars indicate data S.E.
V d = 4 cm3 ,V w = 1.828 cm3 , V o = 0.924 cm3 , V t = 0.092 cm3 (as it is unknown, we assumed it to be equal to 1/10 Vo ), hm = 0.0149 cm, S = 3.46 cm2 , D = 3.34 × 10−6 cm2 /s, r o = 2.7 × 10−6 cm, r t = 2.7 × 10−7 cm, M 0 = 14,360 g, cso = 18,000 g/cm3 , cst = 65,000 g/cm3 . The fitting procedure yields A = 2.03 × 10−4 g/cm3 , s0 = 19.79 g/cm3 , s f = 44.06 g/cm3 , k ow = 4 × 10−7 cm4 /(g s), k wo = 1 × 10−10 cm4 /(g s), k tw = 1 × 10−8 cm4 /(g s) and k wt = 1 × 10−12 cm4 /(g s). Fig. 6 shows the satisfactory agreement between the model best fitting and the permeation data also in the induction period. Due to the numerical nature of the model and its intrinsic complexity (great number of parameters), the fitting results are purely indicative in the sense that the fitting parameters values surely depend on some other parameters values (Vt and rt , for instance) whose correctness is hard to be verified. Nevertheless, our aim was not to use the model to calculate the exact values of kow , kwo , ktw , and kwt , but to check whether the theoretical frame proposed is able to explain the unusual experimental findings. Figs. 7 and 8 illustrate the drug concentration profiles in the four different phases. The Nimesulide concentration in the micellar and oil-phases are almost constant during the whole test, and their values are much higher than those we had in the water and receiver-phases; this was expected, as a consequence of the highly lipophilic character of the drug.
Fig. 7. Drug concentration in aqueous (cw ; model prediction) and receiver (cr ; model best fitting) phases during the permeation experiment.
Fig. 8. Drug concentration in oil (co ; model prediction) and surfactant (ct ; model prediction) phases during the permeation experiment.
5. Conclusions This paper, proposing a theoretical and experimental study about drug release from microemulsions, evidences how the interaction between the drug and the surfactant micelles infers a peculiar characteristic to the release kinetics. Indeed, we verified that the release curve, determined by a permeation experiment
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where microemulsion fills the donor compartment and an aqueous-phase constitutes the receiver compartment, exhibits a typical not linear profile characteristic of diffusion through a thick membrane. This can be explained invoking the possibility that the drug is able to modify the surfactant micelles equilibrium determining a partial micelle disruption due to an initial reduction of the drug concentration in the microemulsion aqueous-phase because of permeation. As a consequence, surfactant molecules coming from micelle disruption are available to increase the drug solubility in the microemulsion aqueous-phase. Interestingly, we verified, by means of an ad hoc developed mathematical model, that also a small solubility variation is sufficient to justify the unexpected release kinetics. This hypothesis has also been verified by means of independent experimental tests such as interfacial tension measurements and release tests from a microemulsion containing small amounts of drug and surfactant, where the above mentioned interactions are surely lowered. Despite the reliability and the correctness of the developed mathematical model, the complexity of the described physical frame prevents from an accurate determination of the water–oil rate constants. Indeed, as some model parameters are very difficult to be independently determined (see micellar volume, for instance), it is possible that the determined absolute values of the kinetics constants (but not their relative ratio) are not completely correct. Nevertheless, as we were mainly interested in explaining the observed strange release kinetics by means of a theoretical frame more than an accurate rate constant calculation, this is not a serious drawback. On the contrary, this works suggests a possible strategy for an accurate determination of the rate constants. Indeed, the reduction of the microemulsion drug and surfactant represents a possibility for the physical frame simplification and the consequent rate constant determination. In this case, indeed, as the model considerably simplifies and the number of required parameters reduces, the rate constant determination recurring to data fitting is surely much more accurate.
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[17] K. Roy, W. Chu, J. McGrath, S.C. Kuo, S.K. Huang, K.W. Leong, Nanoparticle mediated oral gene delivery for DNA vaccination, Proc. Int. Symp. Control. Rel. Bioact. Mater. 26 (1999) 134–135. [18] H.O. Ho, L.C. Chen, H.S. Chiang, B.W. Spur, P.Y.K. Wong, The percutaneous delivery of prostaglandin E1 carried by microemulsion systems, Proc. Int. Symp. Control. Rel. Bioact. Mater. 25 (1998) 579–580. [19] K. Kriwet, C.C. Müller-Goymann, Diclofenac release from phospholipid drug systems and permeation through excised human stratum corneum, Int. J. Pharm. 125 (1995) 231–242. [20] M.R. Gasco, S. Morel, E. Tonso, I. Viano, In vivo and in vitro release of insulin from microemulsion, Proc. Int. Symp. Control. Rel. Bioact. Mater. 19 (1992) 502–503. [21] F. Pattarino, E. Marengo, M.R. Gasco, R. Carpignano, Experimental design and partila least squares in the study of complex mixtures: microemulsions as drug carriers, Int. J. Pharm. 91 (1993) 157–165. [22] S. Ezrahi, A. Aserin, N. Garti, Aggregation behavior in one-phase (Winsor IV) microemulsion systems, in: P. Kumar, K.L. Mittal (Eds.), Handbook of Microemulsion Science and Technology, Dekker, Basel, New York, 1999, pp. 185–246. [23] T. Yotsuyanagi, W.I. Higuchi, A.H. Ghanem, Theoretical treatment of diffusional transport into and through an oil–water emulsion with an interfacial barrier at the oil–water interface, J. Pharm. Sci. 62 (1) (1973) 40–43. [24] R.H. Guy, J. Hadgraft, I.W. Kellaway, M.J. Taylor, Calculation of drug release rates from spherical particles, Int. J. Pharm. 11 (1982) 199–207. [25] H.E. Boddé, J.G.H. Joosten, A mathematical model for drug release from a two-phase system to perfect sink, Int. J. Pharm. 26 (1985) 57–76. [26] D. Friedman, S. Benita, A mathematical model for drug release from O/W emulsions: application to controlled release morphine emulsions, Drug Dev. Ind. Pharm. 13 (9–11) (1987) 2067–2085. [27] C. Washington, K. Evans, Release rate measurements of model hydrophobic solutes from submicron triglyceride emulsions, J. Contr. Rel. 33 (1995) 383–390. [28] Y. Mrestani, R.H.H. Neubert, A. Krauese, Partition behavior of drugs in misroemulsions measured by electrokinetic cromatography, Pharm. Res. 15 (5) (1998) 799–801.
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Modeling of drug release from microemulsions: a peculiar case C. Sirotti a , N. Coceani b , I. Colombo c , R. Lapasin a , M. Grassi a,b,∗ a
Department of Chemical, Environmental and Raw Materials Engineering, DICAMP, Piazzale Europa 1, I-34127 Trieste, Italy b Eurand International S.p.A., via del Follatoio 12, I-34148 Trieste, Italy c Eurand International S.p.A., via Martin Luther King 13, I-20060 Pessano con Bornago, Milan, Italy Received 18 September 2001; received in revised form 18 February 2002; accepted 20 February 2002
Abstract This paper focuses on the experimental and theoretical study of drug release from microemulsions structured as a dispersion of oil droplets in water or vice versa. In particular, drug release kinetics is studied by means of permeation experiments where a synthetic thin (149 m) membrane separates the donor compartment, filled by the drug-loaded microemulsion, from the receiver one, filled by a drug-free aqueous-phase. Experimental trials evidences a peculiar release kinetics resembling that typical of permeation through a thick membrane where the permeated drug amount shows a not linear trend with time. This phenomenon is explained supposing the existence of an interaction between the drug and the surfactant micelles pervading the microemulsion aqueous-phase. This hypothesis is supported by independent experimental tests (critical micellar concentration measurements and release tests from a microemulsion containing small amounts of drug and surfactant) and by means of a mathematical model describing the whole permeation phenomenon. Nimesulide (anti-inflammatory action) is chosen as model drug for its industrial relevance while isopropyl myristate (oil-phase), benzyl alcohol (co-surfactant), Tween 80 (surfactant), compose our microemulsion (45.7% (w/w) water, 30.8% (w/w) surfactant, 11.75% (w/w) oil-phase and 11.75% (w/w) co-surfactant). The results of CMC measurements, release tests from low drug content microemulsion jointly with the good model data fitting ensure about the reliability of our hypothesis. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Drug release; Microemulsion; Mathematical modeling; Oil–water partitioning
1. Introduction Microemulsions are mixtures of oil in water (or vice versa) whose stability essentially comes from the very low interfacial tension due to the presence of the surfactant placed at the water–oil interface. Consequently, microemulsions become thermodynamically stable systems, which are able to form spontaneously without requiring any additional external energy. Very ∗ Corresponding author. Tel.: +39-40-67-63435; fax: +39-40-56-9823. E-mail address: [email protected] (M. Grassi).
often, the presence of a co-surfactant, usually an alcohol, is required to get an optimal formulation, also for the purpose of reducing the amount of surfactant. In this manner, the interfacial tension is generally lowered to less than 1 mN/m, and the formation of oil and/or water dispersed domains ranging from a few to 100 nm is allowed [1]. Accordingly, a huge water–oil interfacial area grows up, indicating that the entropy of mixing compensates the positive interfacial free energy associated to the domains formation. Although strictly depending on the specific components (surfactant, co-surfactant and oil), the energy balance can be heavily affected by temperature, so that a slight
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Nomenclature A A Ao At B C cm co co0 cr cso cst csw ct ct0 c2 cw cw0 D D Fow Fp Ftw Fwo Fwt hm kow kpd
fitting parameter (g/cm3 ) constant (cm3 ) oil–water interface area (cm) micelle–water interface area (cm) constant (g) constant (g2 /cm3 ) Nimesulide concentration in the membrane (g/cm3 ) Nimesulide concentration in the oil-phase (g/cm3 ) initial value of the Nimesulide concentration in the oil-phase (g/cm3 ) Nimesulide concentration in the receiver-phase (g/cm3 ) drug solubility in the oil-phase (g/cm3 ) drug solubility in the surfactantphase (g/cm3 ) time-dependent Nimesulide solubility in the aqueous-phase (g/cm3 ) Nimesulide concentration in the surfactant-phase (g/cm3 ) initial value of the Nimesulide concentration in the surfactant-phase (g/cm3 ) surfactant (Tween 80) bulk concentration (g/cm3 ) Nimesulide concentration in the aqueous-phase (g/cm3 ) initial value of the Nimesulide concentration in the aqueous-phase (g/cm3 ) drug diffusion coefficient inside the membrane (cm2 /s) constant (g3 /cm6 ) drug flux from oil to water-phase (g/cm2 s) drug flux through the membrane (g/cm2 s) drug flux from surfactant to waterphase (g/cm2 s) drug flux from water to oil-phase (g/cm2 s) drug flux from water to surfactant-phase (g/cm2 s) membrane thickness (cm) oil–water rate constant (cm4 /(g s)) partition constant between the microemulsion aqueous-phase and the membrane
kpr ktw kwo kwt M0
ro rt R Row Rwt s0 sf S t T Vd Vm Vo Vr Vt Vw X Greek α γ LV Γ21
partition constant between the receiver-phase and the membrane surfactant micelles–water rate constant (cm4 /(g s)) water–oil rate constant (cm4 /(mg s)) water–surfactant micelles rate constant (cm4 /(mg s)) total drug amount present in the microemulsion at the beginning of the permeation experiment (g) mean radius of the oil droplets (cm) mean radius of the surfactant micelles (cm) universal gas constant (J/mol ◦ K) kow /kwo kwt /ktw initial Nimesulide solubility in the aqueous-phase (g/cm3 ) final Nimesulide solubility in the aqueous-phase (g/cm3 ) membrane surface available for permeation (cm2 ) time (s) temperature (◦ C) donor phase volume (cm3 ) membrane volume (cm3 ) oil-phase volume (cm3 ) receiver-phase volume (cm3 ) surfactant-phase volume (cm3 ) aqueous-phase volume (cm3 ) abscissa (cm) letters parameter (1/s) (Eq. (23)) liquid–air surface tension (mN/m) surfactant molecules number per unit interface area (mol/cm2 )
difference, even lower than 1 ◦ C, can considerably alter the equilibrium concentration of components. Microemulsions can display several structures, such as oil droplets in water, water droplets in oil, random bicontinuous mixtures, ordered droplets, and lamellar mixtures with a wide range of phase equilibria among them and with excess oil and/or water-phases [1–3]. As the formation of a particular structure depends on
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the surfactant, co-surfactant and oil nature, the proper choice and dosage of these components become of primary importance. Depending on the final use of microemulsion, indeed, a particular structure can be specified and other structures have to be avoided. For instance, in the pharmaceutical field, a droplet dispersion (oil in water or water in oil) is normally desired [4,5], whereas, a bicontinuous structure could be of little use for an optimal control on drug delivery. What makes microemulsions fundamental in the pharmaceutical field, apart from their high stability and ease of preparation, is their ability to increase considerably the bioavailability of sparingly water-soluble drugs [6,7]. Indeed, a large amount of a lipophilic drug can be dissolved in the microemulsion oil droplets, so that drug solubility in the whole system is considerably enhanced. Drug diffusion from the oil droplets to the living tissues can take place by crossing the surrounding aqueous medium which essentially acts as a barrier to drug transport owing to the very low drug solubility in water. In this case, microemulsion is used to retard drug delivery [8] and the oil-phase works as a reservoir, but it may also happen that microemulsion speeds up the drug uptake by the living tissues as in the case of oil droplets phagocytosis led by particular biological structures [9]. Moreover, drug-loaded microemulsions are fundamental for delivery systems devoted to topical and transdermal administration [10–12], for solid nanoparticles preparation [13–15], and for loading process of a lipophilic drug into hydrophilic carriers [16], technologies that have a wide employment in the treatment of many diseases and that could have a considerable impact also in the gene delivery field [17]. This great variety of applications gave rise to numerous studies on the microemulsions properties such as the mechanism ruling the drug release [18–21]. Aim of this paper is the study of drug release from a microemulsion resorting to permeation experiments.
2. Modeling Although microemulsions can assume different topological structures [22], we focus our attention on dispersions of oil droplets in water or vice versa, as these should be the best structural conditions for microemulsion-based drug delivery systems. The
403
Fig. 1. Schematic view of the phenomenon to be analyzed. The drug moves from the oil- and micellar-phases to the surrounding hydrophilic phase of the donor compartment and then crosses the interposed membrane to reach the receiver compartment.
analysis of drug release from O/W or W/O microemulsions is conceptually identical, and, then, henceforth we will refer to the case of drug release from an O/W system, which is more interesting for hosting sparingly water-soluble drugs. In the equilibrium state, drug can be distributed among three different phases: the dispersed phase, the continuous phase, and the surfactant micelles (see Fig. 1). The study of drug release from homogenous spherical particles can be discussed using two limiting models [5]: according to the former model, drug diffusion throughout the particle is the rate-determining step of the whole phenomenon, whereas, the latter one considers the interfacial barrier existing between each particle and its surroundings as the rate-determining step, being the drug concentration uniform inside the particle. Undoubtedly, the latter hypothesis fits better our real case because of the liquid state of the disperse phase. Starting from such assumptions and resorting to relevant mass balances, Yotsuyanagi et al. [23] modeled the
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mass transport into an oil–water emulsion in presence of an interfacial barrier between the emulsion and the aqueous-phase. Both fluxes (from oil into water and vice versa) were supposed to be linear functions of concentration. More recently, Guy et al. [24] solved the problem of drug release from an oil droplet phase into an outer aqueous environment not only assuming the same hypotheses of Yotsuyanagi but also considering that, at time zero, aqueous-phase is drug-free. This last condition clearly makes the model not suitable to mimic the real conditions occurring in microemulsions. Boddé and Joosten [25] matched approximately the inverse situation studied by Yotsuyanagi, i.e. drug release from a two-phase system to perfect sink, by starting from the same assumptions (mass balance coupled to linear expression for mass fluxes). Probably, Friedman and Benita [26] developed the most advanced model for drug release from emulsions by considering the existence of three phases: the continuous aqueous-phase, the oil droplets and the surfactant micelles. Also in this case, drug release from an O/W emulsion into an external environment through an interposed membrane is described by combining mass balances and linear dependences of mass fluxes on concentration. As we will explain later, all these approaches based on linear flux–concentration relationships cannot be reliably applied to sparingly water soluble (and/or oil soluble) drugs. As Washington and Evans pointed out [27], the measurement of the drug release from a colloidal system cannot be usually considered a trivial task [28]. Indeed, only two ways do exist for measuring drug release from microemulsions: membrane diffusion technique and in situ method [5]. Indeed, the latter method is disadvantageous since the microemulsion should be put in the release environment (usually an aqueous medium) and then diluted. In this manner, microemulsion will never maintain its original structure (the radius of oil droplets can change) and will surely evolve towards other unknown structural conditions due to its changed location in the phase diagram. As a consequence, this technique does not allow a theoretical analysis of drug release. Conversely, the membrane diffusion technique prevents from variations in the microemulsion structure and that is why a theoretical analysis of drug release is allowed, provided that the membrane effect is properly accounted for. This technique implies a permeation
experiment [29] in which the donor compartment is filled by the drug-loaded microemulsion while the receiver compartment is filled by an aqueous-phase containing a small amount of surfactant in order to resemble the microemulsion water-phase. In this way, we can assume that the drug solubility in the receiver fluid is not the rate-determining step of the whole permeation process. Obviously, we do not know exactly the surfactant and co-surfactant concentrations to be considered (it is virtually impossible to know the real composition of the microemulsion aqueous-phase) and in the light of the huge work developed by Gasco and co-workers [4,11,21], we choose the least amounts of surfactant and co-surfactant which can ensure a good drug solubility in the receiver environment, at least throughout the whole permeation experiment. When the drug-loaded microemulsion is prepared at least 24 h before the beginning of the permeation test, we can reasonably assume that the drug distribution among the three phases (oil, water, surfactant micelles) attains the thermodynamic equilibrium. Thus, the initial difference of drug concentration between the donor and the receiver compartments induce the drug diffusion through the interposed membrane. This process tends to lower the drug concentration in the microemulsion aqueous-phase and alter the drug partition equilibrium and then determines a consequent transfer of drug molecules from surfactant micelles and oil droplets to the surrounding aqueous-phase. As it will be demonstrated hereafter, the drug transfer from the micellar-phase may be combined with the disruption of some micelles and the consequent solubilization of surfactant molecules in the microemulsion aqueous-phase. This, in turn, is responsible for an increase of the drug solubility csw in the aqueous-phase that, for the sake of simplicity, can be conveniently modeled by the following equation: csw (t) = sf + (s0 − sf )(1 − e−at )
(1)
where s0 and sf are the initial and final solubilities, respectively, a an adjustable parameter and t is time. Even if micelle disruption leads to a decrease in the micellar-phase volume and a corresponding increase in the water-phase volume, these changes can be neglected, since, as later on demonstrated, a moderate csw variation, due to the breakup of few micelles, can explain the peculiar behavior we found. Accordingly,
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the drug transfer is governed by the following equations:
Fow = kow co (csw (t) − cw )
405
(9)
Fwt = kwt cw (cst − ct )
(10)
(2)
Ftw = ktw ct (csw (t) − cw )
(11)
At At dct = Fwt − Ftw dt Vt Vt
(3)
Fp =
D (kpd cw − kpr cr ) hm
(12)
Vo dco Vt dct S dcw Fp =− − − dt Vw dt Vw dt Vw
(4)
Vr cr + Vo co + Vw cw + Vt ct + Vm cm = M0
(5)
Ao Ao dco = Fwo − Fow dt Vo Vo
where cm is given by: kpd cw + kpr cr cm = 2
(6)
S is the membrane surface available for permeation, Ao the oil–water interface area, Aw the micelle–water interface area; Vo , Vt , Vw , Vr , Vm are the oil-phase, the surfactant-phase, the water-phase, the receiver-phase and the membrane volumes, respectively; co , ct , cw , cr , cm are the drug concentrations in the oil-phase, the surfactant-phase, the aqueous-phase, the receiver-phase and the membrane, respectively; M0 represents the total drug amount present in the microemulsion at the beginning of the permeation experiment, while kpd and kpr are the partition constants between the microemulsion aqueous-phase and the membrane, and the receiver fluid and the membrane, respectively; Fwo , and Fow , represent the drug fluxes from the aqueous-phase to the oil-phase and vice versa, Fwt , Ftw the drug fluxes from the aqueous-phase to the surfactant-phases and vice versa, while Fp is the drug flux through the membrane. Ao and Aw are defined by Ao =
3Vo ; ro
At =
3Vt rt
(7)
where ro and rt are the mean radii of the oil droplets and the surfactant micelles, respectively. Eqs. (2)–(4) are the equations describing the kinetics of the drug concentration variation in every phase which depends upon the unbalance between the drug fluxes incoming and outcoming each phase, whereas Eq. (5) is the overall mass balance. Fwo , Fow , Fwt , Ftw and Fp can be expressed by the following equations: Fwo = kwo cw (cso − co )
(8)
where kwo is the water–oil rate constant, kow the oil–water rate constant, kwt the water–surfactant micelles rate constant, ktw surfactant micelles–water rate constant, while D is the drug diffusion coefficient inside the membrane (it is supposed independent of concentration) and hm is the membrane thickness. The non-linearity of the drug fluxes (Eqs. (8)–(11)) is required by the fact that, in more general terms, mass transfer between two liquid phases occurs if concentration (≈chemical potential) in the donor phase is greater than zero (trivial condition) and if the solubility threshold is not exceeded in the receiver-phase. One of the simplest ways for assessing both conditions is to consider the product of drug concentration in the donor phase and the difference between the solubility and the current concentration in the receiving phase as shown in Eqs. (8)–(11). Of course, non-linearity for flux expressions is not necessary when the drug is very soluble in both donor and receiver-phases, but it becomes important for poorly water soluble drug like Nimesulide. In a recent paper [30], we demonstrated that, also the simple kinetics of drug partition between two liquid phases (one of which characterized by low drug solubility) cannot be properly described without accounting for non-linearity. It is important to stress that up to now such an aspect was never taken into consideration, at least at our knowledge. The Fp definition implicitly requires the drug diffusion in the membrane to take place only in the x direction and the membrane to be thin (highly permeable to the diffusing drug). Accordingly, a linear concentration profile inside the membrane is assumed [31]. The system of Eqs. (2)–(5) is numerically solved by a five-order Runge–Kutta method, with adaptive stepsize [32]. The values of the initial drug concentration in the three phases (these values are required to perform the numerical solution) can be determined by means of the following equations: dco Ao Ao = Fwo − Fow = 0 dt Vo Vo
(13)
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dct At At Fwt − Ftw = 0 = dt Vt Vt
(14)
Vo co0 + Vw cw0 + Vt ct0 = M0
(15)
where c0 , cw0 and ct0 represent the initial values of co , cw and ct , respectively. These conditions directly descend from the hypothesis about the attainment of the drug partition equilibrium among the three phases at the beginning of the permeation experiment. Rearranging Eqs. (12)–(14) to express ct0 and cw0 as functions of co0 , we get a cubic expression in co0 : 3 2 + Bco0 Aco0 + Cco0 + D = 0
(16)
where the constants are defined as follows: A = Vo (Row − 1)(Rwt Row − 1)
(17)
B = Rwt Row (Vw Row csw + (Row − 1)(cst Vt − M0 ) + Vo cso ) + (Row − 1)(cso Vo + M0 ) − Vw Row csw − Vo cso
(18)
C = cso (Rwt Row (Vt cst − M0 ) + Vw Row csw + Vo cso − M0 (Row − 2))
(19)
2 −cso M0
(20)
D=
with R ow = k ow /kwo , and R wt = k wt /ktw . The only physically consistent root of Eq. (16) represents the starting value of co . Consequently, the initial values of cw and ct are given by cw0 =
Row csw co0 co0 (Row − 1) + cso
(21)
ct0 =
M0 − Vo co0 − Vw cw0 Vt
(22)
Obviously, the initial concentrations are functions of Row and Rwt .
3. Experimental The materials used for the preparation of the microemulsion are: isopropyl myristate (Fluka Chemika, Sigma–Aldrich, Italy) (11.75 wt.%), Tween 80 (polyoxyethylene 20 sorbitan monooleate; Fluka Chemika, Sigma–Aldrich, Italy) as surfactant (30.8 wt.%), benzyl alcohol (Fluka Chemika, Sigma–Aldrich, Italy)
as co-surfactant (11.75 wt.%), and distilled water (45.7 wt.%). Nimesulide (HELSINN, Pambio Noranco, CH; anti-inflammatory action) is chosen as model drug owing to its industrial relevance [33,34]. For the sake of simplicity, the co-surfactant is considered to belong to the oil-phase together with the equal amount of isopropyl myristate. Microemulsion is prepared in a thermostatic vessel by dissolving the drug (3590 g/cm3 in the final microemulsion formulation) in the oil-phase and then dispersing it in a water–surfactant–co-surfactant-phase by gentle stirring, in order to get the final composition. The mixture is left to rest overnight before checking its stability. The droplets size distribution of the oil-phase is determined by using a multiple scattering angle detector (Coulter N4 Plus, Instrumentation Laboratory, Italy). The scattering intensity data are obtained from a prefiltered microemulsion (<0.45 m) at 90◦ and analyzed with a digital correlator (photon correlation spectroscopy (PCS)) to calculate the mean droplet radius (r o = 27 nm). This value is confirmed by images of the microemulsion, obtained by using a transmission electron microscope Philips EM-208. Starting from the same TEM images the surfactant micelles can be assumed to be one-order of magnitude smaller than the oil droplets. The Nimesulide solubility in both the oil and surfactant-phases are measured by adding small drug amounts, under gentle stirring and controlled temperature, in a given solvent volume until the solution becomes permanently turbid. At 37 ◦ C, the solubility in isopropyl myristate–benzyl alcohol (1:1) is 18 mg/cm3 while its solubility in Tween 80 is 65 mg/cm3 . All the permeation experiments are performed at 37 ◦ C by resorting to the Franz cells apparatus, consisting of two (donor and receiver) compartments separated by an interposed silicone rubber membrane (SILASTIC, Dow Corning Corporation, Michigan) whose thickness is 0.0149 cm (Mitutoyo micrometer, Japan) and with a permeation surface S = 3.46 cm2 (we verified its negligible permeability to all the microemulsion components except for Nimesulide). The donor volume (V d = 4 cm3 ) contains the microemulsion loaded by Nimesulide, while the receiver compartment (V r = 22 cm3 ) is filled with a phosphate buffer (pH 7.4), which is initially drug-free and contains Tween 80 (1 wt.%) and benzyl alcohol (1.5 wt.%), in order avoid that the Nimesulide
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solubility in the receiver fluid could become the rate-determining step of the permeation. Inside the receiver and donor compartments homogeneity is ensured by a magnetic stirrer and a rotating impeller, respectively. The receiver solution is continuously sent, by means of a peristaltic pump, through an external circuit to the quartz cell of a double beams computer-aided on-line detector (UV spectrophotometer, Lambda 6/PECSS System, Perkin-Elmer Corporation, Norwalk, CT, wavelength 398 nm) so that the Nimesulide absorbance is measured in every 60 s for a period of 5 h. The conversion into concentration is performed through a calibration curve made up by preparing different reference solutions at different known concentrations (obviously inside the predictable experimental range) and determining the corresponding absorbance values. The droplets and micelles coalescence at the membrane interface is prevented by the intrinsic thermodynamic stability of microemulsions [6], as well as by the scarce affinity of the silicone rubber membrane with the external layer of the oil droplets and surfactant micelles, represented by the hydrophilic part of the surfactant. Moreover, the mixing conditions produced by the magnetic stirrer are unfavorable for the coalescence and the corresponding formation of a stagnant layer adjacent to the membrane. To ensure the reliability of the Nimesulide concentration detection, we verified that the spectrum of the receiver fluid at the end of the permeation experiment does correspond to a Nimesulide aqueous solution with 1% Tween 80 and 1.5% benzyl alcohol concentrations. This proves that no interference arose during permeation. In the attempt of characterizing the diffusive resistance offered by the membrane, the diffusion coefficient (D) of Nimesulide inside the membrane has been determined by means of an ad hoc independent permeation experiment. The donor volume is filled by a buffer surfactant–co-surfactant mixture (with the same composition of the receiver fluid used in the release tests from microemulsion) saturated by the drug and containing an excess of solid drug, while the receiver volume is filled with an identical drug-free aqueous-phase. In this manner, we can assume that the drug solubility in the microemulsion aqueous-phase coincides with that of the fluid filling both the donor and the receiver compartments. Moreover, the excess of solid drug guarantees the constancy of the drug
407
concentration inside the donor liquid along the whole permeation time. The experimental permeation data are then compared with the following equation, suitable for describing drug permeation through a thin membrane [26,30]: cr =
kpd csw (1 − e−akpd t ); kpr
α=
SD Vr hm
(23)
where cr represents the Nimesulide concentration in the receiver fluid, while kpd and kpr (partition coefficients) are set equal to 1. The resulting diffusion coefficient value is D = 3.34 × 10−6 cm2 /s (it is assumed independent of concentration). The surface tension tests are performed by measuring the shape of a liquid drop hanging from a microsyringe with the tensiometer G10 (Krüss GmbH, Hamburg, D).
4. Results and discussion The time variation of Nimesulide concentration in the receiver during the release experiment is represented in Fig. 2. Interestingly, an unexpected behavior is observed since an induction period infers a sigmoidal trend, typical of drug permeation tests through thick membranes [35], to the release curve. Indeed, the drug concentration profile should be linear (or convex) over the whole time range considered in the
Fig. 2. Nimesulide concentration cr in the receiver-phase during the permeation experiment. Vertical bars indicate data S.E.
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light of the measured Nimesulide diffusion coefficient (D = 3.34×10−6 cm2 /s) and the membrane thickness (hm = 149 m, thin membrane). Such a trend could be attributable to electrostatic interactions between drug and membrane [36], but the small thickness of the membrane makes those interactions negligible anyway [37]. Consequently, attention should be focused on the micellar-phase to explain this anomalous behavior. Due to its lipophilic nature, a significant amount of drug could be reasonably assumed as solubilized inside the surfactant micelles (Nimesulide solubility in Tween 80 = 65 mg/cm3 , and in the oil-phase = 18 mg/cm3 ). We can also assume that the drug micelle–aqueous-phases exchange is much faster than that interesting the oil and aqueous-phases. Thus, the decrease in the aqueous-phase Nimesulide concentration cw , due to the drug flux across the membrane, firstly causes the Nimesulide transport from the micellar to the aqueous-phase and then also the internal equilibrium established between the surfactant (co-surfactant) and drug molecules within the micellar-phase is altered. Accordingly, if the critical micellar concentration (CMC) [6] is slowed down, some micelles can disrupt so that more surfactant molecules solubilize in the aqueous-phase. Such a phenomenon should lead to increasing Nimesulide solubility in the aqueous-phase. Due to the transient nature of the permeation phenomenon, a new thermodynamic equilibrium between micelles, drug and aqueous-phase is not established for a long time. In order to validate this hypothesis, permeation tests are performed from a microemulsion containing the minimum surfactant amount sufficient to get the microemulsion. So doing, we assume that the surfactant is placed only at the oil–water interface and no excess is available to form micellar structures (or, at least, the micelles concentration is negligible). Moreover, the microemulsion is loaded with a small amount of Nimesulide (1000 g/cm3 ) in order to minimize the drug–micelle interactions. Higher concentrations would probably result in unstable systems due to the low surfactant concentration. Fig. 3 reports the variation of the drug concentration in the receiver during a time period of 3 h. It is clearly evident that in this case the induction phenomenon in negligible. The differences between two release profiles in the initial
Fig. 3. Nimesulide concentration cr profile in the receiver-phase during the release from a microemulsion containing low amounts of drug and surfactant. Vertical bars indicate data S.E.
time interval can be illustrated more evidently by calculating the numerical derivatives of the concentration curves, and smoothing them with an exponential model. The results are reported in Fig. 4 in a normalized form (with reference to the 3 h value). In the case
Fig. 4. Fitting of the numeric derivates of the concentration curves (normalized on the 3 h values). A: release from a microemulsion containing high amounts of drug and surfactant (Fig. 2 data); B: release from microemulsion containing low amounts of drug and surfactant (Fig. 3 data).
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of low surfactant and Nimesulide contents, the slope variation vanishes after 6 min, while 1 h is needed for the microemulsion with high surfactant concentration to get a linear profile in the release curve. Such a time ratio (10) cannot be ascribed only to the different amounts of loaded drug (drug ratio equal to 3.6) so that we can conclude that surfactant micellar structures are responsible for the anomalous beginning of the drug release process. Additional experimental tests were performed to verify that the presence of Nimesulide affects the CMC of the water–Tween 80–benzyl alcohol system and, hence, to lead further confirmations to the our hypothesis about micelles disruption and consequent surfactant molecules solubilization in response to Nimesulide concentration variation. Liquid– vapor surface tension measurements were made on three systems (buffer–Tween 80, buffer + 2% benzyl alcohol–Tween 80, buffer + 2% benzyl alcohol + 14 g/cm3 Nimesulide–Tween 80) containing different amounts of surfactant. The buffer–Tween 80 system does not pose particular problems in the determination of the CMC value and it is considered as reference. On the contrary, the CMC determination is slightly more complex in the presence of benzyl alcohol (used as co-surfactant in our microemulsion) and Nimesulide. The starting point for the CMC measurement is the Gibbs equation [38]: 1 dγLV Γ21 = − (24) RT d ln c2 where c2 is the surfactant (Tween 80) bulk concentration, T the temperature, R the universal gas constant, Γ21 the excess of surfactant molecules number per unit interface area and γ LV is the surface tension [39]. In a binary system, Γ21 is constant below and above the CMC, with different values in the two concentration ranges. Accordingly, the CMC value can be approximately individuated at the intersection between the tangents to the γ LV versus ln c2 curve before and after the curve slope variation [40]. Similar changes in surface tension occur in multicomponent systems with increasing surfactant concentration, even if the phenomenology appears more complicated by binary interactions. Indeed, while for the buffer–Tween 80 system, the two tangents are easily located (see Fig. 5), in the system containing benzyl alcohol an initial increase in Tween 80 concentration does not generate a
409
Fig. 5. Surface tension γ LV as a function of surfactant concentration c2 , for the three analyzed systems (W: water–Tween 80 (left ordinate axis), W + B: water–benzyl alcohol–Tween 80 (left ordinate axis), W + B + N: water–benzyl alcohol–Nimesulide–Tween 80 (right ordinate axis)).
decrease in surface tension because of the above mentioned Tween 80–benzyl alcohol binary interactions. Reasonably, the surfactant molecules are captured by benzyl alcohol until benzyl alcohol molecules are available and only afterwards the γ LV decrease with c2 takes place. The CMC position can be located in correspondence of the highest γ LV versus ln c2 slope variation [41–43]. The presence of a small amount of Nimesulide smoothes the γ LV versus ln c2 shape and lowers the γ LV value along the whole concentration field examined. The CMC values achieved for the analyzed systems are as follows: buffer–Tween 80 CMC = 276.2 g/cm3 , buffer + 2% benzyl alcohol–Tween 80 CMC = 150 g/cm3 , buffer + 2% benzyl alcohol + 14 g/cm3 Nimesulide–Tween 80 CMC = 87.7 g/cm3 . It is thus possible to observe how the presence of Nimesulide reduces the CMC of the system. This confirms the assumption of micelle breakup occurring during the drug transfer to the receiver when the drug concentration in the aqueous-phase decreases, CMC increases, so causing the solubilization of surfactant molecules previously arranged in micellar structures. On these bases, the proposed model is fitted on the experimental data assuming: V r = 22 cm3 ,
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Fig. 6. Comparison between the model best fitting (solid curve) and the permeation data (open circles). Vertical bars indicate data S.E.
V d = 4 cm3 ,V w = 1.828 cm3 , V o = 0.924 cm3 , V t = 0.092 cm3 (as it is unknown, we assumed it to be equal to 1/10 Vo ), hm = 0.0149 cm, S = 3.46 cm2 , D = 3.34 × 10−6 cm2 /s, r o = 2.7 × 10−6 cm, r t = 2.7 × 10−7 cm, M 0 = 14,360 g, cso = 18,000 g/cm3 , cst = 65,000 g/cm3 . The fitting procedure yields A = 2.03 × 10−4 g/cm3 , s0 = 19.79 g/cm3 , s f = 44.06 g/cm3 , k ow = 4 × 10−7 cm4 /(g s), k wo = 1 × 10−10 cm4 /(g s), k tw = 1 × 10−8 cm4 /(g s) and k wt = 1 × 10−12 cm4 /(g s). Fig. 6 shows the satisfactory agreement between the model best fitting and the permeation data also in the induction period. Due to the numerical nature of the model and its intrinsic complexity (great number of parameters), the fitting results are purely indicative in the sense that the fitting parameters values surely depend on some other parameters values (Vt and rt , for instance) whose correctness is hard to be verified. Nevertheless, our aim was not to use the model to calculate the exact values of kow , kwo , ktw , and kwt , but to check whether the theoretical frame proposed is able to explain the unusual experimental findings. Figs. 7 and 8 illustrate the drug concentration profiles in the four different phases. The Nimesulide concentration in the micellar and oil-phases are almost constant during the whole test, and their values are much higher than those we had in the water and receiver-phases; this was expected, as a consequence of the highly lipophilic character of the drug.
Fig. 7. Drug concentration in aqueous (cw ; model prediction) and receiver (cr ; model best fitting) phases during the permeation experiment.
Fig. 8. Drug concentration in oil (co ; model prediction) and surfactant (ct ; model prediction) phases during the permeation experiment.
5. Conclusions This paper, proposing a theoretical and experimental study about drug release from microemulsions, evidences how the interaction between the drug and the surfactant micelles infers a peculiar characteristic to the release kinetics. Indeed, we verified that the release curve, determined by a permeation experiment
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where microemulsion fills the donor compartment and an aqueous-phase constitutes the receiver compartment, exhibits a typical not linear profile characteristic of diffusion through a thick membrane. This can be explained invoking the possibility that the drug is able to modify the surfactant micelles equilibrium determining a partial micelle disruption due to an initial reduction of the drug concentration in the microemulsion aqueous-phase because of permeation. As a consequence, surfactant molecules coming from micelle disruption are available to increase the drug solubility in the microemulsion aqueous-phase. Interestingly, we verified, by means of an ad hoc developed mathematical model, that also a small solubility variation is sufficient to justify the unexpected release kinetics. This hypothesis has also been verified by means of independent experimental tests such as interfacial tension measurements and release tests from a microemulsion containing small amounts of drug and surfactant, where the above mentioned interactions are surely lowered. Despite the reliability and the correctness of the developed mathematical model, the complexity of the described physical frame prevents from an accurate determination of the water–oil rate constants. Indeed, as some model parameters are very difficult to be independently determined (see micellar volume, for instance), it is possible that the determined absolute values of the kinetics constants (but not their relative ratio) are not completely correct. Nevertheless, as we were mainly interested in explaining the observed strange release kinetics by means of a theoretical frame more than an accurate rate constant calculation, this is not a serious drawback. On the contrary, this works suggests a possible strategy for an accurate determination of the rate constants. Indeed, the reduction of the microemulsion drug and surfactant represents a possibility for the physical frame simplification and the consequent rate constant determination. In this case, indeed, as the model considerably simplifies and the number of required parameters reduces, the rate constant determination recurring to data fitting is surely much more accurate.
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