International Journal of Pharmaceutics 494 (2015) 31–39

Kinetics of drug release from ointments: Role of transient-boundarylayer$

Xiaoming Xu1, Manar Al-Ghabeish1, Yellela S.R. Krishnaiah, Ziyaur Rahman,Mansoor A. Khan*Division of Product Quality Research, OTR/OPQ, Food and Drug Administration, 10903 New Hampshire Avenue, Silver Spring, MD 20993, USA

A R T I C L E I N F O

Article history:Received 24 April 2015Received in revised form 4 July 2015Accepted 29 July 2015Available online 1 August 2015

Keywords:OintmentAcyclovirIn vitro drug releaseKineticsTransient-boundaryLogarithmic time releaseHiguchi model

A B S T R A C T

In the current work, an in vitro release testing method suitable for ointment formulations was developedusing acyclovir as a model drug. Release studies were carried out using enhancer cells on acyclovirointments prepared with oleaginous, absorption, and water-soluble bases. Kinetics and mechanism ofdrug release was found to be highly dependent on the type of ointment bases. In oleaginous bases, drugrelease followed a unique logarithmic-time dependent profile; in both absorption and water-solublebases, drug release exhibited linearity with respect to square root of time (Higuchi model) albeitdifferences in the overall release profile. To help understand the underlying cause of logarithmic-timedependency of drug release, a novel transient-boundary hypothesis was proposed, verified, andcompared to Higuchi theory. Furthermore, impact of drug solubility (under various pH conditions) andtemperature on drug release were assessed. Additionally, conditions under which deviations fromlogarithmic-time drug release kinetics occur were determined using in situ UV fiber-optics. Overall, theresults suggest that for oleaginous ointments containing dispersed drug particles, kinetics andmechanism of drug release is controlled by expansion of transient boundary layer, and drug releaseincreases linearly with respect to logarithmic time.

Published by Elsevier B.V.

Contents lists available at ScienceDirect

International Journal of Pharmaceutics

journal homepage: www.elsev ier .com/locate / i jpharm

1. Introduction

Ointment is one of the commonly used semisolid dosage formsfor dermatological and ophthalmic delivery of pharmaceuticals. Itvaries in type depending on the choice of bases, which includeoleaginous (hydrocarbon) bases, absorption bases, water-solublebases, emulsifying bases, etc. Drug may be present inside theointment as dispersion or as molecular solution. It is expected thatdepending on choice of ointment bases and state of the drug, invivo as well as in vitro drug release from ointment may vary.

From a product quality perspective, in vitro release testing(IVRT) serves many critical roles throughout the life-cycle of a drugproduct. In early product development, it functions as a surrogateof in vivo testing to aid formulation and process development. In

$ This article reflects the views of the author and should not be construed torepresent FDA’s views or policies.* Corresponding author. Fax: +1 301 796 9816.E-mail addresses: Xiaoming.Xu@fda.hhs.gov (X. Xu),

Manar.Al-Ghabeish@fda.hhs.gov (M. Al-Ghabeish), Krishnaiah.Yellela@fda.hhs.gov(Y.S.R. Krishnaiah), Ziyaur.Rahman@fda.hhs.gov (Z. Rahman),Mansoor.Khan@fda.hhs.gov (M.A. Khan).

1 These authors made equal contribution to this work.

http://dx.doi.org/10.1016/j.ijpharm.2015.07.0770378-5173/Published by Elsevier B.V.

late stage development as well as post-marketing phase, itbecomes an integral part of quality control strategy to ensurebatch-to-batch consistency. Additionally, when deemed appropri-ate, it is often used to assess product sameness between differentmanufactures and/or between pre- and post-change products formaking post-approval changes. Despite the significances, thematurity of IVRT methods for semisolid dosage form, in particularpharmaceutical ointment, is considerably lacking and under-utilized as compared to conventional solid oral dosage forms. Inparts, this may be attributed to complex physicochemicalproperties of the ointment formulations as well as the uniquephysiological constraints an IVRT method has to resemble for drugrelease (e.g., through/within the skin or cornea) (Azarmi et al.,2007; Olejnik et al., 2012).

Categorically speaking, most of the reported IVRT methodolo-gies to date have focused on two aspects: (1) to elucidate drugrelease mechanism from different ointment formulations (Chow-han and Pritchard, 1975; Knour-Hekimoglu et al., 1983; Mutimeret al., 1956) and (2) to refine and advance the instrumentationsuitable for testing of semi-solid dosage forms (such as verticaldiffusion cell, Franz cell, Enhancer cell assembly, etc.) (Baranowskiet al., 2014; Nallagundla et al., 2014; Petró et al., 2015; Rege et al.,1998; Thaker and Chern, 2003). The progress of the latter relies on

32 X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39

the implementation of new technologies, and is out of the scope ofthe current report. With regard to the first aspect, depending onchoice of assumptions on the possible rate-limiting step for drugabsorption/permeation in vivo, the effort so far in the first categorycan be further grouped into to two general areas: (1) utilize dialysisor other semi-permeable membranes based techniques to assessthe permeation/diffusion/absorption of drug from ointmentdosage forms, assuming the skin/tissue/membrane, etc. presentsa rate-limiting barrier; or (2) direct analysis of drug release fromdosage forms, assuming the drug permeation does not presentsignificant barrier. The current work was dedicated to the secondarea, with a special focus on understanding the release mechanismof drug from various ointment bases.

Many kinetics models (in the form of a generic equation) havebeen developed (Costa and Sousa Lobo, 2001; Dash et al., 2010;Siepmann and Peppas, 2011) including zero-order, first-order,Higuchi model, Peppas model, etc. to describe the kinetics andmechanism of drug release from drug products. The nature andcomposition of formulation excipients present in a drug productmay affect the kinetics and mechanism of drug release. Forexample, Higuchi has shown that for cream and certain ointmentformulations (later extended to controlled release matrix system)drug release follows a square-root of time profile, and that therelease rate is proportional to square root of the drug solubility, theexposed surface area, the diffusion constant and inverse time(Higuchi, 1960).

Acyclovir was used as a model compound to be incorporatedinto the ointments. It is a synthetic purine nucleoside analoguewith in vitro and in vivo inhibitory activity against herpes simplexvirus types 1 (HSV-1), 2 (HSV-2), and varicella-zoster virus (VZV)(Acosta and Flexner, 2011; Moomaw et al., 2003; Sanjay et al., 2011;Wilhelmus, 2000). Several acyclovir dosage forms are available onthe market, including (oral) tablets, capsules, suspensions,(parenteral) injections, (topical) ointments and creams. Acyclovirointments were prepared with different bases such as oleaginous,absorption and water-soluble bases at a drug load of 4% w/w, andsubjected to in vitro drug release studies using USP Apparatus 2with enhancer cells. The data on the amount of drug released atdifferent time points were analyzed for kinetics and mechanism(s)of drug release.

2. Materials and methods

2.1. Materials

Acyclovir USP (>99%) were purchased from RIA InternationalLLC (East Hanover, NJ, USA). Polyethylene glycol 400 (PEG-400),polyethylene glycol 3350 (PEG-3350), white petrolatum USP, heavymineral oil USP, phosphate buffer saline (PBS, 10X), glacial aceticacid USP, citric acid anhydrous, sodium chloride, and boric acidwere purchased from Fischer Scientific, Norcross, GA. Lanolinalcohol (Ceralan1) was generously provided by Lubrizol (Cleve-land, Ohio). Unless otherwise specified, all materials were ofanalytical grade.

Table 1Formulation compositions for acyclovir ointments.

Ointment prepared with Composition (g)

Acyclovir (g) Mineral oil (g) White pe

Oleaginous base 4.00 7.20 88.80

Absorption base 4.00 14.11 79.97

Water-soluble base 4.00 – –

2.2. High performance liquid chromatography (HPLC) method foracyclovir analysis

The HPLC system consisted of an Agilent 1260 Series (AgilentTechnologies, Wilmington, DE, US) equipped with a binary pump,online degasser, column heater, autosampler and photodiode arrayUV–vis detector. Data collection and analysis were performedusing ChemStation (Agilent Technologies). The current methodwas adapted from literature (Parry et al., 1992), and was validatedper USP guideline (USP36-NF31, 2013). Briefly, the separation wasachieved on a SunFire C18 column (5 mm, 4.6 mm � 150 mm). Theelution was isocratic at 1.2 mL/min with a mobile phase of 0.5% (v/v) acetic acid in water (pH 2.8). The column temperature wasmaintained at 25 �C. The injection volume was 5 mL and detectionwas by UV at 254 nm. Linearity was established in the concentra-tion range of 0.04–10 mg/mL (r2 = 0.999), and the method wasprecise (<1% relative standard deviation for both intra- and inter-day variation) and accurate (99.8% recovery). The limit of detection(LOD) and limit of quantitation (LOQ) were determined to be0.01 mg/mL and 0.03 mg/mL, respectively.

2.3. Preparation of acyclovir ointments

Fine acyclovir particles (d90 = 17 mm determined using HALEOS,Sympatec, Clausthal-Zellerfeld, Germany) were obtained bypassing the raw API (d90 > 100 mm) through an air jet mill (00-Jet-O-Mizer, Fluid Energy, Telford, PA). These drug particles (4% w/w) were dispersed into three types of ointment bases: oleaginous,absorption and water-soluble, via melt fusion method. Briefly,weighed quantity of ointment base (Table 1) and other compo-nents (if needed) were melted at 60 �C in a thermostatically-controlled water bath, after which fine acyclovir particles wereadded into the slurry under 1500 rpm stirring. Agitation wascontinued for another 1.5 h at 60 �C to obtain a homogeneousmixture. The mixture was then allowed to cool under constantstirring (1500 rpm) to 30 �C in a thermostatically-controlled waterbath (15 �C). The rate of cooling was measured at �1.5 � 0.3 �C/min(near the center of the vessel). Once cooled, the ointmentformulations were packed in multiple-dose aluminum tubes(approx. 5 g each tube) and stored at 25 �C/60%RH until further use.

2.4. Drug release using USP Apparatus 2 with enhancer cells

A modified USP Apparatus 2 equipped with 200 mL flat bottomvessels and mini paddles (Agilent Technologies, Santa Clara, CA)was used for drug release studies (Fig. 1). Excess amount of theacyclovir ointment was loaded inside a special semisolid holder,Enhancer cellsTM (Agilent Technologies, Santa Clara, CA) with anexposed area of 4 cm2. Using a spatula, ointment surface wasflattened, smoothed, and excess material removed, after which theexact loaded ointment quantity was determined by weight. A pre-cut and pre-wetted 0.45-mm pore size hydrophilic nylonmembrane (HNWP) (Millipore, Billerica, MA) was placed on topthe ointment before capping the enhancer cell and removingexcess water from the membrane. To eliminate the shearing stressintroduced during sample preparation and its potential impact on

trolatum (g) Lanolin alcohol (g) PEG-400 (g) PEG-3350 (g)

– – –

1.92 – –

– 76.80 19.20

Fig. 1. In vitro drug release setup for ointments (USP Apparatus 2 with enhancercells).

X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39 33

drug release, the capped enhancer cells were left stationary insidethe empty testing vessel for 10 min. To start the test, pre-heatedrelease medium (200 mL) was transferred inside the vessel,followed by immediate activation of the paddle. Unless otherwisenoted, the release medium was pH 7.4 phosphate buffer saline(PBS), the temperature was 37 �C, and the agitation speed was200 rpm. At predefined time (5, 15, 30, 60,120, and 240 min)aliquots of sample (0.5 mL) were withdrawn and analyzed usingHPLC to assess the cumulative amount of drug release.

Fig. 2. Acyclovir drug release from three different ointment bases (oleaginous, absorptio(B) cumulative drug release per unit area plotted against square-root of time; and (C) cum7.4 PBS, 37 �C, n = 6).

2.5. In situ UV fiber optical measurement

An eight-channel mDISS Profiler (Pion Inc., Billerica, MA) wasfitted into the USP Apparatus 2 equipped with enhancer cells forinline measurement of drug concentration. Both agitation speed(200 rpm) and bath temperature (37 �C) were controlled throughdissolution apparatus. Height of the UV probe (the lowest point)was positioned close to the paddle to minimize the response delay.The UV path-length was fixed at 10 mm via a stainless steel tip withmirror. Prior to the in situ measurement, UV signal was calibratedusing various concentrations of standard acyclovir solutions(0.078, 0.156, 0.313, 0.625, 1.250, 2.5, 5.0, and 10.0 mg/mL).Linearity was established in the concentration range of 0.078 to10 mg/mL (r2 = 0.9994), and the method was precise (<2% relativestandard deviation at 2.5 mg/mL) and accurate (99.4% recovery).LOD and LOQ were determined to be 0.11 mg/mL and 0.39 mg/mL,respectively. To start the experiment, enhancer cells (4 cm2 surfacearea) loaded with acyclovir ointment were put inside the glassvessels and paddles lowered to 25 mm above the enhancer cell top.Pre-heated release medium (200 mL) was transferred inside thevessel, followed by immediate activation of the paddle and UVrecording. Spectral scan (200–700 nm) of all channels took lessthan one second with a baseline noise of �0.0002 absorbanceunits. To minimize background interferences, second derivative ofthe spectra in the 250–254 nm range was used for quantitation(Bynum et al., 2001; Toher et al., 2003). Scan frequency varied withtime to account for logarithm scale: 5 s interval in the first minute,10 s interval in the next 9 min, 30 s up to 20 min, 1 min interval upto 60 min, 5 min interval up to 12 h and 10 min interval until 24 h.

n, and water-soluble). (A) Cumulative drug release per unit area in linear time scale;ulative drug release per unit area in logarithm-time scale (4% w/w drug loading, pH

Table

2Mod

el-fi

ttingof

acyc

lovirreleasein

variou

sointm

entba

ses(n

=6).

Ointm

entba

seZe

roorder

Firstorder

Higuch

iKorsm

eyer–Pe

ppas

Loga

rithmic-tim

e

k 0r2

k 1r2

k H/A

r2n

r2K/A

r2

Oleag

inou

s0.04

4�0.005

0.80

7�0.04

0�0

.003

�0.000

0.67

5�0.04

60.87

3�0.09

50.94

4�0.02

40.24

8�0.02

10.98

6�0.01

13.12

2�0.32

70.99

0�0.007

Abs

orption

0.03

3�0.009

0.90

7�0.04

3�0

.002

�0.001

0.86

4�0.04

10.63

4�0.16

90.98

0�0.01

40.13

9�0.03

60.93

3�0.02

92.12

3�0.54

90.90

6�0.03

4W

ater-soluble

13.052

�0.68

10.93

6�0.009

�0.007

�0.000

0.60

2�0.01

429

3.68

2�16

.147

0.99

5�0.003

0.74

7�0.01

70.96

6�0.005

1158

.422

�67

.891

0.92

6�0.006

34 X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39

3. Results and discussion

3.1. In vitro drug release method development

When designing an appropriate in vitro drug release testingmethod, whether it is for quality control or stability assaypurposes, or to simply aid formulation and process development,adequate formulation characterization and sufficient processunderstanding are prerequisites. In the current study, acyclovirwas used as a model drug for understanding the drug releasekinetics from ointments formulated with three types of ointmentbases. All three formulations contained identical drug concentra-tion (4% w/w), and were prepared under similar processingconditions. Quality parameters such as content uniformity,rheology, particle size, etc. were fully characterized (data omittedhere). Present study focuses on the development in vitro releasetesting method and analysis of drug release kinetics. Theexperimental setup used in the in vitro drug release testing ofacyclovir ointments is shown in Fig. 1. It is worth noting thatcontrasting orally or parenterally administered dosage forms,where maximum drug exposure is defined by the total amount ofdrug existing in the product (100% of label or an theoreticalamount), dermatological or ophthalmic applied ointments nor-mally contain drug in excess, in order to account for drug loss dueto skin turnover, pre-corneal clearance (Gaudana et al., 2010), etc.For this reason, monitoring the amount of drug release per(exposed) unit area is a far better indicator for assessingindividual’s drug exposure as compared to percentage of drugrelease which may greatly underestimate the impact of drugrelease (Ueda et al., 2009). Accordingly, in the current work tobenchmark the release profile, cumulative drug amount per unitarea rather than cumulative percentage release was used.

3.2. Release kinetics from ointments with different bases

Drug release profiles from the three ointment bases weredifferent (Fig. 2A). In both oleaginous and absorption bases, limiteddrug amount was released. While the total released drug amountper unit area is comparable for these two ointment bases at 4 h(approx. 20 mg/cm2), their initial release rates differed. In water-soluble base, drug release was several magnitudes higher at 4 h(approx. 4 mg/cm2) than both oleaginous and absorption baseointments. To understand the possible mechanisms governing thedrug release in these ointment bases, various kinetics models werefitted (Table 2), including zero-order, first-order, Higuchi, andKorsmeyer–Peppas models, as well as a newly developedlogarithmic-time release model. Among all, it was determinedthat in absorption base and water-soluble base, acyclovir releaseexhibited linearity with respect to square-root of time andfollowed Higuchi model, as shown in Table 2 and Fig. 2B. Incontrast, in oleaginous base, the amount of drug released waslinear (r2� 0.99) on the logarithmic-time scale, suggesting achange in release mechanism from those described by Higuchi.

Further analysis of the diffusion exponent (n) in Korsmeyer–Peppas equation (Siepmann and Peppas, 2011) revealed that therelease mechanism of drug from water-soluble ointment bases wasof anomalous transport (0.45 < n < 0.89) (i.e., controlled by bothdiffusional mass transport and polymer swelling). For botholeaginous and absorption base ointments, the values of n waslower than 0.45, suggesting that the release process deviated fromFickian diffusion (n = 0.45) (Peppas, 1985). As can be seen above,although both followed Higuchi model, drug release mechanismfrom absorption and water soluble base differed from each other.The better fitting of Korsmeyer–Peppas model than Higuchi modelfor oleaginous ointment suggests that the interfacial boundary isdynamically changing (e.g., expanding) rather than stationary as

Fig. 3. Representation of the transient-boundary at petrolatum/water interface.

X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39 35

assumed in Higuchi theory (Higuchi,1960,1961). Another plausibleexplanation of deviation from Higuchi model release is that it maybe caused by finite dissolution rate, or dissolution-limited drugrelease (Frenning, 2003), rather than being diffusion controlledrelease. In the current work, however, a different approach wastaken, focusing on the role of boundary and its influence on drugsolubilization (e.g., availability of drug for dissolution). It should benoted that the phenomenon is unique to oleaginous ointment. Itdiffers from absorbent and water-soluble base, in both of whichpresence of water absorbing material may allow capillary actionand permit inward moving water boundary. In both oleaginous andabsorption base ointments, the ointment matrix was completelyimmiscible with water. Furthermore, drug particles that weresuspended within the ointment matrix had very limited mobilitybecause of the viscosity of the ointment base. Consequently, mostof the drug dissolution/release likely occurred at or near thephysical boundary. On the contrary, in water-soluble baseointment, the matrix material (i.e., polyethylene glycol) was fullysoluble in water. As the ointment matrix dissolved or eroded, moreand more drug particles were exposed for solubilization, leading toboth faster and greater drug release than from oleaginous andabsorption bases. To further explain the drug release kinetics fromoleaginous ointment base, in particular to find the reason whylogarithmic-time drug release is followed, a transient-boundaryhypothesis is proposed.

3.3. Transient-boundary hypothesis

It is hypothesized that there exists a transient-boundary at thepetrolatum ointment/water interface, consisting of an initialboundary and a dynamically changing transient layer. Thetransient layer is mostly aqueous, and its thickness graduallyexpands over time in the direction of aqueous media. Only drugpresent inside the transient layer can dissolve and further diffuseinto the bulk aqueous media. The interface between transient layerand bulk aqueous media is assumed to be a perfect sink. Arepresentation of the interface is shown in Fig. 3. It should be notedthat the current model is only applicable to oleaginous-baseointments containing solid drug particles. It is not appropriate forabsorption and water-soluble base ointments, or ointmentscontaining molecularly dissolved drugs.

Initial boundary layer exists due to the limited miscibilitybetween petrolatum and water. For this very same reason,thickness of the initial boundary layer should be a constant

characteristic of the equilibrium between the two components.Factors that influence the equilibrium are likely to change the layerthickness, which may include petrolatum’s grade and purity,presence of drug particles and/or modifier (e.g., mineral oil),aqueous media ionic strength, temperature, etc. To simplify thephysical as well as mathematical model, the thickness of the initialboundary layer (Lini) is considered as a constant, h

Lini ¼ h ð1Þ

If the concentration of the drug inside this initial boundary layeris known, the total amount of drug present inside the initialboundary layer, Q0, can then be calculated as

Q0 ¼ m � V ini ¼ m � A � Lini ¼ m � A � h ð2Þwhere, m is the concentration of API (solid state) in petrolatumbase (expressed as mass per unit volume), Vini is the initialboundary layer volume, and A is the exposed surface area.

In this initial boundary layer, API is present in the solid statewith very limited kinetic mobility (e.g., particle diffusion) due tothe extremely high viscosity (>104 Pa s) of the continuous phase(i.e., petrolatum). Hence, release of API from the initial boundarylayer is only possible with progressive advancing of the petrola-tum/water interface followed by rapid dissolution of the API inaqueous media into molecular solution.

It is assumed that change in the total boundary layer thicknessis time-dependent, and that the changing portion of the boundarylayer can be treated as an independent layer, i.e., a transient layer. Itshould be noted that it may be difficult to distinguish this transientlayer from the initial boundary; rather the entire boundary may bephysically expanding. In other words, designation of such transientlayer is a mathematical simplification, rather than an interpreta-tion of the physical system.

As mentioned earlier, the composition of the transient layer ismostly aqueous, and that its thickness (Ltrans) expands over timetowards direction of the bulk aqueous media as a result ofincreasing molecular mobility (i.e., entropy).

Ltrans ¼ f ðtÞ ð3Þ

Considering the thermo-expansion effect at or near the physicalboundary, the time-dependent thickness function, Ltrans, isassumed to follow zero-order for simplification purpose, increas-ing at a constant velocity, v.

Fig. 4. Theoretical concentration profile existing in an ointment containingsuspended drug and in contact with a perfect sink as described by Higuchi,adapted from Higuchi (1961) with permission from Wiley & Sons.

36 X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39

Ltrans ¼ f ðtÞ ¼ v � t ð4Þ

The volume of the resulting transient layer (Vtrans) can becalculated as a product of thickness and exposed surface area, A.

Vtrans ¼ Ltrans � A ¼ v � t � A ð5Þ

Since only dissolved API in the transient layer can furtherdiffuse into bulk aqueous medium, the concentration of the API inthe transient layer (Ctrans) becomes the driving force for drugdiffusion. It is further assumed that the rate-limiting factor for theconcentration change in the boundary layer is transient layerexpansion (Vtrans) rather than drug dissolution, i.e., drug particlesdissolve as soon as they are part of the transient layer. Accordingly,concentration of API in the transient layer can be calculated usingEqs. (2) and (5)

Ctrans ¼ Q0

Vtrans¼ m � A � h

v � t � A¼ m � h

v � tð6Þ

Let’s also assume that Fick’s law of diffusion is followed at alltimes. Once in solution, API diffuses freely into the bulk aqueousmedium.

dQaq

dt¼ J � A ð7Þ

J ¼ �D � @f@x

ð8Þ

where D is the diffusion coefficient, J is the flux, and @f=@x is theconcentration gradient. Given that the sink-condition is main-tained (i.e., API concentration in the bulk medium is negligiblecompared to in the transient layer) and the system is under pseudosteady state conditions, flux can be calculated as

J ¼ P � Ctrans ¼ Dl� Ctrans ð9Þ

where P is the permeation coefficient, and l is the pseudo steadystate diffusion thickness. Expanding the Eq. (7) using Eq. (9) gives

dQaq

dt¼ J � A ¼ D

l� Ctrans � A ¼ D

l�m � h

v � t� A ð10Þ

By rearranging all the constant terms together to a releaseconstant (K), the above Eq. (10) can be written as

dQaq

dt¼ K � 1

tð11Þ

and K ¼ D � m � h � Av � l

ð12Þ

where K has the same unit as drug amount (e.g., mg or mg). Theamount of drug in the bulk medium (Q) can be obtained by solvingthe Eq. (11) as below.

Qaq ¼ K � lnðtÞ þ Q 0 ð13Þ

or Qaq ¼ 2:303K � log10ðtÞ þ Q 0 ð14ÞThis gives rise to logarithmic-time dependent Qaq profile for thedrug release from oleaginous ointments containing dispersed drugparticles, and the slope is the release constant, K. It should be notedthat in the current model (Eqs. (11)–(13)), K is treated as acumulative constant (i.e., a product of multiple independent

constants) under the assumed ideal conditions. This allows use ofsimple linear regression after logarithmic transformation of timeto fit the experimental data. In reality, however, the releaseconstant may become a function of time under certain circum-stances which may lead to various cases of deviations fromlinearity when comparing total amount of drug released againstnatural logarithm of time (refer to later discussion).

3.4. Logarithmic time or square root time?

Scale transformations, such as linear-logarithm, logarithm-linear, etc., are frequently used to explore the underlyingcorrelations between two variables for modelling purposes. Forexample, linearity between independent variable and dependentvariable in linear-linear plot suggests zero-order kinetics, whilelinear-logarithm plot (x-axis in linear scale and y-axis in logarithmscale) with linearity often suggests first-order kinetics.

In drug delivery science, Higuchi drug release model is probablythe most frequently encountered kinetics model where dependentvariable (drug concentration or amount) exhibits linearity withrespect to square-root of time. Interestingly, the initial derivationof the Higuchi model was based on the percutaneous drugabsorption of pharmaceutical creams and ointments (Higuchi,1960, 1961). In the current study, as predicted by Higuchi model,square root of time-dependent release profile was indeed followedby absorption and water-soluble ointment bases. However, foroleaginous ointment, the Higuchi model did not fit (Fig. 2B).Instead, linearity was found between cumulative drug release andlogarithmic time (Fig. 2C). This observation is very unique. First,one might intuitively expect a direct relationship between dQ/dtand concentration as with the most diffusion controlled releaseprocess, but clearly is not the case here. According to Fig. 2C, dQ/dtis expected to be proportional to inverse of time (1/t). Secondly,significant discrepancies exist between Higuchi model predictionsand our results for oleaginous ointments, despite the fact that mostof the Higuchi model assumptions are met: (a) the suspendedparticles are much smaller than the thickness of the layer; (b) theamount of drug present per unit volume is much greater than thesolubility of the drug in the base; and (c) the surface to which theointment is applied is immiscible and constitutes a perfect sink(Higuchi, 1961).

To explain the observed phenomenon, a transient-boundaryhypothesis is proposed, where the inverse-time dependency ofrelease rate is explained by a dynamically changing “transientlayer” (refer to model derivation in previous section). The key

Fig. 5. Effect of pH on acyclovir release from oleaginous ointments (37 �C, n = 6). (A) Cumulative drug release per unit area in linear time scale and (B) cumulative drug releasein logarithm-time scale.

X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39 37

difference between the current proposed model and the Higuchimodel is the direction of the boundary movement. Higuchi modeldescribes an opposite movement for ointment depletion and drugdiffusion (Fig. 4), whereas in our current model these two are in thesame direction (Fig. 3) (Higuchi,1961). Based on the earlier analysisof Korsmeyer–Peppas model, drug release mechanism in watersoluble base was found to be following anomalous transport, verydifferent from absorption base. Yet according to Higuchi modelfitting results, both absorption and water soluble ointmentsexhibited similar boundary movement direction (Fig. 4). Theexistence of these differences was likely caused by formulationdesign. In either absorption or water-soluble ointments, presenceof water-absorbing material means that water can penetrate/diffuse inside the ointment matrix and result in an inward movingboundary, in which case Higuchi’s concentration profile (Fig. 4) canbe perfectly maintained (Fig. 2B). But for oleaginous ointment, inthe absence of any water-soluble component, inward waterpenetration is unlikely as it would otherwise reduce the freedomof both water and petrolatum (i.e., decrease in system’s entropy). Inthis case, an outward moving boundary in the same direction asdrug diffusion is expected.

It is worth noting that this type of logarithmic time in vitro drugrelease correlation holds valid even under different formulationand processing conditions as long as the base material is ofoleaginous type and drug is in suspended state. The findings ofsuch study will be reported elsewhere as a separate publication.

Fig. 6. Effect of temperature on acyclovir release from oleaginous ointments (pH 7.4

cumulative drug release in logarithm-time scale.

3.5. Effect of pH on drug release from oleaginous ointments

In the current proposed transient-boundary hypothesis, onekey assumption is that the transient boundary expansion is therate-limiting step comparing to drug solubilization process. Hence,solubility of the API should have minimal impact on the drugrelease. To verify the validity of this assumption, effect of pH ondrug release (K) from petrolatum ointment was determined, as theequilibrium solubility of acyclovir is known to be pH-dependent(Shojaei et al., 1998).

Due to ionization (two pKa of 2.2 and 9.2), at the acidic andalkaline pH region, acyclovir carries positive and negativenet-charge that results in higher solubility than at the neutralpH range (solubility is approximately 3.2 mg/mL at pH 3.5 and2.6 mg/mL at 7.4 at 37 �C) (Shojaei et al., 1998). The buffers usedwere borate buffer (pH 9.2) and 0.2 M sodium citrate buffer (pH3.5) at 37 �C. Despite the differences in solubility, release constant(calculated as K per unit area, K/A) remained the same under allthree pH conditions (p > 0.05) (Fig. 5B), suggesting the release ofdrug is independent of the drug solubility. There is slightdifference in the intercept term of the release profiles betweenpH 7.4 and pH 3.5 (2.07 � 0.85 vs. 8.56 � 4.59 mg/cm2). However,this may be caused by the initial release (i.e., time-scaling) which isextremely sensitive to the precise onset time of the experiment(even a few seconds delay in start can make a significant on theintercept).

PBS, n = 6). (A) Cumulative drug release per unit area in linear time scale and (B)

Fig. 7. Fiber optic UV data of acyclovir drug release from 6% w/w oleaginous ointment in pH 7.4 PBS @37 �C (n = 5). (A) Cumulative drug release per unit area in linear timescale; (B) cumulative drug release per unit area plotted against square-root of time; and (C) cumulative drug release per unit area in logarithm-time scale. Two dotted arrowindicates 1 min and 4 h time points.

38 X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39

3.6. Effect of temperature on drug release

Under elevated temperature condition (42 �C), acyclovir exhib-ited significantly greater release (Fig. 6) as compared to at 37 �C (K/A = 3.12 � 0.33 mg/cm2 vs. 4.08 � 0.56 mg/cm2, with p < 0.05). Basedon the model equations, it is not immediately evident howtemperature may influence the drug release from oleaginousointment base, as T is not used explicitly. Possibly, temperatureinfluences the drug release through the release constant (K), bychanging the physical boundary conditions at the petrolatum/water interface. Out of the six known parameters (Eq. (12)), threeare possibly temperature-dependent (D,h, and v). Diffusioncoefficient can be expressed through Stokes–Einstein equation

D ¼ kT6phr

ð15Þ

where, k is the Boltzmann constant, T is the temperature, h is theviscosity of the continues phase and r is the radius of the dispersant(drug molecules). Evidently, increase in temperature of applicationarea is likely to accelerate the diffusion of drug molecules, directlythrough the term kT (i.e., the thermal energy) and indirectlythrough additional viscous drag effect (e.g., h is inverselyproportional to temperature for most liquid). Likewise, as thetemperature increases, the thermal energy gain within thetransient-boundary is likely to transform into molecular kineticenergy, and hence result in a faster boundary movement (v).Furthermore, increase in temperature may slightly increasemiscibility between petrolatum and water and lead to a higher

h. Note that the presence of v in the denominator in equation12 indicates a possible negative impact of temperature on K, whichhowever may cancel out with the kT effect in D. This may give riseto a net-effect of release constant being temperature dependentthrough viscosity effect (1/h) and/or by altering the initialboundary thickness (h), both of which defines the interfacialboundary conditions.

3.7. Possible deviations from logarithmic time dependent drug release

To obtain accurate and detailed concentration data, in both fastand slow changing portion of the logarithm-time release profile, insitu UV fiber optics was used. The first data were collected at 5 safter start of the experiment, and last time point was at 24 h. Real-time measurement of the acyclovir concentration allows thedetermination of the range within which logarithmic time releasephenomenon is followed. As shown in Fig. 7B and C, overallacyclovir release from oleaginous ointment follows logarithmictime release better than square-root of time release, confirmingthose observed in Fig. 2. Linearity (of cumulative amount vs.logarithmic time) is most evident after the first minute.

Presence of deviation from linearity is possible for severalreasons. Firstly, the initial boundary layer thickness (h) is only aconstant when the interfacial boundary is at equilibrium. Prior toreaching equilibrium, various time-dependent processes such asmixing, wetting, and temperature equilibrating may all influencethe thickness of the boundary layer. For instance, despite the besteffort, right before the start of the experiment there might be a

X. Xu et al. / International Journal of Pharmaceutics 494 (2015) 31–39 39

slight temperature difference between petrolatum ointment (keptinside the enhancer cell in an empty vessel) and release media(pre-heated to 37 �C). This may cause a slight delay in reaching theconstant h at the initial period and contribute to a relatively slowerdrug release (e.g., lower slope in the first minute) (Fig. 7C). On theother hand, at later time points the boundary may move slightlyinwards petrolatum as it continuously leaches into the aqueousmedia. This may result in an apparent increase in the totalboundary layer thickness and consequently a relatively faster drugrelease towards the end of the experiment (e.g., beyond 4 h).

Furthermore, though not observed, it is possible that thetransient layer thickness expansion may deviate from zero-ordervelocity constant (v) in certain period of time throughout theexperiment. Additionally, the permeation coefficient (P, or D/l) canonly be treated as constant under pseudo-steady-state conditions,which in many cases is very difficult to verify. Last but not least, thedrug concentration (m) inside petrolatum may also be changing ifthe distribution of particles is heterogeneous and/or poly-dispersed.

4. Conclusions

In this study, Higuchi release kinetics was found to be suitablefor two types of ointment bases, absorption and water-solublebases. However, in oleaginous ointment bases, logarithmic timedependent in vitro release kinetics was followed. A novel kineticsmodel was developed based on a transient-boundary hypothesis,and various factors that may influence the in vitro drug releasefrom oleaginous ointment bases were identified. Among themsome of the factors are formulation related, while others may bedependent on the product manufacturing processes as well as thetemperature of the testing conditions. The logarithmic time drugrelease kinetics investigated in the current study may be furtherextended to other similar physical boundary condition systems toprovide mechanistic understanding of the drug release phenome-non when appropriate.

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