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European Journal of Pharmaceutical Sciences 38 (2009) 172–180

Contents lists available at ScienceDirect

European Journal of Pharmaceutical Sciences

journa l homepage: www.e lsev ier .com/ locate /e jps

pplication of dynamic neural networks in the modeling of drug release fromolyethylene oxide matrix tablets

elena Petrovic a,∗, Svetlana Ibric a, Gabriele Betzb, Jelena Parojcic a, Zorica Ðuric a

Institute of Pharmaceutical Technology, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, 11221 Belgrade, SerbiaInstitute of Pharmaceutical Technology, Pharmacenter, University of Basel, Klingelbergstr. 50, 4056 Basel, Switzerland

r t i c l e i n f o

rticle history:eceived 19 April 2009eceived in revised form 17 June 2009ccepted 15 July 2009vailable online 24 July 2009

eywords:ynamic neural networksrug release modelingime series

a b s t r a c t

The main objective of this study was to demonstrate the possible use of dynamic neural networks to modeldiclofenac sodium release from polyethylene oxide hydrophilic matrix tablets. High and low molecularweight polymers in the range of 0.9–5 × 106 have been used as matrix forming materials and 12 differentformulations were prepared for each polymer. Matrix tablets were made by direct compression method.Fractions of polymer and compression force have been selected as most influential factors on diclofenacsodium release profile. In vitro dissolution profile has been treated as time series using dynamic neuralnetworks. Dynamic networks are expected to be advantageous in the modeling of drug release. Networksof different topologies have been constructed in order to obtain precise prediction of release profilesfor test formulations. Short-term and long-term memory structures have been included in the design of

olyethylene oxides (PEOs)ontrolled release

network making it possible to treat dissolution profiles as time series. The ability of network to modeldrug release has been assessed by the determination of correlation between predicted and experimentallyobtained data. Calculated difference (f1) and similarity (f2) factors indicate that dynamic networks arecapable of accurate predictions. Dynamic neural networks were compared to most frequently used staticnetwork, multi-layered perceptron, and superiority of dynamic networks has been demonstrated. Thestudy also demonstrated differences between the used polyethylene oxide polymers in respect to drug

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release and suggests expla

. Introduction

Polyethylene oxides (PEOs) are hydrophilic polymers that haveeen used for designing swellable and controlled release matrixablets. Incorporation of hydrophilic polymers into monolithic

atrices leads to modification of drug release due to swelling androsion of the hydrophilic polymers (Kim, 1998). Being harmlessnd stable makes PEOs suitable carriers for drug delivery systems.heir good compressibility allows the preparation of hydrogelatrices by direct compression (Dimitrov and Lambov, 1999).

ompressibility of polyethylene oxides does not depend on theirolecular weight, chain rigidity or crystallinity (Yang et al., 1996).Polyethylene oxides swell and form compact gel layer on the

urface of the tablet which is responsible for the controlled drug

elease. Only when the gel layer is formed controlled release cane expected—prior to this point formulations have almost imme-iate release dissolution profiles. The controlling mechanism ofrug release from PEO tablets is dependent upon the drug solu-

∗ Corresponding author. Tel.: +381 113951356; fax: +381 113972840.E-mail address: jpetrovic@pharmacy.bg.ac.rs (J. Petrovic).

1

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928-0987/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.ejps.2009.07.007

ns for the obtained results.© 2009 Elsevier B.V. All rights reserved.

ility, drug loading, the addition of a water-soluble excipient, andhe molecular weight of PEOs. For a highly water-soluble drug (e.g.iclofenac sodium), drug diffusion through compact gel layer is theate controlling step (Kim, 1998).

Diclofenac sodium is a potent NSAID (nonsteroidal anti-nflammatory drug) having anti-inflammatory, analgesic andntipyretic properties. It is often used for treating chronic muscu-oskeletal complaints; especially rheumatoid arthritis, osteoarthri-is, spondylarthritis, ankylosing spondylitis, etc. Diclofenac sodiums rapidly dissolved in intestinal fluid and reaches its maximumlood concentration within 30 min. Its mean elimination half-life is.2–1.8 h (Samani et al., 2003). Chronic treatment requires frequentrug administration making diclofenac sodium an ideal candidateor controlled release oral dosage form.

.1. Artificial neural networks

Rigorous regulations in pharmaceutical industry urge for moreophisticated tools that could be used for designing and character-zing dosage forms. It is of great importance to be fully aware ofll the factors impacting the process of dosage form manufacturingnd, if possible, predict the intensity of these impacts on product

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J. Petrovic et al. / European Journal of P

haracteristics. Computer programs based on artificial intelligenceoncepts are proving to be distinctive utilities for this purpose.

Artificial neural networks (ANN) have been introduced intohe field of pharmaceutical technology in 1991 by Hussain et al.1991) and coworkers and gained interest in several pharmaceuti-al applications (Bourquin et al., 1998a,b,c; Murtoniemi et al., 1994;urkoglu et al., 1999). Ever since, they received great attention,specially when it was realized how powerful tools these networksan be. In essential, ANNs are computer programs which utilize theoncept of human brain’s learning. The main difference betweeneural network software and other computer programs is that thelgorithms which are used for data analysis are flexible, i.e. theyan be changed during the analysis itself. This is especially use-ul for nonlinear complex problems. Authors (Chen et al., 1999)ave used ANNs in the design of controlled release formulations.arying formulation variables were used as inputs and in vitroumulative percentages of drug released were used as outputs.ther researchers (Zupancic Bozic et al., 1997) have developed anNN model to optimize diclofenac sodium sustained release matrix

ablets. Trained model was employed to predict release profiles ando optimize the formulation composition. A generalized regressioneural network (GRNN) was used in the design of extended-releasespirin tablets (Ibric et al., 2002). There are many other examples ofpplications of ANN in pharmaceutical technology, cited in Sun etl. (2003). Among the many possible ANN architectures, the multi-ayer perceptron (MLP) network is one of the most widely used (Peht al., 2000; Reis et al., 2004; Rowe and Roberts, 1998). It has beenhown that many artificial intelligence systems, especially neuraletworks, can be applied to the fundamental investigations of theffects of formulation and process variables on the delivery systemSun et al., 2003).

.2. Dynamic neural networks

Generally, ANNs can be divided into static and dynamic net-orks but other classifications are also possible. Dynamic neuraletworks (DNNs) are more advanced than static ones because ofhe fact that data is stored and elaborated in time—the inputs areot independent, moreover they are interacting and influencingach other. Every input is analyzed as a function of the previousne, the network remembers past inputs making the current out-ut integration of past inputs and current response of the system.ast information is therefore used for predicting current and futuretates of the system. This approach is very useful for analyzingrug release from controlled release pharmaceutical formulationsince the amount of drug released is a function where each out-ut depends on the previous input. It is expected that modelingf drug release is more adequate with dynamic than static neuraletworks.

Most often dynamic networks are also referred to as recur-ent networks because of their inner connectedness. The flexibilityf DNNs comes from usage of different processing elements thatontain feedback and delay line taps to express dynamic behav-or (Panerai et al., 2004). The application of feedback enablesiverse usage of DNNs: nonlinear prediction and modeling, adap-ive equalization of communication channels, speech processing,lant control, and automobile engine diagnostics (Haykin, 1999).

Dynamic data is often referred to as time series—a sequencef samples that is spaced at uniform time intervals. Multivariateime series forecasting is still not widely applied despite consider-

ble theoretical advances in this area (De Gooijer and Hyndman,006). For treatment of time series, i.e. dynamic data multiplepproaches have been used: multiple linear regression (MLR), non-inear regression (NLR), artificial neural networks (ANN) and otherpecialized methods, such as SETAR—self-exciting threshold auto

mPpAs

aceutical Sciences 38 (2009) 172–180 173

egression, multivariate exponential smoothing and functionaloefficient autoregressive models (FCAR) (Ghiassi and Nangoy,009).

The recurrent neural networks (RNNs) are multi-layer architec-ures that have been used for a variety of applications includingontrol systems and forecasting of dynamic processes (Ghiassit al., 2005). Aussem (1999) has proposed the usage of RNNsor time series prediction and modeling of small dynamical sys-ems. The idea of classical time series analysis was to replacetatic input–output data with appropriate time histories over aindow of discrete times. Neural network used for time series anal-

sis were memory neuron networks (MNN), dynamic neural unitDNU), feedback networks (FN) and others (Shaw et al., 1997). RNN

odel has been developed (Goh et al., 2002) as an alternative toodel-based approach for the prediction of drug dissolution pro-

les. Authors (Goh et al., 2002) have treated the entire dissolutionrofile as a time series curve in which information contained in oneime point affects further predictions. Elman recurrent network haseen used to predict the dissolution profiles of a matrix controlledelease theophylline pellet preparation.

It is assumed that DNN can be used to model drug release fromydrophilic matrix tablets. Empirical models often used for mod-ling drug release are based on many assumptions and frequentlyail in adequate prediction of drug release profiles. Dynamic net-orks are appreciable for the fact that no assumptions are maderior to analysis of dissolution profiles. Nevertheless, the poten-ial limitation of their usage comes from the fact that they are notapable of elucidating exact mechanism of drug release. The objec-ive of the present work is to demonstrate the usage of DNN for

odeling the drug release from hydrophilic matrix tablets madeith polyethylene oxides (PEOs) of different molecular weights.ynamic networks are compared to conventional, static neuraletworks, and their superiority is demonstrated. Some possiblexplanations for differences in drug release profiles are also given.

. Materials and methods

The following chemicals were obtained from commercial sup-liers: diclofenac sodium (Galenika, Belgrade, Serbia), Sentryolyox WSR 1105-LEO NF Grade and Sentry Polyox WSR Coagulant-EO NF Grade (Dow Chemical Company, Charleston, USA), Avicel PH02 (FMC, Philadelphia, USA) and magnesium stearate (Siegfried,ofingen, Switzerland). Polyethylene oxide (PEO) polymers haveifferent average molecular weights and therefore they differ inontrolling diclofenac sodium release from matrix tablets. PEO

SR 1105 has approximate molecular weight of 0.9 × 106 whereasEO WSR Coagulant approximate molecular weight is 5.0 × 106.

The composition of matrix tablets and the compression forcesed for tableting are given in Table 1. Before compressing each for-ulation of drug powders was mixed in a Turbula mixer type T2C

Willy A Bachofen AG, Basel, Switzerland) for 10 min. Tablets wereompressed using the Zwick® 1478 Universal Testing InstrumentZwick® GmbH, Ulm, Germany). The compression took place withspeed of 20 mm/min. Before each compression cycle, the punchesnd the die wall were lubricated with magnesium stearate.

Tablets diameters and thickness were measured using aicrometer digital caliper Digitcal (Tesa S.A., Renens, Switzerland).

orosity of the tablets has been calculated using true and rela-ive densities of drug and excipients. The hardness of tablets was

easured using Dr. Schleuinger model 8M tester (Dr. Schleuinger,harmatron, Solothurn, Switzerland). The dissolution testing waserformed using an apparatus of type II according to USP (SotaxT7, Sotax AG, Basel, Switzerland) equipped with paddles. Thepeed of paddles was set to constant speed of 50 rpm. 900 ml of

174 J. Petrovic et al. / European Journal of Pharmaceutical Sciences 38 (2009) 172–180

Table 1The composition of matrix tablets and the compression force used for their manufacturing.

Formulation Diclofenac sodium (%, w/w) Polyox WSR 1105 (%, w/w) Polyox WSR Coagulant (%, w/w) Avicel PH 102 (%, w/w) Compression force (kN)

F1 30 10 – 60 5F2 30 10 – 60 7.5F3 30 10 – 60 10F4 30 20 – 50 5F5 30 20 – 50 7.5F6 30 20 – 50 10F7 30 30 – 40 5F8 30 30 – 40 7.5F9 30 30 – 40 10F10 30 20 – 50 7.5F11 30 15 – 55 6F12 30 25 – 45 6.5C1 30 – 5 65 3C2 30 – 5 65 5C3 30 – 5 65 7C4 30 – 10 60 3C5 30 – 10 60 5C6 30 – 10 60 7C7 30 – 15 55 3C8 30 – 15 55 5

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hosphate buffer, pH 6.8 (USP 28) was used as dissolution media.issolution tests were conducted for 8 h. Aliquots of 5 ml were

ampled for analysis, each time the same amount of mediumas replaced to dissolution vessels. Samples were taken at 10

ime points after the beginning of the dissolution test: 0.5 h; 1 h,.5 h; 2 h, 3 h, 4 h, 5 h, 6 h, 7 h and 8 h (where h stands for hours).he amount of diclofenac sodium was determined using UV spec-rophotometer (� = 275 nm).

A screening design was used to determine the most impor-ant formulation and processing parameters for developing PEOontrolled release matrices. Studied parameters were: polymerraction, compression force, addition of a lubricant and mixingime. It was discovered that polymer weight ratio (%, w/w) andhe force used for direct compression of powders mixtures werehe most influential for characteristics of matrices. 32 full factorialesign was used for in-depth analysis of these two parameters:olymer % (w/w) as well as compression force was varied onhree levels (Table 1). PEO 1105 tablets had average weight of49.75 mg (±0.71 mg); porosity was in the range of 13.25–22.56%nd hardness was in the range of 70.3–182.5 N. For PEO Coagu-ant tablets, average weight was 449.83 mg (±1.06 mg); porosity

as in the range of 16.71–30.71% and hardness was in the range of4.8–128.8 N.

Comparison of dissolution profiles was done using differencend similarity factors (f1 and f2 respectively):

1 =∑n

t=1

∣∣Rt − Tt

∣∣∑nt=1Rt

× 100 (1)

2 = 50 log

⎧⎨⎩

[1 + 1

n

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(Rt − Tt)2

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× 100

⎫⎬⎭ (2)

here n is the number of samples, Rt is the percentage of drug

eleased after time t for referent product (in this case those arebserved values) and Tt is the percentage of drug released afterime t for product which is being tested (in this case those are valuesredicted by dynamic neural network). Profiles are considered toe similar for 0 < f1 < 15 and/or 50 < f2 < 100 (Chow and Ki, 1997).

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Commercially available Peltarion® software was used on per-onal computer for designing neural networks.

.1. Topology of dynamic neural networks

Topology of a network consists of blocks connected withinks. Blocks are information processing elements and the centrallement of the block is forward propagator. The role of back prop-gator is usually to mirror the action of the forward propagator inerms of making it possible to conduct support to the system basedn error correction. Links enable communication between differentlocks. Links can be set up to have a memory which is very impor-ant for dynamic networks. The order of the memory says for how

any time steps the signal will be delayed. Treatment of dynamicata requires this kind of temporal dependencies of signal chan-eling. Network topology, together with control system, forms aomplete system. Software control system utilizes the applicationalled back-propagation through time (BPTT) where the back propa-ated signal is buffered and reversed which enables getting forwardnd back propagated signals synchronized in time. Dynamic net-ork feature of the program was used for analyzing drug releaserofiles for matrix tablets made with PEO Coagulant (C1–C12 for-ulations). Topology of network is schematically represented in

ig. 1. Data sources give inputs and outputs to the network. Inputsere % (w/w) of PEO Coagulant and compression force whereas

utputs were fractions of diclofenac sodium released at specificime intervals. Outputs were dynamically treated since they cane considered a time series of events. Gamma memory is a specifichort memory recurrent structure which preserves temporal infor-ation about the system. Distinctive feature of gamma memory is

he number of taps—number of signal delays. For a given numberf taps memory remembers previous system states and integrateshem with current ones. Gamma memory is schematically repre-ented in Fig. 2. From the point of view of signal transmittanceamma memory can be seen as recursive low-pass filter (each out-

ut gives a more filtered version of the original signal) which actss an infinite response filter. It is ideal for adaptive systems sincets interpolation weight � can be adapted using usual algorithms.nterpolation weight controls the depth of Gamma memory andtability is guaranteed when 0 < � < 2. Gamma memory is actually

J. Petrovic et al. / European Journal of Pharmaceutical Sciences 38 (2009) 172–180 175

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Fig. 1. Schematic representation

combination of Tapped-Delay-Line (TDL) and a simple feedbackeuron. So, the signals gk(t) at the taps k in time t of the Gammaemory are convulsions of the impulse response gk tap k.Filters generally are elements that, in predefined way, convert

nputs to outputs. Relationship between inputs and outputs of thepecific filter is defined by convolution integral:

(t) =∫ ∞

0

g(t − �)x(t) dt (3)

here g(t) stands for the impulse response, x(t) is the input and y(t)s the output of the system. Laplace transformation of the convo-uting integral in used to get the relationship between input andutput signals in frequency domain:

(s) = G(s) × X(s) (4)

here s is a complex frequency (transfer functions are usually theatio of two polynomials in s, i.e. a rational function of s).

For Gamma memory, impulse response gk is

k(t) =(

t − 1k − 1

)�k(1 − �)t−k (5)

n the frequency domain transfer function Gk can be written as:

k(z, �) =k∏

i=1

(�z−1

1 − (1 − �)z−1

)(6)

here � is a product operator.The resolution R of the Gamma memory is given by

= K

(K/(1 − �))= 1 − � (7)

ollowing that the order of the memory obeys K the relation:

= D × R (8)

here K is the number of integrators in the memory and D is the

emory depth (De Vries and Principe, 1992).Memory depth D is the temporal mean value of the last taps

mpulse response whereas memory resolution R is the number ofarameters of freedom (i.e. memory state variables) per unit of timePrincipe et al., 1994).

mmnbi

Fig. 2. Schematic representation of Gamma memory. Z−1 is a del

ple built-in dynamic network.

Gamma memory used in the dynamic network has four taps.ince the number of outputs equals number of inputs times numberf taps:

umber of outputs = number of inputs × number of taps (9)

he number of outputs in this case is 8.From Gamma memory signal is transferred to the first Function

ayer, then Weight layer and subsequently to the second Functionayer. Function layers apply a function to their inputs and usuallyntroduce non-linearity to the system. In the network used for ana-yzing PEO Coagulant matrices first Function layer has 8 inputswhich are outputs from Gamma memory) and 8 outputs. Theseutputs are transferred to 10 outputs in Weight layer (since therere 10 time intervals in drug release profile). The second Functionayer elaborates 10 inputs to 10 outputs and sends them to Deltaerminator. Both Function layers apply sigmoid function (Tan h sig-

oid function specifically) as transfer function. Delta terminatorompares two signals—one comes from the data source and rep-esents real, observed outputs; whereas the second signal comesrom the second Function layer and represents outputs predictedy the dynamic system. Data for C1–C10 formulations has beenplit into training and validation subset. Formulations C11 and C12ere used to test the system. It is important to emphasize that testata were not used for development of model.

Software used in this study offers a variety of snippets—a pre-esigned partial topology from which complete adaptive systeman be easily constructed. Dynamic snippets include: Gammaemory, Recurrent and Gamma–Recurrent hybrid snippet. Results

howed that simple Recurrent One Layer dynamic network is theost adequate for analyzing F1–F12 formulations. Fig. 3 represents

ecurrent One Layer network. Some of its elements are the sames in previously described Gamma memory network. From Dataource 1 signals go to the first Weight layer. The first Weight layeras 2 inputs and 17 outputs. The number of outputs has been opti-ized using Monte Carlo simulations in the training mode of the

rogram. Monte Carlo simulations are the simplest tools for opti-

ization of different parameters and will be further described inore details. One Layer Recurrent network is a partially recurrent

etwork since the recurrent connections are sent from hidden layerack to itself. In fully recurrent networks the output is sent back

nto the network. To make it possible to return signals into previ-

ay while � is an interpolation weight. � sums the inputs.

176 J. Petrovic et al. / European Journal of Pharmaceutical Sciences 38 (2009) 172–180

work:

ouoslnMw�eItmm(nhenhow

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Fig. 3. Representation of Reccurent One Layer dynamic neural net

us blocks in the topology it is necessary to have modified linkssed for channeling signals. If links are set up to have a mem-ry then the order of the memory says how many time steps theignal will be delayed (default value is one time step, i.e. −1). Ifocal feedback is constructed, which is the case in partial recurrentetwork studied here, interpolation capabilities become available.andatory memory is added as well as interpolation parameter,eight �. Local feedback is always scaled with 1 − �. In effect,influences the extent to which second-order information influ-

nces the update of the signal processed (Becerikli and Oysal, 2007).n essence, recurrent network is similar to Gamma memory buthere is one great difference—Gamma memory is a short-term

emory whereas recurrent network is foundation for long-termemory structures. In time-lagged networks a short-term memory

i.e. memory filter) is incorporated. However, it is more useful for aetwork to discover, through its internal dynamics the long-termistory of a series of events so that it does not have to depend onxternally provided memory filters. Dynamically driven recurrentetworks with feedback loops attempt to capture such long-termistory in data. Over time, the network stores long-term mem-ry structure in its feedback (recurrent) and regular connections,hose weights are adjusted during training (Samarasinghe, 2006).

From the first Weight layer 17 outputs go to the first Functionayer that has modified links and a feedback connection to itself.his is where the recurrence of the signals takes place. For eachf the 17 outputs there is a separate feedback and default valuesor � are 0.5. �1 to �17 were optimized using Monte Carlo simula-ions (together with the number of outputs from the first Weightayer) making it possible to set up connections that can most ade-uately predict future states of the system. Monte Carlo optimizer

s one of batch processors in the training mode of the software.onte Carlo simulations are another name for random search. It

s rather simple optimization algorithm that takes no assumptionsbout the problem studied (Robert and Casella, 2004). For simula-ions used to construct dynamic network the number of exemplars

(ltia

(a) Peltarion® layout and (b) network’s schematic representation.

nd epochs was varied. In Monte Carlo optimizer exemplars referso number of optimization passes whereas epochs stand for num-er of epochs per optimization pass. When one epoch passes thedaptive system has been presented with available data once. Asdaptive systems are for most part trained iteratively many epochsre usually required to fully train a system. From the first, recur-ent Function layer, signal goes to second Weight layer that has7 inputs and 10 outputs (10 samplings for determining drug dis-olution profile). From the second Weight layer signal goes to theecond Function layer. The second Function layer is an ordinaryunction layer (in comparison to the first Function layer). It has0 inputs and 10 outputs and performs Tan h sigmoid function.he function of the Delta terminator is the same as in previouslyescribed topology.

.2. Topology of static neural networks

In order to evaluate results obtained using dynamic neural net-orks, built-in static neural network software architecture has

een used. Multi-layer perceptron, typical feed forward artificialetwork, was employed for modeling drug release. MLP network

ayout is given in Fig. 4. Distinctive difference between MLP net-ork and previously described dynamic networks is that there areo recurrent connections between elements, each input is analyzed

ndependently. From Data source 1 signals go to the first Weightayer (with 2 inputs and 6 outputs) and first Function layer (with 6nputs and 6 outputs). Function layer applies Tan h sigmoid func-ion to input data and the number of outputs has been optimizedsing Monte Carlo simulations in the training mode of the program.rom the first Function layer signal goes to second Weight layer

with 6 inputs and 10 outputs) and then to the second Functionayer (10 inputs and outputs for 10 sampling points in dissolutionime profile). The function of the Delta terminator is the same asn previously described topologies. Monte Carlo simulations werelso used for variation in number of epochs used for training.

J. Petrovic et al. / European Journal of Pharmaceutical Sciences 38 (2009) 172–180 177

k: (a) Peltarion® layout and (b) network’s schematic representation.

soinsmNsow

3

FimtdFfmrwi1rfirf

Fig. 4. Representation of multi-layer perceptron neural networ

Determination of optimal training conditions for dynamic andtatic networks was done automatically by software. The progressf errors for both training and validation sets were monitored dur-ng training to decide when to stop the training. When there wereo more changes in the training error or when the validation errortarted to diverge, the training was stopped. For all studied casesean standard error did not exceed 2% which is acceptable value.umbers of epochs varied during training of different networks,

ome networks were trained for up to 100 000 epochs in order tobtain minimal error. It is important to emphasize that networksere not over trained.

. Results and discussion

Dissolution of diclofenac sodium from formulations C1–C12 and1–F12 shows dependency of drug release on fraction of polymern the formulation as well as compression force used for tablets

anufacturing. It is reasonable to expect that increase of the frac-ion of polymer and/or compression force leads to decrease of therug release rate but it is not known, a priori, to which extent.ig. 5 shows dissolution profiles of PEO 1105 and PEO Coagulantormulations. Formulations F1–F3 are not sustained release for-

ulations since approximately 40% of diclofenac sodium has beeneleased after 2 h. F4–F9 formulations exhibit sustained releaseith some unexpected profiles, especially formulation F9 is crit-

cal. It is curious that formulation with the highest fraction of PEO105 prepared with the highest compression force (formulation F9)

eleases diclofenac sodium so rapidly. Release of diclofenac sodiumrom PEO Coagulant matrices conforms to expected values—withncrease of fraction of polymer and/or compression force drugelease rate decreases. It is evident that C1–C9 are sustained releaseormulations.

Fig. 5. Dissolution profiles for (a) PEO 1105 formulations and (b) PEO Coagulantformulations.

178 J. Petrovic et al. / European Journal of Pharmaceutical Sciences 38 (2009) 172–180

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ig. 6. Observed values vs. Gamma memory dynamic neural network’s prediction ofercentage of diclofenac sodium relased. Correlation coefficients r2 are: (a) r2 = 0.992nd (b) r2 = 0.993.

Gamma memory network was presented with C1–C10 inputsnd outputs. Fig. 6 shows capability of Gamma memory network toredict fraction of diclofenac sodium released in certain time pointor two test formulations (C11 and C12). To further assess network’sapability of prediction, observed and predicted drug release pro-les were plotted in Fig. 7 and difference and similarity factors werealculated.

From the values for similarity and difference factors it cane concluded that dissolution profiles are similar meaning thatynamic network was successful in predicting drug release pro-le. When the same dynamic network was applied to predict drugelease from PEO 1105 matrices the results were not so good. Exper-ments showed that dissolution of diclofenac sodium from PEO105 matrix tablets is irregular—increase of % (w/w) of polymernd/or compression force does not necessarily lead to decrease ofrug release rate. This irregular dissolution could be the possibleeason for failure of Gamma memory network to predict the releaserofile. Fig. 8 shows observed dissolution profiles for F11 and F12est formulations as well as profiles predicted by Gamma memoryynamic network. It is clear that network is not adequate for pre-icting release profiles, especially for F11 formulation. That was theeason for further application of networks of different topology.

When Recurrent One Layer network was applied to analyze1–F12 formulations, there was improvement in capability of net-ork to predict diclofenac sodium release profiles. In Fig. 9 one can

ee correlation between predicted and observed dissolution pro-les for two test formulations F11 and F12. Correlation is strongetween them and based upon this it could be concluded that mod-

ls are appropriate for dissolution profiles predicting. Nevertheless,t is always recommended to calculate difference and similarity fac-ors since they are far better indicators of potential similarity ofissolution profiles. Fig. 10 shows comparison of dissolution pro-

utpr

ig. 7. Comparisson of dissolution profiles obtained in experiment and predictedy Gamma memory dynamic neural network for C11 and C12 test formulations: (a)

1 = 7.33 and f2 = 73.27 and (b) f1 = 4.12 and f2 = 78.20.

les obtained in experiment and predicted by Recurrent One Layeretwork. It is evident that prediction of dissolution profile for F11

ormulation is still not satisfactory whilst prediction of profile for12 formulation is much better compared to previous results. Thiss good example of how correlation coefficient can be misleading.n this case, experimental and predicted profiles for F11 formu-ation are strongly correlated (r2 = 0.993) but predicted profile ishifted from experimental in such a way that two almost parallelines are obtained with significant differences in absolute values.t should be possible to use this model for predicting dissolutionrofiles keeping in mind that shifting of values could occur. Onef the explanations for this phenomenon is that parameters oformulation F11 are such that it has properties of both immedi-te and modified release formulation. In these formulations theres relatively large amount of drug released in the first period ofhe dissolution test. Network could possibly better recognize thesenstances if it had been trained with more data. In practice, theserossover formulations are always avoided but it would be usefulo have a possibility to predict them. Further research should beddressed in this direction—prediction of attributes of boundaryystem states. It is possible that more complex recurrent networksre needed for such investigations. When MLP static neural net-ork was employed to model diclofenac sodium release from PEOoagulant matrices it proved successful for one of the test formu-

ations but not for the other: values for difference factors were9.16 and 8.94 for formulations C11 and C12 respectively; val-

es for similarity factors were 56.22 and 71.00 respectively. Evenhough MLP networks are highly appreciated because of the sim-licity of their architecture this is a good example of possible lack ofobustness when MLP networks are applied for drug release mod-

J. Petrovic et al. / European Journal of Pharmaceutical Sciences 38 (2009) 172–180 179

Fig. 8. Comparison of dissolution profiles obtained in experiment and predicted byGamma memory dynamic neural network for F11 and F12 test formulations: (a)f1 = 34.26 and f2 = 47.79 and (b) f1 = 17.36 and f2 = 60.72.

Fig. 9. Observed values vs. Recurrent One Layer dynamic neural network’s predic-tion of percentage of diclofenac sodium relased. Correlation coefficients r2 are: (a)r2 = 0.993 and (b) r2 = 0.994.

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ig. 10. . Comparisson of dissolution profiles obtained in experiment and predictedy recurrent dynamic neural network for F11 and F12 test formulations: (a) f1 = 29.03nd f2 = 49.86 and (b) f1 = 5.84 and f2 = 77.54.

ling. This finding was also confirmed when MLP static networkas employed to model diclofenac sodium release from PEO 1105atrices. In this case, network’s prediction ability was not success-

ul for any of the test formulations. Values for difference factorsere 29.23 and 23.78 for formulations F11 and F12 respectively;

alues for similarity factors were 48.97 and 54.91 respectively.rug release should be treated as a time series and it is evident

hat DNNs are appropriate tools for such analysis. Authors wouldlso like to emphasize that prediction ability of dynamic networkss greater than mathematical modeling approach. Details of devel-ped mathematical model for PEO matrices can be found in Petrovict al. (2008) and when developed model is compared to predic-ions of dynamic network, advantages of dynamic networks arelear.

. Conclusions

It has been demonstrated that DNNs are powerful, sophisticatedools for drug release characterization. The ability to accuratelyredict drug release profile using dynamic networks has beenhown. Superiority of dynamic networks over static networks andther modeling approaches is also addressed. Dynamic networksre thus robust tools for drug release characterization. Construct-ng a network with appropriate topology can present an obstacle,ut adequate software packages provide solutions. In terms ofolyethylene oxide matrices, results presented here indicate that

EOs of higher molecular weights (such as PEO Coagulant) are bet-er choice for controlled release dosage forms compared to PEOsith lower molecular weights. Formulations with PEO Coagulant

equired less % (w/w) of polymer to obtain sustained release profile

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80 J. Petrovic et al. / European Journal of P

nd showed fewer variations and unpredicted results in compari-on to PEO 1105 formulations.

cknowledgment

This work was done under the project no. TR 23015 supported byhe Ministry of Science and Technological Development, Republicf Serbia.

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