Application of dynamic neural networks in the modeling of drug release from polyethylene oxide matrix tablets

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

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European Journal of Pharmaceutical Sciences journal homepage: www.elsevier.com/locate/ejps

Application of dynamic neural networks in the modeling of drug release from polyethylene oxide matrix tablets Jelena Petrovic´ a,∗ , Svetlana Ibric´ a , Gabriele Betz b , Jelena Parojˇcic´ a , Zorica Ðuric´ a a b

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

a r t i c l e

i n f o

Article history: Received 19 April 2009 Received in revised form 17 June 2009 Accepted 15 July 2009 Available online 24 July 2009 Keywords: Dynamic neural networks Drug release modeling Time series Polyethylene oxides (PEOs) Controlled release

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 model diclofenac sodium release from polyethylene oxide hydrophilic matrix tablets. High and low molecular weight polymers in the range of 0.9–5 × 106 have been used as matrix forming materials and 12 different formulations 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 diclofenac sodium release profile. In vitro dissolution profile has been treated as time series using dynamic neural networks. Dynamic networks are expected to be advantageous in the modeling of drug release. Networks of different topologies have been constructed in order to obtain precise prediction of release profiles for test formulations. Short-term and long-term memory structures have been included in the design of network making it possible to treat dissolution profiles as time series. The ability of network to model drug release has been assessed by the determination of correlation between predicted and experimentally obtained data. Calculated difference (f1 ) and similarity (f2 ) factors indicate that dynamic networks are capable of accurate predictions. Dynamic neural networks were compared to most frequently used static network, multi-layered perceptron, and superiority of dynamic networks has been demonstrated. The study also demonstrated differences between the used polyethylene oxide polymers in respect to drug release and suggests explanations for the obtained results. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Polyethylene oxides (PEOs) are hydrophilic polymers that have been used for designing swellable and controlled release matrix tablets. Incorporation of hydrophilic polymers into monolithic matrices leads to modification of drug release due to swelling and erosion of the hydrophilic polymers (Kim, 1998). Being harmless and stable makes PEOs suitable carriers for drug delivery systems. Their good compressibility allows the preparation of hydrogel matrices by direct compression (Dimitrov and Lambov, 1999). Compressibility of polyethylene oxides does not depend on their molecular weight, chain rigidity or crystallinity (Yang et al., 1996). Polyethylene oxides swell and form compact gel layer on the surface of the tablet which is responsible for the controlled drug release. Only when the gel layer is formed controlled release can be expected—prior to this point formulations have almost immediate release dissolution profiles. The controlling mechanism of drug release from PEO tablets is dependent upon the drug solu-

∗ Corresponding author. Tel.: +381 113951356; fax: +381 113972840. ´ E-mail address: [email protected] (J. Petrovic). 0928-0987/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2009.07.007

bility, drug loading, the addition of a water-soluble excipient, and the molecular weight of PEOs. For a highly water-soluble drug (e.g. diclofenac sodium), drug diffusion through compact gel layer is the rate controlling step (Kim, 1998). Diclofenac sodium is a potent NSAID (nonsteroidal antiinflammatory drug) having anti-inflammatory, analgesic and antipyretic properties. It is often used for treating chronic musculoskeletal complaints; especially rheumatoid arthritis, osteoarthritis, spondylarthritis, ankylosing spondylitis, etc. Diclofenac sodium is rapidly dissolved in intestinal fluid and reaches its maximum blood concentration within 30 min. Its mean elimination half-life is 1.2–1.8 h (Samani et al., 2003). Chronic treatment requires frequent drug administration making diclofenac sodium an ideal candidate for controlled release oral dosage form. 1.1. Artificial neural networks Rigorous regulations in pharmaceutical industry urge for more sophisticated tools that could be used for designing and characterizing dosage forms. It is of great importance to be fully aware of all the factors impacting the process of dosage form manufacturing and, if possible, predict the intensity of these impacts on product

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characteristics. Computer programs based on artificial intelligence concepts are proving to be distinctive utilities for this purpose. Artificial neural networks (ANN) have been introduced into the field of pharmaceutical technology in 1991 by Hussain et al. (1991) and coworkers and gained interest in several pharmaceutical applications (Bourquin et al., 1998a,b,c; Murtoniemi et al., 1994; Turkoglu et al., 1999). Ever since, they received great attention, especially when it was realized how powerful tools these networks can be. In essential, ANNs are computer programs which utilize the concept of human brain’s learning. The main difference between neural network software and other computer programs is that the algorithms which are used for data analysis are flexible, i.e. they can be changed during the analysis itself. This is especially useful for nonlinear complex problems. Authors (Chen et al., 1999) have used ANNs in the design of controlled release formulations. Varying formulation variables were used as inputs and in vitro cumulative percentages of drug released were used as outputs. Other researchers (Zupancic Bozic et al., 1997) have developed an ANN model to optimize diclofenac sodium sustained release matrix tablets. Trained model was employed to predict release profiles and to optimize the formulation composition. A generalized regression neural network (GRNN) was used in the design of extended-release aspirin tablets (Ibric et al., 2002). There are many other examples of applications of ANN in pharmaceutical technology, cited in Sun et al. (2003). Among the many possible ANN architectures, the multilayer perceptron (MLP) network is one of the most widely used (Peh et al., 2000; Reis et al., 2004; Rowe and Roberts, 1998). It has been shown that many artificial intelligence systems, especially neural networks, can be applied to the fundamental investigations of the effects of formulation and process variables on the delivery system (Sun et al., 2003). 1.2. Dynamic neural networks Generally, ANNs can be divided into static and dynamic networks but other classifications are also possible. Dynamic neural networks (DNNs) are more advanced than static ones because of the fact that data is stored and elaborated in time—the inputs are not independent, moreover they are interacting and influencing each other. Every input is analyzed as a function of the previous one, the network remembers past inputs making the current output integration of past inputs and current response of the system. Past information is therefore used for predicting current and future states of the system. This approach is very useful for analyzing drug release from controlled release pharmaceutical formulations since the amount of drug released is a function where each output depends on the previous input. It is expected that modeling of drug release is more adequate with dynamic than static neural networks. Most often dynamic networks are also referred to as recurrent networks because of their inner connectedness. The flexibility of DNNs comes from usage of different processing elements that contain feedback and delay line taps to express dynamic behavior (Panerai et al., 2004). The application of feedback enables diverse usage of DNNs: nonlinear prediction and modeling, adaptive equalization of communication channels, speech processing, plant control, and automobile engine diagnostics (Haykin, 1999). Dynamic data is often referred to as time series—a sequence of samples that is spaced at uniform time intervals. Multivariate time series forecasting is still not widely applied despite considerable theoretical advances in this area (De Gooijer and Hyndman, 2006). For treatment of time series, i.e. dynamic data multiple approaches have been used: multiple linear regression (MLR), nonlinear regression (NLR), artificial neural networks (ANN) and other specialized methods, such as SETAR—self-exciting threshold auto

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regression, multivariate exponential smoothing and functional coefficient autoregressive models (FCAR) (Ghiassi and Nangoy, 2009). The recurrent neural networks (RNNs) are multi-layer architectures that have been used for a variety of applications including control systems and forecasting of dynamic processes (Ghiassi et al., 2005). Aussem (1999) has proposed the usage of RNNs for time series prediction and modeling of small dynamical systems. The idea of classical time series analysis was to replace static input–output data with appropriate time histories over a window of discrete times. Neural network used for time series analysis were memory neuron networks (MNN), dynamic neural unit (DNU), feedback networks (FN) and others (Shaw et al., 1997). RNN model has been developed (Goh et al., 2002) as an alternative to model-based approach for the prediction of drug dissolution profiles. Authors (Goh et al., 2002) have treated the entire dissolution profile as a time series curve in which information contained in one time point affects further predictions. Elman recurrent network has been used to predict the dissolution profiles of a matrix controlled release theophylline pellet preparation. It is assumed that DNN can be used to model drug release from hydrophilic matrix tablets. Empirical models often used for modeling drug release are based on many assumptions and frequently fail in adequate prediction of drug release profiles. Dynamic networks are appreciable for the fact that no assumptions are made prior to analysis of dissolution profiles. Nevertheless, the potential limitation of their usage comes from the fact that they are not capable of elucidating exact mechanism of drug release. The objective of the present work is to demonstrate the usage of DNN for modeling the drug release from hydrophilic matrix tablets made with polyethylene oxides (PEOs) of different molecular weights. Dynamic networks are compared to conventional, static neural networks, and their superiority is demonstrated. Some possible explanations for differences in drug release profiles are also given.

2. Materials and methods The following chemicals were obtained from commercial suppliers: diclofenac sodium (Galenika, Belgrade, Serbia), Sentry Polyox WSR 1105-LEO NF Grade and Sentry Polyox WSR CoagulantLEO NF Grade (Dow Chemical Company, Charleston, USA), Avicel PH 102 (FMC, Philadelphia, USA) and magnesium stearate (Siegfried, Zofingen, Switzerland). Polyethylene oxide (PEO) polymers have different average molecular weights and therefore they differ in controlling diclofenac sodium release from matrix tablets. PEO WSR 1105 has approximate molecular weight of 0.9 × 106 whereas PEO WSR Coagulant approximate molecular weight is 5.0 × 106 . The composition of matrix tablets and the compression force used for tableting are given in Table 1. Before compressing each formulation of drug powders was mixed in a Turbula mixer type T2C (Willy A Bachofen AG, Basel, Switzerland) for 10 min. Tablets were compressed using the Zwick® 1478 Universal Testing Instrument (Zwick® GmbH, Ulm, Germany). The compression took place with a speed of 20 mm/min. Before each compression cycle, the punches and the die wall were lubricated with magnesium stearate. Tablets diameters and thickness were measured using a micrometer digital caliper Digitcal (Tesa S.A., Renens, Switzerland). Porosity of the tablets has been calculated using true and relative densities of drug and excipients. The hardness of tablets was measured using Dr. Schleuinger model 8M tester (Dr. Schleuinger, Pharmatron, Solothurn, Switzerland). The dissolution testing was performed using an apparatus of type II according to USP (Sotax AT7, Sotax AG, Basel, Switzerland) equipped with paddles. The speed of paddles was set to constant speed of 50 rpm. 900 ml of

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Table 1 The 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 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30

10 10 10 20 20 20 30 30 30 20 15 25 – – – – – – – – – – – –

– – – – – – – – – – – – 5 5 5 10 10 10 15 15 15 10 7.5 12.5

60 60 60 50 50 50 40 40 40 50 55 45 65 65 65 60 60 60 55 55 55 60 62.5 57.5

5 7.5 10 5 7.5 10 5 7.5 10 7.5 6 6.5 3 5 7 3 5 7 3 5 7 5 6 4

phosphate buffer, pH 6.8 (USP 28) was used as dissolution media. Dissolution tests were conducted for 8 h. Aliquots of 5 ml were sampled for analysis, each time the same amount of medium was replaced to dissolution vessels. Samples were taken at 10 time points after the beginning of the dissolution test: 0.5 h; 1 h, 1.5 h; 2 h, 3 h, 4 h, 5 h, 6 h, 7 h and 8 h (where h stands for hours). The amount of diclofenac sodium was determined using UV spectrophotometer ( = 275 nm). A screening design was used to determine the most important formulation and processing parameters for developing PEO controlled release matrices. Studied parameters were: polymer fraction, compression force, addition of a lubricant and mixing time. It was discovered that polymer weight ratio (%, w/w) and the force used for direct compression of powders mixtures were the most influential for characteristics of matrices. 32 full factorial design was used for in-depth analysis of these two parameters: polymer % (w/w) as well as compression force was varied on three levels (Table 1). PEO 1105 tablets had average weight of 449.75 mg (±0.71 mg); porosity was in the range of 13.25–22.56% and hardness was in the range of 70.3–182.5 N. For PEO Coagulant tablets, average weight was 449.83 mg (±1.06 mg); porosity was in the range of 16.71–30.71% and hardness was in the range of 34.8–128.8 N. Comparison of dissolution profiles was done using difference and similarity factors (f1 and f2 respectively):

 n  Rt − Tt  t=1 f1 = × 100 n

(1)

R t=1 t

f2 = 50 log

⎧ ⎨ ⎩

1 1+ (Rt − Tt )2 n n

t=1

−0.5

⎫ ⎬

× 100

⎭

(2)

where n is the number of samples, Rt is the percentage of drug released after time t for referent product (in this case those are observed values) and Tt is the percentage of drug released after time t for product which is being tested (in this case those are values predicted by dynamic neural network). Profiles are considered to be similar for 0 < f1 < 15 and/or 50 < f2 < 100 (Chow and Ki, 1997).

Commercially available Peltarion® software was used on personal computer for designing neural networks. 2.1. Topology of dynamic neural networks Topology of a network consists of blocks connected with links. Blocks are information processing elements and the central element of the block is forward propagator. The role of back propagator is usually to mirror the action of the forward propagator in terms of making it possible to conduct support to the system based on error correction. Links enable communication between different blocks. Links can be set up to have a memory which is very important for dynamic networks. The order of the memory says for how many time steps the signal will be delayed. Treatment of dynamic data requires this kind of temporal dependencies of signal channeling. Network topology, together with control system, forms a complete system. Software control system utilizes the application called back-propagation through time (BPTT) where the back propagated signal is buffered and reversed which enables getting forward and back propagated signals synchronized in time. Dynamic network feature of the program was used for analyzing drug release profiles for matrix tablets made with PEO Coagulant (C1–C12 formulations). Topology of network is schematically represented in Fig. 1. Data sources give inputs and outputs to the network. Inputs were % (w/w) of PEO Coagulant and compression force whereas outputs were fractions of diclofenac sodium released at specific time intervals. Outputs were dynamically treated since they can be considered a time series of events. Gamma memory is a specific short memory recurrent structure which preserves temporal information about the system. Distinctive feature of gamma memory is the number of taps—number of signal delays. For a given number of taps memory remembers previous system states and integrates them with current ones. Gamma memory is schematically represented in Fig. 2. From the point of view of signal transmittance Gamma memory can be seen as recursive low-pass filter (each output gives a more filtered version of the original signal) which acts as an infinite response filter. It is ideal for adaptive systems since its interpolation weight  can be adapted using usual algorithms. Interpolation weight controls the depth of Gamma memory and stability is guaranteed when 0 <  < 2. Gamma memory is actually

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Fig. 1. Schematic representation of simple built-in dynamic network.

a combination of Tapped-Delay-Line (TDL) and a simple feedback neuron. So, the signals gk (t) at the taps k in time t of the Gamma memory are convulsions of the impulse response gk tap k. Filters generally are elements that, in predefined way, convert inputs to outputs. Relationship between inputs and outputs of the specific filter is defined by convolution integral:

∞

y(t) =

g(t − )x(t) dt

(3)

0

where g(t) stands for the impulse response, x(t) is the input and y(t) is the output of the system. Laplace transformation of the convoluting integral in used to get the relationship between input and output signals in frequency domain: Y (s) = G(s) × X(s)

(4)

where s is a complex frequency (transfer functions are usually the ratio of two polynomials in s, i.e. a rational function of s). For Gamma memory, impulse response gk is



gk(t) =

t−1 k−1



k (1 − )t−k

(5)

in the frequency domain transfer function Gk can be written as: Gk (z, ) =

k   i=1

z −1 1 − (1 − )z −1

 (6)

where  is a product operator. The resolution R of the Gamma memory is given by R=

K =1− (K/(1 − ))

(7)

following that the order of the memory obeys K the relation: K =D×R

(8)

where K is the number of integrators in the memory and D is the memory depth (De Vries and Principe, 1992). Memory depth D is the temporal mean value of the last taps impulse response whereas memory resolution R is the number of parameters of freedom (i.e. memory state variables) per unit of time (Principe et al., 1994).

Gamma memory used in the dynamic network has four taps. Since the number of outputs equals number of inputs times number of taps: number of outputs = number of inputs × number of taps

(9)

the number of outputs in this case is 8. From Gamma memory signal is transferred to the first Function layer, then Weight layer and subsequently to the second Function layer. Function layers apply a function to their inputs and usually introduce non-linearity to the system. In the network used for analyzing PEO Coagulant matrices first Function layer has 8 inputs (which are outputs from Gamma memory) and 8 outputs. These outputs are transferred to 10 outputs in Weight layer (since there are 10 time intervals in drug release profile). The second Function layer elaborates 10 inputs to 10 outputs and sends them to Delta terminator. Both Function layers apply sigmoid function (Tan h sigmoid function specifically) as transfer function. Delta terminator compares two signals—one comes from the data source and represents real, observed outputs; whereas the second signal comes from the second Function layer and represents outputs predicted by the dynamic system. Data for C1–C10 formulations has been split into training and validation subset. Formulations C11 and C12 were used to test the system. It is important to emphasize that test data were not used for development of model. Software used in this study offers a variety of snippets—a predesigned partial topology from which complete adaptive system can be easily constructed. Dynamic snippets include: Gamma memory, Recurrent and Gamma–Recurrent hybrid snippet. Results showed that simple Recurrent One Layer dynamic network is the most adequate for analyzing F1–F12 formulations. Fig. 3 represents Recurrent One Layer network. Some of its elements are the same as in previously described Gamma memory network. From Data source 1 signals go to the first Weight layer. The first Weight layer has 2 inputs and 17 outputs. The number of outputs has been optimized using Monte Carlo simulations in the training mode of the program. Monte Carlo simulations are the simplest tools for optimization of different parameters and will be further described in more details. One Layer Recurrent network is a partially recurrent network since the recurrent connections are sent from hidden layer back to itself. In fully recurrent networks the output is sent back into the network. To make it possible to return signals into previ-

Fig. 2. Schematic representation of Gamma memory. Z−1 is a delay while  is an interpolation weight.  sums the inputs.

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Fig. 3. Representation of Reccurent One Layer dynamic neural network: (a) Peltarion® layout and (b) network’s schematic representation.

ous blocks in the topology it is necessary to have modified links used for channeling signals. If links are set up to have a memory then the order of the memory says how many time steps the signal will be delayed (default value is one time step, i.e. −1). If local feedback is constructed, which is the case in partial recurrent network studied here, interpolation capabilities become available. Mandatory memory is added as well as interpolation parameter, weight . Local feedback is always scaled with 1 − . In effect,  influences the extent to which second-order information influences the update of the signal processed (Becerikli and Oysal, 2007). In essence, recurrent network is similar to Gamma memory but there is one great difference—Gamma memory is a short-term memory whereas recurrent network is foundation for long-term memory structures. In time-lagged networks a short-term memory (i.e. memory filter) is incorporated. However, it is more useful for a network to discover, through its internal dynamics the long-term history of a series of events so that it does not have to depend on externally provided memory filters. Dynamically driven recurrent networks with feedback loops attempt to capture such long-term history in data. Over time, the network stores long-term memory structure in its feedback (recurrent) and regular connections, whose weights are adjusted during training (Samarasinghe, 2006). From the first Weight layer 17 outputs go to the first Function layer that has modified links and a feedback connection to itself. This is where the recurrence of the signals takes place. For each of the 17 outputs there is a separate feedback and default values for  are 0.5. 1 to 17 were optimized using Monte Carlo simulations (together with the number of outputs from the first Weight layer) making it possible to set up connections that can most adequately predict future states of the system. Monte Carlo optimizer is one of batch processors in the training mode of the software. Monte Carlo simulations are another name for random search. It is rather simple optimization algorithm that takes no assumptions about the problem studied (Robert and Casella, 2004). For simulations used to construct dynamic network the number of exemplars

and epochs was varied. In Monte Carlo optimizer exemplars refers to number of optimization passes whereas epochs stand for number of epochs per optimization pass. When one epoch passes the adaptive system has been presented with available data once. As adaptive systems are for most part trained iteratively many epochs are usually required to fully train a system. From the first, recurrent Function layer, signal goes to second Weight layer that has 17 inputs and 10 outputs (10 samplings for determining drug dissolution profile). From the second Weight layer signal goes to the second Function layer. The second Function layer is an ordinary Function layer (in comparison to the first Function layer). It has 10 inputs and 10 outputs and performs Tan h sigmoid function. The function of the Delta terminator is the same as in previously described topology. 2.2. Topology of static neural networks In order to evaluate results obtained using dynamic neural networks, built-in static neural network software architecture has been used. Multi-layer perceptron, typical feed forward artificial network, was employed for modeling drug release. MLP network layout is given in Fig. 4. Distinctive difference between MLP network and previously described dynamic networks is that there are no recurrent connections between elements, each input is analyzed independently. From Data source 1 signals go to the first Weight layer (with 2 inputs and 6 outputs) and first Function layer (with 6 inputs and 6 outputs). Function layer applies Tan h sigmoid function to input data and the number of outputs has been optimized using Monte Carlo simulations in the training mode of the program. From the first Function layer signal goes to second Weight layer (with 6 inputs and 10 outputs) and then to the second Function layer (10 inputs and outputs for 10 sampling points in dissolution time profile). The function of the Delta terminator is the same as in previously described topologies. Monte Carlo simulations were also used for variation in number of epochs used for training.

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Fig. 4. Representation of multi-layer perceptron neural network: (a) Peltarion® layout and (b) network’s schematic representation.

Determination of optimal training conditions for dynamic and static networks was done automatically by software. The progress of errors for both training and validation sets were monitored during training to decide when to stop the training. When there were no more changes in the training error or when the validation error started to diverge, the training was stopped. For all studied cases mean standard error did not exceed 2% which is acceptable value. Numbers of epochs varied during training of different networks, some networks were trained for up to 100 000 epochs in order to obtain minimal error. It is important to emphasize that networks were not over trained. 3. Results and discussion Dissolution of diclofenac sodium from formulations C1–C12 and F1–F12 shows dependency of drug release on fraction of polymer in the formulation as well as compression force used for tablets manufacturing. It is reasonable to expect that increase of the fraction of polymer and/or compression force leads to decrease of the drug release rate but it is not known, a priori, to which extent. Fig. 5 shows dissolution profiles of PEO 1105 and PEO Coagulant formulations. Formulations F1–F3 are not sustained release formulations since approximately 40% of diclofenac sodium has been released after 2 h. F4–F9 formulations exhibit sustained release with some unexpected profiles, especially formulation F9 is critical. It is curious that formulation with the highest fraction of PEO 1105 prepared with the highest compression force (formulation F9) releases diclofenac sodium so rapidly. Release of diclofenac sodium from PEO Coagulant matrices conforms to expected values—with increase of fraction of polymer and/or compression force drug release rate decreases. It is evident that C1–C9 are sustained release formulations.

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

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

Gamma memory network was presented with C1–C10 inputs and outputs. Fig. 6 shows capability of Gamma memory network to predict fraction of diclofenac sodium released in certain time point for two test formulations (C11 and C12). To further assess network’s capability of prediction, observed and predicted drug release profiles were plotted in Fig. 7 and difference and similarity factors were calculated. From the values for similarity and difference factors it can be concluded that dissolution profiles are similar meaning that dynamic network was successful in predicting drug release profile. When the same dynamic network was applied to predict drug release from PEO 1105 matrices the results were not so good. Experiments showed that dissolution of diclofenac sodium from PEO 1105 matrix tablets is irregular—increase of % (w/w) of polymer and/or compression force does not necessarily lead to decrease of drug release rate. This irregular dissolution could be the possible reason for failure of Gamma memory network to predict the release profile. Fig. 8 shows observed dissolution profiles for F11 and F12 test formulations as well as profiles predicted by Gamma memory dynamic network. It is clear that network is not adequate for predicting release profiles, especially for F11 formulation. That was the reason for further application of networks of different topology. When Recurrent One Layer network was applied to analyze F1–F12 formulations, there was improvement in capability of network to predict diclofenac sodium release profiles. In Fig. 9 one can see correlation between predicted and observed dissolution profiles for two test formulations F11 and F12. Correlation is strong between them and based upon this it could be concluded that models are appropriate for dissolution profiles predicting. Nevertheless, it is always recommended to calculate difference and similarity factors since they are far better indicators of potential similarity of dissolution profiles. Fig. 10 shows comparison of dissolution pro-

Fig. 7. Comparisson of dissolution profiles obtained in experiment and predicted by Gamma memory dynamic neural network for C11 and C12 test formulations: (a) f1 = 7.33 and f2 = 73.27 and (b) f1 = 4.12 and f2 = 78.20.

files obtained in experiment and predicted by Recurrent One Layer network. It is evident that prediction of dissolution profile for F11 formulation is still not satisfactory whilst prediction of profile for F12 formulation is much better compared to previous results. This is good example of how correlation coefficient can be misleading. In this case, experimental and predicted profiles for F11 formulation are strongly correlated (r2 = 0.993) but predicted profile is shifted from experimental in such a way that two almost parallel lines are obtained with significant differences in absolute values. It should be possible to use this model for predicting dissolution profiles keeping in mind that shifting of values could occur. One of the explanations for this phenomenon is that parameters of formulation F11 are such that it has properties of both immediate and modified release formulation. In these formulations there is relatively large amount of drug released in the first period of the dissolution test. Network could possibly better recognize these instances if it had been trained with more data. In practice, these crossover formulations are always avoided but it would be useful to have a possibility to predict them. Further research should be addressed in this direction—prediction of attributes of boundary system states. It is possible that more complex recurrent networks are needed for such investigations. When MLP static neural network was employed to model diclofenac sodium release from PEO Coagulant matrices it proved successful for one of the test formulations but not for the other: values for difference factors were 19.16 and 8.94 for formulations C11 and C12 respectively; values for similarity factors were 56.22 and 71.00 respectively. Even though MLP networks are highly appreciated because of the simplicity of their architecture this is a good example of possible lack of robustness when MLP networks are applied for drug release mod-

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Fig. 8. Comparison of dissolution profiles obtained in experiment and predicted by Gamma 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.

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

eling. This finding was also confirmed when MLP static network was employed to model diclofenac sodium release from PEO 1105 matrices. In this case, network’s prediction ability was not successful for any of the test formulations. Values for difference factors were 29.23 and 23.78 for formulations F11 and F12 respectively; values for similarity factors were 48.97 and 54.91 respectively. Drug release should be treated as a time series and it is evident that DNNs are appropriate tools for such analysis. Authors would also like to emphasize that prediction ability of dynamic networks is greater than mathematical modeling approach. Details of developed mathematical model for PEO matrices can be found in Petrovic et al. (2008) and when developed model is compared to predictions of dynamic network, advantages of dynamic networks are clear. 4. Conclusions

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

It has been demonstrated that DNNs are powerful, sophisticated tools for drug release characterization. The ability to accurately predict drug release profile using dynamic networks has been shown. Superiority of dynamic networks over static networks and other modeling approaches is also addressed. Dynamic networks are thus robust tools for drug release characterization. Constructing a network with appropriate topology can present an obstacle, but adequate software packages provide solutions. In terms of polyethylene oxide matrices, results presented here indicate that PEOs of higher molecular weights (such as PEO Coagulant) are better choice for controlled release dosage forms compared to PEOs with lower molecular weights. Formulations with PEO Coagulant required less % (w/w) of polymer to obtain sustained release profile

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and showed fewer variations and unpredicted results in comparison to PEO 1105 formulations. Acknowledgment This work was done under the project no. TR 23015 supported by the Ministry of Science and Technological Development, Republic of Serbia. References Aussem, A., 1999. Dynamical recurrent neural networks towards prediction and modeling of dynamical systems. Neurocomputing 28, 207–232. Becerikli, Y., Oysal, Y., 2007. Modeling and prediction with a class of time delay dynamic neural networks. Appl. Soft Comput. 7, 1164–1169. Bourquin, J., Schmidli, H., van Hoogevest, P., Leuenberger, H., 1998a. Comparison of artificial neural networks (ANN) with classical modeling techniques using different experimental designs and data from a galenical study on a solid dosage form. Eur. J. Pharm. Sci. 6, 287–300. Bourquin, J., Schmidli, H., van Hoogevest, P., Leuenberger, H., 1998b. Advantages of Artificial Neural Networks (ANNs) as alternative modeling technique for data sets showing non-linear relationships using data from a galenical study on a solid dosage form. Eur. J. Pharm. Sci. 7, 5–16. Bourquin, J., Schmidli, H., van Hoogevest, P., Leuenberger, H., 1998c. Pitfalls of artificial neural networks (ANN) modeling technique for data sets containing outlier measurements using a study on mixture properties of a direct compressed dosage form. Eur. J. Pharm. Sci. 7, 17–28. Chen, Y., McCall, T.W., Baichwal, A.R., Meyer, M.C., 1999. The application of an artificial neural network and pharmacokinetic simulations in the design of controlled-release dosage forms. J. Control. Release 59, 33–41. Chow, S.C., Ki, F.Y.C., 1997. Statistical comparison between dissolution profiles of drug product. J. Biopharm. Stat. 7, 241–258. De Gooijer, J.G., Hyndman, R.J., 2006. 25 years of time series forecasting. Int. J. Forecasting 22, 443–473. De Vries, B., Principe, J.C., 1992. Short term memory structures for dynamic neural networks. Conference Record of The Twenty-Sixth Asilomar Conference on Signals. Syst. Comput. 2, 26–28. Dimitrov, M., Lambov, N., 1999. Study of Verapamil hydrochloride release from compressed hydrophilic Polyox-Wsr tablets. Int. J. Pharm. 189, 105–111. Ghiassi, M., Nangoy, S., 2009. A dynamic artificial neural network model for forecasting nonlinear processes. Comput. Ind. Eng. 57, 287–297. Ghiassi, M., Saidane, H., Zimbra, D.K., 2005. A dynamic artificial neural network model for forecasting time series events. Int. J. Forecasting 21, 341–362. Goh, W.Y., Lim, C.P., Peh, K.K., Subari, K., 2002. Application of a recurrent neural network to prediction of drug dissolution profiles. Neural Comput. Appl. 10, 311–317. Haykin, S., 1999. Neural Networks—A Comprehensive Foundation. Prentice-Hall, New Jersey.

Hussain, A.S., Yu, X.Q., Johnson, R.D., 1991. Application of neural computing in pharmaceutical product development. Pharm. Res. 8, 1248–1252. Ibric, S., Jovanovic, M., Djuric, Z., Parojcic, J., Solomun, L., 2002. The application of generalized regression neural network in the modeling and optimization of aspirin extended release tablets with Eudragit® RS PO as matrix substance. J. Control. Release 82, 213–222. Kim, C.J., 1998. Effects of drug solubility. Drug loading and polymer molecular weight on drug release from Polyox® tablets. Drug Dev. Ind. Pharm. 24, 645–651. Murtoniemi, E., Yliruusi, J., Kinnunen, P., Merkku, P., Leiviskä, K., 1994. The advantages by the use of neural networks in modeling the fluidized bed granulation process. Int. J. Pharm. 108, 155–164. Panerai, R.B., Chacon, M., Pereira, R., Evans, D.H., 2004. Neural network modeling of dynamic cerebral auto regulation: assessment and comparison with established methods. Med. Eng. Phys. 26, 43–52. Peh, K.K., Lim, C.P., Quek, S.S., Khoh, K.H., 2000. Use of artificial neural networks to predict drug dissolution profiles and evaluation of network performance using similarity factor. Pharm. Res. 17, 1384–1388. Petrovic, J., Jockovic, J., Ibric, S., Parojcic, J., Djuric, Z., 2008. Mathematical modeling of diclofenac sodium’s release from polyethylene oxide matrices. Proceedings of the Tenth European Symposium on Controlled Drug Delivery. J. Control. Release 132, e44–e45. Principe, J.C., Jyh-Ming, K., Celebi, S., 1994. An analysis of the gamma memory in dynamic neural networks. IEEE Trans. Neural Networks 5, 331–337. Reis, M.A.A., Sinisterra, R.D., Belchior, J.C., 2004. An alternative approach based on artificial neural networks to study controlled drug release. J. Pharm. Sci. 93, 418–430. Robert, C.P., Casella, G., 2004. Monte Carlo Statistical Methods. Springer-Verlag, New York. Rowe, R.C., Roberts, R.J., 1998. Artificial intelligence in pharmaceutical product formulation: neural computing and emerging technologies. PSTT 1, 200–205. Samani, S.M., Montaseri, H., Kazemi, A., 2003. The effect of polymer blends on the release profiles of diclofenac sodium from matrices. Eur. J. Pharm. Biopharm. 55, 351–355. Samarasinghe, S., 2006. Neural Networks for Applied Sciences and Engineering. Auerbach Publications, New York. Shaw, A.M., Doyle III, F.J., Schwaber, J.S., 1997. A dynamic neural network approach to nonlinear process modeling. Comput. Chem. Eng. 21, 371–385. Sun, Y., Peng, Y., Chen, Y., Shukla, A., 2003. Application of artificial neural networks in the design of controlled release drug delivery systems. Adv. Drug Deliv. Rev. 55, 1201–1215. Turkoglu, M., Aydin, I., Murray, M., Sakr, A., 1999. Modeling of a roller-compaction process using neural networks and genetic algorithms. Eur. J. Pharm. Biopharm. 48, 239–245. Yang, L., Venkatesh, G., Fassihi, R., 1996. Characterization of compressibility and compatibility of poly(ethylene oxide) polymers for modified release application by compaction simulator. J. Pharm. Sci. 85, 1085–1090. Zupancic Bozic, D., Vrecer, F., Kozjek, F., 1997. Optimization of diclofenac sodium dissolution from sustained release formulations using an artificial neural network. Eur. J. Pharm. Sci. 5, 163–169.