Modelling Drying Time of Candesartan Cilexetil Powder Using Computational Intelligence Technique

The aim of this work was to use two computational intelligence techniques, namely, artificial neural network (ANN) and support vector regression (SVR), to model the drying time of a pharmaceutical powder Candesartan Cilexetil, which is used for arterial hypertension treatment and heart failure. The experimental data set used in this work has been collected from previously published paper of the drying kinetics of Candesartan Cilexetil using vacuum dryer and under different operating conditions. The comparison between the two models has been conducted using different statistical parameters namely root mean squared error (RMSE) and determination coefficient (R2). Results show that SVR model shows high accuracy in comparison with ANN model to predict the non-linear behaviour of the drying time using pertinent variables with {R2 = 0.9991, RMSE = 0.262} against {R2 = 0.998, RMSE = 0.339} for SVR and ANN, respectively.


Introduction
Different studies have been proposed recently in literature concerning the use of different drying technologies and equipment to preserve the final quality of diverse products such as pharmaceuticals. 1 The main objective of the drying process is to remove the impregnated humidity in the products to prevent any type of contamination and alleviate their weight to facilitate their transportation and caking. Taking into account that pharmaceutical powders are heat sensitive, the choice of an appropriate dryer depends on the properties of the powders. Numerous researchers have investigated the effect of diverse operating conditions, namely, vacuum pressure and temperature, on the drying time of various powders. [2][3][4] Since drying experiments are generally costly and tedious, the exact mathematical representation of such complex and highly non-linear behaviour of the drying phenomena, which is usually established based on a lot of hypothesis and multivariable interaction is difficult. Some computational models show their ability to alleviate above limitations and fit and control the drying processes accurately. 5,6 The use of artificial neural networks and support vector machines to model different governing parameters of the drying process of different products and dryers has gained growing interest. 7 For instance, ANNs have been used successfully to model the moisture content of quince slices, 8 also used to study the effect of different drying techniques on different types of root vegetables, 9 another ANN model predicts the dehydration kinetics of pineapple, 10 and an ANN has been used to optimise the drying process of kiwifruit slices in pulsed vacuum dry-ing. 11 In comparison to ANN modelling, SVR is known for its simplicity and optimisation adaptability and handling the complex parameters, 12 for instance, polynomial SVM was employed to estimate the experimental drying performance parameters, 13 also it was applied successfully to describe the drying kinetics of persimmon fruit (Diospyros kaki) during vacuum and hot air drying process. 14 To our knowledge, few works have been focused on modelling of quality indicators of pharmaceutical powders using machine learning techniques ANN and SVR. Therefore, the novelty of this work is to model the drying time of an active ingredient "Candesartan Cilexetil" using artificial neural networks and support vector regression.
2 Results and discussion

Design of experiments
The experimental data for vacuum oven drying kinetics of a thin-layer of active ingredient was reported in our previously published article. 1 MODDE software was used to schedule experiments and generate a second-order fitting model with optimised coefficients. The equation of the response surface methodology (RSM) can be written in the following form: Drying time (min) = 84.5402 − 10.679m 0 + + 0.7556X 0 + 61.2037p − 2.91914T + + 6.02469m 0 From this equation and based on the results found by response surface methodology (see Fig. 1), temperature is shown as the most influencing parameter on drying time. The accuracy of the three models was tested using R² and RMSE as expressed in the following equations: Fig. 2 depicts the observed response vs. the predicted response curve using the RSM model. Results showed that the RSM was found with an acceptable R² and RMSE of 0.9756 and 1.3293 respectively, which demonstrated the acceptable performance of the model to fit the drying time.

Artificial neural network (ANN) modelling
Artificial neural network methods might be employed to implement a non-linear modelling and provide a substitute to logistic regression. 15 The ANN model was designed with the multi-layer feed-forward network (MLP) type and trained with experimental data using back-propagation. The input parameters are initially selected based on system knowledge and availability of reliable data. Several stages are needed for the implementation of ANN in MATLAB software, details of these steps are shown in Fig. 3. The best ANN architecture was determined by optimisation of many parameters, such as the number of hidden layers and neurons, transfer function {tangent sigmoid Eq. (4), Log-sigmoid Eq. (5) and Linear}, number of iterations and network training algorithm {Levenberg-Marquardt, Bayesian regularisation}, as well as the convenient set of weights and biases. To avoid ANN divergence caused by the random initialisation of weights and biases, each ANN architecture was repeated twenty times. The number of neurons in the hidden layer was changed from 5 to 15 neurons. Moreover, three transfer functions were tested, and the best performance was obtained with {sigmoid, linear} transfer function for the hidden and the output layer, respectively. In addition, the ANN with more than one hidden layer was tested, and results showed no significant performance.
Two different types of transfer functions were employed in this work for the hidden layer, hyperbolic tangent sigmoid (named in MATLAB as tansig), log-sigmoid (named in MATLAB as logsig). These functions are defined in Eqs. 4 and 5, respectively. 16,17  This data set will be normalised between [−βγ, (1−β)γ] which leads to the stable convergence of network weights and biases by having all inputs with the same range of values and using premnmx/postmnmx function already programmed in MATLAB software expressed by the following equation: [18][19][20][21] In this work, β = 0.5 and γ = 2 were selected and the scaled values of each input were computed. Output descaling can be performed using the following expression:  Table 1 shows the performance of the ANN model versus the use of two different transfer functions in its hidden layer. The best ANN model was found with the architecture of {4-11-1} (see Fig. 4) neurons in the input, hidden, and output layer, respectively. In this work, tansig was found to be the best function in the hidden layer. The performance of ANN models is depicted in Fig. 5 where k, S, l, are the number of neurons in the input, output, and hidden layer, respectively. Wi (s,k) , Wo (l,s) are the weights, and b1 (s) , b2 (l) are the biases.

Support vector regression (SVR) modelling
Compared with traditional regression and neural networks methods, recently, SVRs have been considered as a powerful technique in solving the nonlinear regression problem, 22,23 the details of the theory and evolution of SVM developed by Vapnik's can be found in ref. 24 The advantages of SVRs are that they do not require a step similar to the selection of ANN topology, do not suffer from a high risk of local minima or overfitting, 25 are not sensitive to starting points, and require less data in comparison to the ANN. 26 The determination of the model depends on the optimization of several parameters, including capacity parameter C, ε-insensitive loss function ε, the kernel function type and its corresponding parameters. 27 The flowchart of modelling using SVM technique is presented in Fig. 6. 28,29 Many kernel functions have been tested and the Gaussian function shows its high capability of representing the complex and non-linear relation between the required drying time and its four operating conditions ( Table 2). The data set was scaled (X in ) based on the proposed expression in this work, which is given by equation Eq. (9): A scatter-plot between the observed against experimental data based on the SVM results is given in Fig. 7. Results show a satisfactory performance with high determination coefficient of 0.9991, and very low RMSE of 0.2616 min in comparison to the above models.  The optimisation of SVR parameters, namely, C, γ, and ε, was performed by varying them in the range of [10 −3 , 10 3 ], [10 −3 , 10 3 ], and [10 −9 , 10 −1 ], respectively. 30 The obtained best SVR parameters are given in Table 3.

SVR-based model versus ANN and RSM methodology
A comparison was performed using a bar plot of R² and RMSE of RSM, ANN, and SVR when estimating vacuum drying time. Figs. 8 and 9 clearly show the high accuracy of support vector regression model. Results confirm that the SVR model highly outsmarts the ANN and RSM with low RMSE of 0.2616 min, and high determination coefficient close to one.   Fig. 9 -Comparison between RSM, ANN, and SVM in terms of determination coefficient Fig. 10 shows that the data predicted by SVR model follow accurately the tendency of the experimental data, which again confirms the superiority of the SVR approach against ANN and RSM methodology.