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Inversely Calibrated Curvilinear Artificial Neural Network Model for Simultaneous Assay of Ternary Cardiovascular Drug Mixture

Novel chemometric design, tailored for pre-clinical multiple drug screening, goals for bioanalytical future scope. A highly sensitive, non-linear multivariate Artificial Neural Network (ANN) is developed and applied for simultaneous spectrophotometric determination of three commonly concomitant cardiovascular drugs in a laboratory made mixtures and spiked human plasma samples. Ticagrelor, Irbesartan, and Hydrochlorothiazide have been simultaneously quantified in the curvilinear ranges of 0-30 μg/mL, 0-10 μg/mL, and 0-3 μg/mL respectively. Highly overlapping Near UV absorption spectra of three drugs, in the region of 215-280 nm, have been recorded 1nm range in synthetic ternary mixtures and trained iteratively. By inversely relating the concentration matrix (xblock) with its corresponding absorption one (y-block), gradient-descent back-propagation ANN calibration could be computed and optimized. All proposed mathematical modeling was manipulated using MATLAB® 2007, reaching down to sixth order exponential Mean Square Error, MSE. To validate, an independent set of ternary synthetic mixtures has been constructed and examined, where excellent recovery results have been obtained. Furthermore, the application of the suggested model to varying ratios of synthetic ternary mixtures as well as spiked plasma samples has resulted in accurate, precise, and robust estimations with no background interference. ANN method was compared to a reference HPLC method; Student's t-test and F-variance ratio were calculated and showed the insignificant difference. This chemometric approach is an eco-friendly green assay, time-saving, and economic method. It initiates a pathway for clinical drug screening through affordable spectroscopic instrumentation.


INTRODUCTION
Although Spectrometric drug assays are still the most applicable in quality control laboratories, their application is highly limited at the demand of high sensitivity and resolving much complicated overlaps. Intelligent spectral data analysis is no longer welfare for analysts [1]. Statistical data analysis, artificial intelligence, mathematical optimization, and machine learning are core competencies of chemometric trials for drug analysis in multicomponent complex formulations [2, 3]. Besides, being ecofriendly and green methods [4], Artificial neural networks (ANNs) or connectionist systems work like human brains, collect joined units or nodes known as artificial neurons, which handle the neurons in the human brain. Each junction, like synapses in real brains, can send a signal to other neurons. In ANN manipulations, the "signal" is data and each neuro signal is calculated by nonlinear function [5].
ANN abilities, as a machine learning computational mathematical pattern, is classified a subcategory of; function approximation, regression analysis, data processing, classification, sequential decision making, and reaching robotics control. Predictive analytics by the ANN calibration model can be efficiently applied for non-linear relationships, quantitative analysis of complex pharmaceutical matrices, and highly overlapped spectral data. Yet unresolved data sets could be identified using ANNs [6,7]. ANNs have processed in vitro in vivo correlations [8,9]. Networks have also been applied to pharmacokinetic data sets [10] and different pharmaceutical drug combinations have been assayed by ANNs [11-13].
Antihypertensive treatment reduces the risk of cardiovascular infarctions. Recent cardiac guidelines recommend combination therapy, rather than monotherapy [14]. Antithrombic agents synergize with antihypertensive combinations for long term treatment [15]. Alternatively, screening for potential drug-drug interactions, contraindications, or both, and by making therapeutic recommendations aimed at achieving optimal response without increasing the potential for adverse drug reactions, especially among elderly patients and those with multiple medical conditions. High demand for accurate and sensitive analysis as well as being economic, affordable, and green one.

Thermo
Spectronic UV-Vis spectrophotometer connected to Harvest computer system was used. Absorption spectra were measured in 1-cm quartz cells. The absorbance data was displayed on EXCEL sheets and processed using MATLAB software.

Materials and Reagents
TICA was purchased from AstraZeneca. IRB and HCT were obtained from Accord-UK LTD, London.

Standard Solutions
Standard stock solutions, 100 µg/mL, of each of TICA, IRB, and HCT were separately and accurately prepared in ethanol. Different aliquots were micropippetted from each stock solution to form a set of 90 standard ternary mixtures. A wide range of drug concentrations was stated in each synthetic mixture as in Table 1.

Preparation of Spiked Plasma Samples
Plasma from the blood bank (Biuret, Lebanon) was purchased and kept at −20 °C. Gentle heating and shaking were required at the time of analysis. K3 EDTA was added for protein precipitation. Here, 400 μL of plasma samples were taken separately into a serial tube and vortexed for 3 min after being spiked with ternary mixture solution (in ethanol) at different concentration ratios. Then, the total amount of ethanol was brought to 1 mL by evaporation under a stream of nitrogen and vortexed for 3 min. The mixtures were centrifuged for 20 min at 4500 rpm, the supernatants were carefully separated using a Pasteur pipette and analyzed.

Construction of ANN Model
Modeling access related both the concentrations of the ternary drug mixture (TICA, IRB, and HCT) and their corresponding absorbance values, in a wide non-linear range, independent of Beer's law. As a start, the multivariate ternary model was constructed based on a training set; 90 mixtures of standard drugs, followed by ANN optimization through a predictive five-level three-factor design. These 135 sample mixtures were split into 90 training mixtures (for building the models) and 45 validation mixtures (for measuring the predictive power of the model). The concentration set; training set, of 90 synthetic mixtures containing TICA, IRB, and HCT in the concentration range of 0-30 µg/mL, 0-10 µg/mL, and 0-3 µg/mL, respectively in ethanol were prepared. Their absorption spectra (A; x-block, conc.; y-block) of the mixture set were plotted and recorded (66wavelength points) in the spectral range of 215-280 nm (Fig. 4).

ANN Optimization
Various topological networks were iteratively run for optimization. A training network of 120 neurons in the input layer, 50 neurons in hidden layers, and three outputs for the calibration and prediction steps was found to be suitable for the construction of ANN calibration for the simultaneous quantitative prediction of the three co-administrated drugs in laboratory prepared mixtures and spiked plasma samples.

Study for ANN Optimization parameters
Transfer function; it is chosen according to the nature of trained data. Being non-linear (A vs conc). Correlation, Log sigmoid activation function has been used for hidden and output layers.
Gradient descent training neural network has been backpropagated (Fig. 5). Thus, the mean square error, MSE, between the network output and the actual values was minimized.

Fig. 5. Training Plot of the proposed Artificial Neural Network
The learning rate initialized for the network was 0.5. The learning coefficient (Lc) masters the connection weights variation during the learning phase. Hidden neurons number (HNN) affected the convoluted performance of the output error function during the learning process.
Different training functions showed no significant difference in their performance (i.e. root mean square error of prediction (RMSEP) was not affected). M-training algorithm was chosen.
Iterative propagations were run to optimize regression of the targeted values versus the real outputs. As shown, Fig. 6 is an illustrative regression plot taken for one of these run propagations.

Fig. 6. Regression Plot of the proposed Artificial Neural Network
Upon application of an optimized calibration model, Mean Square Error (MSE) and network Epochs were correlated. The least MSE recorded a value of 1.49 x10 -6 as shown in the "Performance Plot" of the proposed network (Fig. 7).

Method Validation
To validate the predictability of the present model, ANN was run to estimate the concentration of three analytes in 45 synthetic mixtures (validation set) containing different ratios of drugs within the previously trained ranges.
Validation and training sets are independent. Satisfactory results have been obtained for all mixtures. Mean recovery results and relative standard deviations are shown in Table 2.

Analysis of Laboratory made mixtures
Laboratory made mixtures were prepared and analyzed by the proposed ANN method. The assay results revealed satisfactory accuracy and precision as indicated from % recovery, SD, and RSD % (Table 3). This table also represents a statistical comparison between the assay of TICA, IRB, and HCT in their synthetic mixtures by the proposed assisted ANN method and a developed HPLC method [35], using the student's t-test and the variance ratio F-test. Since the calculated t-and F-values for each drug did not exceed the theoretical ones [37,38], this indicated no significant difference between the applied methods for determination of the three drugs in a laboratory made mixtures.

Analysis of Spiked Plasma Samples
Absorbance data of ternary mixture (full scan), in three spiked human plasma samples, was applied to the ANN calibration model. Each sample was scanned for three successive times, satisfactory results were obtained (Table 4).

Conclusion
As it is known, analysts tend to use linear calibration systems. On the other hand, nonlinear calibration models are necessary for the spectral quantitative analysis of complex pharmaceutical matrices due to small deviations from linearity, some interactions due to excipients or interfering components, and the need for high sensitivity. The proposed method used a feed-forward back propagation neural network to predict blood serum concentration levels of TICA, IRB, and HCT in spiked plasma samples. The results of the study show that the neural network has the predictive capability and able to accurately predict drug concentration levels in spiked human plasma making it interchangeable tools for effectively estimating concentration levels. In addition to accuracy, the neural network application has the advantage of producing results empirically, without the need for developing statistical prediction models.