Introduction

One of the most common non-malignant conditions in older men is benign prostatic hyperplasia (BPH) [1]. It indicates a non-cancerous growth of the prostate that occurs in old age. It has been estimated that a percentage of men over 60 years old (33%) have BPH. Nocturia, intermittent urinary retention, and kidney failure are symptoms of BPH [2]. Also, a higher percentage of this disease is assigned to men over 80 years old [3].

Groups of alpha-adrenergic antagonist drugs and 5-α-reductase inhibitors can be used to treat BPH. Tamsulosin (TAM) (Scheme 1a) as an alpha-adrenergic antagonist prevents the contraction of the smooth muscle of the prostate, which can decrease resistance to bladder neck contraction and urethra in men [4, 5]. Dutasteride (DTS) (Scheme 1b) is a 5a-reductase inhibitor, which is known as a type of anti-androgen. It is a selective inhibitor of both type 1 and type 2 of 5 α-reductase (5-AR) enzyme. DTS is prescribed for the treatment of BPH, as well as it can reduce the production of 5α-dihydrotestosterone (DHT) in the prostate gland [6,7,8]. These drugs are used alone or in combination with each other. The combination of these two drugs reduces the size of the prostate through various mechanisms. The prostate smooth muscle tone is decreased by α-blockers in the short-term and the prostate volume is reduced by 5ARIs over the long term [9].

Scheme 1
scheme 1

Chemical structure of a TAM and b DTS

Full size image

A literature survey indicates that some analytical techniques, including reversed-phase high-performance liquid chromatography (RP-HPLC) [10, 11], thin-layer chromatography (TLC) [12, 13], and liquid chromatography-tandem mass spectrometry (LC–MS-MS) [14] have been developed for simultaneous determination of TAM and DTS in different samples. However, chromatography techniques have several limitations, such as the need in long runtime or large sample volumes [15]. In addition, expensive sample pre-treatment processes and the usage of expensive analytical instrumentation, which are not available in all laboratories, are the other drawbacks of these methods [16]. Compared to the aforesaid methods, the colorimetric approach has become extremely attractive owing to its ease, simplicity, and inexpensive. Also, the response related to the colorimetry is easy to detect with the naked eye without any complicated instrumentation [17, 18].

Gold nanoparticles (AuNPs) have been widely used for colorimetric analysis due to their biocompatibility, great size and distance-dependent surface plasmon resonance (SPR) features, and high molar extinction coefficients, which could display visible color change via aggregation or growth of NPs, even at low concentrations [19,20,21]. The greatest benefit of AuNPs based on colorimetric detection is their changing color in various sizes, which leads to the recognition of diverse analytes. This procedure is based on the two-way approach: (1) the change in color from red to blue/purple can be observed during aggregation and (2) a change from blue/purple to red exists in separation. It can be said that there is a change in SRP peak absorption between the dispersed and aggregation modes of AuNPs, which causes color change [22].

The colorimetric method coupled with the chemometric approach can have good potential for the simultaneous quantification determination of drugs [23]. Artificial intelligence techniques can be useful, including radial basis function neural network (RBF-NN) and fuzzy inference system (FIS). The RBF-NN was represented by Broomhead and Lowe in 1988. It is known as an easy and flexible regression model, which can be introduced as a feedforward neural network (FF-NN) with one hidden layer [24]. One chemometric approach that possesses the potential to deal with an assessment of imprecise and uncertain data is fuzzy inference systems (FIS), which is superior to multi-criteria analysis (MCA) techniques [25].

In this study, a simple, fast, low-cost approach, without the need sample preparation process and expensive apparatus was proposed for the simultaneous determination of TAM and DTS in their binary mixtures in a scale of µg/L. The mentioned features are the advantages of the suggested method compared to the chromatographic techniques. This method is based on the synthesized AuNPs and their aggregation in the presence of the drug. RBF-NN and FIS as chemometrics methods were applied along with the colorimetric technique for solving overlap problem of components. Finally, RBF-NN and FIS were compared with the HPLC using the analysis of variance (ANOVA) test.

Theoretical background

RBF neural network

RBF-NN has a good performance, which includes three layers. The distribution of input to the nodes related to the hidden layer is performed using the input layer. The connection of each node with a center is evident in the hidden layer. The node dimension is equal to the number of input variables. A nonlinear transformation is performed with the hidden layer, and the mapping of the input space to a new high-dimensional space occurs with this layer. After setting the network weight, the generation of the output of the RBF-NN happens through the linear combination of hidden node responses. The RBF is the activation function of the hidden layer. It is a scalar function, which is described as a function of the radial distance between the data center and the sample. Mapping the low-dimensional nonlinear separable input into a high-dimensional linear separable space is done by the radial function. The response of the activation function of the hidden layer node to the input is local. The proximity of the input to the central range of the basis function leads to a larger output by the hidden layer node. Moving away from the center point decreases the output exponentially [26, 27].

FIS model

The FIS as a rule-based system includes three sections: (1) a rule base comprising a collection of fuzzy If–Then rules; (2) a database that describes the membership function (MF) related to the input–output variables; and (3) a reasoning process that sums the output from fuzzy rules to obtain a proper conclusion [28]. The input variables can be shown either as crisp values or a fuzzy set, while the output is generally presented as a fuzzy set. The defuzzification step is required to take decisions based on the FIS output in the fuzzy output. A nonlinear mapping between the input and output space in modeling mode can be facilitated using If–Then rules. The entire input–output space is divided into a number of local regions via fuzzy rules, and the local behavior of the nonlinear mapping is specified by each rule. Hence, the number of fuzzy rules determines the performance of FIS [25]. Two approaches, including Mamdani and the Takagi–Sugeno are defined for the FIS [29, 30]. There are three processes containing fuzzification of the input variables, logic decision, and defuzzification of the FIS output for the Mamdani method. There is no explicit defuzzification process in the Takagi–Sugeno method [25].

Materials and methods

Materials

Pure TAM (99.9%) was provided by Darou Pakhsh Pharma Chem Co. Pure DTS (99.9%) was prepared by Zahravi Co. Avolosin capsule (0.4 mg TAM and 0.5 mg DTS) was purchased from Tasnim Co. Ethanol, tetrachloroauric(III) acid trihydrate (HAucl4.3H2O), and trisodium citrate (Na3C6H5O7) were procured from Merck.

Preparation of AuNPs

0.0214 g of HAucl4.3H2O was dissolved in double-distilled water and made up to a volume of 100 mL in a volumetric flask. Then, the solution was transferred to a 250-mL Erlenmeyer flask and stirred with a magnetic stirrer at a rate of 400 rpm. At the same time, the solution was heated to boiling. While boiling, a watch glass containing some ice was placed on the Erlenmeyer flask to prevent the evaporation of the solution. After boiling, in 4 to 5 steps, 1 mL of trisodium citrate solution (1.1%) was added each time until the color change from light yellow to gray and then wine-red was observed. Heating and stirring continued for 10 min, and then the solution was cooled at room temperature. The obtained AuNPs were stored in dark containers at 4 °C and away from light. Different concentrations of AuNPs were prepared from the stock solution with a concentration of 5 × 10−4 mol/L.

Preparation of standard solution

0.1 g of pure TAM and DTS were dissolved separately in ethanol and made up to volume in a 100-mL volumetric flask. In order to prepare standard solutions with different concentrations, the dilution of the stock solutions of each component was done, and a certain amount of AuNPs was added to each of the solutions and adjusted to volume. Finally, the absorption of these solutions was recorded using T90 + double beam UV–visible from PG Instruments Ltd.

Preparation of mixtures

Various concentrations of TAM and DTS of stock solutions along with a certain amount of AuNPs were used to prepare eight mixtures to evaluate the validity of the RBF and FIS approaches. Afterward, their absorption was recorded.

Preparation of pharmaceutical sample

Ten tablets were weighed and powdered separately. Then, the average weight equivalent of one tablet (1.1 g) was dissolved in ethanol. The solution was placed in an ultrasonic device for 20 min to completely dissolve. Afterward, it was placed in a centrifuge at a rate of 400 rpm for 11 min and the supernatant was passed through filter paper. Then, it was transferred to a 100-mL volumetric flask and made up to the volume. A specific amount of AuNPs was added to the resulting solution, and its absorption was recorded under optimal conditions.

Chromatographic conditions

HPLC Agilent 1200 equipped with an ultraviolet (UV) detector at 274 nm was used to analyze the real sample. Chromatographic separation was conducted using a column Agilent zorbax SB-C18 (15 cm, 3.5 μm) with a temperature of 25 °C. The mobile phase consists of water and acetonitrile (30:70 v/v). Its flow rate was 1 mL/min. The injection volume was 20 μL.

Results and discussion

Characterization

In order to identify the structure and morphology of AuNPs and AuNPs in combination with the drug, TEM analysis (PHILIPS-CM120, Netherlands) was used. The spherical and well-dispersed state of AuNPs is shown in Fig. 1(a). After adding the drug, the aggregation of NPs can be observed (Fig. 1b). Dynamic light scattering (DLS) (MALVERN-ZEN3600, England) was applied to determine the particle size distribution of NPs before and after adding the drug. The average size was found to be 11.49 nm (Fig. 1c) and 122.1 nm (Fig. 1d) for AuNPs and AuNPs + drug, respectively. This increase in the size indicated that NPs were gradually aggregated in the presence of the drug.

Fig. 1
figure 1

TEM images of a AuNPs and b AuNPs + drug. DLS spectra in the c absence and d presence of drug

Full size image

Spectral characteristics

Figure 2 (a) exhibits the UV spectra of TAM (40 µg/mL) and DTS (25 µg/mL). Owing to the strong overlapping of both components, direct and simultaneous spectrophotometric determination of one component in the presence of the other one is not possible. Hence, RBF-NN and FIS methods were used to overcome this problem in the mixtures comprising TAM and DTS.

Fig. 2
figure 2

a The overlay spectrum of TAM and DTS and b UV–Vis spectra of AuNPs and AuNPs + drug

Full size image

The UV–Vis spectrum of synthesized AuNPs displays a SPR band at 524 nm (Fig. 2b). By adding the drug, the absorption intensity was diminished. On the other hand, a remarkable increase in peak wavelength (\(\lambda\) max) around 674 nm was observed. In addition, a color change from red to gray occurred due to the aggregation of AuNPs (Fig. 2b).

RBF-NN results

In this network, the input includes a matrix with a dimension of 401 × 8 containing absorbance of eight mixtures in the range of 400–800 nm. The actual (experimental) concentrations of TAM and DTS existing in the mixtures were considered as RBF-NN targets with a matrix dimension of 8 × 1. In order to write the RBF-NN in a MATLAB R2020b software environment, several parameters such as degree of freedom (df), goal, spread, and the number of neurons (nm) were selected. The degree of freedom was considered equal to 1 (df = 1) so that one neuron is added to the set in each epoch if the network error increases. The error of the network was chosen to be 0.5 (goal = 0.5) to assess the efficiency of the RBF model for predicting concentrations. The spread value was selected 0.9, which was in the range of absorption of mixtures. The “mn” value was 8 because of the eight mixtures made. After writing this program and run of this model, performance (mean square error (MSE)) versus epochs was separately plotted for each component (Fig. 3). Low MSE values (TAM = 1.033 × 10−25 and DTS = 2.854 × 10−26) reveal the high efficiency of this network for the prediction of concentration. The goodness-of-fit of predicted values vs. actual values can be studied using the coefficient of determination (R2) (Fig. 4). The R2 is a statistical measure of how close the predictions are to the actual data. An R2 equal to 1 was obtained for both components, indicating a perfect fit of regression predictions to the data. The non-scattering of the points indicates the closeness of the predicted values to the experimental values. Considering the lack of scattering of points, it can be said that the values obtained from the software are very close to the laboratory values. The accuracy of this model was determined using recovery percentage and mean recovery (Table 1). The percentage of recoveries showed up to 13 decimal digits in Excel software, which is reported here to two decimal digits. These values are close to 100, indicating the great accuracy of the RBF approach. Low root mean square error (RMSE) (Eq. 1) (TAM = 3.69 × 10−13 and DTS = 1.75 × 10−13) represented the high potential of this model for the prediction of concentrations.

$$\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}({y}_{\text{pred}}-{y}_{\text{obs}}{)}^{2}}{n}}$$
(1)

where the predicted and the actual values of the concentrations are shown by ypred and yobs, respectively; the number of mixtures is denoted by “n” [31].

Fig. 3
figure 3

MSE versus the number of epochs for TAM and DTS in RBF-NN model

Full size image
Fig. 4
figure 4

Predicted values (μg/L) versus actual values (μg/L) for TAM and DTS in RBF-NN model

Full size image
Table 1 Obtained recovery, mean recovery, and RMSE of TAM and DTS in RBF-NN model
Full size table

FIS results

In the first step, principal component analysis (PCA) was used to reduce the dimension of absorption of eight mixtures. Two dimensions were obtained, which write as input 1 and input 2 (Table 2). These two columns along with concentrations related to each component in mixtures were individually imported to the MATLAB environment. The Sogno system was applied to the data. Afterward, the Gaussian membership function (MF) was considered among various MFs (trapezoidal, triangular, etc.). The data were sorted from smallest to largest, which is shown on the peaks (Fig. 5). In addition, the sorting of concentration values of both components in eight mixtures was separately performed from small to large. In the next step, the rule of each MF (If–Then rule) was written (Table 3). For example, the second rule is stated as follows:

Table 2 The results obtained related to the absorption of eight mixtures by PCA method
Full size table
Fig. 5
figure 5

Gaussian membership functions related to the inputs of FIS model

Full size image
Table 3 If–Then rules of TAM and DTS in a FIS model
Full size table

If input 1 is equal to 5.32356180 and input 2 is equal to − 2.533441604, then the output will be equal to 200 and 50 μg/L for TAM and DTS, respectively. Other rules are also expressed in the same way. After entering the next stage, inputs were denoted by column 1 and column 2. The predicted concentration of each row (rule) was achieved via a run of this model. These predicted values are shown in the third column (Fig. 6). The value of fuzzy membership is exhibited by the yellow part under the Gaussian curve. The blue lines in the third column show the proximity of predicted values to experimental values.

Fig. 6
figure 6

The rule viewers for the prediction of TAM and DTS concentrations of FIS model

Full size image

R2 values of both components were determined to investigate the goodness of fit of this model (Fig. 7). R squared was found to be 0.9988 and 0.9978 for TAM and DTS, respectively. These results indicate a relatively good closeness of the predicted values to the actual values. As shown in Table 4, the acceptable range of recovery percentage (TAM = 96.5–101.25% and DTS = 98.00–106.00%) and mean recovery percentage (TAM = 99.15% and DTS = 101.76%) indicated appropriate accuracy of FIS model. Relatively low RMSE (TAM = 3.1425 and DTS = 3.1393) expresses the good performance of the proposed method.

Fig. 7
figure 7

Predicted values versus actual values of TAM and DTS in FIS model

Full size image
Table 4 Recovery, mean recovery, and RMSE of mixture analysis by FIS for both components
Full size table

The correlation between input 1, input 2, and output (concentration) is illustrated with a three-dimensional (3D) surface view (Fig. 8). These inputs possess an important role in the prediction of concentrations.

Fig. 8
figure 8

Surface view of correlation between input 1, input 2, and output in the FIS model for TAM and DTS

Full size image

Linear range of calibration curves

The change of color from red to blue related to the AuNPs-TAM and AuNPs-DTS solutions can be easily observed by the bare eyes (Fig. 9a). The calibration curves were obtained in a linear range of 50–200 μg/L for both components. The calibration equations of TAM and DTS were y = 0.0001x + 0.1591 with R2 = 0.9958 and y = 0.0008x + 0.1676 with R2 = 0.9912, respectively (Fig. 9b and c). The limit of detection (LOD) and limit of quantification (LOQ) were calculated using Eqs. (2) and (3), respectively.

$$\text{LOD} =3.3\sigma /S$$
(2)
$$\text{LOQ }=10\sigma /S$$
(3)

where, σ and S are the standard deviation of the response and the slope of the calibration curve, respectively [32]. LOD was obtained at 21.08 and 21.82 μg/L for TAM and DTS, respectively. Also, LOQ was found to be 66.12 and 63.90 μg/L for TAM and DTS, respectively.

Fig. 9
figure 9

a Photographs showing colorimetric images of AuNPs-drug with different concentrations of TAM and DTS 1: 0, 2: 50, 3: 80, 4: 100, 5: 150, 6: 200. b, c UV–Vis spectra and calibration curves of the AuNPs-TAM and AuNPs-DTS

Full size image

HPLC results

Analysis of the Avolosin capsule containing 0.4 mg TAM and 0.5 mg DTS was accomplished using the HPLC technique. Its chromatogram revealed that the retention time of DTS and TAM was 10.546 min and 19.128 min, respectively (Fig. 10).

Fig. 10
figure 10

Obtained chromatogram from the commercial formulation of Avolosin containing TAM and DTS

Full size image

Real sample analysis

The applicability of the suggested methods and HPLC was assessed by analyzing the pharmaceutical sample for the simultaneous determination of TAM and DTS (Table 5). The closeness of the values obtained by the proposed methods and the values on the label claim of the commercial capsule is clearly evident in the results. The mean recovery percentage of TAM for RBF and FIS was 96.91% and 94.08%, respectively, whereas the relative standard deviation (RSD) was lower than 1.5%. On the other hand, the mean recovery percentage of DTS was achieved at 96.33% and 95.06% for RBF and FIS, respectively, while RSD was < 1%. The precision of these methods was proved by the low RSD values. The obtained results demonstrated the potential applicability of these models for the concurrent estimation of TAM and DTS in real samples.

Table 5 Results of analyzing Avolosin by the proposed and reference methods (0.4 mg TAM and 0.5 mg DTS in pharmaceutical formulation)
Full size table

The results obtained from the RBF and FIS were compared with HPLC using the ANOVA test (Table 6). The smaller calculated F values (TAM: 0.489108 and DTS: 0.105180) proved the absence of significant differences between the methods.

Table 6 Statistical analysis using ANOVA test
Full size table

Comparison with other methods

A comparison between the results obtained by the present method and those achieved by other techniques for the simultaneous determination of TAM and DTS was given in Table 7. It can be stated that the colorimetric method has a good linear range, LOD, and LOQ compared to the obtained from the other approaches.

Table 7 Comparison of the proposed method with some of the previously reported methods for the simultaneous determination of TAM and DTS
Full size table

Conclusion

In this study, a novel and simple colorimetric method based on surface plasmon resonance along with chemometric methods (RBF and FIS) were developed for the simultaneous determination of two drugs (tamsulosin and dutasteride) in their pharmaceutical formulations using AuNPs. The synthesized AuNPs represented a colorimetric response upon exposure to the pharmaceutical formulation containing TAM and DTS, which was related to the SPR feature and aggregation of AuNPs. The aggregation of AuNPs induced by the drug was confirmed by TEM and DLS, which results in a change in absorption spectra (524 to 674 nm) and in color (red to gray). RBF-NN and FIS models produced accurate results, and the RSD was almost lower than 1% and 1.5% for RBF and FIS, respectively. This colorimetric approach revealed low LOD and LOQ for the TAM and DTS. It was successfully used to determine two drugs in the Avolosin capsule, which indicates that this proposed method possesses a high potential for the simultaneous detection of TAM and DTS in the pharmaceutical sample. In comparison with available analytical techniques for simultaneous estimation of TAM and DTS, the suggested method had some advantages, including needing smaller amounts of reagents, being easy, rapid, and inexpensive, and it does not require any costly apparatus.