A method for detecting the concentration of acetaminophen and ascorbic acid when they coexist

Abstract

The present invention belongs to the field of electrochemical sensor detection and specifically relates to a method for detecting the concentration of acetaminophen and ascorbic acid when they coexist. The method comprises the following steps: 1: preparing a PBs / cMWCNTs / GCE sensor, mechanically polishing a planar glassy carbon electrode using aluminum oxide powder, ultrasonically cleaning the mechanically polished planar glassy carbon electrode in distilled water, dispersing carboxyl multi-walled carbon nanotubes in DMF and ultrasonically bath treating them, dropping a DMF / cMWCNTs suspension onto GCE and drying it under infrared light, placing the cMWCNTs / GCE electrochemical sensor in a mixed solution containing FeCl3, K3[Fe(cN)6], 0.1 mol / L KCl, and HCl, and preparing a PBs / cMWCNTs / GCE modified electrode using cyclic voltammetry; and 2: using the PBs / cMWCNTs / GCE modified electrode to detect the concentration of the acetaminophen and ascorbic acid mixed solution. The method has high measurement accuracy, simple operation, low cost, and high detection efficiency, and can achieve simultaneous detection of acetaminophen and ascorbic acid in a mixed solution.

Description

Technical Field

[0001] The invention belongs to the field of electrochemical sensor detection, and particularly relates to a concentration detection method when acetaminophen and ascorbic acid coexist. Background Art

[0002] Acetaminophen (AP) is a widely used over-the-counter drug that belongs to the analgesic and antipyretic class and is used to relieve mild to moderate pain and reduce fever. However, excessive intake of acetaminophen may lead to the accumulation of toxic metabolites, which in turn leads to kidney toxicity. Ascorbic acid (AA) is a water-soluble vitamin that is commonly used to supplement insufficient dietary intake. During the metabolism of ascorbic acid in the human body, most of it is metabolized and excreted through the liver. Long-term deficiency of ascorbic acid can lead to diseases such as scurvy.

[0003] Acetaminophen and ascorbic acid are often found in combination in some pharmaceutical formulations. Although these drugs are generally considered relatively safe and effective, they may interact when used simultaneously, potentially affecting their efficacy and safety. Therefore, simultaneous determination of acetaminophen and ascorbic acid is of great significance for both bulk drugs and drug products. Currently, analytical techniques for the analysis of these two mixed drugs include spectrophotometry, high-performance liquid chromatography, luminescence, and titration. However, these techniques require complex extraction procedures prior to detection, resulting in lengthy detection times and significant inconvenience for routine analysis of acetaminophen and ascorbic acid. Because both acetaminophen and ascorbic acid are electroactive compounds, they can be detected and quantified using functional electroanalytical sensors. Compared to other techniques, electrochemical sensing offers advantages such as speed, accuracy, sensitivity, and ease of operation, and can be used in complex samples. However, achieving simultaneous electrochemical detection of both acetaminophen and ascorbic acid is challenging due to the close oxidation potentials of acetaminophen and ascorbic acid in samples at typical electrodes, making it difficult to distinguish their electrochemical signal peaks. This interference between the two signals hinders their simultaneous electrochemical detection. Therefore, if a three-electrode electrochemical detection system could be used to simultaneously measure two or more substances in a mixed solution, it would effectively improve detection efficiency, reduce costs, and enhance accuracy. This would allow for better optimization of the combined effects of acetaminophen and ascorbic acid, minimizing harm to the human body. Summary of the Invention

[0004] The object of the present invention is to provide a detection method for acetaminophen and ascorbic acid in an interference environment.

[0005] A method for detecting the concentration of acetaminophen and ascorbic acid when they coexist, comprising the following steps:

[0006] Step 1: PBs / cMWCNTs / GCE sensor preparation

[0007] 1-1. A flat glassy carbon electrode was mechanically polished using aluminum oxide powder, and the mechanically polished flat glassy carbon electrode was ultrasonically cleaned in distilled water to obtain a GCE;

[0008] 1-2. Disperse carboxyl multi-walled carbon nanotubes in DMF and treat in an ultrasonic bath to obtain a DMF / cMWCNTs suspension;

[0009] 1-3. The DMF / cMWCNTs suspension was dropped onto GCE and dried under infrared light to obtain a cMWCNTs / GCE electrochemical sensor;

[0010] 1-4. The cMWCNTs / GCE electrochemical sensor was placed in a mixed solution containing FeCl3, K3[Fe(cN)6], 0.1 mol / L KCl and HCL, and a PBs / cMWCNTs / GCE modified electrode was prepared by cyclic voltammetry;

[0011] Step 2: Using the PBs / cMWCNTs / GCE modified electrode, the concentration of acetaminophen and ascorbic acid mixed solution was detected.

[0012] Preferably, the step 2 specifically includes the following steps:

[0013] 2-1. Using the PBs / cMWCNTs / GCE modified electrode, several groups of mixed solution samples with known acetaminophen and ascorbic acid concentrations were tested using three electrochemical methods: CV, DPV, and CA, to obtain detection data.

[0014] 2-2. Obtaining characteristic parameters from the detection data;

[0015] 2-3. Correlation analysis was performed between the extracted characteristic parameters and the concentrations of acetaminophen and ascorbic acid in the mixed solution using PCA to obtain strongly correlated characteristic parameters with a correlation coefficient greater than 0.9;

[0016] 2-4. Constructing an artificial neural network consisting of an input layer, a hidden layer, and an output layer, with the strongly correlated feature parameters described in step 2-3 as input to the artificial neural network;

[0017] 2-5. Train the artificial neural network constructed in step 2-4 to obtain a trained PCA-ANN model;

[0018] The PBs / cMWCNTs / GCE modified electrode was used to detect a sample solution with unknown concentrations of ascorbic acid and acetaminophen using the trained PCA-ANN model.

[0019] Preferably, in step 1-2, the amount of the carboxyl multi-walled carbon nanotubes is 5 mg, the amount of DMF is 10 mL, and the ultrasonic bath treatment time is 24 h;

[0020] In steps 1-3, the amount of the DMF / cMWCNTs suspension used is 3 μL.

[0021] Preferably, in steps 1-4,

[0022] The cyclic voltammetry was performed in a three-electrode electrochemical workstation, wherein the three electrodes included: a cMWCNTs / GCE electrochemical sensor as a working electrode, a platinum electrode as an auxiliary electrode, and a saturated Ag / AgCl as a reference electrode;

[0023] The cyclic voltammetry process includes: performing electrochemical polymerization at a scanning rate of 50 mV / s, a potential range of -0.2 to 1.3 V, and performing 10 cycles of cyclic scanning.

[0024] Preferably, in steps 1-4, the cMWCNTs / GCE electrochemical sensor is placed in a mixed solution containing 0.02 mol / L FeCl3, 0.02 mol / L K3[Fe(cN)6], 0.1 mol / L KCl and 0.01 mol / L HCL.

[0025] Preferably, in step 2-1, the step of testing several groups of mixed solution samples of known acetaminophen and ascorbic acid concentrations to obtain test data comprises:

[0026] Prepare 0.1mM, 0.2mM, 0.4mM, 0.6mM, 0.8mM and 1.0mM acetaminophen sample solutions; prepare 1mM, 2mM, 4mM, 6mM, 8mM and 10mM ascorbic acid sample solutions; cross-mix the 6 concentrations of acetaminophen solution with the 6 concentrations of ascorbic acid solution in sequence to obtain 36 mixed test sample solutions; use CV, DPV and CA methods to repeat the test for each mixed solution sample 10 times, and obtain a total of 360 sets of test data. In step 2-2, the characteristic parameters are as follows:

[0027]

[0028]

[0029] In the steps 2-3, the characteristic parameters strongly correlated with the concentration of acetaminophen are: Icv_o_ap, Icv_r_ap, Kcv_o_ap, Kcv_r_ap, Vs_cv_aa, Vs_cv_o_ap, Vs_cv_r_ap, Idpv_ap, Ve_dpv_ap and I_ca; the characteristic parameters strongly correlated with the concentration of ascorbic acid are: Icv_aa, Kcv_aa, Vs_cv_aa, Vs_cv_o_ap and Vs_cv_r_ap, Idpv_aa, Vdpv_aa, Vdpv_ap, Vs_dpv_aa, Vs_dpv_ap and I_ca.

[0030] Preferably, the step 2-4 of constructing an artificial neural network consisting of an input layer, a hidden layer, and an output layer comprises the following steps:

[0031] 2-4-1. The input layer is an n-dimensional vector P composed of feature parameters 1×N , calculated and outputted by the hidden layer to obtain the result variable Y out , where the input variable x i ∈P 1×N , output variable Y out ∈P 1×1 ;

[0032] 2-4-2. The hidden layer has M neurons and the weight matrix w∈P M×N Responsible for connecting the input layer and the hidden layer neurons, in between which a bias unit b0∈P is required 1×M , then the hidden layer neurons receive the vector γ as:

[0033] γ=xw T +b0 (1)

[0034] Then the hidden layer neurons need to calculate the activation function, as shown below

[0035] γ′=σ(γ) (2)

[0036] 2-4-3. The hidden layer neurons need to be multiplied by the weight matrix θ to the output layer, and then add the bias unit b1, and the output concentration value Y out That is:

[0037] Y out =σ(z)θ+b1 (3)

[0038] The input-output relationship finally established by the artificial neural network is:

[0039] Y out =σ(xw T +b)θ+b1 (4)

[0040] The neural network can obtain the above-mentioned network parameters such as w, b, θ through BP back propagation training;

[0041] 2-4-4. Each layer of neurons uses Levenberg-Marquardt optimized Bayesian regularization to train the BP network function, as shown in the following formula

[0042] J′e=(J T J+μI m )δ (5)

[0043] Where J is the Jacobian matrix, the first-order derivative of the J matrix to the network error is represented by J′e, and J T is the transpose of matrix J, the Levenberg damping factor is defined by μ, and I m is the identity matrix, and δ is the update vector variable;

[0044] Then, the loss function is obtained by comparing the network forward propagation output with the true value, as shown in the following formula:

[0045]

[0046] Taking partial derivatives of the neural network parameters in turn, we get the following formula

[0047]

[0048] Then update the model parameters as shown below

[0049]

[0050] Where r is the learning rate of the neural network, which affects the training speed and quality of the ANN.

[0051] Preferably, in steps 2-4, the number of neurons in the input layer is 11, two hidden layers are used, each with 4 neurons, and the output layer has 1 neuron.

[0052] Preferably, in steps 2-5, the learning rate of the training is 0.0005, the regularization parameter is 0.001, and the loss function is a square error loss function.

[0053] Beneficial effects of the present invention:

[0054] 1. The present invention is based on the three-electrode detection principle. By modifying the electrode and using machine learning methods, a single electrode can be used to simultaneously detect acetaminophen and ascorbic acid in a mixed solution. The present invention has high measurement accuracy, R 2The detection accuracy is 99.4%, the root mean square error is 0.259 mM, and the mean absolute error is 0.222 mM. The method has the advantages of simple operation, low cost, and high detection efficiency, and can realize the simultaneous detection of acetaminophen and ascorbic acid in a mixed solution.

[0055] 2. Compared with the prior art, the present invention has simple and quick electrode modification, low modification cost, fast response, small size, can effectively separate the oxidation peaks of acetaminophen and ascorbic acid, has high measurement accuracy, and is conducive to the simultaneous detection of acetaminophen and ascorbic acid.

[0056] 3. The present invention realizes the simultaneous detection of acetaminophen and ascorbic acid based on an electrochemical detection system, improves the balance of data by combining voltammetry and amperometry, and reduces the accidental error of a single method.

[0057] 4. The present invention is based on the detection results of simultaneous detection of acetaminophen and ascorbic acid. There is severe nonlinearity between the peak current and the concentration of the mixed solution. The strongly correlated characteristic parameters are extracted by PCA to train and predict the artificial neural network, achieving a prediction accuracy of more than 99% for the concentrations of acetaminophen and ascorbic acid in the mixed solution.

[0058] 5. The present invention is based on the principle of simultaneous detection of acetaminophen and ascorbic acid. It can not only be used for the decoupled analysis of acetaminophen and ascorbic acid, but also expands the applicability of traditional electrochemical methods in multi-component detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the workflow of the present invention;

[0060] Figure 2 Cyclic voltammograms of acetaminophen (0.6 mM) and ascorbic acid (4.0 mM) mixed solutions on bare GCE (a), cMWCNTs / GCE (a), and PBs / cMWCNTs / GCE (a);

[0061] Figure 3 CV responses of different concentrations of acetaminophen (0.1, 0.2, 0.4, 0.6, 0.8, and 1.0 mM) on PBs / cMWCNTs / GCE, and the linear relationship between CV oxidation peak current and acetaminophen concentration;

[0062] Figure 4 CV responses of different concentrations of ascorbic acid (1, 2, 4, 6, 8, and 10 mM) on PBs / cMWCNTs / GCE, and the linear relationship between CV oxidation peak current and ascorbic acid concentration;

[0063] Figure 5is the DPV response of different concentrations of acetaminophen (0.1, 0.2, 0.4, 0.6, 0.8 and 1.0 mM) on PBs / cMWCNTs / GCE, and the linear relationship between the DPV response peak current and the acetaminophen concentration;

[0064] Figure 6 is the DPV response of different concentrations of ascorbic acid (1, 2, 4, 6, 8, and 10 mM) on PBs / cMWCNTs / GCE, and the linear relationship between the DPV response peak current and the ascorbic acid concentration;

[0065] Figure 7 Figure 2 shows the CA response of PBs / cMWCNTs / GCE to different concentrations of acetaminophen (0.1, 0.2, 0.4, 0.6, 0.8, and 1.0 mM). The inset shows the linear relationship between the current value and the square root of time in the chronoamperometric detection data, and the relationship between acetaminophen concentration and I and t. -1 / 2 The linear relationship between the slopes of

[0066] Figure 8 Figure 2 shows the CA response of PBs / cMWCNTs / GCE to different concentrations of ascorbic acid (1, 2, 4, 6, 8, and 10 mM). The inset shows the linear relationship between the current value and the square root of time in the chronoamperometric detection data, and the relationship between ascorbic acid concentration and I and t. -1 / 2 The linear relationship between the slopes of

[0067] Figure 9 is the PCA of the characteristic parameters of the electrochemical detection curve and the acetaminophen concentration, and the PCA of the characteristic parameters of the electrochemical detection curve and the ascorbic acid concentration;

[0068] Figure 10 The following are the relationship plots between the predicted concentration of acetaminophen and the actual concentration of acetaminophen by the PCA-ANN model, and the relationship plots between the predicted concentration of ascorbic acid and the actual concentration of ascorbic acid by the PCA-ANN model;

[0069] Figure 11 It is the PCA-ANN model network structure; DETAILED DESCRIPTION

[0070] The simultaneous detection of ascorbic acid and acetaminophen is further described in detail below with reference to the accompanying drawings and specific implementation examples:

[0071] The following are the English-Chinese translations of some of the names used below: Prussian blue / multi-walled carbon nanotubes / glassy carbon (PBs / cMWCNTs / GCE), dimethylformamide (DMF), cyclic voltammetry (CV), differential pulse voltammetry (DPV), chronoamperometry (CA), Pearson correlation coefficient (PCA), correlation coefficient (R 2), root mean square error (RMSE), and mean absolute error (MAE).

[0072] Example 1

[0073] Step 1: Preparation and characterization of PBs / cMWCNTs / GCE sensors.

[0074] 1-1. A flat glassy carbon electrode was mechanically polished using aluminum oxide powder and ultrasonically cleaned in distilled water.

[0075] 1-2. Disperse 5 mg of carboxyl multi-walled carbon nanotubes in 10 mL of DMF and ultrasonicate for 24 h to form a uniform suspension.

[0076] 1-3. Take 3 μL of DMF / cMWCNTs suspension and drop it on GCE. Dry it under infrared light to construct a cMWCNTs / GCE electrochemical sensor.

[0077] 1-4. The cMWCNTs / GCE was placed in a mixed solution containing 0.02 mol / L FeCl3+0.02 mol / L K3[Fe(cN)6]+0.1 mol / L KCl+0.01 mol / L HCl. Electrochemical polymerization was performed at a scan rate of 50 mV / s in the potential range of -0.2 to 1.3 V. The cyclic scanning treatment was repeated for 10 cycles to obtain a PBs / cMWCNTs / GCE modified electrode.

[0078] 1-5. Prepare acetaminophen solutions, ascorbic acid solutions and mixed solutions of different concentrations, and characterize the electrochemical behaviors of acetaminophen and ascorbic acid on different electrodes.

[0079] 1-5-1. Prepare 0.1 mM, 0.2 mM, 0.4 mM, 0.6 mM, 0.8 mM and 1.0 mM acetaminophen sample solutions.

[0080] 1-5-2. Prepare 1 mM, 2 mM, 4 mM, 6 mM, 8 mM and 10 mM ascorbic acid sample solutions.

[0081] 1-5-3. Six concentrations of acetaminophen solutions and six concentrations of ascorbic acid solutions were cross-mixed in sequence to obtain 36 mixed test sample solutions.

[0082] 1-5-4. Each mixed solution sample was tested 10 times using the CV, DPV and CA methods, and a total of 360 sets of test data were obtained.

[0083] 1-5-5. Record the changes in the oxidation peak spacing, peak potential and oxidation peak current of ascorbic acid and acetaminophen on the three modified electrodes to prepare for the subsequent signal decoupling analysis.

[0084] 1-5-6. Cyclic voltammetry was performed in a mixed solution of 0.6 mM acetaminophen and 4.0 mM ascorbic acid using three working electrodes: GCE, cMWCNTs / GCE, and PBs / cMWCNTs / GCE. The scan rate was 50 mV / s. The electrochemical curves are shown in Figure 1-5-6. Figure 2 On the unmodified glassy carbon electrode, the voltammetric responses of ascorbic acid and acetaminophen partially overlapped, with a small peak spacing, making it difficult to distinguish the two. However, when using PBs / cMWCNTs / GCE, the cyclic voltammetric response observed that the oxidation peak potentials of ascorbic acid and acetaminophen were clearly separated, and their oxidation peak currents were significantly enhanced, with the peak shapes becoming sharp, narrow, and high.

[0085] 1-6. Electrochemical detection of acetaminophen and ascorbic acid separately using PBs / cMWCNTs / GCE sensor.

[0086] 1-6-1. CV detection was performed on acetaminophen sample solutions and ascorbic acid sample solutions with six different concentrations in the potential range of -0.2 to 0.8 V at a scan rate of 0.1 V / s.

[0087] 1-6-2. Observe the CV result curve of acetaminophen (such as Figure 3 a), each CV curve has a redox peak pair, where the oxidation peak is at 271mV and the reduction peak is at about 349mV, and the peaks become larger with increasing concentration. Determine the positions of the oxidation peaks and reduction peaks for 6 concentration gradients. Determine the relationship between the acetaminophen concentration and the oxidation peak current value within the six concentration gradients, and perform regression fitting (such as Figure 3 b), the linear regression equation is Ipa (μA) = 58.76C (mM) + 9.15, and the correlation coefficient is R 2 =0.992.

[0088] Observe the ascorbic acid CV result curve (such as Figure 4 a), it can be seen from the figure that ascorbic acid does not have a reduction peak. The oxidation peak current of the cyclic voltammetry curve increases with the increase of ascorbic acid concentration, and the ascorbic acid concentration is linear with the oxidation peak current value. Do regression fitting (such as Figure 4 b), the linear regression equation was I (μA) = 25.4C (mM) - 25.6, and the correlation coefficient R 2 =0.994.

[0089] 1-6-3. DPV tests were performed on acetaminophen sample solutions and ascorbic acid sample solutions of six different concentrations in the potential range of -0.2 to 0.8 V, amplitude of 0.05 V, and pulse width of 0.05 s.

[0090] 1-6-4. Observe the DPV curve of acetaminophen (such as Figure 5 a) Determine the position of the oxidation peak. A clear oxidation peak can be observed at approximately 315 mV. The current of this peak gradually increases with the increase of acetaminophen concentration. Determine the relationship between acetaminophen concentration and oxidation peak current value, and perform regression fitting (such as Figure 5 b), the linear regression equation is Ipa (μA) = 55.7C (mM) + 19.0, and the correlation coefficient is R 2 =0.971.

[0091] Observe the ascorbic acid DPV result curve (such as Figure 6 a), the peak value of the oxidation peak corresponding to the oxidation of ascorbic acid appears at about 20mV, and the peak current is proportional to the ascorbic acid concentration. Figure 6 b), the linear regression equation was I(μA)=8.53C(mM)+3.21, and the correlation coefficient R 2 =0.994.

[0092] 1-6-5. At a potential of 0.6 V and a running time of 30 s, CA detection was performed on six acetaminophen sample solutions and ascorbic acid sample solutions with different concentrations.

[0093] 1-6-6. Observe the acetaminophen CA result curve (such as Figure 7 a) When the response current decreases and reaches a steady state, the Cottrell equation (as shown below) is used.

[0094]

[0095] Calculate the diffusion coefficient of acetaminophen on the modified electrode and determine the current value and t -1 / 2 The linear fitting diagram (such as Figure 7 a illustration). And determine the slope t -1 / 2 The fitting diagram of acetaminophen concentration I (such as Figure 7 b), the linear regression equation is Slope(μAs 1 / 2 )=6.85C(mM)+3.30, correlation coefficient R 2 =0.990.

[0096] Observe the ascorbic acid CA result curve (such as Figure 8 a) In the early stage of the chronoamperometric response to ascorbic acid, the response current is large, and then the current gradually decreases and reaches a steady state. When the response current decreases and reaches a steady state, determine the slope t obtained by plotting -1 / 2 The fitting diagram of acetaminophen concentration I (such as Figure 8 b), the linear regression equation is Slope(μAs 1 / 2)=6.43C(mM)-0.51, correlation coefficient R 2 =0.997. The diffusion coefficient of ascorbic acid on PBs / cMWCNTs / GCE was calculated using the Cottrell equation to be 2.36×10 -5 cm 2 s -1 .

[0097] Step 2: Prediction of the concentration of acetaminophen and ascorbic acid mixed solution.

[0098] 2-1. 36 groups of mixed solution samples were tested 10 times using the three electrochemical methods of CV, DPV, and CA, and a total of 360 sets of test data were obtained.

[0099] 2-2. Feature extraction of 360 sets of original data is performed as follows:

[0100]

[0101]

[0102] 2-3. Use PCA to analyze the correlation between the extracted characteristic parameters and the concentration of the mixed solution, and take the characteristic parameters with strong correlation (such as Figure 9 a. Figure 9 b).

[0103] 2-3-1. PCA can be used to measure the degree of linear relationship between two variables. Therefore, it can be used to describe the correlation between the extracted feature parameters and the solution concentration, generate a correlation matrix, and remove irrelevant and redundant features from the original data set. Before calculating the correlation based on PCA, the feature set is normalized. For the feature vectors X and Y, the Pearson correlation calculation expression is:

[0104]

[0105] Among them, X i Indicates the value of X under sample i, Y i It represents the value of Y under sample i. The larger the absolute value of COR, the stronger the correlation between the two variables.

[0106] 2-3-2. PCA can reduce the dimensionality of input variables by eliminating some correlated variables that are unimportant to the estimated results. Using an orthogonal transformation matrix, the original data is transformed into a projection matrix by generating a combination of linear correlation numbers between each input variable. Correlation numbers are composed of eigenvalues ​​and eigenvectors that contain a large amount of information about the original data. If a variable has a large eigenvalue, it has a greater impact on the model output, and vice versa. The mathematical objective function of principal component analysis is expressed by the following equation:

[0107] PC i =v i x (13)

[0108] Among them, PC i is the i-th PC, the matrix of the original input data is represented by x, v i The covariance matrix of x is the coefficient of x. jk ) can be calculated by the following method

[0109]

[0110] In this expression, and are samples x ij and x ik The mean of , l is the length of the vector data.

[0111] 2-3-3. Because Icv_o_ap, Icv_r_ap, Kcv_o_ap, Kcv_r_ap, Vs_cv_aa, Vs_cv_o_ap and Vs_cv_r_ap in the cyclic voltammetry curve, Idpv_ap and Ve_dpv_ap in the differential pulse voltammetry curve, and I_ca in the chronoamperometry curve have a high correlation with the acetaminophen concentration; Icv_aa, Kcv_aa, Vs_cv_aa, Vs_cv_o_ap and Vs_cv_r_ap in the cyclic voltammetry curve, Idpv_aa, Vdpv_aa, Vdpv_ap, Vs_dpv_aa and Vs_dpv_ap in the differential pulse voltammetry curve, and I_ca in the chronoamperometry curve have a high correlation with the ascorbic acid concentration, the above characteristics are retained.

[0112] 2-4. Construct an artificial neural network consisting of an input layer, a hidden layer, and an output layer.

[0113] 2-4-1. The input layer is an n-dimensional vector P composed of feature parameters 1×N , calculated and outputted by the hidden layer to obtain the result variable Y out , where the input variable x i ∈P 1×N , output variable Y opt ∈P 1×1 .

[0114] 2-4-2. The hidden layer has M neurons and the weight matrix w∈P M×N Responsible for connecting the input layer and the hidden layer neurons, in between which a bias unit b0∈P is required 1×M , then the hidden layer neurons receive the vector γ as:

[0115] γ=xwT +b0 (15)

[0116] Then the hidden layer neurons need to calculate the activation function, as follows

[0117] γ′=σ(γ) (16)

[0118] 2-4-3. The hidden layer neurons to the output layer also need to be multiplied by the weight matrix θ, and then add the bias unit b1, and the output concentration value Y out That is

[0119] Y out =σ(z)θ+b1 (17)

[0120] The input-output relationship finally established by the artificial neural network is:

[0121] Y out =σ(xw T +b)θ+b1 (18)

[0122] The neural network can obtain the above-mentioned network parameters such as w, b, θ through BP (Back Propagation) back propagation training.

[0123] 2-4-4. The BP back propagation algorithm propagates the error back from the output to the input layer, calculates the contribution of each neuron's weight to the error, and then updates the weight and bias value of each neuron through the gradient descent algorithm. In order to optimize and evaluate the output, each layer of neurons uses Levenberg-Marquardt optimized Bayesian regularization to train the BP network function, as shown below

[0124] J′e=(J T J+μI m )δ (19)

[0125] Where J is the Jacobian matrix, the first-order derivative of the J matrix to the network error is represented by J′e, and J T is the transpose of matrix J, the Levenberg damping factor is defined by μ, and I m is the identity matrix, and δ is the update vector variable.

[0126] Then, the loss function is obtained by comparing the network forward propagation output with the true value, as shown below:

[0127]

[0128] Taking partial derivatives of the neural network parameters in turn, we get the following formula

[0129]

[0130]

[0131] Then update the model parameters by

[0132]

[0133] Where r is the learning rate of the neural network, which affects the training speed and quality of the ANN.

[0134] 2-5. In the PCA-ANN model, the number of system inputs is only the PCs from the PCA output. Figure 11 The figure shows the network structure of the PCA-ANN model. The extracted feature parameter dataset was divided into training and test sets with an 8:2 ratio. In a multilayer perceptron, the feature parameter dimension is the number of input neurons. Two hidden layers were selected, each with four neurons, and the output layer had one neuron. The artificial neural network model was trained multiple times with a learning rate of 0.0005, a regularization parameter of 0.001, and a squared error loss function. The trained PCA-ANN model was used to predict the concentration of a sample solution with unknown ascorbic acid and acetaminophen concentrations.

[0135] 2-6. In the ANN model, when the concentrations of ascorbic acid and acetaminophen are unknown, the ANN model can predict the concentration of acetaminophen solutions in the concentration ranges of 0.1mM, 0.2mM, 0.4mM, 0.6mM, 0.8mM and 1.0mM, and the concentration of ascorbic acid samples in the concentration ranges of 1mM, 2mM, 4mM, 6mM, 8mM and 10mM.

[0136] 2-7. The ANN model predicts the concentration of acetaminophen on the data set without PCA feature selection. The prediction accuracy of the ANN model is 96.2% (R 2 =0.962), RMSE and MAE were 0.054 mM and 0.043 mM, respectively. Figure 10 a shows the prediction results of the ANN model on the data set with PCA feature selection. The predicted values ​​of acetaminophen concentration have a higher fit with the calibration values. The prediction accuracy of the PCA-ANN model is 99.1% (R 2 =0.991), RMSE was 0.033mM, and MAE was 0.028mM. When PCA feature selection was performed, RMSE and MAE values ​​were reduced by 0.021mM and 0.015mM, respectively. When the concentrations of ascorbic acid and acetaminophen were unknown, the concentrations of 1mM, 2mM, 4mM, 6mM, 8mM and 10mM ascorbic acid samples were predicted by the ANN model, and the differences between the predicted concentrations and the calibrated concentrations were compared (e.g. Figure 10b), it can be seen that when PCA feature selection is performed, the RMSE and MAE values ​​are reduced by 0.224mM and 0.093mM respectively.

[0137] The present invention is a comprehensive application of electrochemical detection and machine learning algorithms in the simultaneous detection of acetaminophen-ascorbic acid mixed solutions. It is mainly divided into three parts: electrode modification, experimental data acquisition, and data decoupling. First, a conventional three-electrode electrochemical detection system is selected, with a glassy carbon electrode as the working electrode, a platinum electrode as the auxiliary electrode, and saturated Ag / AgCl as the reference electrode; a multi-walled carbon nanotube dispersion is used to construct a cMWCNTs / GCE electrode by a drop coating method, and then the cMWCNTs / GCE is placed in a solution containing 0.02moL / L FeCl3+0.02moL / L K3[Fe(cN)6]+0.1moL / L KCl+0.01moL / L The working electrode surface was modified by electrochemical deposition in a mixed solution of HCL to obtain a PBs / cMWCNTs / GCE modified electrode; then 36 groups of mixed solutions of acetaminophen and ascorbic acid with different concentrations were tested separately by cyclic voltammetry, differential pulse voltammetry and chronoamperometry; by extracting features from the electrochemical curves of acetaminophen solutions and ascorbic acid solutions with known concentrations and establishing a regression fitting relationship, it was demonstrated that the concentrations of acetaminophen and ascorbic acid were linearly related to the peak current; by extracting features from the electrochemical curves of mixed solutions of acetaminophen and ascorbic acid with unknown concentrations, and using PCA to eliminate low-correlation and redundant feature parameters, the ANN model was used for prediction to obtain the concentrations of acetaminophen and ascorbic acid, respectively, with a prediction accuracy of over 99%.

[0138] Example 2

[0139] Step 1: Preparation of PBs / cMWCNTs / GCE sensor.

[0140] Step 2: Prepare acetaminophen solutions, ascorbic acid solutions, and mixed solutions of acetaminophen and ascorbic acid at different concentrations to characterize the electrochemical behaviors of acetaminophen and ascorbic acid at different electrodes.

[0141] Step 3: Electrochemical detection of acetaminophen and ascorbic acid separately.

[0142] Step 4: Prediction of the concentration of acetaminophen and ascorbic acid mixed solution.

[0143] Furthermore, the step 1 includes:

[0144] 1-1. A flat glassy carbon electrode was mechanically polished with aluminum oxide powder and ultrasonically cleaned in distilled water.

[0145] 1-2. Disperse 5 mg of carboxyl multi-walled carbon nanotubes in 10 mL of DMF and ultrasonicate for 24 h to form a uniform suspension.

[0146] 1-3. Take 3 μL of DMF / cMWCNTs suspension and drop it on GCE. Dry it under infrared light to construct a cMWCNTs / GCE electrochemical sensor.

[0147] 1-4. cMWCNTs / GCE was placed in a mixed solution containing 0.02 mol / L FeCl3+0.02 mol / L K3[Fe(cN)6]+0.1 mol / L KCl+0.01 mol / L HCl. Electrochemical polymerization was carried out at a scan rate of 50 mV / s in the potential range of -0.2 to 1.3 V. The cyclic scanning treatment was repeated for 10 cycles to obtain a Prussian blue / multi-walled carbon nanotube / glassy carbon (PBs / cMWCNTs / GCE) modified electrode.

[0148] Furthermore, the step 2 includes:

[0149] 2-1. Acetaminophen sample solutions of 0.1 mM, 0.2 mM, 0.4 mM, 0.6 mM, 0.8 mM, and 1.0 mM were prepared.

[0150] 2-2. Ascorbic acid sample solutions of 1 mM, 2 mM, 4 mM, 6 mM, 8 mM, and 10 mM were prepared.

[0151] 2-3. Six acetaminophen solutions of different concentrations were cross-mixed with six ascorbic acid solutions of different concentrations to obtain 36 mixed test sample solutions.

[0152] 2-5. Cyclic voltammetry was performed in a mixed solution of 0.6 mM acetaminophen and 4.0 mM ascorbic acid using three working electrodes: GCE, cMWCNTs / GCE, and PBs / cMWCNTs / GCE.

[0153] 2-6. Each mixed solution sample was tested 10 times using the three electrochemical methods: CV, DPV, and CA, and a total of 360 sets of test data were obtained.

[0154] 2-7. Record the changes in the oxidation peak spacing, peak potential, and oxidation peak current of ascorbic acid and acetaminophen on the three modified electrodes.

[0155] Furthermore, the step 3 includes:

[0156] 3-1. CV detection was performed on acetaminophen sample solutions and ascorbic acid sample solutions with six different concentrations in the potential range of -0.2 to 0.8 V at a scan rate of 0.1 V / s.

[0157] 3-2. Observe the CV result curve and determine the positions of the oxidation peak and reduction peak.

[0158] 3-3. Determine the relationship between acetaminophen concentration and ascorbic acid concentration and oxidation peak current value within six concentration gradient ranges, and perform regression fitting.

[0159] 3-4. DPV tests were performed on acetaminophen sample solutions and ascorbic acid sample solutions with six different concentrations in the potential range of -0.2 to 0.8 V, amplitude of 0.05 V, and pulse width of 0.05 s.

[0160] 3-5. Observe the DPV result curve, determine the position of the oxidation peak, determine the relationship between the acetaminophen concentration and ascorbic acid concentration and the oxidation peak current value, and perform regression fitting.

[0161] 3-6. CA detection was performed on acetaminophen sample solutions and ascorbic acid sample solutions with six different concentrations at a potential of 0.6 V and a running time of 30 s.

[0162] 3-7. When the response current decreases and reaches a steady state, the diffusion coefficients of acetaminophen and ascorbic acid on the modified electrode are calculated using the Cottrell equation. The expression of the Cottrell equation is:

[0163]

[0164] Where I is the current, n is the number of electrons exchanged by the reactant molecule, F is the Faraday constant (96,500 C / mol), and C is the analyte concentration (mol cm -3 ), D is the analyte diffusion coefficient (cm 2 / s), A is the geometric area (0.04cm 2 ). Determine the current value and t -1 / 2 Linear fitting graph. And determine the slope t in the graph -1 / 2 Fitted plots with acetaminophen concentration and ascorbic acid concentration.

[0165] Furthermore, the step 4 includes:

[0166] 4-1. 36 groups of mixed solution samples were tested 10 times using the three electrochemical methods: CV, DPV, and CA, and a total of 360 sets of test data were obtained.

[0167] 4-2. Feature extraction was performed on 360 sets of raw data. The anodic peak current, cathodic peak current, oxidation curve baseline slope, reduction curve baseline slope, oxidation peak area, and reduction peak area in the cyclic voltammetry curve, the anodic peak current, cathodic peak current, peak area, oxidation reaction start potential, and oxidation reaction end potential in the differential pulse voltammetry curve, the steady-state current value, the initial time of the steady-state current, and the relationship between the current value I and the time t were selected. -1 / 2 The slope of is extracted as a feature parameter.

[0168] 4-3. Construct an artificial neural network consisting of an input layer, a hidden layer, and an output layer. The input layer is an n-dimensional vector P composed of feature parameters. 1×N , calculated and outputted by the hidden layer to obtain the result variable Y out , where the input variable x i ∈P 1×N , output variable Y out ∈P 1×1 .

[0169] 4-4. The hidden layer has M neurons and the weight matrix w∈P M×N Responsible for connecting the input layer and the hidden layer neurons, in between which a bias unit b0∈P is required 1×M , then the hidden layer neurons receive the vector γ as:

[0170] γ=xw T +b0 (26)

[0171] Then the hidden layer neurons need to calculate the activation function, as shown in formula (3)

[0172] γ′=σ(γ) (27)

[0173] 4-5. The hidden layer neurons to the output layer also need to be multiplied by the weight matrix θ, and then add the bias unit b1, and the output concentration value Y out That is

[0174] Y out =σ(z)θ+b1 (28)

[0175] The input-output relationship finally established by the artificial neural network is:

[0176] Y out =σ(xw T +b)θ+b1 (29)

[0177] The neural network can obtain the above-mentioned network parameters such as w, b, θ through BP (Back Propagation) back propagation training.

[0178] 4-6. The BP back propagation algorithm propagates the error back from the output to the input layer, calculates the contribution of each neuron's weight to the error, and then updates the weight and bias value of each neuron through the gradient descent algorithm. In order to optimize and evaluate the output, each layer of neurons uses Levenberg-Marquardt optimized Bayesian regularization to train the BP network function, as shown below

[0179] J′e=(J T J+μI m )δ (30)

[0180] Where J is the Jacobian matrix, the first-order derivative of the J matrix to the network error is represented by J′e, and J T is the transpose of matrix J, the Levenberg damping factor is defined by μ, and I m is the identity matrix, and δ is the update vector variable.

[0181] Then, the loss function is obtained by comparing the network forward propagation output with the true value, as shown below:

[0182]

[0183] Taking partial derivatives of the neural network parameters in turn, we get the following formula

[0184]

[0185] Then update the model parameters by

[0186]

[0187] Where r is the learning rate of the neural network, which affects the training speed and quality of the ANN.

[0188] 4-7. PCA can be used to measure the degree of linear relationship between two variables. Therefore, it can be used to describe the correlation between the extracted feature parameters and the solution concentration, generate a correlation matrix, and remove irrelevant and redundant features from the original data set. Before calculating the correlation based on PCA, the feature set is normalized. For the feature vectors X and Y, the Pearson correlation calculation expression is:

[0189]

[0190] Among them, X i Indicates the value of X under sample i, Y i It represents the value of Y under sample i. The larger the absolute value of COR, the stronger the correlation between the two variables.

[0191] 4-8. PCA can reduce the dimensionality of input variables by eliminating some correlated variables that are unimportant to the estimated results. Using an orthogonal transformation matrix, the original data is transformed into a projection matrix by generating a combination of linear correlation numbers between each input variable. Correlation numbers consist of eigenvalues ​​and eigenvectors that contain a large amount of information about the original data. If a variable has a large eigenvalue, it has a greater impact on the model output, and vice versa. The mathematical objective function of principal component analysis is expressed by the following equation:

[0192] PC i =v i x (37)

[0193] Among them, PC i is the i-th PC, the matrix of the original input data is represented by x, v i The covariance matrix of x is the coefficient of x. jk ) can be calculated by the following method

[0194]

[0195] In this expression, and are samples x ij and x ik The mean of , l is the length of the vector data.

[0196] 4-9. Split the dataset from which feature parameters were extracted into training and test sets with an 8:2 ratio. In a multilayer perceptron, the dimension of the feature parameters is the number of input neurons. Select two hidden layers, each with four neurons, and one output neuron. Perform multiple training runs using an artificial neural network model with a learning rate of 0.0005, SGD as the optimizer, a regularization parameter of 0.001, and a squared error loss function. Use the trained ANN model to predict acetaminophen concentrations.

[0197] 4-10. Use principal component analysis (PCA) to analyze the correlation between the extracted characteristic parameters and the concentration of the mixed solution, and select characteristic parameters with strong correlation.

[0198] In the PCA-ANN model, the system inputs were only the 11 PCs from the PCA output. To determine the impact of the PCA method on neural network model training time, the feature parameter datasets before and after extraction were divided into training and test sets at an 8:2 ratio. Training and prediction were performed using the PCA-ANN model and the ANN model, and the differences between the predicted concentrations and the calibrated concentrations were compared.

[0199] 4-12. Using R 2The prediction results of ANN model and PCA-ANN model were evaluated by the root mean square error (RMSE) and mean absolute error (MAE). The above parameters are obtained by the following formula:

[0200]

[0201]

[0202] The present invention combines electrochemical detection methods and machine learning algorithms with the detection of acetaminophen and ascorbic acid separately to achieve simultaneous detection of acetaminophen and ascorbic acid using the same modified electrode, effectively improving detection efficiency and reducing detection costs. Furthermore, the detection accuracy is high, the sensitivity is high, and the operation is easy. Simultaneous detection of ascorbic acid and acetaminophen can optimize the combined effect of acetaminophen and ascorbic acid, minimize the adverse effects of drug combination on the human body, and maximize the positive effects of drug combination on the human body.

Claims

1. A method for detecting the concentration of acetaminophen and ascorbic acid when they coexist, characterized in that: The following steps are involved: Step 1: PBs / cMWCNTs / GCE sensor preparation 1-1. A flat glassy carbon electrode was mechanically polished using aluminum oxide powder, and the mechanically polished flat glassy carbon electrode was ultrasonically cleaned in distilled water to obtain a GCE; 1-2. Disperse carboxyl multi-walled carbon nanotubes in DMF and treat in an ultrasonic bath to obtain a DMF / cMWCNTs suspension; 1-3. The DMF / cMWCNTs suspension was dropped onto GCE and dried under infrared light to obtain a cMWCNTs / GCE electrochemical sensor; 1-4. The cMWCNTs / GCE electrochemical sensor was placed in a mixed solution containing FeCl3, K3[Fe(cN)6], 0.1 mol / L KCl and HCL, and a PBs / cMWCNTs / GCE modified electrode was prepared by cyclic voltammetry; Step 2: Using the PBs / cMWCNTs / GCE modified electrode, the concentration of the acetaminophen and ascorbic acid mixed solution is detected; Step 2 specifically includes the following steps: 2-1. Using the PBs / cMWCNTs / GCE modified electrode, three electrochemical methods, CV, DPV and CA, were used to test several groups of known acetaminophen and ascorbic acid concentrations of mixed solution samples to obtain test data; 2-2. Obtaining characteristic parameters from the detection data; 2-3. Correlation analysis was performed between the extracted characteristic parameters and the concentrations of acetaminophen and ascorbic acid in the mixed solution using PCA to obtain strongly correlated characteristic parameters with a correlation coefficient greater than 0.9; 2-4. Constructing an artificial neural network consisting of an input layer, a hidden layer, and an output layer, with the strongly correlated feature parameters described in step 2-3 as input to the artificial neural network; 2-5. Train the artificial neural network constructed in step 2-4 to obtain a trained PCA-ANN model; The PBs / cMWCNTs / GCE modified electrode was used to detect a sample solution with unknown concentrations of ascorbic acid and acetaminophen using the trained PCA-ANN model.

2. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 1, wherein: In the step 1-2, the amount of the carboxyl multi-walled carbon nanotubes is 5 mg, the amount of DMF is 10 mL, and the ultrasonic bath treatment time is 24 h; In steps 1-3, the amount of the DMF / cMWCNTs suspension used is 3 μL.

3. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 1, wherein: In the steps 1-4, The cyclic voltammetry was performed in a three-electrode electrochemical workstation, wherein the three electrodes included: a cMWCNTs / GCE electrochemical sensor as a working electrode, a platinum electrode as an auxiliary electrode, and a saturated Ag / AgCl as a reference electrode; The cyclic voltammetry process includes: performing electrochemical polymerization at a scanning rate of 50 mV / s, a potential range of -0.2 to 1.3 V, and performing 10 cycles of cyclic scanning.

4. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 1, wherein: In steps 1-4, the cMWCNTs / GCE electrochemical sensor is placed in a mixed solution containing 0.02 mol / L FeCl3, 0.02 mol / L K3[Fe(cN)6], 0.1 mol / L KCl and 0.01 mol / L HCL.

5. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 1, wherein: In step 2-1, the test data obtained by testing several groups of mixed solution samples of known acetaminophen and ascorbic acid concentrations include: Acetaminophen sample solutions of 0.1mM, 0.2mM, 0.4mM, 0.6mM, 0.8mM and 1.0mM were prepared; ascorbic acid sample solutions of 1mM, 2mM, 4mM, 6mM, 8mM and 10mM were prepared; 6 concentrations of acetaminophen solutions were cross-mixed with 6 concentrations of ascorbic acid solutions in sequence to obtain 36 mixed test sample solutions; each mixed solution sample was tested 10 times using the CV, DPV and CA methods, and a total of 360 sets of test data were obtained.

6. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 5, wherein: In step 2-2, the characteristic parameters are as follows: In the steps 2-3, the characteristic parameters strongly correlated with the concentration of acetaminophen are: Icv_o_ap, Icv_r_ap, Kcv_o_ap, Kcv_r_ap, Vs_cv_aa, Vs_cv_o_ap, Vs_cv_r_ap, Idpv_ap, Ve_dpv_ap and I_ca; the characteristic parameters strongly correlated with the concentration of ascorbic acid are: Icv_aa, Kcv_aa, Vs_cv_aa, Vs_cv_o_ap and Vs_cv_r_ap, Idpv_aa, Vdpv_aa, Vdpv_ap, Vs_dpv_aa, Vs_dpv_ap and I_ca.

7. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 6, wherein: The step 2-4 of constructing an artificial neural network consisting of an input layer, a hidden layer, and an output layer comprises the following steps: 2-4-1. The input layer is an n-dimensional vector P composed of feature parameters 1×N , calculated and outputted by the hidden layer to obtain the result variable Y out , where the input variable x i ∈P 1×N , output variable Y out ∈P 1×1 ; 2-4-2. The hidden layer has M neurons and the weight matrix w∈P M×M Responsible for connecting the input layer and the hidden layer neurons, in between which a bias unit b0∈P is required 1×M , then the hidden layer neurons receive the vector γ as: γ=xw T +b0 Then the hidden layer neurons need to calculate the activation function, as shown below γ′=σ(γ) 2-4-3. The hidden layer neurons need to be multiplied by the weight matrix θ to the output layer, and then add the bias unit b1, and the output concentration value Y out That is: Y out =σ(z)θ+b1 The input-output relationship finally established by the artificial neural network is: Y out =σ(xw T +b)θ+b1 The neural network can obtain the above-mentioned network parameters such as w, b, θ through BP back propagation training; 2-4-4. Each layer of neurons uses Levenberg-Marquardt optimized Bayesian regularization to train the BP network function, as shown in the following formula J′e=(J T J+μI m )δ Where J is the Jacobian matrix, the first-order derivative of the J matrix to the network error is represented by J′e, and J T is the transpose of matrix J, the Levenberg damping factor is defined by μ, and I m is the identity matrix, and δ is the update vector variable; Then, the loss function is obtained by comparing the network forward propagation output with the true value, as shown in the following formula: Taking partial derivatives of the neural network parameters in turn, we get the following formula Then update the model parameters as shown below Where r is the learning rate of the neural network, which affects the training speed and quality of the ANN.

8. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 7, wherein: In the steps 2-4, the number of neurons in the input layer is 11, two hidden layers are used, each with 4 neurons, and the output layer has 1 neuron.

9. The method for detecting the concentration of acetaminophen and ascorbic acid when they coexist as claimed in claim 8, wherein: In steps 2-5, the learning rate of the training is 0.0005, the regularization parameter is 0.001, and the loss function is the square error loss function.

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