The data used for training, validation, and testing in this study were obtained from Beijing Savant Biotechnology Co., Ltd. These data are the result of testing a variety of items. The detection items mainly included human ferritin, vitamin D, D-dimer, and C-reactive protein and so on. The sample types mainly included whole blood, serum, and plasma.

A double-antibody sandwich test strip with fluorescent microspheres (FMS) as the carrier was used to illustrate the detection principle of LFIA. The double-antibody sandwich structure is shown in Figure 1. The test strip was composed of a sample pad, conjugate pad, nitrocellulose membrane (NC membrane), absorbent pad, and plastic backing card. After the sample was dripped into the sample pad, it was subjected to immunochromatography under capillarity. The detection antibody-FMS (DAb-FMS) and rabbit IgG antibody-FMS (Rabbit-Ab-FMS) were placed on the conjugate pad. There are T and C lines on the NC membrane; the T line is coated with capture antibody (CAb), and the C line is coated with goat anti-rabbit IgG antibody (GAR-Ab). The absorbent pad causes liquid to flow via capillary action. The plastic backing card plays the role of fixing and supporting.

When the sample solution containing the analyte was added to the sample pad, it was laterally transferred along the NC membrane via capillary action. When the sample flowed through the conjugate pad, the Antigen in the sample reacted with DAb to form a DAb-FMS/Antigen complex. When the complex flows to the T line in the NC membrane, the Antigen and CAb on the T line are immunized to form a DAb-FMS/Antigen/CAb complex. Rabbit-Ab-FMS, which does not participate in the reaction, continues to flow forward to the C line and reacts with GAR-Ab.

Generally, the entire reaction process takes approximately 15 min. After immunochromatography is completed, the excitation light generated by the scanning mechanism irradiates the T and C lines, and fluorescence is generated. In the process of scanning the NC membrane, the fluorescence intensity produced at each point of the scan was recorded using a photodiode, and the peak data shown in Figure 1 were finally formed. The ratio of the fluorescence intensities of the two lines can be obtained by calculating the ratio of the peak areas of the T- and C-peaks. The concentration of the antigen detected in the sample was proportional to the T/C. By establishing a standard curve, the concentration of the antigen detected in the sample can be calculated.

During the testing of clinical samples, four different peak shape data were obtained: noise (class 1), only C-peak (class 2), only T-peak (class 3), and double-peaks (C-peak and T-peak, class 4). Class 1 was generated by a fluorescence analyzer scanning the fouled NC membrane, whereas class 2 was generated by detecting the sample with a concentration of 0. However, the data of class 3 were very few, and were generally generated from the test strips with the disappearance of the C-peak. To better train the model, the C-peak of the double-peaks (class 4) was deleted and transformed into the background by a cubic spline interpolation method; thus, a large amount of data containing only the T-peak was generated manually.

To train the model, a large amount of labeled data is required. Data annotation is a complex process, and the quality of the annotation directly affects the results of the model training. This method includes two steps corresponding to a classification and a segmentation model, and the training data of the two models must be annotated separately. The labeled dataset was randomly divided into training and verification sets.

The entire dataset for the classification model includes approximately 4,100 detection data, including four types of peak shapes, namely, noise, only C-peak, only T-peak, and double-peaks. These four types of data were encoded according to one-hot, which were noise (class 1), only C-peak (class 2), only T-peak (class 3), and double-peaks (class 4), as shown in Figures 2–4. There were approximately 900 data for noise (class 1), 900 for only C-peak (class 2), 900 for only T-peak (class 3), and 1,400 for double-peaks (class 4). The peak shape of the detection data is particularly complex and diverse, and only a few typical ones are selected for display here.

The dataset of the segmentation model includes approximately 1,400 pieces of detection data, that is, all the data of class 4. In this study, based on the Python language, software was designed to annotate the integral regions of the T-peak and C-peak, and the integral regions of the C-peak and T-peak of 1,400 fluorescence detection data were annotated.

Convolutional neural network is an artificial neural network specially designed to process data such as images or videos. It generally has three layers, namely, convolution, pooling and full connection layer. In the convolution layer, input samples are convolved with kernel, and the discrete convolution function is defined as:

where f and g are two functions.

Pooling is used to extract high-dimensional features, and the most commonly used ones are maximum and average pooling. In a fully connected layer, all neurons in the current layer are interconnected with every neuron in the next layer.

As shown in Figure 5, the entire data-processing flow consists of two steps. First, a classification model was used to classify the input data. Second, after analyzing the input data, if the output result was class 4 (double-peaks), the data were imported into the next segmentation model to realize the data segmentation of the C-peak and T-peak areas.

The input of the classification model had two channels. Because the fluorescent signal has strong background noise, we subtracted the background and then normalized it as the first channel. It was achieved by the following formula.

where Y₁ is the first channel, X is raw input data, x_min is minimum value, and x_max is maximum value of raw data. In order to make the model learn the peak shape rather than intensity, we performed a logarithmic operation on the signal which was deducted background as the second channel. It was achieved by the following formula.

where Y₂ is the second channel, X is raw input data, x_min is minimum value, and x_max is maximum value of raw data.

The network architecture of the classification model is illustrated in Figure 5A. The entire network architecture consisted of 10 layers; the first seven layers were conv1d + ReLU + MaxPool1d (Acharya et al., 2017; Gu et al., 2018; Zhang et al., 2019), and the input data were extracted into four features of high-dimensional 1,024 channels. The eighth layer extended the number of channels to 2,048. Next, Max + Transposition was used to extract the maximum value from the four high dimension features (Gu et al., 2018). To improve the accuracy of classification, we used dropout layer before fully connected layers. The last layer (Dropout + Fully-connected + SoftMax) classified the data into one of four classes (Srivastava et al., 2014).

We designed an improved U-Net segmentation model with reference to the classic U-Net model (Ronneberger et al., 2015); the network architecture is shown in Figure 5B. We changed the input data into two channels. This model had four parts: input unit, encoding structure, decoding structure, and output unit (Ronneberger et al., 2015; Oh et al., 2019; Wang et al., 2021; Zheng et al., 2021; Zunair and Ben Hamza, 2021). The encoding structure used four units to reduce the dimensions, and the number of feature maps was increased gradually. In order to reduce training time, we added batch normalization after each convolution (Melnikov et al., 2020). In the decoding structure, each step was symmetrical with the encoding part to recover data. The upsampling section allowed the network to propagate the context information to a higher-resolution layer. In the last layer, the discrimination of whether each point in fluorescence data belonged to an integral region was realized.

The classification model classified the data into one of four classes, which is a problem of four classes. Multi-classification neural networks generally use cross-entropy loss as a loss function. The mathematical expression of this loss function in the program is:

where M is the batch size, C is the total number of classes (four), y_ij is the real label, and o_ij is the predictive output.

The Dice coefficient (also known as the Dice score or DSC) is a function of the set similarity measurement, which is usually used to calculate the similarity between two sets (Saeedizadeh et al., 2021), with values ranging from 0 to 1. Here, it was used to measure the overlap between the ground-truth and predicted masks, where 0 indicates no overlap and 1 indicates complete overlap.

where A and B denote the predicted and ground-truth masks.

To minimize the loss function, we used the 1-DSC as the final loss function. The mathematical expression of this loss function in the program is:

where M is the batch size, N is the number of sample data, y_ij is the ground-truth mask, and o_ij is the predictive mask.

For unbalanced sample data, weighted binary cross entropy can be used as the training loss function. Therefore, compared with the standard cross-entropy loss, better results can be obtained when the number of positive and negative points is unbalanced (Zhu et al., 2019). The mathematical expression of this loss function in the program is:

where M is the batch size, N is the number of sample data, y_ij is the ground-truth mask, and o_ij is the predictive mask. w₁ and w₀ correspond to the weights labeled 1 and 0, respectively.

In this study, the mathematical expression for the weight parameter w_c is:

where N represents the total number of data points for each sample and N_c represents the number of data points in class c.

After labeling the data, we trained the model. The classification and segmentation models were trained separately. The training parameters of the classification and segmentation model are listed in Table 1.

Accuracy, which is the proportion of correctly predicted samples to the total number of samples, is generally used as the evaluation metric of a multi-classification model. The mathematical expression of accuracy in the program is:

where M denotes the batch size, y_i denotes the real label, and o_i is the predictive output.

The intersection over union (IoU), also known as the Jaccard index, calculates the ratio of the intersection and union of the ground-truth and predicted segmentation masks (Saeedizadeh et al., 2021). It can be used to measure the similarity between the ground-truth and predicted segmentation masks; the higher the similarity, the higher the value.

where A and B denote the predicted and ground-truth masks. The mathematical expression of IoU in the program is:

where M is the batch size, N is the number of sample data, y_ij is the ground-truth mask, and o_ij is the predictive mask.

Both the weight coefficients of the weighted binary cross-entropy and cut-off threshold have a certain influence on the performance of the model. To obtain appropriate weights and cut-off thresholds, this study conducted cross experiments on weights and cut-off thresholds. As presented in Table 2, when w₀ : w₁ = 0.6 : 0.4 and the cut-off threshold = 0.6, the IoU achieved a maximum value of 0.9680. The other parameters used during the training are listed in Table 1.

We also compared the three loss functions of WBCE, DSC, and WBCE + DSC. When the other conditions were the same, the combined loss function (WBCE + DSC) was used to obtain the maximum IoU, as illustrated in Table 3.

Figure 6A shows the loss curves of different epochs during the classification model training process, and Figure 6B shows the accuracy of the training and validation sets corresponding to different epochs. The maximum accuracy of the model validation set was 99.59%.

To analyze which samples were misclassified, we built confusion matrix. As in Figure 6C, only five samples were misclassified, two class 1 and three class 2 data were misclassified as class 4. These five samples had the characteristics of two different classes, which leaded to misclassification. In general, such samples are rare.

Figure 7A shows the loss curves of different epochs during the segmentation model training process, and Figure 7B shows the IoU of the training and validation sets corresponding to different epochs. The maximum IoU of the model validation set was 0.9680.

There are many types of peak detection methods, such as the direct peak location, Fourier transform, cumulative sum derivative, curve fitting, devolution, and wavelet transform (CWT) methods (Deng et al., 2021). The direct peak location according to the properties of peak and continuous wavelet transform are two classical methods in traditional methods. The principle of direct peak location is to find out all the local maxima of the signal through the simple comparison method, and then select the subset of these peaks according to the specified peak properties. The method principle of CWT is that the signal is first transformed by CWT in certain scales, and then the ridges are found in the CWT matrix. The positions of these ridges correspond to the positions of all peaks (Du et al., 2006). Using the verification set, method proposed in this paper was compared with the two traditional methods. These two methods have been implemented in SciPy library based on Python, so we directly used the related functions (find_peaks() and find_peaks_cwt()) in SciPy library.

Classical peak-finding methods can only find the local maxima of the signal, and do not have the ability to classify the signal. Here, after obtaining the local maxima through the classical methods, some subsequent processing steps were adopted to make it have the classification ability, and then compared with the classification model proposed in this study. These subsequent processing steps are as follows:

The comparison results are shown in Table 4. It can be seen that the performance of the two classical methods is similar in term of accuracy, one is 80.10%, the other is 80.76%. Accuracy of the method proposed in this study is 99.59%, which is much better than classical methods.

For two classical methods, the function of peak_widths() in the SciPy library can be used to identify the integral region. Compared with the segmentation method in this study in terms of IoU, Dice, Recall and Precision. The results are shown in Table 4. As can be seen from the table, no matter which evaluation term it is, the method proposed in this paper is much better than two classical methods.

The method proposed in this study was tested using instrument test data. First, the ability of the segmentation model to segment various peak shapes was tested. Next, three most important indicators (standard curve, repeatability, and recovery) were tested.

After training, the method can classify raw input data into one of four classes and perform data segmentation on data belonging to Class 4. The segmentation model could effectively segment C- and T-peak regions from fluorescence intensity of 512 data points. Figure 8 shows examples of data segmentation results for some typical peak shapes, where the orange shaded areas are segmented C- and T-peak regions. Figure 8A shows segmentation of the normal peak shape, and C -and T-peak regions were accurately extracted and obtained. Figures 8B, C show that in the presence of overlapping and interference peaks, C- and T-peaks can be accurately segmented. Figures 8D–F show the segmentation results for weak T-peak with baseline drift, tailing or interference peak. As shown in the figure, baseline drift, tailing and interference peaks did not affect accurate segmentation of the data; the detection of weak T-peak region is also excellent. After data were imported into the segmentation model, they were first normalized. The network model only focused on learning the shape of entire data set and did not learn the value of fluorescence intensity. The experimental results indicate that it can meet the requirements of LFIA for data processing.

The method was tested using Ferritin. A standard curve was established using a range of concentrations (0, 15, 50, 200, 300, and 500 ng/ml) of the standards. Each concentration of the standard was tested three times using test strips. The detection data were processed using proposed method. First, data were classified, then segmented, and finally, the segmented regions were integrated and T/C was calculated. The method accurately classified the detection data of 0 ng/ml as class 2 (only C-peak), and the corresponding T/C values were 0. The remaining data were classified as class 4 (double-peaks) and then segmented. Using T/C as the ordinate and concentration as the abscissa, a standard curve was established using four parameters, as shown in Figure 9. It can be observed that the T/C and concentration have a good correlation with a correlation coefficient of 0.9986. This shows that the method is effective in dealing with LFIA data.

Three concentrations (20, 220, and 400 ng/ml) of the reference standards were tested for repeatability using the same batch of test strips. Each concentration was tested 10 times, and the CV values were calculated. The data were processed using the method described in this study. The data for all the three concentrations were classified as class 4 (double-peaks). The data were segmented, and concentrations were calculated; the results are listed in Table 5. It can be observed that the CV values of three concentrations are all good, and the maximum does not exceed 1.37%. This shows that the stability of the method is good.

Recovery was tested using samples of three concentrations (40, 100, and 150 ng/ml). Each sample was tested thrice. The method in this study was used to process the data, and all the data were classified as class 4 (double-peaks); the results are listed in Table 6. The calculated recovery rates were 105.07, 96.37, and 99.67%, respectively. This shows that concentration calculated by the method is very accurate.