Epileptic seizure prediction method and system based on power spectrum and phase spectrum of electroencephalogram

Abstract

The application provides an epilepsy seizure prediction method and system based on electroencephalogram power spectrum and phase spectrum, comprising: an electroencephalogram signal acquisition module configured to acquire and preprocess multi-channel electroencephalogram signals; a power spectrum and phase spectrum extraction module configured to divide the electroencephalogram signals into multiple segments of a set time, transform each segment of the set time, and extract power spectrum and phase spectrum based on the transformation; a model construction module configured to construct a double-flow convolutional neural network model, wherein the model comprises a first network flow and a second network flow; a feature fusion module configured to splice output features of the first network flow and the second network flow in the channel dimension, fuse power and phase information, and obtain a fused feature map; and a prediction module configured to convert the fused feature map into a one-dimensional feature vector through further processing, and calculate the one-dimensional feature vector to output the probability of epilepsy seizure and non-seizure.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of biomedical signal processing and artificial intelligence, and particularly relates to an electroencephalogram (EEG)-based seizure prediction method and system based on power spectrum and phase spectrum. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] Epilepsy is a common neurological disease affecting hundreds of millions of people worldwide. Accurate detection of seizures is crucial for the diagnosis, treatment and management of patients. Traditional seizure detection mainly relies on neurologists' manual analysis of electroencephalogram (EEG) signals, but this method is both time-consuming and susceptible to subjective factors, making it difficult to detect seizures in a timely and accurate manner.

[0004] To improve the efficiency and accuracy of seizure detection, researchers have developed various automated detection methods. Among them, time-frequency analysis methods such as short-time Fourier transform (STFT) and wavelet transform (WT) have been widely used to extract time-frequency features of EEG signals. However, these methods have a trade-off between time and frequency resolution, making it difficult to achieve high time and frequency resolution simultaneously.

[0005] S-transform (ST) is an improved time-frequency analysis method that combines the advantages of STFT and WT, with a frequency-dependent Gaussian window function, providing better time-frequency resolution while preserving phase information.

[0006] In recent years, deep learning, especially convolutional neural networks (CNN), has made significant progress in image classification and signal processing. CNN can automatically learn deep features of data, reducing the dependence on manual feature extraction.

[0007] However, in seizure detection, how to effectively combine the power spectrum and phase spectrum information of EEG signals to build a high-performance deep learning model remains a challenge.

[0008] In the prior art, for example: CN113397561B_A brain electrical detection system based on S-transform and Bayesian convolutional neural network and its working method and device; Thesis, Shandong University, Automatic detection of epilepsy based on S-transform and bidirectional LSTM network. Most methods only use the power spectrum information of EEG signals, ignoring the importance of phase spectrum in seizure detection. SUMMARY

[0009] In order to overcome the above-mentioned deficiencies of the prior art, the present application provides an epilepsy seizure prediction method based on power spectrum and phase spectrum of electroencephalogram, which can make full use of power and phase information of EEG signal, and improve the accuracy and robustness of epilepsy seizure detection by combining deep learning technology.

[0010] In order to achieve the above-mentioned purpose, one or more embodiments of the present application provide the following technical solutions:

[0011] In the first aspect, an epilepsy seizure prediction system based on power spectrum and phase spectrum of electroencephalogram is disclosed, comprising:

[0012] An electroencephalogram signal acquisition module configured to acquire and preprocess multi-channel electroencephalogram signals;

[0013] A power spectrum and phase spectrum extraction module configured to divide the preprocessed electroencephalogram signals into multiple segments of a set time, transform each segment of the set time, and extract power spectrum and phase spectrum based on the transformation;

[0014] A model construction module configured to construct a double-flow convolutional neural network model, wherein the model comprises a first network flow and a second network flow, the first network flow processes power spectrum, and the second network flow processes phase spectrum;

[0015] A feature fusion module configured to splice the output features of the first network flow and the second network flow in the channel dimension, fuse power and phase information, and obtain a fused feature map;

[0016] A prediction module configured to convert the fused feature map into a one-dimensional feature vector through further processing, and calculate the probability of epilepsy seizure and non-seizure for the one-dimensional feature vector.

[0017] As a further technical solution, in the electroencephalogram signal acquisition module, the multi-channel electroencephalogram signals are acquired and preprocessed, specifically including:

[0018] Electroencephalogram signal data is collected at a set sampling rate, and signal segments of each set time are extracted;

[0019] Discrete wavelet transform is performed using wavelet, detail coefficients are selected, a filtered signal is reconstructed, and the signal segments with eye and muscle artifact removed are filtered based on the filtered signal.

[0020] As a further technical solution, in the model construction module, the first network flow and the second network flow have the same structure and are used to extract deep features, and each of them comprises a multi-layer convolutional layer, a batch normalization layer, an activation function layer and a pooling layer.

[0021] The first layer convolutional layer receives a power spectrum or a phase spectrum, and gradually reduces the size of a feature map and gradually increases the number of channels through a series of convolution and pooling operations.

[0022] As a further technical solution, in the prediction module, the fused feature map is converted into a one-dimensional feature vector through further processing, and the specific process is:

[0023] The fused feature map is subjected to further convolution and pooling operations, and finally converted into a one-dimensional feature vector through a global average pooling layer.

[0024] As a further technical solution, in the prediction module, the one-dimensional feature vector is calculated to output the probability of seizure and non-seizure, specifically:

[0025] The global average pooling layer is connected to a fully connected layer, and an activation function is used to output the probability of seizure and non-seizure.

[0026] As a further technical solution, the constructed double-flow convolutional neural network model adopts a leave-one-out strategy in the model training process to ensure that the data of the test subjects are not involved in the training.

[0027] As a further technical solution, it further includes a post-processing module configured to post-process the output probability, specifically by adding the output scores of adjacent multiple set time segments to obtain a comprehensive score.

[0028] A moving average filter is used to filter the scores to smooth the score sequence.

[0029] A threshold is set to determine the smoothed score, and a score higher than the threshold is determined as a seizure.

[0030] In a second aspect, an electroencephalogram-based power spectrum and phase spectrum seizure prediction method is disclosed, comprising:

[0031] Obtain multi-channel electroencephalogram signals and pre-process them;

[0032] Divide the pre-processed electroencephalogram signals into multiple set time segments, transform each set time segment, and extract power spectrum and phase spectrum based on the transformation;

[0033] Construct a double-flow convolutional neural network model, which includes a first network flow and a second network flow, the first network flow processes the power spectrum, and the second network flow processes the phase spectrum;

[0034] Splice the output features of the first network flow and the second network flow in the channel dimension, fuse the power and phase information, and obtain a fused feature map;

[0035] The fused feature map is further processed and converted into a one-dimensional feature vector, and the probability of epilepsy seizure and non-seizure is calculated for the one-dimensional feature vector.

[0036] The above one or more technical solutions have the following beneficial effects:

[0037] The present application comprehensively extracts the time-frequency feature information of power spectrum and phase spectrum by performing S transform on the EEG signal. The double-flow convolutional neural network is used to process the power and phase features respectively, and the features are fused at the feature level, which overcomes the shortcomings of traditional methods that only rely on power spectrum and ignore phase spectrum information. In this way, not only the feature expression is enriched, but also the model's ability to capture complex patterns of seizures is improved, and the accuracy and sensitivity of seizure detection are significantly improved.

[0038] The advantages of the additional aspects of the present application will be partially given in the following description, partially become obvious from the following description, or be known by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0039] The drawings accompanying the specification of this application form a part thereof, serve to provide further understanding of the application, and together with the description of the exemplary embodiments of the application and explanations thereof, to explain the application, and do not constitute improper limitations on the application.

[0040] Figure 1 The overall flowchart of the seizure detection method based on S transform and double-flow convolutional neural network according to the embodiment of the present application is shown in the figure.

[0041] Figure 2 The structure diagram of the double-flow convolutional neural network according to the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0042] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0043] It should be noted that the terms used herein are only for the purpose of describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present application.

[0044] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0045] Embodiment one

[0046] Referring to the accompanying Figure 1 The present embodiment discloses an electroencephalogram-based power spectrum and phase spectrum seizure prediction system, which comprises:

[0047] An electroencephalogram signal acquisition module configured to acquire and pre-process multi-channel electroencephalogram signals;

[0048] A power spectrum and phase spectrum extraction module configured to divide the pre-processed electroencephalogram signals into multiple segments of a set time, transform each segment of the set time, and extract power spectrum and phase spectrum based on the transformation;

[0049] A model construction module configured to construct a dual-flow convolutional neural network model, the model including a first network flow and a second network flow, the first network flow processing power spectrum and the second network flow processing phase spectrum;

[0050] A feature fusion module configured to splice output features of the first network flow and the second network flow in a channel dimension, fuse power and phase information, and obtain a fused feature map;

[0051] A prediction module configured to convert the fused feature map into a one-dimensional feature vector through further processing, and calculate the one-dimensional feature vector to output probabilities of seizures and non-seizures.

[0052] First, in the electroencephalogram signal acquisition module, multi-channel EEG signals are acquired and pre-processed.

[0053] In this module, when implemented specifically: 18-channel EEG data is collected at a sampling rate of 256 Hz, and non-overlapping signal segments of 4 seconds are extracted, each segment containing 1024 sampling points. Then, for each segment, each EEG signal segment is decomposed and reconstructed by DWT to achieve filtering. Specifically: Daubechies-4 (Db4) wavelet is used for 5-layer discrete wavelet transform (DWT), and the formula is:

[0054]

[0055] where ψ j,k (t) is the Db4 wavelet function with a scale of 2 j and a shift of k. Through DWT, the signal is decomposed into approximation coefficients and five detail coefficients.

[0056] In order to remove high-frequency noise and artifacts such as electrooculogram (EOG) and electromyogram (EMG), the detail coefficients d3 (16-32 Hz), d4 (8-16 Hz) and d5 (4-8 Hz) are selected, and the filtered signal with a frequency range of 4-32 Hz is reconstructed. The formula of the reconstructed signal x recon (t) is:

[0057]

[0058] where c j,kThe detail coefficient corresponding to the scale and position.

[0059] Secondly, the filtered signal is divided into four 1-second segments, each containing 256 sampling points. For each 1-second segment, S transform is performed to extract the power spectrum and phase spectrum.

[0060] The definition of S transform is as follows:

[0061]

[0062] Where p is a parameter that controls the width of the Gaussian window, p = 0.5 to balance between time and frequency resolution, x(t) is the time signal, τ is the time variable, and f is the frequency variable.

[0063] Calculate the power spectrum |S(τ,f)| 2 and the phase spectrum φ(τ,f):

[0064] |S(τ,f)| 2 = |S x (τ,f)| 2 = [Re(S x (τ,f))] 2 + [Im(S x (τ,f))] 2

[0065]

[0066] Through the above calculation, the power spectrum and phase spectrum of each 1-second segment are obtained, and the size of the power spectrum and phase spectrum is 32x32x18. The dimension is a two-dimensional time-frequency feature matrix. Among them, 32 represents the frequency dimension, 32 represents the time dimension, and 18 represents the number of EEG channels.

[0067] Then, a double-flow convolutional neural network model is constructed to process the power spectrum and phase spectrum respectively. The structure of the two network flows is the same, and the multi-layer convolutional layer, batch normalization layer, activation function layer and pooling layer of each network flow are used to extract deep features.

[0068] Referring to FIG. 1, the specific structure of the double-flow CNN model is as follows: Figure 2

[0069] Input layer: the input size is 32x32x18.

[0070] First convolutional layer: the convolution kernel size is 3x3, the number of convolution kernels is 32, the step is 1, and the padding method is "same". The output size is 32x32x32.

[0071] Batch normalization layer: standardize the convolution output.

[0072] ​ReLU activation function layer: apply nonlinear activation.

[0073] Max pooling layer: pooling window size is 2x2, stride is 2. Output size is 16x16x32.

[0074] Second convolutional layer: convolution kernel size is 3x3, number of convolution kernels is 64, stride is 1, padding mode is "same". Output size is 16x16x64.

[0075] Batch normalization layer.

[0076] ReLU activation function layer.

[0077] Max pooling layer: pooling window size is 2x2, stride is 2. Output size is 8x8x64.

[0078] Dropout layer: Dropout probability is 0.5.

[0079] Third convolutional layer: convolution kernel size is 3x3, number of convolution kernels is 128, stride is 1, padding mode is "same". Output size is 8x8x128.

[0080] Batch normalization layer.

[0081] ReLU activation function layer.

[0082] At the same time, add a shortcut connection including a convolutional layer (convolution kernel size is 3x3, number of 128) and a max pooling layer (pooling window size is 4x4, stride is 4), directly reduce the input from 32x32x18 to 8x8x128, and add it to the main branch to improve the feature expression ability.

[0083] Feature fusion and classification: the output features of the two network streams of power spectrum and phase spectrum are spliced in the channel dimension to obtain a fusion feature map with a size of 8x8x256.

[0084] Fourth convolutional layer: convolution kernel size is 3x3, number of convolution kernels is 256, stride is 1, padding mode is "same". Output size is 8x8x256.

[0085] Batch normalization layer.

[0086] ReLU activation function layer.

[0087] Max pooling layer: pooling window size is 2x2, stride is 2. Output size is 4x4x256.

[0088] Fifth convolutional layer: convolution kernel size is 3x3, number of convolution kernels is 512, stride is 1, padding mode is "same". Output size is 4x4x512.

[0089] Batch normalization layer.

[0090] ReLU activation function layer.

[0091] Max pooling layer: the pooling window is 4x4, and the step is 4. The output size is 1x1x512.

[0092] Global average pooling layer (GAP): converts the feature map into a feature vector with a length of 512.

[0093] Fully connected layer: the number of neurons is 2, corresponding to the seizure and non-seizure categories.

[0094] SoftMax activation function: outputs the probability of each category.

[0095] In particular, referring again to Figure 2 As shown, the first layer of convolutional layers receives an input feature map with a size of 32x32x18, which is a power spectrum or a phase spectrum. After a series of convolution and pooling operations, the size of the output feature map gradually decreases, and the number of channels gradually increases. To prevent overfitting, a Dropout layer is added to the network.

[0096] Next, the output features of the two network streams are spliced in the channel dimension to fuse the power and phase information. The fused feature map is further subjected to convolution and pooling operations, and finally passes through a global average pooling (GAP) layer to convert the feature map into a one-dimensional feature vector. Then, a fully connected layer is connected, and a SoftMax activation function is used to output the probability scores of seizure and non-seizure.

[0097] During model training, the Leave-One-Subject-Out (LOSO) strategy is used to test each subject individually, and its data does not participate in training, ensuring that the test subject's data does not participate in training and improving the model's generalization ability. The optimizer is Adam, the learning rate is 0.001, the batch size is 512, the maximum number of training rounds is 320, and the L2 regularization coefficient is 0.0001.

[0098] During model training, the input EEG channel order is randomly shuffled in each small batch of data to prevent the model from overfitting to a specific channel order.

[0099] Finally, the probability scores output by the model are post-processed. The output scores of the adjacent four 1-second segments are added to obtain a comprehensive score. To smooth the score sequence, a 7-length moving average filter is used to filter the scores. A threshold is set to distinguish the smoothed scores, and the score higher than the threshold is determined as a seizure. The threshold Thr is adjusted according to the characteristics of the patient's EEG signal to achieve the best balance between sensitivity and specificity. Considering the time delay caused by filtering, the segment determined as a seizure is extended by a certain number of points on the time axis.

[0100] In an embodiment, specifically, the score is accumulated: the output probability scores of the adjacent four 1-second segments are added, and the comprehensive score ranges from -4 to +4.

[0101] Moving average filtering: a 7-length (N=3) moving average filter is used, and the formula is:

[0102]

[0103] where x(i) is the i-th comprehensive score.

[0104] Threshold determination: a threshold Thr is set, and when the smoothed score Z(i)>Thr, it is determined as a seizure.

[0105] Boundary compensation: for the segment determined as a seizure, it is extended by 12 points on both sides of the time axis to compensate for the time delay caused by filtering, thereby improving the sensitivity index of the seizure detection.

[0106] Through the above method, the present application realizes high-accuracy detection of seizures, fully utilizes the power and phase characteristics of EEG signals, and has important clinical application value.

[0107] The technical scheme of the embodiment can improve the accuracy and robustness of seizure detection. The method fully utilizes the power spectrum and phase spectrum information of electroencephalogram (EEG) signals, and combines deep learning technology to overcome the defects of insufficient utilization of phase information and low detection accuracy in traditional methods.

[0108] Application of the model on the CHB-MIT dataset:

[0109] The model is trained and tested on the CHB-MIT database, which contains EEG data of 23 patients with a total duration of about 979.93 hours, including EEG records of seizure and non-seizure states. The model performance evaluation indexes include segment-level accuracy, segment-level sensitivity, segment-level specificity, event-level sensitivity, and event-level false detection rate (FDR). These evaluation indexes are defined as follows:

[0110] Segment-level accuracy (Accuracy):

[0111]

[0112] Segment-level sensitivity (Sensitivity):

[0113]

[0114] Segment-level specificity (Specificity):

[0115]

[0116] Event-level sensitivity: the percentage of correctly detected seizure events in the total number of seizure events.

[0117] Event-level false detection rate (FDR): the average number of false detections per hour.

[0118] The experimental results on the CHB-MIT database are shown in Table 1, with an average accuracy of 92.00%, an average sensitivity of 79.59%, an average specificity of 92.23%, an average event-level sensitivity of 85%, and an average false detection rate of 2.52 times per hour.

[0119] Table 1: Seizure detection results of the model on the CHB-MIT database

[0120]

[0121]

[0122] Example Two

[0123] Referring again to the drawings, the purpose of the present embodiment is to provide an electroencephalogram-based seizure prediction method based on power spectrum and phase spectrum, comprising: Figure 1

[0124] Obtaining and preprocessing multi-channel electroencephalogram signals;

[0125] Dividing the preprocessed electroencephalogram signals into multiple segments of a set time, transforming each segment of the set time, and extracting power spectrum and phase spectrum based on the transformation;

[0126] Constructing a dual-stream convolutional neural network model, the model comprising a first network stream and a second network stream, the first network stream processing power spectrum and the second network stream processing phase spectrum;

[0127] Concatenating the output features of the first network stream and the second network stream in the channel dimension, fusing power and phase information, and obtaining a fused feature map;

[0128] ​The fused feature map is further processed and converted into a one-dimensional feature vector, and the one-dimensional feature vector is calculated to output the probability of a seizure and a non-seizure.

[0129] Embodiment three

[0130] The purpose of this embodiment is to provide a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the program.

[0131] Embodiment four

[0132] The purpose of this embodiment is to provide a computer-readable storage medium.

[0133] A computer-readable storage medium, having stored thereon a computer program, which is executed by a processor to perform the steps of the above method.

[0134] Embodiment five

[0135] The purpose of this embodiment is to provide a computer program product containing instructions, which, when executed on a computer, causes the computer to perform the method and functions involved in any of the above embodiments.

[0136] The steps and methods involved in the above embodiments correspond to embodiment two, and the specific embodiments can refer to the relevant description of embodiment one. The term "computer-readable storage medium" should be understood to include a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry instruction sets for execution by a processor and cause the processor to perform any of the methods in the present application.

[0137] Those skilled in the art should understand that the above modules or steps of the present application can be implemented by a general computer device, alternatively, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device for execution by a computing device, or they can be made into individual integrated circuit modules, or a plurality of modules or steps among them can be made into a single integrated circuit module. The present application is not limited to any specific combination of hardware and software.

[0138] The above describes the specific embodiments of the present application in conjunction with the accompanying drawings, but is not a limitation on the scope of protection of the present application, and those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the scope of protection of the present application.

Claims

1. A seizure prediction system based on power spectrum and phase spectrum of electroencephalogram characterized by, The method comprises the following steps: An electroencephalogram signal acquisition module is configured to acquire and preprocess multi-channel electroencephalogram signals; A power spectrum and phase spectrum extraction module is configured to divide the preprocessed electroencephalogram signals into multiple segments of a set time, transform each segment of the set time, and extract power spectrum and phase spectrum based on the transformation; A model construction module is configured to construct a dual-flow convolutional neural network model, which comprises a first network flow and a second network flow, the first network flow processes power spectrum, and the second network flow processes phase spectrum; A feature fusion module is configured to splice the output features of the first network flow and the second network flow in the channel dimension, fuse power and phase information, and obtain a fused feature map; A prediction module is configured to convert the fused feature map into a one-dimensional feature vector through further processing, and calculate the probability of a seizure and a non-seizure for the one-dimensional feature vector.

2. The electroencephalogram-based power spectrum and phase spectrum of seizure prediction system as claimed in claim 1, wherein, In the electroencephalogram signal acquisition module, the multi-channel electroencephalogram signals are acquired and preprocessed, specifically including the following steps: Collecting electroencephalogram signal data at a set sampling rate, and extracting signal segments of a set time; Performing discrete wavelet transform on the signal segments using a wavelet, selecting detail coefficients, reconstructing a filtered signal, and filtering the signal segments to remove electrooculogram and electromyogram artifacts based on the filtered signal.

3. The electroencephalogram-based power spectrum and phase spectrum of seizure prediction system as claimed in claim 1, wherein, In the model construction module, the first network flow and the second network flow have the same structure and are used to extract deep features, and each of the first network flow and the second network flow comprises a multi-layer convolutional layer, a batch normalization layer, an activation function layer, and a pooling layer; The first convolutional layer receives power spectrum or phase spectrum, and the size of the output feature map gradually decreases and the number of channels gradually increases through a series of convolution and pooling operations.

4. The electroencephalogram-based power spectrum and phase spectrum of seizure prediction system as claimed in claim 1, wherein, In the prediction module, the fused feature map is converted into a one-dimensional feature vector through further processing, and the specific process is as follows: The fused feature map is further convolved and pooled, and finally converted into a one-dimensional feature vector through a global average pooling layer.

5. The electroencephalogram-based power spectrum and phase spectrum of seizure prediction system as claimed in claim 1, wherein, In the prediction module, the probability of a seizure and a non-seizure is calculated for the one-dimensional feature vector, specifically as follows: The global average pooling layer is connected to a fully connected layer, and an activation function is used to output the probability of a seizure and a non-seizure.

6. The electroencephalogram-based power spectrum and phase spectrum of seizure prediction system as claimed in claim 1, wherein, In the model training process of the constructed dual-flow convolutional neural network model, a leave-one-out strategy is adopted to ensure that the data of the test subjects do not participate in the training. Further comprising a post-processing module configured to post-process the output probability, specifically by adding the output scores of adjacent multiple set time segments to obtain a comprehensive score; A moving average filter is used to filter the scores to smooth the score sequence; A threshold is set to determine whether the smoothed score is higher than the threshold to determine whether a seizure occurs.

7. A computer processing method based on power spectrum and phase spectrum of electroencephalogram, characterized in that, The method comprises the following steps: Acquiring and preprocessing multi-channel electroencephalogram signals; Dividing the preprocessed electroencephalogram signals into multiple segments of a set time, transforming each segment of the set time, and extracting power spectrum and phase spectrum based on the transformation; Constructing a dual-flow convolutional neural network model, which comprises a first network flow and a second network flow, the first network flow processes power spectrum, and the second network flow processes phase spectrum; The output features of the first network stream and the second network stream are spliced in the channel dimension to fuse the power and phase information, and a fused feature map is obtained; The fused feature map is further processed and converted into a one-dimensional feature vector, and the one-dimensional feature vector is calculated to output the probabilities of seizures and non-seizures.

8. A computer program product comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the method described in claim 7.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the method described in claim 7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by a processor, executes the steps of the method described in claim 7.

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