Anesthesia consciousness state assessment system and method based on information integration theory

Abstract

The present invention discloses an anesthesia consciousness state assessment system and method based on information integration theory. The system obtains resting-state EEG data under anesthesia and uses bandpass filtering to obtain alpha frequency segments after preprocessing. The continuous EEG signal is converted into discrete variables using a binning method to avoid the Gaussian assumption. The effective information of the multi-channel EEG system is estimated using the definition of discrete multi-channel EEG time series and discrete conditional entropy. Atomic partitioning is used to obtain the maximum normalized integrated information Φ under different time delays in the alpha frequency segment of the multi-channel EEG signal. EEG As a new indicator for the assessment of anesthetic consciousness state. Starting from the problem of anesthetic consciousness state assessment, the present invention is based on the integrated information theory and uses the binning method to solve the problem that the integrated information estimation cannot be applied to the measured EEG signals, thus assessing the anesthetic consciousness state from a theoretical perspective.

Description

Technical Field

[0001] The present invention belongs to the technical field of electroencephalogram (EEG) signals, and relates to an anesthesia consciousness state assessment system and method based on information integration theory, and relates to an anesthesia consciousness state assessment system and method based on information integration theory for multi-channel EEG data under general anesthesia and sedation. Background Art

[0002] Every year, tens of millions of patients have their consciousness suppressed during surgery under general anesthesia, a condition known as loss of consciousness (LOC) / unconsciousness, to ensure their safety during surgery.

[0003] Current clinical assessment and monitoring of different states of consciousness during anesthesia relies on subjective scoring, which is often based on the patient's response to external disturbances. However, after severe brain injury or surgical anesthesia, the patient may remain awake but unresponsive to external disturbances. In these cases, it is impossible to assess whether the patient is still in an appropriate anesthetic state. Another major issue affecting the effectiveness of existing assessment and monitoring algorithms is the large individual differences in sensitivity to anesthetic concentrations among different patients. Due to individual differences, moderate concentrations of anesthetics will not necessarily induce unconsciousness in all patients.

[0004] The bispectral index (BIS) is a typical spectral index that assists anesthesiologists in administering general anesthesia and has been widely used in clinical practice. However, BIS values ​​show significant variability between individual patients and vary significantly with different anesthetic agents. Currently, many available algorithms have been developed, such as M-entropy and auditory evoked potentials. However, these methods all have limitations to varying degrees, and their assessment and monitoring of consciousness under anesthesia are affected by different anesthetic agents and individual differences.

[0005] In addition to clinical indicator research, anesthesia consciousness is supported by different consciousness theories, including global neuronal workspace theory, predictive coding theory, attention schema theory, etc. Among them, the integrated information theory (IIT) provides a quantifiable measure for evaluating the state of anesthesia consciousness (integrated information, i.e. ), and several versions have been developed in recent years. The main assumption of information integration theory is that consciousness is related to the brain's ability to integrate information. It believes that consciousness is supported by the balance between integration and differentiation in the brain. Defined as the maximum effective information of the system .

[0006] Currently, clinical assessment of different states of consciousness under anesthesia is mostly limited to subjective scoring and BIS monitoring. The accuracy of these assessments and monitoring of anesthetic consciousness needs to be improved. Furthermore, there is a lack of an anesthetic consciousness assessment algorithm supported by a theoretical basis for consciousness. Summary of the Invention

[0007] In order to solve the problems existing in the background technology, the present invention proposes an anesthesia consciousness state assessment system and method based on information integration theory. The present invention includes a multi-channel electroencephalogram (EEG) data acquisition device. The present invention involves using multi-channel EEG to record the brain activity of participants under anesthesia in a resting state, and using integrated information (EEG) improved for non-Gaussian EEG data. )Assess the state of consciousness during anesthesia.

[0008] The technical solutions specifically adopted in the present invention are as follows:

[0009] In a first aspect, the present invention provides a method for assessing anesthesia consciousness state based on information integration theory, comprising:

[0010] S1: Data Collection

[0011] Collect resting-state multi-channel EEG data from subjects under anesthesia;

[0012] S2: Data Preprocessing

[0013] Preprocess the resting-state multi-channel EEG data, and then use bandpass filtering to filter the preprocessed multi-channel EEG data to obtain alpha band EEG data;

[0014] S3: EEG discretization processing

[0015] Since the continuous EEG signal after data preprocessing is non-Gaussian and non-stationary, each sampling point of the alpha frequency band EEG signal is discretized to obtain the discretized EEG time series;

[0016] S4: Effective Information Estimation

[0017] According to the above discretized EEG time series, combined with formula (1), the effective information of the alpha band multi-channel EEG signal is Make estimates;

[0018] Formula (1)

[0019] In the formula Represents effective information, which is defined as the difference between the information generated by multi-channel EEG and the information generated by each single channel EEG; is a multi-channel EEG signal. is the time delay between the current time state and the past time state, for The preset division ratio, for After the division Individual EEG signals, is the number of sub-EEG signals, is the discrete conditional entropy;

[0020] Using the discrete version of conditional entropy Make an estimate:

[0021] Formula (2)

[0022] In the formula and is a discrete variable, and n is and Discrete states in ;

[0023] S5: Integrated Information Computing

[0024] 5-1 Effective information based on multi-channel EEG signals , use atomic partition (AP) as the preset partition ratio , according to formula (3) we can get the integrated information ;

[0025] Formula (3)

[0026] 5-2 Considering that each EEG signal of different EEG channels has different ability to generate information, the normalization coefficient is used to Normalize it and get ;

[0027] Formula (4)

[0028] Where: is the estimate of mutual information, For the The amount of information generated by each brain signal;

[0029] 5-3 The maximum normalized integration information of all delays As the final integrated information ;

[0030] Formula (5)

[0031] S6: Based on the final integrated information Make a judgment to identify the subject's state of anesthesia consciousness.

[0032] Preferably, the preprocessing specifically corrects the DC bias of the resting-state multi-channel EEG data, performs a 0.5–45 Hz bandpass filter, removes power frequency interference, re-references the electrodes through an average reference, downsamples the EEG data to 250 Hz, uses an inverse filter to detect and eliminate interference from muscle activity, uses a wavelet filtering-based algorithm to remove electrooculogram interference, segments the EEG signals into segments of 4 s and 50% overlap, and identifies abnormal EEG channels by calculating the normalized variance of the EEG signals.

[0033] Preferably, in step S3, a binning method is used for discretization.

[0034] In a second aspect, the present invention provides an anesthesia consciousness state assessment system, comprising:

[0035] Data acquisition module, used to collect resting-state multi-channel EEG data of subjects under anesthesia;

[0036] The data preprocessing module is used to preprocess the resting-state multi-channel EEG data collected by the data acquisition module, and then use bandpass filtering to filter the preprocessed multi-channel EEG data to obtain alpha frequency band EEG data;

[0037] The EEG discretization processing module is used to discretize each sampling point of the alpha frequency band EEG signal output by the data preprocessing module to obtain the discretized EEG time series;

[0038] The effective information estimation module is used to extract the effective information of the alpha frequency band multi-channel EEG signal from the discretized EEG time series output by the EEG discretization processing module. ;

[0039] Integrated information calculation module, used to calculate the effective information of multi-channel EEG signals , use atomic partition (AP) as the preset partition ratio , get integrated information ; Use normalization coefficients to Normalize it and get ; The maximum normalized integration information of all delays As the final integrated information ;

[0040] Anesthesia consciousness state recognition module is used to identify the state of anesthesia based on the final integrated information Make judgments and identify the subject's state of consciousness under anesthesia;

[0041] The display screen is used to display the recognition results of the anesthesia consciousness state recognition module.

[0042] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed in a computer, the computer is caused to execute the method described above.

[0043] In a fourth aspect, the present invention provides a computing device comprising a memory and a processor, wherein the memory stores executable code, and the processor implements the described method when executing the executable code.

[0044] The beneficial effects of the present invention are:

[0045] The present invention introduces information integration theory into the assessment of anesthetic consciousness state, avoiding the limitations of existing anesthetic consciousness state assessment technology in anesthetic assessment under different anesthetic drugs and individual differences, making the assessment results more theoretically based and credible.

[0046] The present invention introduces a binning method into multi-channel EEG signals to calculate the integrated information value, avoiding the Gaussian requirement of existing integrated information calculation methods for data, so that information integration theory can be used in anesthesia monitoring based on EEG signals.

[0047] The present invention uses EEG information from seven electrodes covering the entire brain and atomic partitioning to calculate the integrated information value, which greatly reduces the amount of calculation of the integrated information and enables it to be more conveniently applied in clinical environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the EEG binning method and multi-channel EEG system of the present invention; A is the schematic diagram of the EEG signal binning method, B is the schematic diagram for estimating Schematic diagram of multi-channel EEG signals and sub-EEG signals.

[0049] Figure 2 Middle (A)- Figure 2 Middle (B) shows the dynamics of participants who lost consciousness during propofol anesthesia. and the corresponding statistical results.

[0050] Figure 3 Middle (A)- Figure 3 Middle (B) shows the dynamics of participants who were anesthetized with propofol but did not lose consciousness. and the corresponding statistical results.

[0051] Figure 4 Middle (A)- Figure 4 Middle (B) are the statistical results of eBIS for participants who lost consciousness during propofol anesthesia and those who did not lose consciousness. DETAILED DESCRIPTION

[0052] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, the following detailed description of the specific embodiments of the present invention is provided in conjunction with the accompanying drawings. The following description sets forth numerous specific details to facilitate a full understanding of the present invention. A set of publicly available EEG data from propofol anesthesia is used as an example for illustration.

[0053] Participants: Twenty-two healthy adults participated in this study. Due to technical issues, data from two participants were unavailable; data from the remaining 20 participants (9 males; 11 females) (mean age = 30.85; SD = 10.98) were analyzed.

[0054] Anesthesia Protocol: Each experimental run began with a 25-30 minute awake baseline period, followed by a target-controlled propofol infusion initiated via an automated syringe driver (Alaris Asena PK, Carefusion, Berkshire, UK). Using this system, the anesthesiologist inputs the target plasma concentration, and the system determines the infusion rate required to achieve and maintain the target concentration. Three propofol plasma levels were targeted: 0.6 μg / ml (mild sedation), 1.2 μg / ml (moderate sedation), and recovery. The mild sedation state was designed to produce a relaxed yet still responsive behavioral state. At each target level, 10 minutes were allowed for plasma propofol concentration to reach steady state before behavioral testing and EEG recordings were initiated. After cessation of the infusion, plasma propofol concentrations declined exponentially to zero. In silico pharmacokinetics simulations using TIVATrainer indicated that propofol plasma concentrations approached zero within 15 minutes, leading to behavioral recovery; therefore, behavioral assessments were resumed 20 minutes after cessation of sedation.

[0055] Behavioral Data Collection: At each of the four steady-state levels described above, participants were asked to perform a simple behavioral task involving the rapid discrimination of two auditory stimuli. Specifically, participants were asked to respond by pressing a button to indicate whether the stimulus presented binaurally was a buzz or a noise. Forty such stimuli, twenty of each type, were presented in a randomized order with an average interstimulus interval of 3 seconds. Participants' cognitive processing of these stimuli at each sedation level was calculated based on their hit rate (i.e., the percentage of correct responses). In addition, reaction time (the delay between the onset of the auditory stimulus and the correct button press) was measured.

[0056] Behavioral Assessment: A binomial model was used to distinguish participants whose behavior was impaired during moderate sedation from those whose reaction times remained responsive despite slower response times. Specifically, a binomial distribution was fitted to each participant's hit rate during baseline and moderate sedation. For each fitted model, the distribution parameter p, the probability of a correct response, and its 95% confidence interval were estimated. For a given participant, if the confidence interval during moderate sedation was lower than the confidence interval at baseline and did not overlap with the confidence interval at baseline, their consciousness was considered significantly impaired and they were classified as unconscious under anesthesia. If the confidence intervals overlapped, they were classified as not unconscious under anesthesia. Of the 20 participants, 7 were unconscious under anesthesia and 13 were not. Therefore, an accurate metric for assessing consciousness during anesthesia should show significant differences during anesthesia in the 7 participants who were unconscious but not in the 13 participants who were not unconscious.

[0057] EEG signals were acquired using a Net Amps 300 amplifier (Electrical Geodesics Inc., Eugene, Oregon, USA), encompassing seven EEG channels (Fp1, Fp2, T3, Cz, T4, O1, and O2) based on the 10-20 international scale. Multi-channel EEG signals were acquired for 4 minutes at baseline, 0.6 μg / ml (mild), 1.2 μg / ml (moderate), and recovery from sedation. EEG data were preprocessed by first performing DC offset correction and bandpass filtering from 0.5 to 45 Hz to remove power frequency interference. Anomalous data segments were identified and removed by calculating the normalized variance. The electrodes were re-referenced using an average reference, and the EEG data were downsampled to 250 Hz. In neuroelectrophysiology, different EEG frequency bands are thought to represent neuronal integration at different spatial scales: slower oscillations synchronize brain networks over longer distances, while faster oscillations are thought to synchronize cell assemblies over relatively short spatial scales. In addition, slower oscillations (theta, alpha) represent higher-level top-down cognitive processes, while faster oscillations (beta, gamma) represent local bottom-up processes. The preprocessed multi-channel EEG data were filtered using bandpass filtering into five frequency bands: delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), beta (12-25 Hz), and gamma (25-45 Hz); the EEG signals in each frequency band were segmented into 4 s segments with 50% overlap to estimate .

[0058] The original estimation algorithm of integrated information is designed for Gaussian system and is not suitable for non-Gaussian EEG data. The present invention uses the binning method to convert the continuous EEG signal into discrete variables to avoid the Gaussian assumption. In simple terms, since the sampling points of the EEG signal are all continuous values, the entropy cannot be directly estimated for the EEG signal sequence. For each sampling point of the EEG signal in different frequency bands, a simple rounding method is used to obtain its discrete value, and then the next step of entropy-based integrated information estimation can be carried out. The binning method and the EEG system are shown in the attached figure. Figure 1 As shown. The multi-channel EEG signals of each frequency band are processed using the binning method to obtain discrete EEG signals.

[0059] According to the above discretized EEG time series, combined with formula (1), the effective information of the alpha band multi-channel EEG signal is Make estimates;

[0060] Formula (1)

[0061] In the formula Represents effective information, which is defined as the difference between the information generated by multi-channel EEG and the information generated by each single channel EEG; is a multi-channel EEG signal. is the time delay between the current time state and the past time state, for The preset division ratio, for After the division Individual EEG signals, is the number of sub-EEG signals, is the discrete conditional entropy;

[0062] Using the discrete version of conditional entropy Make an estimate:

[0063] Formula (2)

[0064] In the formula and is a discrete variable, and n is and Discrete states in ;

[0065] According to the effective information of multi-channel EEG signals , use atomic partition (AP) as the preset partition ratio , according to formula (3) we can get the integrated information ;

[0066] Formula (3)

[0067] Considering that each EEG signal of different EEG channels has different ability to generate information, the normalization coefficient is used to Normalize it and get ;

[0068] Formula (4)

[0069] Where: is the estimate of mutual information, For the The amount of information generated by each brain signal;

[0070] Integrate information Based on delay For example, if the time delay is set to 20 milliseconds, then It is possible to estimate how much information a multi-channel EEG system integrates within 20 milliseconds. Based on previous research, the human brain's conscious perception should be within a rough time scale. In other words, there is a specific time scale for the integration of information. Therefore, the present invention will delay Set it to 12 ms to 200 ms, with an interval of 4 ms (this interval is the minimum because the sampling rate of our multi-channel EEG data is 250 Hz). As the final integrated information ;

[0071] Formula (5)

[0072] According to the final integrated information Make a judgment to identify the subject's state of anesthesia consciousness.

[0073] The alpha frequency band is believed to provide the most features of consciousness in the brain and is dominant during surgery under general anesthesia. In addition, the long-range integration of top-down processing (which supports consciousness) gradually develops with the temporal dynamics of the alpha frequency band. Therefore, the alpha frequency band Represents the consciousness of the multi-channel EEG system, which is a new evaluation index of anesthesia consciousness state proposed in this invention. The larger the value, the more conscious the participant is, and the smaller the value, the less conscious the participant is. When it reaches around 7.0, it means that the participant is beginning to lose consciousness.

[0074] All data processing is completed in the terminal device, which includes a host, a panel, a display, and a power connector. The front end of the host is provided with a panel, a display is embedded in the panel, and the power connector is located on the right side of the host. The host includes a power supply, a data processing chip, a connecting mechanism, and an external mechanism. The power supply is connected to the power connector, and the data processing chip is connected to the display through the connecting mechanism. The original EEG signal and The calculated value is displayed on the monitor. When the EEG signal is abnormal, the monitor will prompt the abnormal signal. When the value is higher than 7.0, the displayed value is green. When it is lower than 7.0, the displayed value will turn orange. When it drops to 0, the displayed value turns red and an alarm occurs.

[0075] Calculate eBIS (estimated Bispectral index) and Comparing performance: The effectiveness of the bispectral index (BIS) and the eBIS in distinguishing various states of consciousness under anesthesia was investigated. The bispectral index (BIS) is a combination of time-domain (burst suppression ratio, BSR) and frequency-domain (beta ratio, beta_ratio and fast-slow synchronization, synch_fast_slow) parameters. All time-domain and frequency-domain subparameters were calculated for each 4-second window and averaged for each participant. The eBIS was calculated by summing the subparameters:

[0076]

[0077] Statistical analysis: Considering the small sample size of this study, we used the accelerated bootstrap procedure to analyze the dynamics of all patients and participants. Resampling was performed. In this process, the data of all participants were resampled 1000 times. The original data before bootstrap were tested. The significant differences: The normal distribution of the data was tested using the Shapiro-Wilk test and the traditional repeated measures analysis of variance (ANOVA) combined with the least significant difference (LSD) test was used to verify the To investigate the differences in the eBIS and sedation status between different states of consciousness, a Bayesian repeated measures ANOVA was performed to further validate the statistical results. Only the differences between baseline and moderate sedation, and between moderate sedation and sedation recovery, were compared. The p-values ​​were corrected for multiple comparisons using the false discovery rate (FDR). SPSS version 23.0 software was used for conventional repeated measures ANOVA. JASP software was used for Bayesian repeated measures ANOVA. Bayes factor (BF) was used. 10>100 indicates decisive evidence that H1 occurs under the conditions compared with H0, 30< BF 10 <100 indicates very strong evidence, 10< BF 10 <30 indicates strong evidence, 3< BF 10 <10 indicates moderate evidence, 1< BF 10 <3 means the evidence is weak, BF 10 <1 means no evidence.

[0078] Comparison of statistical results: Figure 2 Showing the dynamics of unconscious participants under propofol anesthesia The changes and corresponding statistical results during anesthesia are in the delta, theta, alpha, beta and gamma bands. Four states of consciousness (baseline, mild sedation, moderate sedation and sedation recovery) are distinguished based on the plasma levels during anesthesia. Figure 2 The dynamics of the alpha band can be observed The sedation process was consistent with propofol-induced anesthesia, and there was a significant difference between baseline and moderate sedation (p = 0.016, BF 10 = 3.58). Figure 3 Shows the dynamics of propofol-anesthetized participants who did not lose consciousness The changes and corresponding statistical results during anesthesia are in the delta, theta, alpha, beta and gamma bands. Figure 3 The dynamics of the alpha band can be observed There was no significant change during anesthesia, and there was no significant difference between baseline and moderate sedation, because for participants who did not lose consciousness during anesthesia, although the plasma concentration of propofol changed, their consciousness state did not change. It is an accurate indicator for evaluating anesthesia awareness. Figure 4 The statistical results of eBIS are shown in order to compare Performance comparison shows that eBIS can well simulate the performance of real BIS value in anesthesia awareness assessment. Figure 4 A shows that for participants who lost consciousness during propofol-induced anesthesia, the eBIS at moderate sedation was significantly different from that at baseline (p = 0.005, BF 10 = 11.59). However, among participants who did not lose consciousness during propofol-induced anesthesia, moderate sedation was significantly different from baseline (p = 0.03, BF 10 = 2.41) also showed significant differences (Appendix Figure 4B) It can be seen that when propofol plasma concentration changes but does not cause changes in the participant's consciousness, the eBIS misjudged the participant's consciousness state. The results show that for the assessment of different consciousness states during anesthesia, the eBIS is more sensitive to anesthetic concentration, while the alpha frequency band is more sensitive to anesthetic concentration. It can better monitor the consciousness state of participants under anesthesia than eBIS.

[0079] The embodiment described above is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Persons skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent substitution or equivalent transformation falls within the scope of protection of the present invention.

Claims

1. A method for assessing anesthesia consciousness state based on information integration theory, characterized in that: The method comprises the following steps: S1: Data Collection Collect resting-state multi-channel EEG data from subjects under anesthesia; S2: Data Preprocessing Preprocess the resting-state multi-channel EEG data, and then use bandpass filtering to filter the preprocessed multi-channel EEG data to obtain alpha-band EEG signals; S3: EEG discretization processing Since the continuous EEG signal after data preprocessing is non-Gaussian and non-stationary, each sampling point of the alpha band EEG signal is discretized to obtain the discretized EEG time series; S4: Effective Information Estimation According to the above discretized EEG time series, combined with formula (1), the effective information of the alpha band multi-channel EEG signal is Make estimates; Formula (1) In the formula Represents effective information, which is defined as the difference between the information generated by multi-channel EEG and the information generated by each single channel EEG; is a multi-channel EEG signal. is the time delay between the current time state and the past time state, for The preset division ratio, for After the division Individual EEG signals, is the number of sub-EEG signals, is the discrete conditional entropy; Using the discrete version of conditional entropy Make an estimate: Formula (2) In the formula and is a discrete variable, and n is and Discrete states in ; S5: Integrated Information Computing 5-1 Effective information based on multi-channel EEG signals , use atomic partition (AP) as the preset partition ratio , according to formula (3) we can get the integrated information ; Formula (3) 5-2 Considering that each EEG signal of different EEG channels has different ability to generate information, the normalization coefficient is used to Normalize it and get ; Formula (4) Where: is the estimate of mutual information, For the The amount of information generated by each brain signal; 5-3 The maximum normalized integration information of all delays As the final integrated information ; Formula (5) S6: Based on the final integrated information Make a judgment to identify the subject's state of anesthesia consciousness.

2. The method according to claim 1, characterized in that The preprocessing specifically includes correcting the DC bias of resting-state multi-channel EEG data, performing a 0.5-45 Hz bandpass filter to remove power frequency interference, re-referencing the electrodes through an average reference, downsampling the EEG data to 250 Hz, using an inverse filter to detect and eliminate interference from muscle activity, using a wavelet filtering-based algorithm to remove electrooculogram interference, segmenting the EEG signals into 4-second segments with 50% overlap, and identifying abnormal EEG channels by calculating the normalized variance of the EEG signals.

3. The method according to claim 1, characterized in that In step S3, the binning method is used for discretization.

4. An anesthetic consciousness state assessment system implementing the method according to any one of claims 1 to 3, characterized in that include: Data acquisition module, used to collect resting-state multi-channel EEG data of subjects under anesthesia; The data preprocessing module is used to preprocess the resting-state multi-channel EEG data collected by the data acquisition module, and then use bandpass filtering to filter the preprocessed multi-channel EEG data to obtain alpha-band EEG signals; The EEG discretization processing module is used to discretize each sampling point of the alpha frequency band EEG signal output by the data preprocessing module to obtain the discretized EEG time series; The effective information estimation module is used to extract the effective information of the alpha frequency band multi-channel EEG signal from the discretized EEG time series output by the EEG discretization processing module. ; Integrated information calculation module, used to calculate the effective information of multi-channel EEG signals , use atomic partition atomicpartition as the preset partition ratio , get integrated information ; Use normalization coefficients to Normalize it and get ; The maximum normalized integration information of all delays As the final integrated information ; Anesthesia consciousness state recognition module is used to identify the state of anesthesia based on the final integrated information Make judgments and identify the subject's state of consciousness under anesthesia; The display screen is used to display the recognition results of the anesthesia consciousness state recognition module.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that When the computer program is executed in a computer, the computer is caused to execute the method according to any one of claims 1 to 3.

6. A computing device comprising a memory and a processor, characterized in that The memory stores executable code, and when the processor executes the executable code, the method according to any one of claims 1 to 3 is implemented.

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