Characteristic value calculation method based on electrocardiogram data

Abstract

The invention discloses a characteristic value calculation method based on electrocardio data, belongs to the field of medical data analysis, and provides an electrocardio data analysis and processing method. Comprising the following steps: decomposing different frequency components of an electrocardiosignal by using wavelet transform, and analyzing on different time scales. Wavelet transformation is relatively suitable for detecting QRS wave groups, and due to the fact that the wavelet transformation can highlight transient characteristics of signals on different frequency bands, complex electrocardiosignal processing is more efficient. In addition, wavelet transform is not only suitable for wave crest detection, but also can help to remove signal noise and improve signal definition. The deep learning technology is used for automatically extracting the features from the electrocardiosignals, a feature extractor does not need to be manually designed, related medical professional knowledge and the artificial intelligence technology are combined, wave crests in the electrocardiosignals can be more accurately detected, and meanwhile anomaly detection can be carried out, such as early signs of heart diseases such as sinus arrhythmia and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of medical data analysis, and in particular to a method for calculating characteristic values ​​based on electrocardiogram data. Background Art

[0002] In the context of modern medicine, resting electrocardiogram (ECG) is a basic and commonly used tool for assessing heart health and has important clinical significance. The basic function of resting electrocardiogram is to help detect and diagnose cardiovascular diseases such as arrhythmia, myocardial ischemia, and myocardial infarction by recording the electrical activity of the heart at rest. With the increase in the incidence of cardiovascular diseases, especially as cardiovascular diseases have become one of the main causes of death worldwide, the application of electrocardiogram has become more extensive. However, traditional resting electrocardiogram analysis methods have many shortcomings and cannot fully meet the requirements of efficiency, accuracy, and automation in modern medical environments. First, traditional electrocardiogram analysis mainly relies on manual interpretation by medical staff. This method is highly subjective, especially for complex or marginal cases, misdiagnosis or missed diagnosis may occur. This subjective analysis process is also affected by the doctor's personal experience and judgment, resulting in large differences in the interpretation results between different doctors. In addition, manual interpretation of electrocardiogram data often takes a long time, especially when facing a large number of patients, which easily leads to a waste of medical resources and is not conducive to timely treatment of the disease.

[0003] With the rapid development of information technology, automated ECG eigenvalue calculation methods have emerged to improve the efficiency and accuracy of diagnosis. These methods are usually based on signal processing technology, machine learning algorithms and biostatistics models, and automatically extract and analyze the eigenvalues ​​of ECG signals by computers to identify cardiac abnormalities. However, although these methods have significantly improved the analysis efficiency, they still face many challenges in practical applications. One major challenge is the complexity of ECG signals. Resting ECG signals are affected by many factors, such as the patient's physiological state, environmental interference, equipment noise, etc., which may cause noise and baseline drift in the signal. How to effectively remove these interferences and accurately extract key ECG eigenvalues, such as P waves, QRS waves and T waves, is a technical challenge faced by automated analysis methods. In addition, the nonlinear and non-stationary characteristics of ECG signals increase the complexity of algorithm design, requiring more efficient computing resources and more advanced algorithms to deal with. Another significant problem is the generalization ability of the algorithm. Many automated eigenvalue calculation methods perform well on specific data sets, but when applied to different groups, the effect may not be satisfactory. ECG data may show significant differences due to race, age, gender or health status, which requires the algorithm to have good generalization ability and maintain high accuracy and reliability in different patient groups. This limitation not only limits the universality of the algorithm, but also increases the risk of clinical application.

[0004] In this context, it is crucial to develop a computational method that can read ECG data files in a standard format and improve the generalization ability of the algorithm. It is necessary not only to fully utilize the content of the ECG data, but also to reduce the complexity of feature extraction, while integrating clinical standards to reduce the compatibility between different systems and the limitations on the consistency of results. Summary of the invention

[0005] In order to solve the technical problems existing in the above-mentioned prior art that the accurate extraction of key electrocardiogram eigenvalues ​​and the automated eigenvalue calculation method perform well on specific data sets, but the effect is unsatisfactory when applied to different groups, the present invention provides a eigenvalue calculation method based on electrocardiogram data.

[0006] To implement the above technical solution, the present invention provides a method for calculating characteristic values ​​based on electrocardiogram data, comprising the steps of:

[0007] S1: Obtain the patient data who has undergone static electrocardiogram. First, the electrocardiogram data comes from the hospital. The electrocardiogram data is exported in batches from the hospital information system. The electrocardiogram machine configured by the hospital can adapt to both 12-lead and 18-lead detection needs. It uses a 1000Hz sampling rate and an inspection time of 10s. Select the xml file for saving the file format, and there will be a file fda.xml file exported at the same time; then use the custom function readXML in the PyCharm software to read the Ⅰ lead, Ⅱ lead, Ⅲ lead, AVR lead, AVL lead, AVF lead, V1 lead, V2 lead, V3 lead, V4 lead, V5 lead and V6 lead in turn, a total of 120,000 data points; finally, the 18-lead further reads the V3R lead, V4R lead, V5R lead, V7 lead, V8 lead and V9 lead, a total of 18,000 data points

[0008] 0 data points;

[0009] S2: Through the customized wavelet denoising filter function and wavelet multi-resolution decomposition function, the wavelet transform method is used to remove the interference of 50Hz noise from the read ECG data, and the wavelet multi-resolution decomposition is used to remove the baseline drift;

[0010] S3: The BioSPPy library is used to measure each measurement point of a single wave of each lead. The purpose is to mark the starting point, peak value, and end point of each wave, and then manually check and verify to obtain labeled ECG data.

[0011] S4: Expanding the parameters that cannot be directly measured from the electrocardiogram through the measurement points obtained in step S3;

[0012] S5: The ECG data with the calculated feature points and labeled are stored in a CSV file;

[0013] S6: After reading the labeled data, normalize the data;

[0014] S7: After dividing the labeled ECG data into training and test sets, the one-dimensional signal is converted into a

[0015] The shape of the deep learning model is then reshaped into two-dimensional data.

[0016] S8: By using the improved semantic segmentation U-net network structure, after encoding and decoding, the output model

[0017] Visualization results of the type;

[0018] S9: After training the model, evaluate the performance of the model on the test set, make predictions through the model, and extract cardiac telegrams

[0019] The characteristic value of the number;

[0020] S10: Analyze and compare the calculated characteristic values ​​with the expert consensus standard values, determine reasonable parameter standard values ​​based on the local conditions, and feed back to step S3 to update more accurate annotation points.

[0021] Furthermore, step S2 includes: wavelet decomposition, using discrete wavelet transform (DWT) to decompose the ECG signal into multiple levels; threshold selection, estimating the noise standard deviation through the absolute median, and calculating the soft threshold based on this value; denoising, using the threshold to process the detail coefficients; wavelet reconstruction, inversely transforming the processed coefficients into time domain signals to achieve the purpose of denoising.

[0022] Further, step S3 includes: baseline, R wave detection, processing the electrocardiogram signal using the biosppy.signals.ecg function, and calculating the peak value of the T wave using the BioSPPy library.

[0023] Furthermore, the baseline is a line connecting the starting points of two QRS complexes; in the process of processing the electrocardiogram signal using the biosppy.signals.ecg function, it is assumed that the P wave is in the window before the R wave.

[0024] Further, in step S3, the measurement points include baseline, P wave peak, P wave starting point, P wave ending point, QRS wave starting point, R wave peak, QRS wave ending point, T wave starting point, T wave peak, T wave ending point, Q point peak, Q point ending point, S wave starting point, S wave peak and QRS electrical axis.

[0025] Further, in step S4, the parameters include heart rate HR, P wave width, P wave amplitude, PR interval, QRS duration, Q wave width, Q wave amplitude, S wave width, S wave amplitude, R wave amplitude, QT interval, QTc interval, ST interval, T wave amplitude, RR interval, PP interval, RR interval difference and PP interval difference.

[0026] Furthermore, the calculation formula of QTc interval is:

[0027]

[0028] Furthermore, the method for confirming the T wave is as follows: draw a tangent at the steepest point of the T wave terminal branch along the apex of the T wave, and the intersection of the tangent and the isoelectric line is determined as the end point of the T wave. When the amplitudes of the double-peak T wave are equivalent, the QT interval is measured to the intersection of the maximum tangent of the second peak of the T wave and the baseline; at this time, the period between the two peaks of the T wave can be measured, ≤150ms is the notch of the T wave, and >150ms is the overlap of the TU wave.

[0029] Furthermore, in step S5, the label includes the starting point, ending point, peak value, and width of each wave.

[0030] In summary, the present invention has the following beneficial effects compared with the prior art:

[0031] The present invention proposes a new method for analyzing and processing ECG data. This method includes using wavelet transform to decompose the different frequency components of ECG signals and analyze them on different time scales. Wavelet transform is more suitable for detecting QRS complexes because wavelet transform can highlight the transient characteristics of signals in different frequency bands, making the processing of complex ECG signals more efficient. In addition, wavelet transform is not only suitable for peak detection, but also can help remove signal noise and improve signal clarity. Deep learning technology is used to automatically extract features from ECG signals without the need for manually designed feature extractors. It combines relevant medical expertise and artificial intelligence technology to enable more accurate detection of peaks in ECG signals, while enabling abnormality detection, such as early signs of heart disease such as sinus arrhythmia.

[0032] This newly proposed ECG data analysis and processing method has undoubtedly brought important innovations and breakthroughs to the field of ECG monitoring. By combining wavelet transform and deep learning technology, this method can not only efficiently decompose and analyze the different frequency components of ECG signals, but also show excellent performance in denoising and feature extraction. This advanced technical means will greatly improve the accuracy and efficiency of ECG data analysis, and provide strong support for the early diagnosis of clinical heart disease. Especially in today's rapid development of artificial intelligence, the application potential of this method is undoubtedly huge. It will promote the development of the medical industry in a more intelligent direction, help doctors better identify and diagnose heart disease, and ultimately benefit the majority of patients and make important contributions to improving public health. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0034] Figure 1 It is a schematic diagram of the overall process of applying an algorithm for calculating eigenvalues ​​using ECG data;

[0035] Figure 2 This is a schematic diagram of the content of the central electrical data file of this application;

[0036] Figure 3 It is a schematic diagram of the U-net model in this application. DETAILED DESCRIPTION

[0037] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0038] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0039] See also Figures 1 to 3 As shown, the present invention provides an algorithm for calculating characteristic values ​​based on electrocardiogram data, comprising the steps of:

[0040] S1: Get the patient data who has done a static ECG. First, the ECG data comes from the hospital. The ECG data is exported in batches from the hospital information system. The ECG machine configured by the hospital can adapt to both 12-lead and 18-lead detection requirements, using a 1000Hz sampling rate and a 10s inspection time. Select the XML file as the file format to save, and the fda.xml file will be exported at the same time. The XML file contains the basic information of the ECG machine, the patient's basic personal information, the start and end time of the static ECG test, and also includes the patient's ECG diagnosis and description. The fda.xml file also contains most of the content in the XML file, but the fda.xml file also covers the ECG data points of each lead, which are saved in digits. A digits content contains 10,000 data points. Through the custom function readXML function in PyCharm software, a total of 120,000 data points of lead I, lead II, lead III, AVR lead, AVL lead, AVF lead, V1 lead, V2 lead, V3 lead, V4 lead, V5 lead and V6 lead are read in sequence. For 18 leads, a total of 180,000 data points of lead V3R, lead V4R, lead V5R, lead V7, lead V8 and lead V9 are read.

[0041] S2: The 50Hz noise is removed from the read ECG data using the wavelet transform method, and the baseline drift is removed using wavelet multi-resolution decomposition. This can be achieved through the custom wavelet denoising filter function and wavelet multi-resolution decomposition function in the PyCharm software, which is conducive to the subsequent determination of the baseline position.

[0042] For example, after removing the noise of ECG data with 10,000 data points at a sampling frequency of 1000 Hz, the data is decomposed, the level can be selected as 5 as shown, and the soft threshold is 0.5, but the most appropriate value needs to be determined based on the specific data, and then the baseline drift removal part is continued.

[0043] As a preferred embodiment, step S2 needs to be coded. During the code programming process, four methods are used in step S2, namely wavelet decomposition: using discrete wavelet transform (DWT) to decompose the ECG signal at multiple levels, the purpose is to obtain the approximation component and detail component of the signal. Threshold selection: the noise standard deviation is estimated by the absolute median, and the soft threshold is calculated based on this value. The selection of threshold is the key to denoising, which controls the ratio of noise to signal. Denoising processing: using threshold processing detail coefficients, soft threshold processing makes the signal smooth without losing important features. Wavelet reconstruction: the processed coefficients are inversely transformed into time domain signals to achieve the purpose of denoising.

[0044] S3. Measure individual waves of each lead, including baseline, P wave peak, P wave start point, P wave end point, QRS wave start point, R wave peak, QRS wave end point, T wave start point, T wave peak, T wave end point, Q point peak, Q point end point, S wave start point, S wave peak, and QRS axis.

[0045] As a preference, step S3 includes:

[0046] Baseline, the baseline is the basic line segment, usually the line connecting the starting points of two QRS wave groups. The judgment of the direction of each wave of the electrocardiogram and the measurement of the amplitude are all based on the electrocardiogram baseline as the reference level. Under normal circumstances, the isoelectric line includes three parts: PR segment, ST segment and TP segment, and the baseline and the isoelectric line are on the same horizontal line. When affected by certain factors (such as tachycardia, myocardial ischemia, etc.), the PR segment or ST segment no longer reflects the isoelectric line, and there is a deviation between the three, and the isoelectric line deviates from the baseline.

[0047] R wave detection uses the derivative of the signal to detect the position of the R wave. This method detects the change in the peak value and can be used to identify the R wave. The subsequent extraction of waveform features (extract_wave_features function) can extract the features of the P wave, Q wave, R wave, S wave, and T wave from the position of the R wave.

[0048] Use the biosppy.signals.ecg function to process the ECG signal and obtain information such as the R wave position and the filtered signal. Use the find_p_wave_features function to extract the peak, start point, and end point of the P wave. Here, it is assumed that the P wave is in the window before the R wave.

[0049] Use the BioSPPy library to calculate the peak of the T wave. The T wave usually follows the R wave and can be extracted by analyzing the shape of the ECG signal. BioSPPy provides powerful ECG signal processing functions that can help us identify the T wave.

[0050] S4: Parameters that cannot be measured directly from the electrocardiogram are expanded through the measurement points calculated by S3, such as HR (heart rate), which is obtained by calculating the time interval between two adjacent R waves. In addition, it also includes P wave width, P wave amplitude, PR interval, QRS duration, Q wave width, Q wave amplitude, S wave width, S wave amplitude, QRS amplitude, QT interval, QTc, ST interval, T wave amplitude, RR' interval (R' indicates the next R wave) and PP' (P' indicates the next P wave) interval, and RR interval difference.

[0051] R wave peak extraction: Use info['ECG_R_Peaks'] to extract the position of the R wave.

[0052] RR interval calculation: Use np.diff() function to calculate the time interval between adjacent R peaks, and the result is in samples.

[0053] Heart rate calculation: Calculate heart rate based on RR interval. The formula is heart rate (bpm) = 60 / (RR interval (seconds)). To convert to seconds, the RR interval needs to be divided by the sampling frequency. The data sampling frequency used in the experiment is 1000 Hz.

[0054] P wave width = P wave starting point (P-start) - P wave ending point (P-end).

[0055] P wave amplitude = P wave peak (P-peak) - baseline (baseline)

[0056] PR interval = P wave starting point (P-start) - QRS wave starting point (QRS-start)

[0057] QRS duration = QRS wave starting point (QRS-start) - QRS wave ending point (QRS-end)

[0058] Q wave width = QRS wave starting point (QRS-start) - Q wave ending point (Q-end)

[0059] Q wave amplitude = Q wave peak (Q-peak) - baseline (baseline)

[0060] S wave width = S wave starting point (S-start) - QRS wave ending point (QRS-end)

[0061] S wave amplitude = S wave peak (S-peak) - baseline (baseline)

[0062] QRS amplitude = R wave amplitude (R-peak) - baseline

[0063] QT interval = QRS wave starting point (QRS-start) - T wave ending point (Q-end)

[0064] RR' interval = R wave starting point (R-start) - R' wave starting point (R' starting point)

[0065] RR interval difference = maximum RR' interval - minimum RR' interval

[0066] QTc (corrected QT interval) is a correction value of the QT interval in the electrocardiogram (ECG) to eliminate the effect of heart rate on the interval. The QT interval is the time from the start of the QRS to the end of the T wave. Since heart rate has a significant effect on the QT interval, c is used to standardize the QT intervals under different heart conditions to make them comparable. The calculation formula is as follows:

[0067]

[0068] When the T wave morphology is variable and the T wave end point is difficult to determine, a tangent is drawn from the T wave apex along the steepest part of the T wave terminal branch. The intersection of the tangent and the isoelectric line is determined as the T wave end point. When the amplitude of the bimodal T wave is equal, the QT interval is measured to the intersection of the maximum tangent of the second peak of the T wave and the baseline. The overlap of the T and U waves is similar to the notch of the T wave. At this time, the period between the two peaks of the T wave can be measured. If it is ≤150ms, it is the notch of the T wave. If it is >150ms, it is caused by the overlap of the TU waves. For most patients, the 12-lead synchronous electrocardiograph can automatically and accurately determine the starting point of the QRS wave and the end point of the T wave, and distinguish the U wave from the T wave. Its measurement results are accurate and reliable.

[0069] T wave amplitude = T wave peak (T-peak) - baseline (baseline)

[0070] S5: Label the ECG data whose characteristic values ​​have been calculated, including the starting point, end point, peak value, and width of each wave. Store the ECG data in a CSV file.

[0071] S6: After reading the labeled data, normalize the data.

[0072] S7: The ECG data is divided into training and test sets. In order to input the data into the neural network, we need to convert the one-dimensional signal into a shape suitable for the deep learning model and reshape the data into two-dimensional data (number of samples, time steps, number of features).

[0073] S8: By using the improved semantic segmentation U-net network structure, after encoding and decoding, the visualization results of the model are output;

[0074] S9: After training the model, the performance of the model is evaluated on the test set, and the model is used to make predictions and extract the characteristic values ​​of the ECG signal;

[0075] S10: Analyze and compare the calculated characteristic values ​​with the expert consensus standard values, determine reasonable parameter standard values ​​based on the local conditions, and feed back to step S3 to update more accurate annotation points.

[0076] Through the present invention, we successfully extracted the feature values ​​of P wave, QRS complex and T wave from the electrocardiogram signal with annotation marks using U-net. The U-net model accurately segments features to help identify normal and abnormal heartbeats and locate problem areas. The encoder gradually extracts features, reduces resolution, and increases the number of feature maps; the decoder gradually restores resolution and combines the features of the encoder to restore details. The convolution operation extracts important features from the signal, the pooling layer reduces the dimension of the data, and finally predicts through the fully connected layer. This method not only reduces the workload of manual feature design, but also can handle complex signal patterns and improve the accuracy of feature extraction.

[0077] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating characteristic values ​​based on electrocardiogram data, characterized in that: Includes steps: S1: Obtain the patient data who has undergone static electrocardiogram. First, the electrocardiogram data comes from the hospital. The electrocardiogram data is exported in batches from the hospital information system. The electrocardiogram machine configured by the hospital can adapt to both 12-lead and 18-lead detection requirements. It uses a 1000Hz sampling rate and an inspection time of 10s. Select the xml file as the file format for saving, and there will be an fda.xml file exported at the same time; then use the custom function readXML in the PyCharm software to read the Ⅰ lead, Ⅱ lead, Ⅲ lead, AVR lead, AVL lead, AVF lead, V1 lead, V2 lead, V3 lead, V4 lead, V5 lead and V6 lead in turn, a total of 120,000 data points; finally, the 18-lead further reads the V3R lead, V4R lead, V5R lead, V7 lead, V8 lead and V9 lead, a total of 180,000 data points; S2: Through the customized wavelet denoising filter function and wavelet multi-resolution decomposition function, the wavelet transform method is used to remove the interference of 50Hz noise from the read ECG data, and the wavelet multi-resolution decomposition is used to remove the baseline drift; S3: Use the BioSPPy library to measure each measurement point of a single wave of each lead, with the goal of marking the starting point, peak value, and end point of each wave, followed by manual inspection, verification, and supplementation to obtain labeled ECG data; S4: Expanding the parameters that cannot be directly measured from the electrocardiogram through the measurement points obtained in step S3; S5: The ECG data with the measured feature points and labeled are stored in a CSV file; S6: After reading the labeled data, normalize the data; S7: After dividing the labeled ECG data into training and test sets, the one-dimensional signal is converted into a shape suitable for the deep learning model, and finally the data is reshaped into two-dimensional data; S8: By using the improved semantic segmentation U-net network structure, after encoding and decoding, the visualization results of the model are output; S9: After training the model, the performance of the model is evaluated on the test set, and the model is used to make predictions and extract the characteristic values ​​of the ECG signal; S10: Perform reasonable analysis and comparison on the calculated characteristic value and the expert consensus standard value, determine reasonable parameter standard value in combination with the local situation, and feed it back to step S3 to update more accurate annotation points.

2. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 1, characterized in that: Step S2 includes: wavelet decomposition, using discrete wavelet transform (DWT) to decompose the ECG signal into multiple levels; threshold selection, estimating the noise standard deviation through the absolute median, and calculating the soft threshold based on this value; denoising, using the threshold to process the detail coefficients; wavelet reconstruction, inversely transforming the processed coefficients into time domain signals to achieve the purpose of denoising.

3. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 1, characterized in that: Step S3 includes: baseline, R wave detection, processing of ECG signals using the biosppy.signals.ecg function, and calculation of the peak of the T wave using the BioSPPy library.

4. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 3, characterized in that: The baseline is a line connecting the starting points of two QRS complexes; in the process of processing electrocardiogram signals using the biosppy.signals.ecg function, it is assumed that the P wave is in the window before the R wave.

5. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 1, characterized in that: In step S3, the measurement points include baseline, P wave peak, P wave starting point, P wave ending point, QRS wave starting point, R wave peak, QRS wave ending point, T wave starting point, T wave peak, T wave ending point, Q point peak, Q point ending point, S wave starting point, S wave peak and QRS electric axis.

6. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 1, characterized in that: In step S4, the parameters include heart rate HR, P wave width, P wave amplitude, PR interval, QRS duration, Q wave width, Q wave amplitude, S wave width, S wave amplitude, R wave amplitude, QT interval, QTc interval, ST interval, T wave amplitude, RR interval, PP interval, RR interval difference and PP interval difference.

7. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 6, characterized in that: The calculation formula of the QTc interval is:

8. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 6, characterized in that: The method for confirming the T wave is as follows: draw a tangent at the T wave apex along the steepest part of the T wave terminal branch, and the intersection of the tangent and the isoelectric line is determined as the T wave end point. When the amplitudes of the double-peak T waves are equal, the QT interval is measured to the intersection of the maximum tangent of the second peak of the T wave and the baseline; at this time, the period between the two peaks of the T wave can be measured, ≤150ms is the notch of the T wave, and >150ms is the TU wave overlap.

9. The method for calculating characteristic values ​​based on electrocardiogram data according to claim 1, characterized in that: In step S5, the label includes the starting point, ending point, peak value, and width of each wave.

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