Method and system for analyzing synergy degree and participation degree of pelvic floor multiple muscles

Abstract

The invention discloses a method and system for analyzing the synergy degree and participation degree of multiple pelvic floor muscles, and relates to the technical field of pelvic floor multiple muscle data analys.The method comprises the following steps that S100, electromyographic signals of the pelvic floor, rectus abdominis, gluteus and hip adductor are collected, and normalization processing is conducted on the collected signals; step S200, carrying out synergy analysis on the plurality of muscles by adopting the normalized electromyographic signals; step S300, performing independent muscle participation degree analysis according to a collaborative analysis result; step S400, evaluating the similarity between the rectus abdominis, the hip adductor and the gluteus and the pelvic floor muscle activity in different contraction stages by calculating the Pearson correlation coefficient of each muscle in different time windows; and step S500, calculating the reference total work amount of the muscles and combining the window similarity to obtain the participation degree of each muscle in different time windows.

Description

Technical Field

[0001] The present invention relates to the technical field of pelvic floor multi-muscle data analysis, and in particular to a method and system for analyzing the coordination and participation of pelvic floor multi-muscles. Background Art

[0002] The International Continence Society (ICS) defines urinary incontinence as any complaint of involuntary urine leakage, of which the most common type of urinary incontinence in women is stress urinary incontinence (SUI). SUI is particularly noticeable when exerting force, being tired, sneezing or coughing, and has become a major obstacle for women to participate in sports and fitness activities, thus affecting their overall health. In response to this problem, Kegel proposed pelvic floor muscle (PFM) training, which has shown a high cure rate for urinary incontinence in non-controlled, non-randomized studies. However, in actual application, the effect of Kegel training varies from person to person, partly because participants often have difficulty in properly controlling the pelvic floor muscles and often mistakenly contract the gluteal muscles, hip adductor muscles or rectus abdominis muscles.

[0003] Studies have shown that about 30% of women cannot accurately control their pelvic floor muscles, resulting in poor training results. In addition, existing assessment methods, such as maximum voluntary contraction (MVC) and regional muscle engagement assessment based on JS divergence, can reflect the degree of muscle activation and engagement to a certain extent, but they still have limitations. The MVC method mainly relies on the amplitude of the electromyographic signal during muscle contraction, but different muscle contraction types (such as concentric contraction and isometric contraction) will produce different EMG signal amplitudes, which makes the MVC method in assessing the degree of activation of the pelvic floor muscles during Kegel exercises. Although the assessment method based on JS divergence can measure the differences between different muscle signals, it does not fully consider the synergy between muscles and changes in different contraction stages.

[0004] Therefore, the problem existing in the prior art is that there is a lack of an effective method that can accurately evaluate the coordination and participation of the pelvic floor muscles and other related muscles (such as the rectus abdominis, gluteal muscles, and hip adductor muscles) in Kegel training. The lack of this method makes it difficult for participants to judge whether their training is correct, and they cannot know which muscles play a leading role in the training, thereby affecting the training effect. Summary of the invention

[0005] The purpose of the present invention is to provide a method and system for analyzing the coordination and participation of multiple pelvic floor muscles to solve the problems raised in the prior art.

[0006] To achieve the above object, the present invention provides the following technical solution: a method for analyzing the coordination and participation of multiple pelvic floor muscles, the method comprising the following steps:

[0007] Step S100: collecting electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles, and performing normalization processing on the collected signals;

[0008] Step S200: using the normalized electromyographic signals to perform synergy analysis on multiple muscles;

[0009] Step S300: performing independent muscle engagement analysis based on the synergy analysis results;

[0010] Step S400: evaluating the similarity of the activities of the rectus abdominis, hip adductor muscles, gluteal muscles and pelvic floor muscles at different contraction stages by calculating the Pearson correlation coefficient of each muscle in different time windows;

[0011] Step S500: obtaining the participation degree of each muscle in different time windows by calculating the total reference work amount of the muscle and combining the window similarity;

[0012] Furthermore, the step S100 includes the following two steps:

[0013] Step S101 obtains a reference electromyographic signal through a formulated reference action, wherein the reference action is to place the hand on the abdomen for feedback, and to contract the abdomen, hip adductor muscles and pelvic floor muscles at the same time, and collect the combined contraction electromyographic signal of the abdomen, hip adductor muscles and pelvic floor muscles generated in the action; at the same time, the Glazer pelvic floor assessment is used to perform Kegel training, and the electromyographic signal during the training process is collected;

[0014] Step S102 normalizes the electromyographic signal EMG extracted from the pelvic floor combined muscles, and calculates the ratio of the electromyographic signal EMG of multiple muscles including the pelvic floor muscles, transverse abdominal muscles, internal oblique abdominal muscles, external oblique abdominal muscles, rectus abdominis and hip adductor muscles during Kegel training to the maximum value EMGmax of the corresponding muscle contraction during joint contraction to obtain a normalized electromyographic signal.

[0015] In the above technical solution, by collecting the electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles and normalizing these signals, a unified standard is provided for subsequent analysis; this step ensures that the signals between different muscles can be compared fairly and eliminates the interference caused by differences in signal strength; the normalization process makes the electromyographic signals comparable in time and amplitude, laying a solid foundation for subsequent synergy and participation analysis.

[0016] Furthermore, the step S200 specifically includes the following steps:

[0017] Step S201 uses a non-negative matrix decomposition method to decompose the muscle reference activation level matrix into a linear combination of a synergistic element matrix and an activation coefficient matrix:

[0018] M m×n=W m×r ×H r×n ;

[0019] Among them, M m×n is the muscle reference activation level matrix, which indicates the activation level of each muscle at different time points; W m×r Indicates different muscle coordination modes; H r×n represents the activation degree of each co-element at different time points; m is the number of channels of the electromyographic signal, n is the number of sampling points, and r represents the decomposition of the muscle activation level into r co-element; the non-negative matrix decomposition is converted into an optimization problem, and W is solved by iterative means. m×r and H r×n , the matrix decomposition process must satisfy the constraint that all matrix elements are non-negative;

[0020] Step S202 measures the similarity between different muscle signals by Euclidean distance, and calculates the Euclidean distance between two muscle matrices according to the following formula:

[0021]

[0022] Where A and B represent two different muscle signal matrices, E(A||B) represents the Euclidean distance between matrices A and B; A ij and B ij Respectively represent the values ​​of matrices A and B recorded from the i-th muscle to the j-th dimension. If and only if A=B, E(A||B) reaches the minimum value of 0;

[0023] Step S203 measures the difference between the probability distributions of different muscle signals by using the KL divergence function:

[0024]

[0025] Where S and Q represent two probability distribution matrices, D(S||Q) represents the KL divergence from the distribution matrix S to the distribution matrix Q; S ij and Q ij It represents the probability that the i-th muscle signal in the distribution matrix S and Q takes the j-th value; D(S||Q) reaches the minimum value 0 if and only if S=Q.

[0026] In the above technical solution, the non-negative matrix decomposition method is used to perform synergy analysis on the normalized electromyographic signals, revealing the collaborative working mode between muscles, which not only helps to understand the interaction mechanism of muscles during movement, but also provides a basis for subsequent participation analysis; the similarities and differences between different muscle signals are measured by Euclidean distance and KL divergence function, which further enhances the accuracy and reliability of the analysis, and helps to identify which muscles play a dominant role in specific movements and the synergistic relationship between them.

[0027] Furthermore, the step S300 includes the following steps:

[0028] Step S301 collects the electromyographic signals of the rectus abdominis, hip adductors, and gluteal muscles during joint contraction, and the electromyographic signals of the rectus abdominis, hip adductors, gluteal muscles, and pelvic floor muscles during Glazer pelvic floor assessment training. While collecting the electromyographic signals, the electromyographic signals are sent to an electromyographic signal amplifier for amplification and signal adjustment; the amplified analog signals are converted into digital signals through AD sampling, and the digital signals are sent to an MCU for signal data processing;

[0029] Step S302 converts the original electromyographic signal represented as a function of time x(n) into an RMS signal, and calculates the RMS value of all contractions using a 200 ms sliding window, moving in increments of 1 ms in each data set, according to the formula:

[0030]

[0031] Where X rms Expressed as RMS signal value, X i It is represented by the original electromyographic signal value, and N represents the number of sampling points in the window;

[0032] The combined contraction of the abdomen, hip adductor muscles and pelvic floor muscles was used as the reference value of the muscles. The maximum values ​​of the abdomen and hip adductor muscles during combined contraction were calculated respectively, and the resting electromyographic value was subtracted from the maximum value to obtain the final muscle activity signal value M.

[0033] In the above technical solution, by calculating the activity level of muscles in different time windows, the contribution of each muscle to the overall movement is quantified; by converting the original electromyographic signal into an RMS root mean square signal and using the sliding window technology to calculate the RMS value, the dynamic changes of muscle activity can be accurately captured; it helps to identify which muscles are more active at a specific stage and their contribution to the overall movement effect;

[0034] The step S400 includes the following steps:

[0035] Step S401 calculates the Pearson correlation coefficient and the electromyographic integral map of each muscle in different time windows. This algorithm uses a total of 11 time windows, which are numbered in sequence in stages and represented by i. When i=1, 2, 3, 4, 5, it represents 5 windows of staged light contraction; when i=6, 7, 8, 9, 10, it represents 5 windows of tonic contraction; when i=11, it represents 1 window of endurance contraction;

[0036] Step S402 calculates the covariance and standard deviation of the root mean square signals of the pelvic floor muscles and the rectus abdominis, hip adductors, and gluteal muscles, and divides them to obtain the Pearson correlation coefficient of each muscle in different time windows, which is used to evaluate the similarity of the rectus abdominis, hip adductors, and gluteal muscles with the pelvic floor muscle activities at different contraction stages, according to the formula:

[0037] Cov(X,Y)=E[(XE[X])(YE[Y])];

[0038]

[0039] Where X and Y represent the electromyographic signal values ​​of the pelvic floor muscles and other muscles, respectively. E[X] and E[Y] are the average values ​​of the electromyographic signal values ​​of the pelvic floor muscles and other muscles in the window, respectively. Cov(X,Y) represents the covariance of X and Y, and σ X and σ Y are the standard deviations of X and Y, respectively, and R i represents the Pearson correlation coefficient between each muscle and the pelvic floor muscle in the i-th window, i = 1, 2, …, 11;

[0040] In the above technical solution, the Pearson correlation coefficient of each muscle in different time windows is calculated to evaluate the similarity of the activities of the rectus abdominis, hip adductor muscles, gluteal muscles and pelvic floor muscles in different contraction stages; this not only helps to understand the coordination relationship between muscles, but also provides an important basis for evaluating the synchronization and consistency of muscle activities; by calculating the Pearson correlation coefficient, the similarity of muscle activities can be quantitatively evaluated, which helps to identify which muscles are more synchronized with the pelvic floor muscle activities at a specific stage, and whether the coordination relationship between them is good;

[0041] Furthermore, the step S500 includes the following steps:

[0042] Step S501 calculates the myoelectric integral graph of each muscle in different time windows. First, the myoelectric signal of the previous resting stage is calculated according to the formula:

[0043]

[0044] Where v represents the resting EMG signal value, n represents the number of EMG signal sampling points, and v 1 Indicates the sampling value of the electromyographic signal;

[0045] Step S502 calculates the maximum value A of the five windows flicked and shrunk in stages i , where i = 1, 2, 3, 4, 5;

[0046] Step S503 calculates the electromyographic integral graphs of the six windows in the tetanic contraction and endurance contraction stages respectively, according to the formula:

[0047]

[0048] IEMG i represents the electromyographic integral value of the i-th window, i = 6, 7, 8, 9, 10, 11, t 1 and t 2 are the start and end time of the window, respectively, and EMG(t) represents the value of the EMG signal in the window at time t minus the value of the resting EMG signal;

[0049] Step S504 calculates the total muscle reference work volume using the formula:

[0050]

[0051] Where W represents the total reference work of the muscle, and M(t) represents the normalized electromyographic signal value of each muscle at time t;

[0052] Step S505 calculates the muscle participation degree of the phased flick contraction window by the following formula:

[0053]

[0054] Where i = 1, 2, 3, 4, 5, P i Indicates the muscle engagement of 5 windows of phase flick contraction;

[0055] Step S506 calculates the muscle participation in the mandatory contraction and endurance contraction phases by the following formula:

[0056]

[0057] Where i = 6, 7, 8, 9, 10, 11, P i Indicates the muscle engagement in 6 windows during the forced contraction and endurance contraction phases;

[0058] Step S507 The overall Glazer pelvic floor assessment muscle participation P is expressed as:

[0059]

[0060]

[0061] Where P I represents the muscle engagement of the I-th window, where I is the number of windows, I=1, 2, 3, …, 11.

[0062] In the above technical scheme, a comprehensive muscle engagement evaluation method is given by integrating the analysis results of the previous steps. By calculating the electromyographic integral graph and the normalized electromyographic signal value, the activity level of the muscle at different stages can be accurately quantified; at the same time, combined with the window similarity calculated by the Pearson correlation coefficient, the calculation result of the muscle engagement can be further adjusted to make it more in line with the actual situation, greatly improving the accuracy of muscle engagement, and providing more accurate and reliable feedback for Kegel training.

[0063] A pelvic floor multi-muscle coordination and participation analysis system, the system comprising a signal acquisition and processing module, a coordination analysis module, a participation analysis module, and a data output module;

[0064] The signal acquisition and processing module is used to collect electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles, and perform normalization processing on the collected signals;

[0065] The synergy analysis module performs muscle synergy analysis on the normalized electromyographic signal;

[0066] The participation analysis module evaluates the participation of different muscles according to the synergy analysis results;

[0067] The data output module is used to output the results of the muscle participation assessment.

[0068] The signal acquisition and processing module includes a reference action electromyographic signal acquisition unit and an electromyographic signal processing unit;

[0069] The reference action electromyographic signal acquisition unit obtains a reference electromyographic signal through a specified reference action; the Glazer pelvic floor assessment is used to perform Kegel training, and the electromyographic signal during the training process is collected; the electromyographic signal processing unit normalizes the electromyographic signal EMG extracted from the pelvic floor combined muscles.

[0070] The collaborative analysis module includes a signal non-negative matrix decomposition unit and a collaborative analysis unit; the signal non-negative matrix decomposition unit uses a non-negative matrix decomposition method to decompose the muscle reference activation level matrix into a linear combination of a collaborative element matrix and an activation coefficient matrix;

[0071] The synergy analysis unit measures the similarity between different muscle signals by Euclidean distance, and measures the difference between the probability distributions of different muscle signals by KL divergence function:

[0072] The engagement analysis module includes a signal feature extraction unit and a muscle engagement analysis unit;

[0073] The signal feature extraction unit performs independent muscle participation analysis based on the synergy analysis result, collects the electromyographic signals of the rectus abdominis, hip adductor muscles, and gluteal muscles during joint contraction, and the electromyographic signals of the rectus abdominis, hip adductor muscles, gluteal muscles, and pelvic floor muscles during Glazer pelvic floor assessment training, and sends the electromyographic signals to an electromyographic signal amplifier for amplification and signal adjustment while collecting the electromyographic signals; converts the amplified analog signals into digital signals through AD sampling, and sends the digital signals to an MCU for signal data processing;

[0074] The raw EMG signal represented as a function of time x(n) was converted into an RMS signal and the RMS values ​​of all contractions were calculated using a 200 ms sliding window, moving in increments of 1 ms in each data set, according to the formula:

[0075]

[0076] Where X rms Expressed as RMS signal value, X i It is represented by the original electromyographic signal value, and N represents the number of sampling points in the window;

[0077] The combined contraction of the abdomen, hip adductor muscles and pelvic floor muscles was used as the reference value of the muscles. The maximum values ​​of the abdomen and hip adductor muscles during combined contraction were calculated respectively, and the resting electromyographic value was subtracted from the maximum value to obtain the final muscle activity signal value M.

[0078] The muscle participation analysis unit is used to calculate the Pearson correlation coefficient and the electromyographic integral map of each muscle in different time windows. This algorithm uses a total of 11 time windows, which are numbered in sequence in stages and represented by i. When i=1, 2, 3, 4, 5, it represents 5 windows of staged light contraction; when i=6, 7, 8, 9, 10, it represents 5 windows of tonic contraction; when i=11, it represents 1 window of endurance contraction;

[0079] The covariance and standard deviation of the root mean square signals of the pelvic floor muscles and the rectus abdominis, hip adductors, and gluteal muscles were calculated and divided to obtain the Pearson correlation coefficient of each muscle in different time windows, which was used to evaluate the similarity of the activities of the rectus abdominis, hip adductors, and gluteal muscles with the pelvic floor muscles at different contraction stages.

[0080] Calculate the myoelectric integral graph of each muscle in different time windows. First, calculate the myoelectric signal in the previous resting stage according to the formula:

[0081]

[0082] Where v represents the resting EMG signal value, n represents the number of EMG signal sampling points, and v 1 Indicates the sampling value of the electromyographic signal;

[0083] Calculate the maximum value A of the five windows that are flicked and shrunk in stages i , where i = 1, 2, 3, 4, 5;

[0084] Calculate the electromyographic integral graphs of six windows in the tetanic contraction and endurance contraction stages respectively, according to the formula:

[0085]

[0086] IEMG i represents the electromyographic integral value of the i-th window, i = 6, 7, 8, 9, 10, 11, t 1 and t 2 are the start and end time of the window, respectively, and EMG(t) represents the value of the EMG signal in the window at time t minus the value of the resting EMG signal;

[0087] The total muscle reference work is calculated by the formula:

[0088]

[0089] Where W represents the total reference work of the muscle, and M(t) represents the normalized electromyographic signal value of each muscle at time t;

[0090] The phasic flick contraction window muscle engagement was calculated using the following formula:

[0091]

[0092] Where i = 1, 2, 3, 4, 5, P i Indicates the muscle engagement of 5 windows of phase flick contraction;

[0093] The muscle engagement during the mandatory and endurance contraction phases was calculated using the following formula:

[0094]

[0095] Where i = 6, 7, 8, 9, 10, 11, P i Indicates the muscle engagement in 6 windows during the forced contraction and endurance contraction phases;

[0096] The total Glazer pelvic floor assessment muscle involvement P is expressed as:

[0097]

[0098] Where P I represents the muscle engagement of the I-th window, where I is the number of windows, I=1, 2, 3, …, 11.

[0099] Compared with the prior art, the present invention has the following beneficial effects:

[0100] The present invention obtains reference electromyographic signals through a well-established reference action, and uses the normalized electromyographic signals obtained therefrom to perform collaborative analysis of multiple muscles, decomposing the normalized electromyographic signals of multiple muscles into a collaborative matrix (W) and an activation coefficient matrix (H), effectively distinguishing the collaborative working modes of different muscles, and being able to clearly identify which muscles play a leading role at each time point; by analyzing the collaborative elements, the present invention can accurately identify which muscles contribute more to a specific contraction action, thereby better evaluating the participation of the muscles;

[0101] The present invention introduces an adaptive myoelectric normalization method and a participation calculation method, which adjusts the participation assessment according to the personalized myoelectric signal characteristics of the participants, especially combining the contraction types of different muscles (rectus abdominis, pelvic floor muscles, hip adductor muscles, etc.), avoiding the use of a single MVC as a reference, thereby greatly improving the accuracy and reliability of the assessment;

[0102] The present invention introduces adaptive electromyography normalization and multi-muscle synergy analysis, and performs participation analysis through waveform similarity and normalized electromyography values, thereby effectively solving the problems of low accuracy and insufficient feedback in Kegel training muscle participation assessment in the prior art, and greatly improving the training effect and clinical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 A method flow chart of a method for analyzing the coordination and participation of multiple pelvic floor muscles of the present invention;

[0104] Figure 2 This is a system module diagram of a pelvic floor multi-muscle coordination and participation analysis system of the present invention. DETAILED DESCRIPTION

[0105] Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without making any creative work shall fall within the scope of protection of the present invention.

[0106] Example: Figure 1-Figure 2 As shown, the present invention provides a technical solution, a method for analyzing the coordination and participation of multiple pelvic floor muscles, the method comprising the following steps:

[0107] Step S100: collecting electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles, and performing normalization processing on the collected signals;

[0108] Step S200: using the normalized electromyographic signals to perform synergy analysis on multiple muscles;

[0109] Step S300: performing independent muscle engagement analysis based on the synergy analysis results;

[0110] Step S400: evaluating the similarity of the activities of the rectus abdominis, hip adductor muscles, gluteal muscles and pelvic floor muscles at different contraction stages by calculating the Pearson correlation coefficient of each muscle in different time windows;

[0111] Step S500: obtaining the participation degree of each muscle in different time windows by calculating the total reference work amount of the muscle and combining the window similarity;

[0112] Furthermore, the step S100 includes the following two steps:

[0113] Step S101 obtains a reference electromyographic signal through a specified reference action. The reference action is to place the hand on the abdomen for feedback, requiring the participant to simultaneously contract the abdomen, hip adductor muscles and pelvic floor muscles to the maximum extent, as if trying to prevent vaginal insertion for 5 seconds, and collect the combined contraction electromyographic signals of the abdomen, hip adductor muscles and pelvic floor muscles generated in the action; at the same time, the Glazer pelvic floor assessment is used to perform Kegel training, and the electromyographic signals during the training are collected. The specific evaluation process is as follows:

[0114] 1. One 60-second rest period (before baseline): Instruct women to feel the PFM while resting.

[0115] 2. Five phased flick contractions: Instruct women to contract the PFM as quickly as possible (2 seconds of contraction, 2 seconds of rest in between);

[0116] 3. Five 10-second tetanic contractions with 10 seconds of rest in between: Instruct the woman to contract the PFM as strongly as possible, hold the contraction for 10 seconds, and then completely relax the PFM after holding the contraction for 10 seconds.

[0117] 4. One 60-second endurance contraction: Women were instructed to contract the PFM to a level that could be held for 60 seconds;

[0118] 5. One 60-second rest period (after baseline): Instruct women to feel the PFM while resting.

[0119] Step S102 normalizes the electromyographic signal EMG extracted from the pelvic floor combined muscles, and calculates the ratio of the electromyographic signal EMG of multiple muscles including the pelvic floor muscles, transverse abdominal muscles, internal oblique abdominal muscles, external oblique abdominal muscles, rectus abdominis and hip adductor muscles during Kegel training to the maximum value EMGmax of the corresponding muscle contraction during joint contraction to obtain a normalized electromyographic signal.

[0120] In the above technical solution, by collecting the electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles and normalizing these signals, a unified standard is provided for subsequent analysis; this step ensures that the signals between different muscles can be compared fairly and eliminates the interference caused by differences in signal strength; the normalization process makes the electromyographic signals comparable in time and amplitude, laying a solid foundation for subsequent synergy and participation analysis.

[0121] Furthermore, the step S200 specifically includes the following steps:

[0122] Step S201 uses a non-negative matrix decomposition method to decompose the muscle reference activation level matrix into a linear combination of a synergistic element matrix and an activation coefficient matrix:

[0123] N m×n =W m×r ×H r×n ;

[0124] Among them, M m×n is the muscle reference activation level matrix, which indicates the activation level of each muscle at different time points; W m×r Indicates different muscle coordination modes; H r×n represents the activation degree of each co-element at different time points; m is the number of channels of the electromyographic signal, n is the number of sampling points, and r represents the decomposition of the muscle activation level into r co-element; the non-negative matrix decomposition is converted into an optimization problem, and W is solved by iterative means. m×r and H r×n , the matrix decomposition process must satisfy the constraint that all matrix elements are non-negative;

[0125] Step S202 measures the similarity between different muscle signals by Euclidean distance, and calculates the Euclidean distance between two muscle matrices according to the following formula:

[0126]

[0127] Where A and B represent two different muscle signal matrices, E(A||B) represents the Euclidean distance between matrices A and B; A ij and B ij Respectively represent the values ​​of matrices A and B recorded from the i-th muscle to the j-th dimension. If and only if A=B, E(A||B) reaches the minimum value of 0;

[0128] Step S203 measures the difference between the probability distributions of different muscle signals by using the KL divergence function:

[0129]

[0130] Where S and Q represent two probability distribution matrices, D(S||Q) represents the KL divergence from the distribution matrix S to the distribution matrix Q; S ij and Q ij It represents the probability that the i-th muscle signal in the distribution matrix S and Q takes the j-th value; D(S||Q) reaches the minimum value 0 if and only if S=Q.

[0131] In the above technical solution, the non-negative matrix decomposition method is used to perform synergy analysis on the normalized electromyographic signals, revealing the collaborative working mode between muscles, which not only helps to understand the interaction mechanism of muscles during movement, but also provides a basis for subsequent participation analysis; the similarities and differences between different muscle signals are measured by Euclidean distance and KL divergence function, which further enhances the accuracy and reliability of the analysis, and helps to identify which muscles play a dominant role in specific movements and the synergistic relationship between them.

[0132] Furthermore, the step S300 includes the following steps:

[0133] Step S301 collects the electromyographic signals of the rectus abdominis, hip adductors, and gluteal muscles during joint contraction, and the electromyographic signals of the rectus abdominis, hip adductors, gluteal muscles, and pelvic floor muscles during Glazer pelvic floor assessment training. While collecting the electromyographic signals, the electromyographic signals are sent to an electromyographic signal amplifier for amplification and signal adjustment; the amplified analog signals are converted into digital signals through AD sampling, and the digital signals are sent to an MCU for signal data processing;

[0134] Step S302 converts the original electromyographic signal represented as a function of time x(n) into an RMS signal, and calculates the RMS value of all contractions using a 200 ms sliding window, moving in increments of 1 ms in each data set, according to the formula:

[0135]

[0136] Where X rms Expressed as RMS signal value, X i It is represented by the original electromyographic signal value, and N represents the number of sampling points in the window;

[0137] The combined contraction of the abdomen, hip adductor muscles and pelvic floor muscles was used as the reference value of the muscles. The maximum values ​​of the abdomen and hip adductor muscles during combined contraction were calculated respectively, and the resting electromyographic value was subtracted from the maximum value to obtain the final muscle activity signal value M.

[0138] In the above technical solution, by calculating the activity level of muscles in different time windows, the contribution of each muscle to the overall movement is quantified; by converting the original electromyographic signal into an RMS root mean square signal and using the sliding window technology to calculate the RMS value, the dynamic changes of muscle activity can be accurately captured; it helps to identify which muscles are more active at a specific stage and their contribution to the overall movement effect;

[0139] The step S400 includes the following steps:

[0140] Step S401 calculates the Pearson correlation coefficient and the electromyographic integral map of each muscle in different time windows. This algorithm uses a total of 11 time windows, namely, 5 windows of phased flick contraction: 70-80s, 80-90s, 90-100s, 100-110s, 110-120s, 5 windows of tetanic contraction: 139-151s, 159-171s, 179-191s, 199-211s, 219-231s, and 1 window of endurance contraction: 250-310s;

[0141] In step S402, taking the rectus abdominis as an example, the covariance and standard deviation between the pelvic floor muscles and the rectus abdominis are calculated and divided to obtain the Pearson correlation coefficient of each muscle in different time windows, which is used to evaluate the similarity between the rectus abdominis and the pelvic floor muscle activities in different contraction stages, according to the formula:

[0142] Cov(X,Y)=E[(XE[X])(YE[Y])];

[0143]

[0144] Where X and Y represent the electromyographic signal values ​​of the pelvic floor muscles and the rectus abdominis muscles, respectively. E[X] and E[Y] are the average values ​​of the electromyographic signal values ​​of the pelvic floor muscles and the rectus abdominis muscles in the window, respectively. Cov(X,Y) represents the covariance of X and Y, and σ X and σ Y are the standard deviations of X and Y, respectively, and R i represents the Pearson correlation coefficient between the rectus abdominis and pelvic floor muscles in the i-th window, i = 1, 2, …, 11;

[0145] In the above technical solution, the Pearson correlation coefficient of each muscle in different time windows is calculated to evaluate the similarity of the activities of the rectus abdominis, hip adductor muscles, gluteal muscles and pelvic floor muscles in different contraction stages; this not only helps to understand the coordination relationship between muscles, but also provides an important basis for evaluating the synchronization and consistency of muscle activities; by calculating the Pearson correlation coefficient, the similarity of muscle activities can be quantitatively evaluated, which helps to identify which muscles are more synchronized with the pelvic floor muscle activities at a specific stage, and whether the coordination relationship between them is good;

[0146] Furthermore, the step S500 includes the following steps:

[0147] Step S501 calculates the electromyographic integral map of the rectus abdominis in different time windows. First, the electromyographic signal in the previous resting stage is calculated according to the formula:

[0148]

[0149] Where v represents the resting EMG signal value, n represents the number of EMG signal sampling points, and v 1 Indicates the sampling value of the electromyographic signal;

[0150] Step S502 calculates the maximum value A of the five windows flicked and shrunk in stages i , where i = 1, 2, 3, 4, 5;

[0151] Step S503 calculates the electromyographic integral graphs of the six windows in the tetanic contraction and endurance contraction stages respectively, according to the formula:

[0152]

[0153] IEMG i represents the electromyographic integral value of the i-th window, i = 6, 7, 8, 9, 10, 11, t 1 and t 2 are the start and end time of the window, respectively, and EMG(t) represents the value of the EMG signal in the window at time t minus the value of the resting EMG signal;

[0154] Step S504 calculates the total muscle reference work volume using the formula:

[0155]

[0156] Where W represents the total reference work of the muscle, and M(t) represents the normalized electromyographic signal value of each muscle at time t;

[0157] Step S505 calculates the muscle participation degree of the phased flick contraction window by the following formula:

[0158]

[0159] Where i = 1, 2, 3, 4, 5, P i Indicates the muscle engagement of 5 windows of phase flick contraction;

[0160] Step S506 calculates the muscle participation in the mandatory contraction and endurance contraction phases by the following formula:

[0161]

[0162] Where i = 6, 7, 8, 9, 10, 11, P i Indicates the muscle engagement in 6 windows during the forced contraction and endurance contraction phases;

[0163] Step S507 The overall Glazer pelvic floor assessment muscle participation P is expressed as:

[0164]

[0165] Where P I represents the muscle engagement of the I-th window, where I is the number of windows, I=1, 2, 3, …, 11.

[0166] In the above technical scheme, a comprehensive muscle engagement evaluation method is given by integrating the analysis results of the previous steps. By calculating the electromyographic integral graph and the normalized electromyographic signal value, the activity level of the muscle at different stages can be accurately quantified; at the same time, combined with the window similarity calculated by the Pearson correlation coefficient, the calculation result of the muscle engagement can be further adjusted to make it more in line with the actual situation, greatly improving the accuracy of muscle engagement, and providing more accurate and reliable feedback for Kegel training.

[0167] A pelvic floor multi-muscle coordination and participation analysis system, the system comprising a signal acquisition and processing module, a coordination analysis module, a participation analysis module, and a data output module;

[0168] The signal acquisition and processing module is used to collect electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles, and perform normalization processing on the collected signals;

[0169] The synergy analysis module performs muscle synergy analysis on the normalized electromyographic signal;

[0170] The participation analysis module evaluates the participation of different muscles according to the synergy analysis results;

[0171] The data output module is used to output the results of the muscle participation assessment.

[0172] The signal acquisition and processing module includes a reference action electromyographic signal acquisition unit and an electromyographic signal processing unit;

[0173] The reference action electromyographic signal acquisition unit obtains a reference electromyographic signal through a specified reference action; the Glazer pelvic floor assessment is used to perform Kegel training, and the electromyographic signal during the training process is collected; the electromyographic signal processing unit normalizes the electromyographic signal EMG extracted from the pelvic floor combined muscles.

[0174] The collaborative analysis module includes a signal non-negative matrix decomposition unit and a collaborative analysis unit; the signal non-negative matrix decomposition unit uses a non-negative matrix decomposition method to decompose the muscle reference activation level matrix into a linear combination of a collaborative element matrix and an activation coefficient matrix;

[0175] The synergy analysis unit measures the similarity between different muscle signals by Euclidean distance, and measures the difference between the probability distributions of different muscle signals by KL divergence function:

[0176] The engagement analysis module includes a signal feature extraction unit and a muscle engagement analysis unit;

[0177] The signal feature extraction unit performs independent muscle participation analysis based on the synergy analysis result, collects the electromyographic signals of the rectus abdominis, hip adductor muscles, and gluteal muscles during joint contraction, and the electromyographic signals of the rectus abdominis, hip adductor muscles, gluteal muscles, and pelvic floor muscles during Glazer pelvic floor assessment training, and sends the electromyographic signals to an electromyographic signal amplifier for amplification and signal adjustment while collecting the electromyographic signals; converts the amplified analog signals into digital signals through AD sampling, and sends the digital signals to an MCU for signal data processing;

[0178] The raw EMG signal represented as a function of time x(n) was converted into an RMS signal and the RMS values ​​of all contractions were calculated using a 200 ms sliding window, moving in increments of 1 ms in each data set, according to the formula:

[0179]

[0180] Where X rms Expressed as RMS signal value, X i It is represented by the original electromyographic signal value, and N represents the number of sampling points in the window;

[0181] The combined contraction of the abdomen, hip adductor muscles and pelvic floor muscles was used as the reference value of the muscles. The maximum values ​​of the abdomen and hip adductor muscles during combined contraction were calculated respectively, and the resting electromyographic value was subtracted from the maximum value to obtain the final muscle activity signal value M.

[0182] The muscle participation analysis unit is used to calculate the Pearson correlation coefficient and the electromyographic integral map of each muscle in different time windows. This unit uses a total of 11 time windows, which are 5 windows of phased flick contraction: 70-80s, 80-90s, 90-100s, 100-110s, 110-120s, 5 windows of tetanic contraction: 139-151s, 159-171s, 179-191s, 199-211s, 219-231s, and 1 window of endurance contraction: 250-310s.

[0183] The covariance and standard deviation of the root mean square signals of the pelvic floor muscles and the rectus abdominis, hip adductors, and gluteal muscles were calculated and divided to obtain the Pearson correlation coefficient of each muscle in different time windows, which was used to evaluate the similarity of the activities of the rectus abdominis, hip adductors, and gluteal muscles with the pelvic floor muscles at different contraction stages.

[0184] Calculate the myoelectric integral graph of each muscle in different time windows. First, calculate the myoelectric signal in the previous resting stage according to the formula:

[0185]

[0186] Where v represents the resting EMG signal value, n represents the number of EMG signal sampling points, and v 1 Indicates the sampling value of the electromyographic signal;

[0187] Calculate the maximum value A of the five windows that are flicked and shrunk in stages i , where i = 1, 2, 3, 4, 5;

[0188] Calculate the electromyographic integral graphs of six windows in the tetanic contraction and endurance contraction stages respectively, according to the formula:

[0189]

[0190] IEMG i represents the electromyographic integral value of the i-th window, i = 6, 7, 8, 9, 10, 11, t 1 and t 2 are the start and end time of the window, respectively, and EMG(t) represents the value of the EMG signal in the window at time t minus the value of the resting EMG signal;

[0191] The total muscle reference work is calculated by the formula:

[0192]

[0193] Where W represents the total reference work of the muscle, and M(t) represents the normalized electromyographic signal value of each muscle at time t;

[0194] The phasic flick contraction window muscle engagement was calculated using the following formula:

[0195]

[0196] Where i = 1, 2, 3, 4, 5, P i Indicates the muscle engagement of 5 windows of phase flick contraction;

[0197] The muscle engagement during the mandatory and endurance contraction phases was calculated using the following formula:

[0198]

[0199] Where i = 6, 7, 8, 9, 10, 11, P i Indicates the muscle engagement in 6 windows during the forced contraction and endurance contraction phases;

[0200] The total Glazer pelvic floor assessment muscle involvement P is expressed as:

[0201]

[0202] Where P I represents the muscle engagement of the I-th window, where I is the number of windows, I=1, 2, 3, …, 11.

[0203] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. 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 analyzing the coordination and participation of multiple pelvic floor muscles, characterized by: The method comprises the following steps: Step S100: collecting electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles, and performing normalization processing on the collected signals; Step S200: using the normalized electromyographic signals to perform synergy analysis on multiple muscles; Step S300: performing independent muscle engagement analysis based on the synergy analysis results; Step S400: evaluating the similarity of the activities of the rectus abdominis, hip adductor muscles, gluteal muscles and pelvic floor muscles at different contraction stages by calculating the Pearson correlation coefficient of each muscle in different time windows; Step S500: The participation degree of each muscle in different time windows is obtained by calculating the total reference work amount of the muscle and combining the window similarity.

2. A method for analyzing the coordination and participation of multiple pelvic floor muscles according to claim 1, characterized in that: The step S100 includes the following two steps: Step S101 obtains a reference electromyographic signal through a formulated reference action, wherein the reference action is to place the hand on the abdomen for feedback, and to contract the abdomen, hip adductor muscles and pelvic floor muscles at the same time, and collect the combined contraction electromyographic signal of the abdomen, hip adductor muscles and pelvic floor muscles generated in the action; at the same time, the Glazer pelvic floor assessment is used to perform Kegel training, and the electromyographic signal during the training process is collected; Step S102 normalizes the electromyographic signal EMG extracted from the pelvic floor combined muscles, and calculates the ratio of the electromyographic signal EMG of multiple muscles including the pelvic floor muscles, transverse abdominal muscles, internal oblique abdominal muscles, external oblique abdominal muscles, rectus abdominis and hip adductor muscles during Kegel training to the maximum value EMGmax of the corresponding muscle contraction during joint contraction to obtain a normalized electromyographic signal.

3. A method for analyzing the coordination and participation of multiple pelvic floor muscles according to claim 1, characterized in that: The step S200 specifically includes the following steps: Step S201 uses a non-negative matrix decomposition method to decompose the muscle reference activation level matrix into a linear combination of a synergistic element matrix and an activation coefficient matrix: M m×n =W m×r ×H r×n ; Among them, M m×n is the muscle reference activation level matrix, which indicates the activation level of each muscle at different time points; W m×r Indicates different muscle coordination modes; H r×n represents the activation degree of each synergist at different time points; m is the number of channels of the electromyographic signal, n is the number of sampling points, and r means decomposing the muscle activation level into r co-elements; Convert the non-negative matrix decomposition into an optimization problem and use iterative means to solve W m×r and H r×n , the matrix decomposition process must satisfy the constraint that all matrix elements are non-negative; Step S202 measures the similarity between different muscle signals by Euclidean distance, and calculates the Euclidean distance between two muscle matrices according to the following formula: Where A and B represent two different muscle signal matrices, E(A||B) represents the Euclidean distance between matrices A and B; A ij and B ij Respectively represent the values ​​of matrices A and B recorded from the i-th muscle to the j-th dimension. If and only if A=B, E(A||B) reaches the minimum value of 0; Step S203 measures the difference between the probability distributions of different muscle signals by using the KL divergence function: Where S and Q represent two probability distribution matrices, D(S||Q) represents the KL divergence from the distribution matrix S to the distribution matrix Q; S ij and Q ij It represents the probability that the i-th muscle signal in the distribution matrix S and Q takes the j-th value; D(S||Q) reaches the minimum value 0 if and only if S=Q.

4. A method for analyzing the coordination and participation of multiple pelvic floor muscles according to claim 1, characterized in that: The step S300 includes the following steps: Step S301 collects the electromyographic signals of the rectus abdominis, hip adductors, and gluteal muscles during joint contraction, and the electromyographic signals of the rectus abdominis, hip adductors, gluteal muscles, and pelvic floor muscles during Glazer pelvic floor assessment training. While collecting the electromyographic signals, the electromyographic signals are sent to an electromyographic signal amplifier for amplification and signal adjustment; the amplified analog signals are converted into digital signals through AD sampling, and the digital signals are sent to an MCU for signal data processing; Step S302 converts the original electromyographic signal represented as a function of time x(n) into an RMS signal, and calculates the RMS value of all contractions using a 200 ms sliding window, moving in increments of 1 ms in each data set, according to the formula: Where X rms Expressed as RMS signal value, X i It is represented by the original electromyographic signal value, and N represents the number of sampling points in the window; The combined contraction of the abdomen, hip adductor muscles and pelvic floor muscles was used as the reference value of the muscles. The maximum values ​​of the abdomen and hip adductor muscles during combined contraction were calculated respectively, and the resting electromyographic value was subtracted from the maximum value to obtain the final muscle activity signal value M.

5. The method for analyzing the coordination and participation of multiple pelvic floor muscles according to claim 1, characterized in that: The step S400 includes the following steps: Step S401 calculates the Pearson correlation coefficient of each muscle in different time windows. This algorithm uses 11 time windows in total, which are numbered in sequence in stages and represented by i. When i=1, 2, 3, 4, 5, it represents 5 windows of staged light contraction; when i=6, 7, 8, 9, 10, it represents 5 windows of tonic contraction; when i=11, it represents 1 window of endurance contraction; Step S402 calculates the covariance and standard deviation of the root mean square signals of the pelvic floor muscles and the rectus abdominis, hip adductors, and gluteal muscles, and divides them to obtain the Pearson correlation coefficient of each muscle in different time windows, which is used to evaluate the similarity of the rectus abdominis, hip adductors, and gluteal muscles with the pelvic floor muscle activities at different contraction stages, according to the formula: Cov(X,Y)=E[(XE[X])(YE[Y])]; Where X and Y represent the electromyographic signal values ​​of the pelvic floor muscles and other muscles, respectively. E[X] and E[Y] are the average values ​​of the electromyographic signal values ​​of the pelvic floor muscles and other muscles in the window, respectively. Cov(X,Y) represents the covariance of X and Y, and σ X and σ Y are the standard deviations of X and Y, respectively, and R i represents the Pearson correlation coefficient between each muscle and the pelvic floor muscle in the i-th window, i = 1, 2, …, 11.

6. A method for analyzing the coordination and participation of multiple pelvic floor muscles according to claim 1, characterized in that: The step S500 includes the following steps: Step S501 calculates the myoelectric integral graph of each muscle in different time windows. First, the myoelectric signal of the previous resting stage is calculated according to the formula: Where v represents the resting EMG signal value, n represents the number of EMG signal sampling points, and v1 represents the EMG signal sampling value; Step S502 calculates the maximum value A of the five windows flicked and shrunk in stages i , where i = 1, 2, 3, 4, 5; Step S503 calculates the electromyographic integral graphs of the six windows in the tetanic contraction and endurance contraction stages respectively, according to the formula: IEMG i represents the electromyographic integral value of the i-th window, i = 6, 7, 8, 9, 10, 11, t1 and t2 are the start and end time of the window respectively, and EMG(t) represents the value of the electromyographic signal in the window at time t minus the value of the resting electromyographic signal; Step S504 calculates the total muscle reference work volume using the formula: Where W represents the total reference work of the muscle, and M(t) represents the normalized electromyographic signal value of each muscle at time t; Step S505 calculates the muscle participation degree of the phased flick contraction window by the following formula: Where i = 1, 2, 3, 4, 5, P i Indicates the muscle engagement of 5 windows of phase flick contraction; Step S506 calculates the muscle participation in the mandatory contraction and endurance contraction phases by the following formula: Where i = 6, 7, 8, 9, 10, 11, P i Indicates the muscle engagement in 6 windows during the forced contraction and endurance contraction phases; Step S507 The overall Glazer pelvic floor assessment muscle participation P is expressed as: Where P I represents the muscle engagement of the I-th window, where I is the number of windows, I=1, 2, 3, …, 11.

7. A pelvic floor multi-muscle coordination and participation analysis system, characterized by: The system includes a signal acquisition and processing module, a collaborative analysis module, a participation analysis module, and a data output module; The signal acquisition and processing module is used to collect electromyographic signals of the pelvic floor, rectus abdominis, gluteal muscles, and hip adductor muscles, and perform normalization processing on the collected signals; The synergy analysis module performs muscle synergy analysis on the normalized electromyographic signal; The participation analysis module evaluates the participation of different muscles according to the synergy analysis results; The data output module is used to output the results of the muscle participation assessment.

8. A pelvic floor multi-muscle coordination and participation analysis system according to claim 7, characterized in that: The signal acquisition and processing module includes a reference action electromyographic signal acquisition unit and an electromyographic signal processing unit; The reference action electromyographic signal acquisition unit obtains a reference electromyographic signal through a specified reference action; the Glazer pelvic floor assessment is used to perform Kegel training, and the electromyographic signal during the training process is collected; the electromyographic signal processing unit normalizes the electromyographic signal EMG extracted from the pelvic floor combined muscles; The collaborative analysis module includes a signal non-negative matrix decomposition unit and a collaborative analysis unit; the signal non-negative matrix decomposition unit uses a non-negative matrix decomposition method to decompose the muscle reference activation level matrix into a linear combination of a collaborative element matrix and an activation coefficient matrix; the collaborative analysis unit measures the similarity between different muscle signals through the Euclidean distance and measures the difference between the probability distributions of different muscle signals through the KL divergence function.

9. A pelvic floor multi-muscle coordination and participation analysis system according to claim 7, characterized in that: The engagement analysis module includes a signal feature extraction unit and a muscle engagement analysis unit; The signal feature extraction unit performs independent muscle participation analysis based on the synergy analysis result, collects the electromyographic signals of the rectus abdominis, hip adductor muscles, and gluteal muscles during joint contraction, and the electromyographic signals of the rectus abdominis, hip adductor muscles, gluteal muscles, and pelvic floor muscles during Glazer pelvic floor assessment training, and sends the electromyographic signals to an electromyographic signal amplifier for amplification and signal adjustment while collecting the electromyographic signals; converts the amplified analog signals into digital signals through AD sampling, and sends the digital signals to an MCU for signal data processing; The raw EMG signal represented as a function of time x(n) was converted into an RMS signal and the RMS values ​​of all contractions were calculated using a 200 ms sliding window, moving in increments of 1 ms in each data set, according to the formula: Where X rms Expressed as RMS signal value, X i It is represented by the original electromyographic signal value, and N represents the number of sampling points in the window; The combined contraction of the abdomen, hip adductor muscles and pelvic floor muscles was used as the reference value of the muscles. The maximum values ​​of the abdomen and hip adductor muscles during combined contraction were calculated respectively, and the resting electromyographic value was subtracted from the maximum value to obtain the final muscle activity signal value M.

10. A pelvic floor multi-muscle coordination and participation analysis system according to claim 9, characterized in that: The muscle participation analysis unit is used to calculate the Pearson correlation coefficient and the electromyographic integral map of each muscle in different time windows. This algorithm uses a total of 11 time windows, which are numbered in sequence in stages and represented by i. When i=1, 2, 3, 4, 5, it represents 5 windows of staged light contraction; when i=6, 7, 8, 9, 10, it represents 5 windows of tonic contraction; when i=11, it represents 1 window of endurance contraction; The covariance and standard deviation of the root mean square signals of the pelvic floor muscles and the rectus abdominis, hip adductors, and gluteal muscles were calculated and divided to obtain the Pearson correlation coefficient of each muscle in different time windows, which was used to evaluate the similarity of the activities of the rectus abdominis, hip adductors, and gluteal muscles with the pelvic floor muscles at different contraction stages; Calculate the myoelectric integral graph of each muscle in different time windows. First, calculate the myoelectric signal in the previous resting stage according to the formula: Where v represents the resting EMG signal value, n represents the number of EMG signal sampling points, and v1 represents the EMG signal sampling value; Calculate the maximum value A of the five windows that are flicked and shrunk in stages i , where i = 1, 2, 3, 4, 5; Calculate the electromyographic integral graphs of six windows in the tetanic contraction and endurance contraction stages respectively, according to the formula: IEMG i represents the electromyographic integral value of the i-th window, i = 6, 7, 8, 9, 10, 11, t1 and t2 are the start and end time of the window respectively, and EMG(t) represents the value of the electromyographic signal in the window at time t minus the value of the resting electromyographic signal; The total muscle reference work is calculated by the formula: Where W represents the total reference work of the muscle, and M(t) represents the normalized electromyographic signal value of each muscle at time t; The phasic flick contraction window muscle engagement was calculated using the following formula: Where i = 1, 2, 3, 4, 5, P i Indicates the muscle engagement of 5 windows of phase flick contraction; The muscle engagement during the mandatory and endurance contraction phases was calculated using the following formula: Where i = 6, 7, 8, 9, 10, 11, P i Indicates the muscle engagement in 6 windows during the forced contraction and endurance contraction phases; The total Glazer pelvic floor assessment muscle involvement P is expressed as: Where P I represents the muscle engagement of the I-th window, where I is the number of windows, I=1, 2, 3, …, 11.

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