CN113499049B - Method for analyzing heart rate variability data based on self-adaptive multi-scale entropy - Google Patents
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Abstract
The invention belongs to the technical field of medical treatment, and relates to a method for analyzing heart rate variability data based on self-adaptive multi-scale entropy; the method overcomes the defect of fixed dimension of the complexity of the MSE quantization HRV, and comprehensively and accurately quantizes the complexity of the HRV; in the method, integral mean modal decomposition is adopted to carry out self-adaptive decomposition on HRV, so as to obtain a series of multi-scale mean value substitution data sets of original data; secondly, coarsely granulating each element in the mean value substitution data set and obtaining the corresponding self-adaptive scale; finally, calculating the SampEn value of each element in the coarsely granulated mean value substitution data set to obtain a self-adaptive multi-scale entropy; the HRV complexity can be comprehensively and accurately evaluated by the self-adaptive multi-scale entropy.
Description
Technical Field
The invention relates to the technical field of medical treatment, in particular to a method for analyzing heart rate variability data based on self-adaptive multi-scale entropy.
Background
Heart Rate Variability (HRV) is the temporal variation between successive cardiac cycles (N-N or R-R). HRV contains rich individual cardiovascular regulation information, and reflects the synthetic regulation influence of sinoatrial node autonomy from multiple physiological aspects such as sympathetic nerve, vagus nerve, central nervous system, carotid artery pressure and chemoreceptor. By detecting and analyzing HRV, diseases related to autonomic nerve functions, such as coronary heart disease, heart failure, hypertension and the like, can be evaluated.
HRV analysis methods are generally classified into linear and nonlinear analysis methods. The linear analysis method comprises the following steps: statistical or geometric graphical analysis of HRV data in the time domain and HRV-based spectral analysis in the frequency domain. Since the HRV is a complex non-stationary signal and the linear analysis method cannot reflect its time-varying characteristics, the HRV non-linear analysis method, including Poincar scattergram, correlation dimension, lyapunov index, detrended fluctuation analysis and various entropies, has been widely regarded and studied.
Most HRV nonlinear dynamics analysis methods require that the HRV data volume is large enough, and the application limit is not overcome until Pincus proposes approximate entropy (ApEn) which can be applied to a short and noisy clinical data time series. However, ApEn belongs to biased estimation and the measurement is heavily influenced by the data length, the result lacks consistency. Sample entropy (SampEn) is not calculated as a self-match and is largely independent of data length, showing good relative consistency. However, SampEn, like ApEn, is based on single-scale analysis and does not take into account the multi-scale characteristics of biological systems, especially when quantifying the complexity of biological systems in certain pathological situations, which may lead to erroneous results. To this end, Costa proposes a Multiscale Sample Entropy (MSE) based on taking SampEn after multiscale coarse-grained granulation of data. MSE quantifies the information expressed by physiological dynamics explicitly at multiple scales, showing the multi-scale characteristics of biological systems ignored by ApEn or SampEn, and is one of the leading edges of current HRV nonlinear analysis methods.
Firstly, the MSE method carries out multiscale on data to obtain a multiscale mean value substitution data set of original data; secondly, coarsely granulating each element in the mean value substitution data set; finally, the SampEn value of each element in the coarsely granulated mean-value substitution data set is calculated to obtain MSE (see fig. 1 for steps).
The first step is as follows: and (4) carrying out multiscale on data.
The MSE method is used for multi-scaling of data, and essentially implements non-overlapping window mean filtering on a data sequence, and data in a window is replaced by a data mean. Changing the window scale τ to 1-20, a multi-scale mean value substitution data (or called low frequency "trend") set of the original data sequence can be obtained, and y (n) { y ═ y (1) (n),…,y (20) (n) }, schematic diagram is shown in FIG. 1. The formula is as follows:
wherein x is i Is a data sequence; tau is a scale value and is generally 1-20. Fig. 2 shows exemplary scale replacement data obtained by MSE of a real HRV.
The second step is that: and coarsely granulating the multi-scale mean value substitution data set. For each alternative data sequence y (τ) (n), all mean substitution data are coarsely granulated to unit length 1, as shown schematically in FIG. 1.
The third step: all multi-scale coarse-grained substitution data were taken as SampEn.
Let the discrete sequence of substitute data be [ x ] 1 ,x 2 ,...,x N ](N is data length), and generating N-m-1 m-dimensional vectors X by m-dimensional embedding m (1)，…，X m (N-m +1) in which the vector X m (i)＝[x i ,x i+1 ,...,x i+m-1 ](i is more than or equal to 1 and less than or equal to N-m). The vector distance is defined as the maximum scalar value of the difference of the corresponding elements in the two vectors, and the distance threshold is set as r. SampEn is defined as [11 ]]：
Wherein the content of the first and second substances,
when the embedding dimension is m and the distance between every two vectors is less than or equal to a threshold value r, the number of the vectors is B i The probability average of (a);
when the embedding dimension is m +1 and the distance between every two vectors is less than or equal to a threshold value r, the number of the vectors A i Is calculated from the probability average of (1).
Finally, the SampEn of all elements after y (n) coarse granulation is solved to obtain MSE.
The data multi-scale coarse graining is crucial to MSE, and the essence is that original data substitution data is obtained after a fixed scale window moving average value filtering is applied to the data; changing the window scale (generally 1-20) to obtain original data multi-scale substitute data; the multiscale substitution data is coarsely granulated to unit length. However, factors such as age, sex, psychology, drugs, and especially a wide variety of arrhythmias (tachyarrhythmias, bradyarrhythmias, atrial fibrillation, heart failure, etc.) will all complexly affect the multiscale properties of HRV. MSE coarse grain is equivalent to performing non-overlapping window moving average filtering on a data sequence, and the window width is the MSE time scale. Fixed scale (window width) and fixed scale entropy, the analysis of nonlinear non-stationary data has limited effect, MSE is not enough to study and represent real data of different dynamic processes. Therefore, the number of scales and their sizes are difficult to predict and estimate, and the fixed scale MSE cannot fully and accurately quantify the HRV.
Disclosure of Invention
The invention overcomes the defect of MSE fixed scale, fully and accurately quantifies HRV complexity, and provides a method for analyzing heart rate variability data based on adaptive multiscale entropy (AMSE); in the method, an Integral Mean Mode Decomposition (IMMD) method is adopted to carry out IMMD self-adaptive decomposition on the HRV to obtain a series of multi-scale mean value substitution data sets of original data; secondly, coarsely granulating each element in the mean value substitution data set and obtaining the corresponding self-adaptive scale; finally, the SampEn value of each element in the coarsely granulated mean replacement data set is calculated.
Because IMMD is equivalent to data self-adaptive local mean filtering, after the HRV is coarsely granulated in multiple scales by IMMD, the obtained AMSE scale has self-adaptability, and the HRV complexity can be comprehensively and accurately quantified.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for analyzing heart rate variability data based on adaptive multi-scale entropy specifically comprises the following steps:
the first step is as follows: performing self-adaptive decomposition on heart rate variability data by an integral mean modal decomposition method IMMD to obtain a multi-scale alternative data set R (n); the method specifically comprises the following steps:
1) definition of X jk (j、k＝1,2,…；k>j) Is a heart rate variability data sequence x (n) ═ x 1 ,x 2 ,…,x i ,…,x N ]Adjacent to two extreme values x j And x k In the middle part, X jk Length τ ═ j-k + 1; determining integral to obtain local sequence X jk The mean value is:
m jk fixed at a local midpoint
And (4) solving all local mean value points of the data sequence based on the formula (3).
2) And (3) constructing a data mean sequence m (n) by all local mean points of the cubic spline interpolation data sequence.
3) The prototype pattern function PMF is:
PMF(n)＝x(n)-m(n) (4)
1) to 3) above are called a primary mean screening process, and PMF is denoted as PMF 1 。
4)PMF 1 The mean screening process was repeated iteratively k-1 ( k 2,3, …) times as a new data sequence to yield PMFs k (ii) a When PMF k The cauchy screening stop criterion is met:
stop of screening, PMF k I.e., IMF 1.
5) Residual component r 1 (n) ═ x (n) -IMF1 as a new signal, and all the above processes were repeated to obtain IMF2 and r 2 (n); similarly, the remaining IMFk (k ═ 3, …, n) component and the remaining component r of the signal are obtained k (n)。
6) Residual component set r (n) { r ═ r 0 (n),r 1 (n),r 2 (n),…,r n And (n) is the data multi-scale mean value substitution data sequence set.
The second step is that: r (n) coarse graining and self-adaptive scale thereof;
1) will r is k (n) performing step 1) of the first step to obtain r k (n) all local means, the sequence formed by the local means being the coarse grain r k (n)。
2) Definition of
Is the ith local scale in the IMFk; definition of r k (n) the corresponding scale is the mean or average period of all local scales of the IMFk:
the third step: r (n) after coarse graining, all elements calculate sample entropy SampEn to obtain self-adaptive multi-scale entropy AMSE.
Furthermore, in the second step, in order to avoid the statistical error generated by solving the sample entropy SampEn, when r is k (n) after coarse granulation the length is less than 1X 10 3 And (4) discarding.
Compared with the prior art, the invention has the following beneficial effects:
1. the IMMD method is particularly suitable for nonlinear and non-stationary data, and in the AMSE method provided based on the IMMD method, scale self-adaptive data is local, so that the AMSE is more practical than MSE.
2. The AMSE entropy values are more accurate in quantifying HRV sequence complexity than the MSE entropy values: 1) the statistical average AMSE entropy value of HRV sequence samples of Normal Sinus Rhythm (NSR) is highest in a large-scale adaptive scale, which is consistent with the most widely recognized NSR having the strongest complexity, but the traditional MSE may not be obtained by analysis on an empirical scale; 2) AMSE analysis indicates that the dynamics of the heart of a healthy person are the most complex; atrial Fibrillation (AF) pathology transforms the heart system from complex to chaotic, with the most severe loss of complexity; sympathetic and vagal activity is impaired to varying degrees in patients with Congestive Heart Failure (CHF).
3. The AMSE adaptation scale may reflect HRV sequence complexity. For the challenge2008HRV dataset given in the examples: all mean adaptation scales of AF, CHF patient HRV sequence samples were reduced relative to NSR, and the reduction in all mean adaptation scales of AF patient HRV sequence samples was greater than for CHF patients. This is consistent with the statistical differences of the power spectrum of HRV sequence samples of AF and CHF patients and the statistical mean difference of AMSE entropy values, so that the AMSE adaptive scale can indirectly reflect the complexity of HRV data sequences.
In a word, based on the fact that IMMD is equivalent to continuous adaptive local mean filtering, multi-scale coarse granulation can be carried out on data, the AMSE method provided by the invention can comprehensively and accurately reflect the complexity of a biological system on an adaptive scale and a scale entropy value, and has remarkable advantages compared with MSE.
Drawings
Fig. 1 is a schematic diagram of MSE multi-scale coarse granulation, in which (a) scale is 2; (b) the scale is 3.
FIG. 2 is a plurality of typical scale replacement data obtained by MSE of HRV.
FIG. 3 is a schematic diagram of AMSE adaptive multi-scale coarse grain employed in the present invention; in the figure, (a) 1 st scale; (b) dimension 2.
FIG. 4 is a plurality of representative scale replacement data obtained by the AMSE for the HRV.
FIG. 5 is three HRVsStatistical mean AMSE entropy for sequence samples
Corresponding statistical mean adaptive scale
Error bar graph.
FIG. 6 is a block diagram of the statistical mean MSE error of three HRV sequence samples
Figure (a).
FIG. 7 is a graph of three HRV sample AMSE adaptive scale error bars
Fig. 8 is a Lomb power spectrum of all samples of three HRVs, wherein (a) AF; (b) CHF; (c) NSR.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present invention more clearly apparent, the present invention is further described in detail with reference to the embodiments and the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The technical solution of the present invention is described in detail below with reference to the embodiments and the drawings, but the scope of protection is not limited thereto.
The embodiment is a method for analyzing heart rate variability data based on adaptive multi-scale entropy AMSE: firstly, carrying out IMMD self-adaptive decomposition on data by an AMSE method to obtain a series of multi-scale mean value substitution data sets of original data; secondly, coarsely granulating each element in the mean value substitution data set and obtaining the corresponding self-adaptive scale; finally, calculating the SampEn value of each element in the coarsely granulated mean value substitution data set to obtain AMSE; and processing the heart rate variability HRV sequence sample by self-adaptive multi-scale entropy AMSE to obtain the self-adaptive scale.
The data used in this example came from 2008, with PhysioNet as chaos, "is the normal heart rate chaotic? "topical challenge provided a set of R-R interval sequence datasets (see Glass L2009 Chaos 19028501-1). Which comprises the following steps: normal Sinus Rhythm (NSR) (age 30 ± 10, 2 men and 3 women), patients with Congestive Heart Failure (CHF) (age 59 ± 9, 5 men), patients with Atrial Fibrillation (AF) (age, gender unknown) each 5 cases with R-R interval data sequences of 20-24 h.
The first step is as follows: and (3) adaptively decomposing the heart rate variability data by the IMMD method to obtain a multi-scale alternative data set R (n).
1) Definition of X jk (j、k＝1,2,…；k>j) Is a heart rate variability data sequence x (n) ═ x 1 ,x 2 ,…,x i ,…,x N ]Adjacent to two extreme values x j And x k In the middle part, X jk The length is τ j-k + 1. Determining integral to obtain local sequence X jk The mean value is:
m jk fixed at a local midpoint
And (4) solving all local mean value points of the data sequence based on the formula (3).
2) And (3) constructing a data mean sequence m (n) by all local mean points of the cubic spline interpolation data sequence.
3) The Prototype Mode Function (PMF) is:
PMF(n)＝x(n)-m(n) (4)
1) to 3) above are called a primary mean screening process, and PMF is denoted as PMF 1 。
4)PMF 1 The mean screening process was repeated iteratively k-1 ( k 2,3, …) times as a new data sequence to yield PMFs k . When PMF k The cauchy screening stop criterion is met:
stop of screening, PMF k I.e., IMF 1.
5) Residual component r 1 Repeating the above processes to obtain IMF2 and r as new signal (n) ═ x (n) -IMF1 2 (n) of (a). Similarly, the remaining IMFk (k ═ 3, …, n) component and the remaining component r of the signal are obtained k (n)。
6) Residual component set r (n) { r ═ r 0 (n),r 1 (n),r 2 (n),…,r n And (n) is the data multi-scale mean value substitution data sequence set.
The HRV sequence data in FIG. 2 is subjected to AMSE method to obtain adaptive multi-scale alternative data, which is shown in FIG. 4.
The second step is that: r (n) coarse graining and adaptive scaling thereof.
1) Will r is k (n) performing step 1) of the first step to obtain r k (n) all local means, the sequence formed by the local means being the coarse grain r k (n)。
2) According to the literature: costa M, Goldberger a L, Peng C K2005 phys.rev.e 71021906, in order to avoid statistical errors in SampEn, the MSE should generally have at least 1 × 10 after multi-scale coarse-grained data 3 A data point. Therefore, if r k (n) after coarse granulation the length is less than 1X 10 3 And (4) discarding.
3) Definition of
Is the ith local (local part between the ith and i +1 extreme values of the IMFk) dimension in the IMFk. Because the IMFk spectrum has narrow-band characteristics, the IMFk local scale
Approximately equal. IMFk and its corresponding residual component r k (n) local dimensions are the same, thus, r is defined k (n) the corresponding scale is the mean (or average period) of all local scales of the IMFk:
as can be seen by comparing fig. 2 and fig. 4, the MSE scale is a fixed value, and the trend change step sizes are equal; the AMSE scale is defined as the average value of all local scales of the substituted data obtained by IMMD self-adaptation, has self-adaptation, and has approximately equal trend change step length.
The third step: r (n) after coarse granulation, all elements are subjected to SampEn to obtain AMSE.
The fourth step: AMSE analysis of HRV
1. Experimental results and analysis of AMSE entropy on HRV:
each HRV sequence sample is similar in sequence by obtaining the self-adaptive scale through AMSE, so that the self-adaptive scale and the corresponding entropy value statistical average can be respectively carried out on the three HRV sequence samples in sequence. The statistical mean AMSE entropy and statistical mean adaptive scale correlation curve for each of the three HRV sequence samples is shown in fig. 5.
AMSE analysis results: 1) the HRV sequence entropy of NSR decreases rapidly on the 1 st (τ ═ 1) and 2 st (τ ═ 3.52) scales, then increases on the 2 nd to 4 th (τ ═ 7.29) scales, and then begins to decrease slowly as the scales increase and is approximately constant. In general, except for the 1 st scale, the HRV sequence AMSE entropy values for NSR fluctuate very little over all the remaining scales and can be considered approximately constant. 2) HRV sequence entropy values in CHF patients decrease rapidly on the 1 st (τ -1) and 2(τ -3.13) scales, increase with increasing scale, and begin to decrease slowly and approximately constant on the 7 th (τ -13.31) scale. 3) The HRV sequence entropy of the AF patient is monotonically reduced on all scales along with the increase of the scales and is similar to white noise.
Fig. 6 shows a statistical mean MSE error bar graph of three HRV sequence samples, and as can be seen from comparison with fig. 5, the mean MSE variation trend of the three HRV sequence samples is almost consistent with the mean AMSE variation trend when the mean MSE variation trend is smaller than 20. It can be observed that: the HRV sequence single scale SampEn values (entropy corresponding to scale 1 in fig. 6) for NSR are higher for CHF patients and lower for AF patients, and their empirical multi-scale (1-20) MSE entropy values are also higher for CHF patients and lower for AF patients. This is clearly in conflict with the general consensus that NSR has the greatest complexity, and that many diseases will attenuate individual complexity conclusions. The change trend of the MSE curve of the three HRV sequences can be reasonably inferred: when the scale is larger than a certain value (>20), the MSE entropy value for NSR may be higher than for AF and CHF patients. However, it is obviously impractical to gradually expand the MSE scale to an unknown value. MSE cannot accurately analyze chanllenge2008HRV datasets in full.
And (3) analyzing an experimental result: the HRV sequence entropy of NSR is highest in a large scale (17.54-67.17), so the AMSE method indicates that the NSR cardiac dynamics is most complex.
Relative to NSR, AF patient AMSE entropy values exhibit substantial variability at all scales. The multi-scale entropy of patients with AF decreases exponentially with increasing scale, reflecting the degradation of the control mechanisms that regulate heart rate on higher-order scales. This behavior resembles white noise, consistent with the phenomenon of absolutely unequal R-R intervals (meaning complete disruption of R-R intervals) in the pathological state of AF, reflecting the pathological state of atrial fibrillation which converts the heart system from complex to chaotic.
CHF patients have AMSE entropy values below NSR on all scales. On the lower order (2-4) scale, the difference in entropy between CHF patients and NSR is greater than on the higher order (4-8) scale. The data multiscale in the AMSE method is equivalent to continuous adaptive low-pass filtering on the data, so the entropy value on a high-order scale is determined by the low-frequency component of the original data, and the entropy value on a low-order scale is determined by the low-frequency component and the relatively high-frequency component together, so that the reduction of the AMSE entropy value on the low-order scale of a CHF patient is more obvious relative to NSR. The method is corresponding to the reduction of 0.04-0.15 Hz low-frequency power (LF) and 0.15-0.40 Hz high-frequency power (HF) in the HRV frequency domain index of the CHF patient, especially the reduction of HF is more obvious (see table 1; based on IMMD decomposition characteristics, 0.40Hz approximately corresponds to the 1 st-2 nd scale, 0.15Hz approximately corresponds to the 4 th scale, and 0.04Hz approximately corresponds to the 8 th scale), and reflects that the sympathetic nerve activity and the vagal nerve activity are damaged to different degrees, especially the vagal nerve injury is more serious. In addition, the low-order scale AMSE entropy difference between CHF patients and NSR may also result in part from NSR respiratory modulation (sinus rhythm) amplitudes higher than CHF patients.
TABLE 1 Lomb power spectrum related parameters (mean. + -. sd) of three HRV sequence samples
2. HRV analysis with adaptive scaling
HRV contains rich cardiovascular regulation information, and the nervous system, body fluid, and the body organs regulate themselves, which affect HRV. The complexity of the human biological system HRV sequence enables the scale of multi-scale entropy to increase nonlinearly, and pathological states can cause the scale change of the HRV sequence entropy. The MSE scale is linearly increased in fixed step length, and cannot reflect the nonlinear increase of the HRV sequence entropy scale, and even cannot reflect the change of the human HRV sequence entropy nonlinear scale in different physiological states; the AMSE can be equivalent to continuous adaptive low-pass filtering based on IMMD, and the multi-scale entropy value is obtained by data driving corresponding to the adaptive scale, so that the complexity of the HRV sequence can be reflected.
Fig. 7 is a bar graph of three HRV sequence samples AMSE adaptive scale statistical mean error. As can be seen in fig. 7, all mean adaptive scales of AMSE for the three HRV sequence samples are NSR, CHF patients, and AF patients in order from large to small. The average adaptive scale corresponds to the IMF component average period of the HRV sequence, so that the IMF component average periods are NSR, CHF patients and AF patients from large to small. This is consistent with the statistical mean of the frequency ranges (or highest frequencies) of the three HRV samples being NSR, CHF patients, AF patients, in order from small to large in the Lomb power spectrum (see fig. 8); and indirectly via frequency with power spectrum differences (e.g., Total Power (TP) in the frequency domain, LF, HF power spectrum parameter statistical mean differences in table 1).
If NSR is taken as a criterion, the change in the average adaptation scale for AF patients is greater in nearly all patients with CHF (see FIG. 7), which is consistent with AF patients having a greater change in the average AMSE entropy value over nearly all average adaptation scales than CHF patients (see Table 2).
TABLE 2 change in mean AMSE entropy for AF, CHF versus NSR
The AMSE adaptive scale change of the human HRV is consistent with the AMSE entropy change and the power spectrum change, and the HRV sequence complexity can be indirectly described and analyzed.
The above is a further detailed description of the present invention with reference to specific preferred embodiments, which should not be considered as limiting the invention to the specific embodiments described herein, but rather as a matter of simple derivation or substitution within the scope of the invention as defined by the appended claims, it will be understood by those skilled in the art to which the invention pertains.
Claims (2)
1. The method for analyzing the heart rate variability data based on the adaptive multi-scale entropy is characterized by specifically comprising the following steps of:
the first step is as follows: performing self-adaptive decomposition on heart rate variability data by an integral mean modal decomposition method IMMD to obtain a multi-scale alternative data set R (n); the method specifically comprises the following steps:
1) definition of X jk (j、k＝1,2,…；k>j) Is a heart rate variability data sequence x (n) ═ x 1 ,x 2 ,…,x i ,…,x N ]Adjacent to two extreme values x j And x k In the middle part, X jk Length τ ═ j-k + 1; determining integral to obtain local sequence X jk The mean value is:
m jk fixed at a local midpoint
Based on the formula (3), all local mean value points of the data sequence are obtained;
2) constructing a data mean sequence m (n) by all local mean points of the cubic spline interpolation data sequence;
3) the prototype pattern function PMF is:
PMF(n)＝x(n)-m(n) (4)
1) to 3) above were screened as a primary averageProgram, PMF is denoted as PMF 1
4)PMF 1 The mean screening process was repeated iteratively k-1 (k 2,3, …) times as a new data sequence to yield PMFs k (ii) a When PMF k The cauchy screening stop criterion is met:
stop of screening, PMF k Namely IMF 1;
5) residual component r 1 (n) ═ x (n) -IMF1 as a new signal, and all the above processes were repeated to obtain IMF2 and r 2 (n); similarly, the remaining IMFk (k ═ 3, …, n) component and the remaining component r of the signal are obtained k (n)；
6) Residual component set r (n) ═ r 0 (n),r 1 (n),r 2 (n),…,r n (n) the data sequence set is replaced by the data multi-scale mean value;
the second step is that: coarse granulating each element in R (n) and obtaining a corresponding adaptive scale, specifically:
1) will r is k (n) performing step 1) of the first step to obtain r k (n) all local means, the sequence formed by the local means being the coarse grain r k (n)；
2) Definition of
Is the ith local scale in the IMFk; definition of r k (n) the corresponding scale is the mean or average period of all local scales of the IMFk:
the third step: r (n) after coarse graining, all elements calculate sample entropy SampEn to obtain self-adaptive multi-scale entropy AMSE.
2. The adaptive multi-scale based on claim 1A method for entropy analysis of heart rate variability data, characterized in that in the second step, in order to avoid statistical errors in the sample entropy SampEn, when r is k (n) after coarse granulation the length is less than 1X 10 3 And (4) discarding.
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