Software for GMSE analysis

Download gmse.c, the C language source for a program that performs multiscale entropy analysis. The program can be compiled using any ANSI/ISO C compiler, and should be linked to the C math library (it uses only the sqrt function from that library). For example, using the freely available GNU C compiler, mse.c can be compiled into an executable mse by the command:

    gcc -o gmse -O gmse.c -lm

Preparing data for GMSE analysis

The program to compute GMSE processes text formatted input files with either one or two columns. Files with one column can be a list of RR intervals or any time series of interest. Files with two columns should be the time of occurrence of an R wave, t(i), and the corresponding RR intervals, t(i+1) - t(i). This type of RR interval file can be obtained from a beat annotation file using ann2rr:

    ann2rr -r nsrdb/16265 -a atr -c -p N -P N  -i s3  -V s3 > 16265.RR

Example of a two-column input file (16265.RR):

t(i)	RR(i) = t(i+1) - t(i)
0.406	0.602
1.008	0.609
1.617	0.602
2.219	0.625
2.844	0.609
3.453	0.625
4.078	0.594
4.672	0.602
⋮	⋮
300.914	0.547
301.461	0.539
302.539	0.547
303.086	0.539
⋮	⋮

The two-column file, 16265.RR can be filtered using filt from the HRV Toolkit:

    filt 0.3 20 -x 0.3 2.0

In this example, all points below 0.3 and above 2.0 are first removed. Next, to decide one whether the data point x_i should be filtered out or kept, the mean value of the 20 data points to the left and the 20 data points to the right is calculated. The central point x_i is deleted if it is below of above 30% (0.3) of the computed average value. The process is repeated for all data points.

When given two column input files (time and RR intervals), the GMSE program excludes RR intervals that are not consecutive. In the example above, there is an interruption in the time series between 301.461 and 302.539 s (values highlighted in yellow): 302.539 - 301.461 = 1.078 ≠ 0.539. Thus, the RR interval 0.539 will be excluded from the analysis. In addition, no vectors comprising the intervals immediately preceding (0.547) and following (0.547) the interruption will be considered.

Summary of options and default values for GMSE

-n:

largest scale. Default: 20.

-a:

difference between consecutive scales. Default: 1.

-c:

coarse-graining method: 1) mean; 2) standard deviation (SD); 3) variance; 4) mean absolute deviation. Default: SD.

-x:

sample entropy noise tolerance value: fixed. Two data points, u_i, u_j match if |u_i - u_j| ≤ x

-r:

sample entropy noise tolerance value: a number between 0 and 1 that represents a percent. Two data points, u_i, u_j match if |u_i - u_j| ≤ r * SD. Default: r = 0.15. For mean coarse-graining analysis (traditional MSE), SD is the standard deviation of the original (scale 1) time series. For all other cases, SD is the standard deviation of scale 4 (default) coarse-grained time series.

-m:

sample entropy vector length. Default: m = 2.

-i:

starting data point. Default: 0.

-I:

ending data point. Default: end of file.

Examples of command lines

1. gmse -i 0 -I 50000 -c 1 < 16265.RR-filt > output

   Coarse-graining method: mean (traditional MSE). Sample entropy parameters values m = 2, r = 0.15 (15% of SD of the original time series). The first 50,000 data points are considered.

   The output values are:

   Scale	SampEn	m3/m2	r * SD
   1	1.1897	7253987/23837718	0.013203
   2	1.3032	1600494/5891466	0.013203
   3	1.4956	473897/2114637	0.013203
   4	1.6527	179051/934800	0.013203
   5	1.6506	117176/610500	0.013203
   6	1.6294	85533/436301	0.013203
   7	1.6505	57324/298632	0.013203
   8	1.6164	47163/237466	0.013203
   9	1.5821	40749/198244	0.013203
   10	1.5895	31764/155689	0.013203
   11	1.5332	28626/132628	0.013203
   12	1.5297	24666/113877	0.013203
   13	1.5189	21291/97245	0.013203
   14	1.4899	18804/83427	0.013203
   15	1.4710	16822/73235	0.013203
   16	1.4687	14703/63866	0.013203
   17	1.4734	12977/56633	0.013203
   18	1.4482	11873/50527	0.013203
   19	1.4621	9992/43114	0.013203
   20	1.4319	9591/40155	0.013203

2. gmse -i 0 -I 50000 -r 0.2 -c 2 < 16265.RR-filt > output

   Coarse-graining method: SD. Sample entropy parameters m = 2, r = 0.20 (20% of the coarse-grained time series for scale 5). This is the command line used to derive the results shown on the left panel of Fig. 2 and on the right panel of Fig. 5.

   The output values are:

   Scale	SampEn	m3/m2	r * SD
   5	1.4648	307814/1331797	0.003835
   6	1.5233	168245/771816	0.003835
   7	1.5829	99565/484806	0.003835
   8	1.6365	62961/323456	0.003835
   9	1.7058	40966/225554	0.003835
   10	1.7258	30256/169946	0.003835
   11	1.7605	21967/127745	0.003835
   12	1.8010	16915/102437	0.003835
   13	1.8103	13668/83541	0.003835
   14	1.8485	10580/67189	0.003835
   15	1.8309	9132/56979	0.003835
   16	1.8727	7565/49216	0.003835
   17	1.8786	6460/42275	0.003835
   18	1.8836	5632/37041	0.003835
   19	1.8833	4867/32000	0.003835
   20	1.9080	4180/28171	0.003835

3. gmse -i 0 -I 50000 -x 0.008 -c 4 < 16265.RR-filt > output

   Mean absolute deviation is the chosen metric for coarse-graining. Sample entropy parameters m = 2, r = 0.008 (fixed, not a % of SD). This is the command line used to derive the results plotted on the right side panel of Fig. 3.

   The output values are:

   Scale	SampEn	m3/m2	r * SD
   5	0.7032	3594655/7261796	0.008000
   6	0.7591	2008629/4291038	0.008000
   7	0.8139	1186303/2677237	0.008000
   8	0.8624	767179/1817262	0.008000
   9	0.9165	506521/1266507	0.008000
   10	0.9311	380264/964870	0.008000
   11	0.9756	273555/725658	0.008000
   12	0.9891	217627/585165	0.008000
   13	0.9915	177947/479594	0.008000
   14	1.0232	140291/390320	0.008000
   15	1.0296	117161/328049	0.008000
   16	1.0236	104222/290078	0.008000
   17	1.0395	89258/252412	0.008000
   18	1.0468	77024/219414	0.008000
   19	1.0332	68169/191564	0.008000
   20	1.0375	60541/170863	0.008000