Calculation of XapEn. Short excerpt of raw data from three channels shown to illustrate the computation of XApEn. Parameters were set to r = 23 μV (tolerance) and m = 1 (sequence length). Thus, the 'sequence' length is one data point. For illustration purposes we choose data point i = 10 of Channel 1. Similar sequences (data points of similar amplitude) of Channels 2 and 3 are found within the upper rectangle representing tolerance r, i.e. data points 6 and 7 of Channel 2 and data point 15 of Channel 3. This leads to coefficients and . In the second pass, sequence length is extended to m+1 = 2 points so that now the two point-sequence Channel 1 (10,11) is under consideration. For all previously identified data points in channels 2 and 3 (namely, those similar to Channel 1 (10)) the algorithm checks if the consecutive data point is similar to Channel 1 (11) and hence a pattern similar to Channel 1 (10, 11) exists. Graphically this means that two consecutive data points of channels 2 and 3 have to reside within the upper and lower rectangle, respectively. Only Channel 2 (7, 8) fulfils this requirement. This leads to coefficients and .
This pattern matching procedure is performed for all possible sequences so that:
If a specific pattern in one channel can not be detected in the other, as in the example above, the corresponding is undefined. In the analyzed data sets and with the parameters chosen, this case did not occur.
Kreuzer et al. BMC Neuroscience 2010 11:122 doi:10.1186/1471-2202-11-122