Figure 2.

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 <a onClick="popup('http://www.biomedcentral.com/1471-2202/11/122/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2202/11/122/mathml/M1">View MathML</a> and <a onClick="popup('http://www.biomedcentral.com/1471-2202/11/122/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2202/11/122/mathml/M2">View MathML</a>. 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 <a onClick="popup('http://www.biomedcentral.com/1471-2202/11/122/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2202/11/122/mathml/M3">View MathML</a> and <a onClick="popup('http://www.biomedcentral.com/1471-2202/11/122/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2202/11/122/mathml/M4">View MathML</a>.

This pattern matching procedure is performed for all possible sequences so that:

<a onClick="popup('http://www.biomedcentral.com/1471-2202/11/122/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2202/11/122/mathml/M5">View MathML</a>


If a specific pattern in one channel can not be detected in the other, as in the example above, the corresponding <a onClick="popup('http://www.biomedcentral.com/1471-2202/11/122/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2202/11/122/mathml/M6">View MathML</a>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
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