Sample entropy reveals high discriminative power between young and elderly adults in short fMRI data sets

Some studies have placed Sample entropy on the same data length constraint of 10m–20m (m: pattern length) as approximate entropy, even though Sample entropy is largely independent of data length and displays relative consistency over a broader range of possible parameters (r, tolerance value; m, pattern length; N, data length) under circumstances where approximate entropy does not. This is particularly erroneous for some fMRI experiments where the working data length is less than 100 volumes (when m = 2). We therefore investigated whether Sample entropy is able to effectively discriminate fMRI data with data length, N less than 10m (where m = 2) and r = 0.30, from a small group of 10 younger and 10 elderly adults, and the whole cohort of 43 younger and 43 elderly adults, that are significantly (p < 0.001) different in age. Ageing has been defined as a loss of entropy; where signal complexity decreases with age. For the small group analysis, the results of the whole brain analyses show that Sample entropy portrayed a good discriminatory ability for data lengths, 85 ≤ N ≤ 128, with an accuracy of 85% at N = 85 and 80% at N = 128, at q < 0.05. The regional analyses show that Sample entropy discriminated more brain regions at N = 128 than N = 85 and some regions common to both data lengths. As data length, N increased from 85 to 128, the noise level decreased. This was reflected in the accuracy of the whole brain analyses and the number of brain regions discriminated in the regional analyses. The whole brain analyses suggest that Sample entropy is relatively independent of data length, while the regional analyses show that fMRI data with length of 85 volumes is consistent with our hypothesis of a loss of entropy with ageing. In the whole cohort analysis, Sample entropy discriminated regionally between the younger and elderly adults only at N = 128. The whole cohort analysis at N = 85 was indicative of the ageing process but this indication was not significant (p > 0.05).