The Tsallis Entropy in the EEGs of Normal and Demented Individuals

Abstract

The electroencephalogram (EEG) is a recording of the brain's total electrical activity. Since the brain processes information, the information in the brain's total electrical activity probably corresponds to the information processing in the brain. This assumption was used to study the entropy or 'self-information' in the EEGs of participants who were performing a short-term memory task. There were two groups of participants in this study; one group had a medical diagnosis of "normal aging,"(Normal) and the other group had a diagnosis of "very mild dementia," (Dementia). The dementia diagnosis means that they have short-term memory impairment. The EEG of each participant was recorded while they performed a short-term memory task; face recall. Their EEG was also recorded while they performed a second short-term memory task; object recall. These EEG data were used to test a basic hypothesis; the entropy in the EEGs of the Dementia group would be significantly different than the entropy in the EEGs of the Normal group. When choosing a method to test this hypothesis, it is important to account for how the brain processes a recall stimulus. The brain information processing that occurs during a recall task has informational, temporal and spatial properties. Therefore, to accurately analyze the entropy in the EEG data three things must be specified: 1) which entropy measure to use, 2) which time intervals of the EEG data to use, and 3) what locations on the participant's scalp (choice of EEG electrodes) to use. The specifications used are: 1) Entropy measure. The entropy measure used was the Tsallis entropy. Tsallis entropy is a generalization of the Shannon entropy to a non-additive entropy measure. An additive entropy measure assumes that the entropy of a whole system is equal to the sum of the entropies of each part of the system. EEG data may not conform to this assumption, so we used the Tsallis entropy instead of the Shannon entropy. 2) EEG time interval. The EEG data used were those data that occurred during the first 300 milliseconds (ms) after the appearance of the recall stimulus. A participant's response is purely perceptual/cognitive for about 300 ms after the appearance of the recall stimulus (Sternberg 1966, 1969). Muscle movement responses, responses which are more variable, begin later in the task. This suggests that the first 300 ms of the EEG data will be more specific to the task. 3) Spatial component - the choice of EEG electrodes. Electrodes chosen for this EEG data analysis should correspond with the way that information moves through the brain during the first 300 ms of the recall task. The task began with a visual stimulus. The information from this stimulus enters the posterior cortex at V1 (Broadman area 17). After about 150 ms, this (transformed and partially altered) information enters the anterior cortex. Therefore, the EEG data which correspond to the recall task are those data recorded by posterior electrodes during the first 150 ms and those data recorded by anterior electrodes for the next 150 ms. The entropy analysis of these data was accomplished by computing the Tsallis entropy in two posterior electrodes; P3 and P4 for the first 150 ms after the appearance of the stimulus. Then, the Tsallis entropy of the EEG data in the second, contiguous 150 ms time interval was computed. The EEG data for this second entropy measurement were recorded by two anterior electrodes: T7Fp3 and T8Fp4 (electrodes placed slightly behind the temples). Thus, the EEG data analyzed were data which corresponded to the flow of brain information during the first 300 ms of the recall task. It has been assumed that the entropy in an EEG corresponds to brain information processing during the recall task. However, these entropies, alone, do not show how brain information changes when moving from posterior cortex to anterior cortex. A commonsense solution to this difficulty would be to compute the mutual entropy (mutual information) measure. However, this measure is based on the assumption of a closed information channel. This assumption does not hold true for the brain. The neural information pathway from early visual cortex to anterior cortex is not a closed pathway. For this reason, a relative entropy measure, a measure of the amount of anterior EEG entropy relative to the amount of posterior EEG entropy is more appropriate. This relative entropy measure is the ratio of the anterior EEG entropy to the posterior EEG entropy. This ratio of entropies or "entropy ratio" was the measure used to compare Normal and Dementia participants. Normal participants were expected to have larger entropy ratios than those with dementia. Thus, the quantitative hypothesis is, the entropy ratios of the Normal participants will be higher than the entropy ratios of the Dementia participants. For the most part, this hypothesis was formulated before the testing of the 47 participants. It was ante hoc. To be more exact, the specifics of the method for testing the hypothesis were formulated during the EEG testing of the first few participants; about eight participants. A total of 33 normal aging participants and 14 very mildly demented participants were tested. The results are: 31 of the 33 Normals had higher entropy ratios than the 14 entropy ratios of the Dementia group. These 31 entropy ratios were all greater than one. 14 of the 14 entropy ratios of the Dementia group were less than or equal to one (at two decimal places of precision). Participant's entropy ratios can be used to discriminate between the Normal and Dementia groups. Assume that entropy ratios greater than one denote normal aging and entropy ratios less than or equal to one denote dementia (impaired short-term memory). Then these criteria distinguish between the Normal and Dementia groups with a specificity of 100% (14 of 14) and a sensitivity of 94% (31 of 33). This means that two Normal participants were incorrectly classified as having dementia. However, both of these participants have a family history of Alzheimer's Disease dementia. One participant had a parent, now deceased, who had severe dementia. This participants other parent has Alzheimer's Disease. The second participant also has a parent with Alzheimer's a genetic predisposition to Alzheimer's Disease dementia. For this reason, these two participants may have very early Alzheimer's Disease. This remains to be seen, as does further refinement and testing of this hypothesis.