A characteristic feature of these learning curves is the large scatter of the trial values around the curve

There are at least two possible sources of such variability.First, as with most cognitive tests, the participant is apt to develop test-taking strategies with repeated exposures to the same procedure. Benedict & Zgaljardicrefer to this as “test-specific” practice. Second,the participant’s state of health might be changed due to any external or internal factors acting before or during test performance, such as exposure to marijuana. Thus, it is advisable to conduct several repeated tests for each participant. We advocate repeating the test three times. Mathematical modeling of the learning curve offers a quantitative description of learning and memory abilities when a participant is exposed to marijuana or consumes a plant based product purported to improve learning and memory. Moreover, values of the model’s coefficients B3 and B4 give the opportunity to characterize short- and long-term memory status quantitatively. For this purpose, it is necessary to separate the initial set of B3 and B4 values into disjointed subsets.

When the model was applied to patients with multiple sclerosis, about half of the patients were shown to exhibit cognitive impairment . Thus, when working with patients suffering from multiple sclerosis,it is possible to obtain a spectrum from “normal memory status” to “severely impaired”. The multiples clerosis group included 365 patients with clinically defined multiple sclerosis and was tested with the CVLT-II . The raw learning data were modeled and the sets of B3 and B4 values were used for further analysis . Female and male sets of B3 values, as well as B4 values, were analyzed separately because it was shown that females scored significantly higher than males on the CVLT .SPSS 17 was used for cluster and discriminant analysis. Initial values of B3 or B4 were classified based on hierarchical cluster analysis. This procedure identifies relatively homogeneous groups of B3 or B4values, using an algorithm that starts with each value in a separate cluster, and combines clusters until only one is left. At each step, the two clusters separated by the shortest distance are combined. After separating raw coefficient values into six clusters of B3 values or six clusters of B4 values, discriminant analysis is applied to the clusters.

Discriminant analysis creates a linear function of B3 or B4 that provides the best discrimination between two samples, in particular, between neighboring clusters. With discriminant analysis, it is possible to calculate cut-off values B3 and B4 for assigning the obtained B3 or B4 value to one or another memory state level. In other words, the cut-off values allow the determination of to what extent the short- and long-term memory is impaired. The data were gathered at the Institute for Experimental Medicine, St. Petersburg Russia between January and April, 2013. The research was conducted in accordance with the National Standard of the Russian Federation “Good Clinical Practice” with the permission of the Institutional Board on Biomedical Ethics of the Institute for Experimental Medicine. Participants were recruited from the Institute’s clinic who were undergoing drug rehabilitation and wanted to continue their treatment. Healthy volunteers were recruited from the surrounding area. Two groups were used. The first group was 15 healthy volunteers and was comprised of seven females within the age range of 22 – 27 years old and eight males within the age range of 23 – 31 years old. The second group was 15 drug addicts and was comprised of four females within the age range of 23 – 31 years old and 11 males within the age range of 22 – 44 years old who all under wentrehabilitation courses. The drug addicts used Amphetamine-like psychostimulant drugs.Each participant was examined three times with an inter test interval of one to two days. Three different lists of words were used.

The senior authors are grateful to Professor Sergey Tsikunov, Pavlov’s Department of Physiology, Institute for Experimental Medicine, St. Petersburg, Russia who conducted clinical examinations of the subjects. Based on this assessment, participants were assigned either to the healthy volunteer group or the drug addicted group. Here we see that in each drug addicted male the learning curves differ from each other much more than those of the healthy male participants.Instead of a monotonous increase in trial values as the test continues,often these values decrease in the middle of the test—a concave curve or a convexity in the middle of the test, a convex curve, or even an S-shaped curve. Such a deviation in the location of points is a consequence of memory impairment under the influence of drug abuse. Thus, averaging over three tests is even more necessary in drug addicts than in healthy participants. The results presented here show how the model can be used to characterize the effect of marijuana on learning and memory.

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