With application of the Higuchi algorithm, fractal dimension (FD) values of the electrocortical activity of the rat parietal cerebral and paravermal cerebellar cortex were calculated, before and after unilateral discrete injury of the left parietal cortex. Immediately following the first acute injury, in a group of six rats, a reversible increase in mean FD was found at the left (ipsilateral side to the injury) cerebral cortex, from 1.38 to 1.59, and at the left cerebellar cortex from 1.51 to 1.73. In addition, an indication of plastic changes after repeated (third) injury was found as an irreversible increase in mean FD: 1.54 on the left and 1.48 on the right side of parietal cortex.

We propose a new method for calculating fractal dimension (DF) of a signal y(t), based on coefficients m (n) y , mean absolute values of its nth order derivatives (consecutive finite differences for sampled signals). We found that logarithms of m (n) y , n = 2, 3, . . . , n max , exhibited linear dependence on n:with stable slopes and Y -intercepts proportional to signal DF values. Using a family of Weierstrass functions, we established a link between Y -intercepts and signal fractal dimension:and calculated parameters A(n max ) and B(n max ) for n max = 3, . . . , 7. Compared to Higuchi's algorithm, advantages of this method include greater speed and eliminating the need to choose value for k max , since the smallest error was obtained with n max = 3. 283 Fractals 2005.13:283-292. Downloaded from www.worldscientific.com by EMORY UNIVERSITY on 07/30/15. For personal use only.

We recorded electrocortical activity in anesthetized rats and constructed k(max) new self-similar time series, applying Higuchi's algorithm. The aim of this study was to estimate value of the parameter k(max) in order to obtain fractal dimension values as an optimum measure of biosignal change. After our analysis, electrocortical activity recordings resulted in a family of curves f(k(max)). Three regions could be distinguished 2 < or = k(max) < 8, with a U-shape; 8 < or = k(max) < or = 30, with a steeper quasilinear increase; and k(max) > or = 30, with a smaller slope quasilinear increase. We suggest the optimum region for k(max): 8 < k(max) < 18, specifically k(max) = 8.

The cerebellum, even when not directly damaged, is potentially interesting for understanding the adaptive responses to brain injury. Cerebellar electrocortical activity (ECoG) in rats was studied using spectral and fractal analysis after single and repeated unilateral injury of the parietal cortex. Local field potentials of cerebellar paravermal cortex were recorded before brain injury, in the acute phase (up to 2.5 hours) after a first injury of anesthetized rats, and then before and after second, third, and, in some cases, fourth injury. Relative gamma power (32.1-128.0 Hz) and fractal dimension of ECoGs were temporarily increased after the first injury. However, there was a permanent mild increase in gamma activity and a mild increase in the fractal dimension of cerebellar activity as a chronic change after repeated remote brain injury. There was a negative linear correlation between the normalized difference in fractal dimensions and normalized difference in gamma powers of cerebellar activity only in the case of repeated brain injury. This is the first study showing that correlation between the parameters of spectral and fractal analyses of cerebellar activity can discriminate between single and repeated brain injuries, and is, therefore, a promising approach for identifying specific pathophysiological states.

Cerebellar involvement in cognitive functions has been revealed in numerous anatomical, clinical and neuroimaging studies and several hypotheses about potential the role of the cerebellum in higher level brain function have been established. The aim of this study was to show involvement of the cerebellum in simple cognitive tasks. For this matter, we contrasted two tasks from the same semantic domain with specific cognitive content and level of practice: counting forward and counting backward. Twelve volunteers participated in this fMRI study and they were asked to perform both tasks within the same number range (1 to 30 and vice versa). Results showed greater activation in the right cerebellum for the task of counting forward than for counting backward, while for counting backward greater activation was found in prefrontal cortex, supplementary motor area, and anterior cingulate of both hemispheres. Our results correlate with already established hypotheses about cerebellar role in precise and smooth control, not only in well-trained motor but in well trained cognitive tasks as well.