Medical & Biological Engineering & Computing

, Volume 48, Issue 7, pp 671–679

Fractal dimension values of cerebral and cerebellar activity in rats loaded with aluminium


    • Institute for Biological Research “S. Stankovic”University of Belgrade
  • Milka Culic
    • Institute for Biological Research “S. Stankovic”University of Belgrade
  • Ljiljana Martac
    • Institute for Biological Research “S. Stankovic”University of Belgrade
  • Gordana Stojadinovic
    • Institute for Biological Research “S. Stankovic”University of Belgrade
  • Ivan Capo
    • Medical FacultyUniversity of Novi Sad
  • Dusan Lalosevic
    • Medical FacultyUniversity of Novi Sad
  • Slobodan Sekulic
    • Medical FacultyUniversity of Novi Sad
Original Article

DOI: 10.1007/s11517-010-0620-3

Cite this article as:
Kekovic, G., Culic, M., Martac, L. et al. Med Biol Eng Comput (2010) 48: 671. doi:10.1007/s11517-010-0620-3


Aluminium interferes with a variety of cellular metabolic processes in the mammalian nervous system and its intake might increase a risk of developing Alzheimer’s disease (AD). While cerebral involvement even at the early stages of intoxication is well known, the role of cerebellum is underestimated. Our aim was to investigate cerebral and cerebellar electrocortical activity in adult male rats exposed to chronic aluminium treatment by nonlinear analytic tools. The adult rats in an aluminium-treated group were injected by AlCl3, intraperitoneally (2 mg Al/kg, daily for 4 weeks). Fractal analysis of brain activity was performed off-line using Higuchi’s algorithm. The average fractal dimension of electrocortical activity in aluminium-treated animals was lower than the average fractal dimension of electrocortical activity in the control rats, at cerebral but not at cerebellar level. The changes in the stationary and nonlinear properties of time series were more expressed in cerebral electrocortical activity than in cerebellar activity. This can be useful for developing effective diagnostic and therapeutic strategies in neurodegenerative diseases.


AluminiumCerebral and cerebellar electrocortical activityFractal dimensionAlzheimer’s disease

1 Introduction

Aluminium (Al) is one of the most widely distributed metals in the environment and may enter into the body mostly from the water, diet and medication. Al has been shown to interfere with a variety of cellular metabolic processes in animals and humans. It is interesting that neurobehavioral changes in developing mice exposed to Al, beginning at puberty and extending to young adulthood, differed from those in animals exposed to treatment in the adult stage [17]. A great body of evidence has implicated Al as a neurotoxin, which may be involved in the etiology of neurodegenerative disorders, such as Alzheimer’s disease (AD) and dialysis dementia, which are manifested with progressive cognitive impairments such as learning and memory loss [5, 15, 42]. Toxic damage to brain induced by Al has been investigated as a possible cause of neurodegenerative disorders in humans as already reviewed [45] although brain has been found to accumulate lower concentrations of aluminium than many other tissues—bone, muscles, liver, spleen [46]. Neurophysiological investigations of workers chronically exposed to aluminium have raised the question of whether pre-clinical detection of aluminium neurotoxicity and consequent early treatment might help to prevent or retard the onset of AD or other neurological and cognitive impairments [33, 36]. Much of data analysis related to AD has been directed towards investigation of underlying nonlinear dynamics and main findings of reduced coherence among cortical regions [21]. Our electrophysiological and histological approaches confirmed that aluminium has neurotoxic effects in adult rats parenterally treated with aluminium (2 g/kg daily) for 4 weeks [11, 27]. The aim of this study was to use fractal analysis of cerebral and cerebellar electrocortical activity for exploring brain dynamics in the rat model of Al toxicity. The preliminary account on this study has already appeared [10].

2 Materials and methods

2.1 Experimental animals, aluminium treatment regime and histological verification

The experiments were performed on adult male rats of the Wistar strain. All animal treatments were conducted in accordance with the European Communities Council Directive of 24 November 1986 (86/609/EEC). The animals were subjected to a 12 h light–dark cycle and housed one per cage at 22°C with free access to food and water. There were 10 animals in each of two groups—the control group (the rats were injected by 1 ml saline, i.p, per day, for 4 weeks) and the aluminium-treated group. For developing a model of chronic aluminium neurotoxicity a lower dose variant of the rat model [4, 27] was used and the rats were chronically treated by intraperitoneal administration 1 ml of 0.445% AlCl3·6H20 in saline, i.e. 2 mg Al/kg, per day, for 4 weeks. The age of the examined rats at the days of electrophysiological recordings was about 3.5 months in the control group and did not differ on the average age of the age of aluminium-treated rats. All rats survived acute experimentation well (first testing and the one repeated after a week). Thereafter, some animals were killed and underwent neurohistological verifications and neuronal cell loss, many dying (“dark”) neurons and endogenous aluminium in subcellular structures were noticed in neocortical, hippocampal regions and occasionally in cerebellum of rats loaded with aluminium [11].

2.2 Electrophysiological recording procedure

Electrophysiological procedure was performed under anaesthesia (pentobarbital sodium, Serva, Heidelberg; initial doses—35 mg/kg, subsequent doses, as required, ~8 mg/kg, i.p) while each animal was fixed in a stereotaxic frame. Round-shaped craniotomy allowed epidural positioning of the silver ball electrodes on the cerebral/cerebellar areas or intracortical positioning of the tungsten microelectrodes into the superficial brain areas (at the coordinates in mm, according to bregma: P: 2.5; L/R: 2.0; H: 0 and P: 10.5; L/R 1.5; H: −1.0). Thus, local field potentials (ECoGs) as 4 brain signals (from the left and right parietal cortex as well as from the left and right paravermal cortex) of each animal were simultaneously recorded, monitored continuously during acute experimentation and digitized sequentially.

2.3 Signal processing

Brain signals in each experimental animal were amplified by the multi-channel processor (MCP Module, Alpha-Omega Eng, Nazareth) and filtered by the same hardware of low and high band pass filters (pass between DC and 1 kHz) and by the 50 Hz notch filter. The signals were sequentially acquired at 5–15 min pauses between acquisition sessions into a PC via an analogue-to-digital converter (SIGVIEW package and CB2DN program). Each acquired sequence lasted up to 241 s. The signals were sampled at the sampling rate of 256 Hz. Especially important aspect of our data acquisition was the elimination of ECoG artefacts due to movements and other non-brain sources of electric activity (which could mostly occur at 61, 100, 107 and 121 Hz). Thus, the digitized signals were filtered off-line by our software (FMBS program).

2.4 Stationarity of brain signals

Spectral analysis of brain signals was performed by FFT [9] and the wavelet tools [12, 13, 26, 29], (program WAVE1). For this purpose we used the relative wavelet energy (RWE) in discrete wavelet transform as the parameter that describes the distribution of signal energy [34]. We found that around 70% of the energy of each of the recorded brain signals in this study was concentrated in the field below 12 Hz. This could mean that frequencies above 12 Hz are not relevant and thus a minimum width of the window corresponded to 1/12 Hz = 83.3 ms was needed in order to examine the stationarity of these signals. According to [8] the optimum window length should be more than three times than this value, in order to avoid underlying trend of time series, so we have chosen the window of 312.5 ms. The nonparametric test, the so called, runs test [6] was used in purpose of examining of stationarity of brain signals. Standard procedure was applied: in the first step, we calculated the median value of each epoch and each sample was classified as a unit (above median value) or zero (below median value). Further, the number of sequences (the so-called, “runs”) of units or zeroes within the epoch compared to the values in table [24] which are derived from distribution function of independent, ergodic and stationary data. If the number of runs falls within the region of acceptance at the given significance level (usually 0.05), the epoch is considered to be stationary.

2.5 Nonlinearity of brain signals

We applied the surrogate method in order to establish the existence of nonlinear dynamics in rat brain activity and to justify the use of nonlinear tools in time series analysis. Surrogates have the same linear properties as well as the originals, but not the nonlinear properties [39]. For each signal, we generated 15 surrogates and determined their fractal dimensions (program SUR1G), so that the average value is used as a representative in the statistical tests. According to the theory of statistical errors, the probability to find the value of fractal dimension of surrogate (FDsur) within the interval [<FD>sur − 2σ, <FD>sur + 2σ] is about 95%, where <FD>sur is the mean of fractal dimension values of a surrogate group and σ is the standard deviation. It follows that the real signal can be considered as a non-linear if its fractal dimension is outside this interval. Thus, we determined the value of the parameter with the statistical significance S [35], defined by the formula (1) where FD is a fractal dimension of the original signal:
$$ S = {\frac{{\left| {\left\langle {\text{FD}} \right\rangle^{\text{sur}} - {\text{FD}}} \right|}}{\sigma }}. $$

If the value of this parameter is S > 2, it means that there are significant differences between the originals and surrogates and the real signal is regarded as a nonlinear.

2.6 The calculation of fractal dimensions

The fractal dimension (FD) values of recorded, nonlinear and in the wide sense stationary sequences of up to 241 s (divided into epochs of 781 ms, without overlap) were calculated off-line by the original Higuchi algorithm [19] and slightly modified one [37], (DFHIG and DFHIGK programs). We shall briefly describe this algorithm which is one of the most accurate methods for the determination of fractal dimensions. For a given time series {x(1), x(2),…, x(N)} a new time series were constructed:
$$ X_{k}^{m} = \left\{ {x(m),\;x(m + 1),\; \ldots \;,x\left( {m + {\text{int}}\left[ {(N - m)/k} \right]k} \right)} \right\};\quad m = \{ 1,\;2,\; \ldots \;,k\} $$
where: m is initial time, k time interval, k = {1, 2, … , kmax} and int(r) integer part of real number r. The length Lm(k) was computed for each of the Xkm series or curves according to the formula:
$$ L_{m} (k) = \frac{1}{k}\left[ {\left( {\sum\limits_{i = 1}^{{\text{int} \left[ {{\frac{N - m}{k}}} \right]}} {\left| {x(m + ik) - x(m + (i - 1)k)} \right|} } \right){\frac{N - 1}{{\text{int} \left[ {{\frac{N - m}{k}}} \right]k}}}} \right] $$
and Lm(k) was averaged for all m:
$$ L(k) = {\frac{{\sum_{m = 1}^{k} {L_{m} (k)} }}{k}} $$
giving the mean value of the curve length L(k) for each k = {1, 2, … , kmax}. Finally, FD was determined from the plot log (L(k)) versus 1/k as a slope of the straight line. We used epochs of width of 200 experimental points (781 ms). According to the study [37], the optimum range of kmax was 8 < kmax < 18. The value kmax = 8 as the minimum in that range was used for the fractal analysis of electrocortical activity. Individual FD values from all epochs were averaged in order to obtain a final FD value for a particular signal during a certain sequence (mostly of 121 s duration). Means and variances of FDs of each signal were obtained sequentially in the time course of a stable anaesthesia. We used two-way MANOVA and post-hoc Least Significant Difference (LSD) to compare the mode FD values in brain activity of the aluminium-treated and control rats.

3 Results

We have started with visual inspection, spectral and wavelet analysis of signals recorded at the cerebral and cerebellar level in different experimental conditions. At the significance level of p = 0.05, we found that nearly 82% of the epochs were stationary, while the others were eliminated, as shown in the Fig. 1a, b. Clearly, changes in stationarity were higher in the case of cerebral signals related to the cerebellar ones and the percentage of stationary epochs was greater in the case of aluminium-treated animals compared to the control rats. Concerning nonlinearity of time series, we have determined that 96% of surveyed signals were non-linear as shown in Fig. 1c, d. Spectral characteristics of typical brain signals are shown in Figs. 2 and 3. The greater part of the mean power spectrum of considered signals was concentrated in the low frequency range; it was the expected result, because all signals were recorded in the anaesthetized animals. As the recorded signals in this study had non-linear properties, we have focused on changes of fractal dimension values of cerebral (parietal) and cerebellar (paravermal) electrocortical activities. Fractal dimension values of these brain signals could help us to differentiate brain states of aluminium loaded rats from the physiological control rats. We should mention that there was an inter-experimental variability of fractal parameters in control animals, as well as in aluminium-treated ones. However, it turned out that FD values of particular brain activity could be lower in aluminium-treated rats than in controls. Examples of pronounced changes in FD values of cerebral electrocortical activity are shown in Fig. 4, while FD values of cerebellar activity are presented in Fig. 5. In accordance with our previous findings in rats before and after brain injury it is noteworthy that the mean fractal dimension is lower at the parietal cerebral level than at paravermal cerebellar level in this control animal and in the aluminium-intoxicated one. All calculated FD values of activity of particular brain areas in each animal were fairly stable during the 2.5 h of recordings and are shown in Fig. 6. A two-way ANOVA showed that aluminium treatment was a factor inducing significant changes (F = 11.70, df = 1, dferror = 70, p < 0.01) in the FD values of brain electrocortical activity. It means in statistical considerations, that an extreme value F = 11.70 could occur by chance less than one in a hundred (p < 0.01), if the FD values of brain signals in aluminium-treated rats are truly equal to the FD values in signals of control animals. Simply stated, it means that FD values could be used as a discriminative factor between these two group of signals. The impact of brain structure on FD values was relevant also (F = 14.61, df = 3, dferror = 70, p < 0.01). Post-hoc data comparisons by LSD test showed that the average FD value of the left cerebral electrocortical activity was lower (p < 0.05) than that of the right cerebral cortex (p < 0.05) in aluminium-treated rats, compared to control rats, but there were no significant changes at the cerebellar levels (Fig. 7).
Fig. 1

The stationary and nonlinear properties of time series in 4 control and 4 aluminium-treated rats: percentage of accepted epochs of cerebral (a) and cerebellar signals (b); corresponding values of parameter S of statistical significance for differentiation between the real signals and their surrogates (c), (d)
Fig. 2

Typical signals recorded at the cerebral level in the control animal (a) and Al-treated animal (b) and their corresponding mean power spectra (c), (d)
Fig. 3

Typical signals recorded at the cerebellar level of the same animals as in Fig. 1: control animal (a) and Al-treated animal (b) and their corresponding mean power spectra (c), (d)
Fig. 4

The properties of cerebral electrocortical activity. LFPs, i.e. ECoGs of parietal cerebral cortex in (a) the control rat K4D and (b) the Al-treated rat A2P during a period of ~20 s; corresponding FD values: in (c) the control rat K4D and (d) the Al-treated rat A2P
Fig. 5

The properties of cerebellar electrocortical activity. LFPs, i.e. ECoGs of paravermal cerebellar cortex in (a) the control rat and (b) the Al-treated rat from Fig. 1; corresponding FD values: in (c) the control rat K4D and (d) the Al-treated rat A2P
Fig. 6

Fractal dimension values of brain activity from particular areas. The means and standard deviations of FD values of (a, b) cerebral and (c, d) cerebellar activities during 10 periods (each lasting 121 s) obtained during 2.5 h of continuous recordings in one control rat and one Al-treated rat
Fig. 7

Comparisons of FD values of cerebral and cerebellar signals in different experimental conditions. Means and standard deviations of mode FD values of cerebellar and cerebellar signals during periods of 121 s in the group of 10 control rats and the group of 10 Al-treated rats

4 Discussion

Aluminium neurotoxicity and its possible impairment of cognitive performance have been extensively studied. We considered the fractal dimension as a measure of electrocortical signal complexity in order to test nonlinearity of cerebral and cerebellar signals in Al loaded animals and to discriminate non-linear time series from random-like stationary time series. Our study could show that there are clear changes in cerebral signal complexity and that there are not so clear cerebellar changes under low aluminium intoxication suggesting electrophysiological signs of developing a neurodegenerative process which could have some similarities with developing AD. Our findings are in accordance with the study in which FD was used to quantify the complexity of electroencephalographic time series [1] and particularly with the recent study [18] which suggests that spontaneous magnetoencephalographic rhythms are less complex in AD patients than in healthy control subjects. Our results are also consistent with those found in patients with AD with significantly lower dimensional complexity than age-approximated non-demented control rats [7]. It is interesting that quantitative EEG changes in humans with mild cognitive impairment showed non-overlapping features between controls and AD patients and dynamic changes as the disease progressed [23]. A multiscale profile also revealed that EEG background activity was less complex in AD patients than in control subjects [14].

Concerning spectral changes, we have noticed the increased activity of slow frequencies in the mean power spectra of brain activity in aluminium-treated rats. Moreover, the power of delta and theta range were increased in comparison to the power in control animals, while the higher frequency ranges (alpha and beta band) decreased. These results in aluminium-intoxicated animals are in agreement with the spectral EEG changes in patients suffering from AD [2, 3, 20, 25, 41].

Concerning regional specificity of obtained FD values in our study, the FD values of cerebellar activity were greater than those of cerebral activity in each animal as in the study on the animal model of brain injury [38], but consistent decrease in the FD values of cerebellar signals could not be always correlated with the aluminium treatment. There could be at least two reasons for not finding the electrophysiological effect of Al toxicity at the cerebellar level in adults animals: one is technical and the other neurobiological. Namely, the cerebellar ECoGs could be picked up from different cell layers whose spectral and fractal characteristics may differ as the recording microelectrode was positioned with an imprecision of ~100 μm. The other, neurobiological reason, implies that the cerebellum may be less affected by aluminium toxicity than the cerebrum at least when the animals grew up and were not aged. Thus, Al concentrations were higher in hippocampus than in cerebellum or cortex in Tg2576 mice exposed to Al or Al plus melatonin [16]. Cerebellum is a brain region which may be more resistant to many of the neurodegenerative disorders, such as stroke or AD, because cerebellum appears to be ‘equipped with the tools’ necessary to protect itself against these types of assaults [44]. Alterations of amino acids metabolism in brain are also region specific in response to aluminium exposure [31]. The importance of cerebro-cerebellar connections could be investigated on brain signal processing in young rats (whose mothers were intoxicated by aluminium via drinking water during gestation and lactation period) where we have noticed an extreme predominance of slow ECoG power spectra at the parietal cortical level [28, 32]. Early electrophysiological findings under mild aluminium intoxication could be of even greater importance, as characteristic AD morphological changes cannot be found in vivo. It should be also pointed out that no senile plaques [4] were found in rat brains intoxicated even by Al doses of 10 mg/kg (60 intraperitoneal injections), and no tau aggregation was detected in the mouse AD model in vivo, but only in vitro [30]. Some authors raise the question of whether pre-clinical detection of Al neurotoxicity and cholesterol/copper toxicity [43] may extend the validity of these models to treatment modalities and help to prevent or retard the onset of AD or other types of dementia. Therefore, early detection of quantitative EEG changes in humans with probable AD [22] and our proposal on spectral and fractal analysis of cerebral and cerebellar signals after various exposures to aluminium may be useful for developing effective diagnostic and therapeutic strategies. It should be kept in mind that increased variability of EEG signals of specific cortical areas may be due to the replacement of the coherent information obtained during eyes open by noise [40].


This study was financed by the Serbian Ministry of Science and Technological Development (Project Grant No. 143021). The kindness of Dr. S. Spasic, from the Institute for Multidisciplinary Studies in Belgrade for ceding us the software for FD calculation, is appreciated.

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© International Federation for Medical and Biological Engineering 2010