Chaos, Solitons & Fractals 45 (2012) 619–628

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Chaos, Solitons & FractalsNonlinear Science, and Nonequilibrium and Complex Phenomena

journal homepage: www.elsevier .com/locate /chaos

Dopaminergic modulation of the spectral characteristics in the ratbrain oscillatory activity

Miguel Valencia a, Jon López-Azcárate a, María Jesús Nicolás a, Manuel Alegre a,b,Julio Artieda a,b,⇑a Neurophysiology Laboratory, Neurosciences Area, CIMA, University of Navarra, Pamplona, Spainb Clinical Neurophysiology Section, Clínica Universidad de Navarra, Pamplona, Spain

a r t i c l e i n f o

Article history:Available online 30 January 2012

0960-0779/$ - see front matter � 2012 Elsevier Ltddoi:10.1016/j.chaos.2011.12.019

⇑ Corresponding author at: Neurophysiology LaboArea, CIMA, University of Navarra, Pamplona, Spain

E-mail address: jartieda@unav.es (J. Artieda).

a b s t r a c t

Oscillatory activity can be widely recorded in the brain. It has been demonstrated to playan important role not only in the physiology of movement, perception and cognition, butalso in the pathophysiology of a variety of diseases. In frequency domain, neurophysiologi-cal recordings show a power spectrum (PSD) following a log (PSD) / log (f)�b, that revealsan intrinsic feature of many complex systems in nature: the presence of a scale-freedynamics characterized by a power-law component (PLC).

Here we analyzed the influence of dopaminergic drugs over the PLC of the oscillatoryactivity recorded from different locations of the rat brain. Dopamine (DA) is a neurotrans-mitter that is required for a number of physiological functions like normal feeding, locomo-tion, posturing, grooming and reaction time. Alterations in the dopaminergic system causevast effects in the dynamics of the brain activity, that may be crucial in the pathophysiol-ogy of neurological (like Parkinson’s disease) or psychiatric (like schizophrenia) diseases.

Our results show that drugs with opposite effects over the dopaminergic system, induceopposite changes in the characteristics of the PLC: DA agonists/antagonists cause the PLC toswing around a fulcrum point in the range of 20 Hz. Changes in the harmonic component ofthe spectrum were also detected. However, differences between recordings are betterexplained by the modulation of the PLC than by narrow peak activities in particular fre-quency ranges.

Our findings suggest that the brain operates in a state of self-organized criticality (SOC)that is sensitive to dopaminergic stimulation. Nevertheless, understanding of the interac-tions between the rhythmic (harmonic component) and arhythmic component (fractalcomponent) of brain activity remains as a challenge, which should motivate future studiesto explore these phenomena.

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1. Power-law characteristic of the oscillatory brainactivity

The synchronization of neuronal activity may be mecha-nistically important for information processing acrossdifferent levels of the sensory and motor systems [1,2]. Syn-chronized activity within a large population can be detected

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ratory, Neurosciences.

as oscillatory activity in the electro/magneto-encephalo-gram (EEG/MEG) or in local field potentials (LFP) recordings.Changes in oscillatory activity are related to the pathophys-iology of neurological and psychiatric diseases and arethought to play a significant role in cognitive functions.

Attending to its functional role, oscillatory activity iscommonly spliced into bands (d,h,a,b,c, . . .) related withmotor states, cognitive functions or pathological signs[3,4]. Nevertheless, the power spectrum of brain activityfollows a straight line when plotted in log–log coordinates(log of power versus log of frequency): log (PSD) / log (f)�b

620 M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628

with 0 < b < 4. This feature constitutes the so called power-law or fractal component of the power spectrum [1,5]. It iscommonly not considered in many EEG and LFP studiessince power at each frequency is routinely normalized byits value during a pre-task baseline, or simply becausethe PSD is analyzed in linear coordinates and only periodicoscillations (the harmonic component) are taken intoaccount.

However, brain activity at rest presents this ubiquitous‘‘1/f-like’’ feature of complex systems. Even when subjectsperform an active task, neural activities can exhibit apower-law distribution. A number of recent works havetried to elucidate the role of this arrhythmic, 1/fb brainactivity that seems to be critical if a full understanding ofbrain function is required [6].

One possibility about the origin of this power-lawdistribution is related to an hypothetical state of self-organized criticality (SOC) in the brain, a state that wouldbe maintained in order to optimize function [7–9]. Somemodels for this dynamics have been constructed, but it isnot evident if these models describe the neurophysiologi-cal processes actually involved in the brain [5,8,10,11].The possibility of a noisy origin from instruments [12], isnot considered anymore. There are plenty of features inthe brain showing scale-free dynamics with hard explana-tion according to this instrument noise paradigm. Studiesinvolving real brain data have detected scale-free proper-ties in LFP’s, MEG, EEG and in functional magnetic reso-nance imaging (fMRI) signals recorded from the brain[1,13,14]. Dynamics of neurotransmitter release, neuronaltopology, and the speed of action potentials together withthe human behavior represent also manifestations of thisfeature [4].

On the other hand, it is well known that variations inthe amount of neurotransmitters cause changes in bothbrain activity and function [15]. In Parkinson’s disease,DA transmission in the circuits that connect the frontalcortex and the basal ganglia is altered due to the dopami-nergic depletion caused by the degeneration of the dopa-minergic cells from the substantia nigra pars compacta[16]. This deficit provokes an important impact in theexpression of motor behavior. Alterations in rhythmicityand synchrony of brain activity have been studied as po-tential signatures of parkinsonian deficits [17–21]. Wepropose that DA modulation will affect both, the har-monic and the fractal characteristics of brain activity.Changes in dopaminergic transmission in the brain areexpected to have a solid effect in the activity in the basalganglia and therefore in the spectral properties of thesignals.

To validate our hypothesis, we analyzed the effect oftwo different dopaminergic drugs, apomorphine andhaloperidol. Apomorphine is a non-selective dopamineagonist. Historically, apomorphine has been tried for avariety of uses including the treatment of Parkinson’sdisease as it increases the excitability of the DA pathways.Haloperidol is a typical antipsychotic that producesakinesia, and can be used to model PD in rodents. Itsstrong antidopaminergic action in the nigrostriatal path-way underlies side effects like parkinsonism, dystonia orakathisia.

2. Preparation and recording procedures

We analyzed the effect of different dopaminergic drugson the electrocorticographic (ECoG) activity of the motorcortex and in the LFP from three nuclei from the basalganglia (CPU, STN and SNr) in 16 adult male Wistar rats(250–300 gr).

Animals were recorded in three conditions: saline injec-tion (1 ml/kg), after the administration of 5 mg/kg of apo-morphine (dopamine receptors agonist) and finally underthe effect of 1 mg/kg of haloperidol (dopamine antagonist).

The whole protocol was approved by the institutionalanimal ethics committee, ‘‘Comité de Ética para la Experi-mentación Animal, Universidad de Navarra, approval ID088-06’’.

2.1. Electrode implantation surgery

Rats were anesthetized with ketamine (75 mg/kg i.p.)and xylazine (11 mg/kg i.p.) and held in a stereotaxicframe. Blunt ear bars were used to avoid any damage inthe tympanic membrane of the animals. Target coordinatesfor electrode placement were selected according to theatlas Paxinos and Watson (1998): [anterior (AP):2.20 mm and lateral (L): 3.20 mm] for the motor cortex,[AP: �4.8 mm and L: 7.4 mm] for the auditory cortex(reference for motor cortex recording), [AP: 0.20 mm andL: 3 mm, V: �6 mm] for caudate-putamen, [AP: �3.80 mm,L: 2.5 mm, V:�7.8 mm] for STN and finally [AP: �5.80 mm,L: 2 mm, V: �8 mm] for SNr.

Two different types of electrodes were used in order torecord local field potentials from the mentioned brainstructures. Concentric microelectrodes with two contacts(Model SNE-100, Kopf Instruments, Tujunga, California,USA) were stereotactically placed in the CPU, STN andSNr. Cortical local field potentials were recorded by meansof stainless steel screws (1.6 mm diameter, Plastics One,Roanoke, VA, USA, Ref. E363) placed in the skull. Activeelectrode was placed in the primary motor cortex referredto an electrode placed in the auditory cortex. An additionalscrew placed in the frontal region was used as groundelectrode. The wires of the electrodes were connected toa custom-made small ten-channel socket that was firmlyheld with dental cement (Faciden, Olot, Spain) to the ratskull. Only the terminal male pins of the socket wereuncovered by the skin.

Pharmacological experiments began five days aftersurgery. Antibiotic (enrofloxacin, Alsir 10%, Esteve, Spain)was administrated orally during one week to avoid infec-tions. Postoperative analgesia was also administrated(Ketoprophen, 2 mg/kg sc, Ketofen 1%, Lab, Spain).

2.2. Recording procedure

Animals were recorded inside a custom-made Faradaycage shielded from external electrical fields and wereconnected to the recording equipment by two cables whichhanged from the top of the cage (Ref. 363–363 50 cm 6TCS,spring, Plastics One, Roanoke, VA, USA). A multi-channelrotary commuter (SL12C/SB, Plastics One, Roanoke, VA,

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USA) was used to allow the animals free movement insidethe cage.

The recording procedure started from five to seven daysafter electrode implantation and it began 45 min after theconnection of the cables in order to let the animals habit-uate to the Faraday cage.

All recordings were carried out in the same order for allthe animals, and they extended for three days. The firstday, animals were recorded after saline injection (1 ml/kg; 0.9%, B Braun, Barcelona, Spain). The second day oscil-latory activity was studied under the effect of 5 mg/kg ofapomorphine (Apo-go Pen, Italfarmaco, Madrid, Spain),and finally the third day animals received an intraperito-neal bolus of 1 mg/kg of haloperidol (Haloperidol, Esteve,Barcelona, Spain). Two (out of 16) animals didn’t receivehaloperidol injection.

2.3. Signal conditioning

The signals were filtered 0.3–1000 Hz, amplified 20000-fold using Grass P511 amplifiers (Grass, W Worwick, RI,USA), sampled at 2500 Hz, and stored in a personalcomputer using Spike2 software and a CED 1401 poweranalog-to-digital converter (Cambridge Electronic Design).

Misplaced electrodes (detected in postmortem histolog-ical analysis) and recording channels with suboptimalsignal quality were also excluded from further analysis.In summary, a total of 16 motor cortex, 15 CPU, 11 STNand 10 SNr were studied in both, saline and apomorphineconditions and 14 motor cortex, 13 CPU, 9 STN and 8 SNrafter the administration of haloperidol.

3. Fractal vs. harmonic components of PSD

For each animal and condition, 300 s segments free ofartifacts were selected. Then, frequency content of the

Fig. 1. PSD of the CPU recorded in one representative animal under two diffadministration of an apomorphine dose (red trace). When plotted in log–log u(PSD) / log (f)�b. Comparison of the two PSD reveals how the slope of the PLC (b)the PSD is also altered, with the rising/vanishing/modification of oscillatory acticauses that some oscillatory activities present differences in terms of absolute powremoved, relative powers (i.e, related to the fractal component) result into comparthis figure legend, the reader is referred to the web version of this article.)

signals was characterized by means of the Welch periodo-gram using a fast Fourier transform of 5 seconds length anda Hanning window, giving a resolution of 0.2 Hz per bin[22]. Power spectrums for each channel, treatment andanimal were computed and plotted in double logarithmicscale.

In this representation, all the PSDs roughly followed astraight line with a decreasing trend in power whilefrequency increases. Over this linear trend, differentbumps (oscillatory modes or frequency bands) wereobserved. Fig. 1 shows the PSD of the signal recorded inthe CPU of one representative animal under saline (bluetrace) and apomorphine (red trace) conditions. Differencesare clearly observed in both, the fractal and harmoniccomponents. The most significant change is related to thechange in the slope (b) of the PLC, that would change theinterpretation of the relative power in the harmoniccomponent (see Fig. 1).

Although this view is not new, here we propose to splitthe PSD into these two elements, one accounting for thefractal features and the other related to the harmoniccomponent of the PSD, and to study them separately. Thisway, the fractal component can be characterized by astraight line in double logarithmic axes, while theharmonic part results in a normalized version of the PSD,decomposable into a series of oscillatory modes atdifferent frequencies.

3.1. Power-law component (PLC)

To characterize the power-law component of the PSD,we adopted a slight modification of the coarse-grainingspectral analysis approach (CGSA). CGSA was proposed toseparate the harmonic/oscillatory from the scale-free/frac-tal components of the power spectrum [6,23]. Thisprocedure takes advantage of the self-affinity property of

erent conditions: after saline administration (blue trace) and after thenits (left side), the PSD roughly follows an straight line according to logchanges with the effect of the apomorphine. The harmonic component of

vities superimposed over the PLC. Changes in the b exponents (right, top)er (e.g. red trace peak�80 Hz vs. blue trace peak�50 Hz). When the PLC isable values (right, bottom). (For interpretation of the references to color in

622 M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628

a scale-free time series, i.e., the statistical distribution ofthe data remains the same when sampled at different

3

scales, and the fact that this is not true for harmonic timeseries [24].

Considering the dynamics of a self-affine time seriesx(t), it satisfies the relation:

xðht þ t0Þ � xðt0Þ $ hHxðt þ t0Þ � xðt0Þ ð1Þ

for any h > 0 and t0, where $ implies that both hands of $have the same distribution function characterized bydetermining the Hurst exponent H(0 < H < 1).

The actual implementation of CGSA relies in the compu-tation of the auto-power spectrum SXX(f) of x[n], the dis-crete version of the original series, x(t). In a similarmanner, the cross-power spectrum from the so called‘‘coarse grained series’’ and the original time series, namelySXXhðf Þ is calculated, where the coarse grained time series

xh[n] is constructed by taking every h samples from a partof the original time series x[n] (attention should be paid inusing a suitable antialiasing filtering scheme).

If x[n] is a simple harmonic signal with a frequency ofx, xh[n] is also a simple harmonic series with a frequencyof hx. When h – 1, this results in SXXh

ðf Þ ! 0. On the otherhand, if x[n] is self-affine satisfying Eq. (1), the quantitykSXXh

k (cross-spectral gain) never tends to be zero.Indeed, considering that xh[n] has the same distribution

as x[n] by the factor hH, we can expect that in case of self-affine time series, the quantity kSXXh

k normalized by thefactor hH could be equivalent to the auto-power spectrumSXX(f) of the original series. Therefore, kSXXh

k=hH can be re-garded as self-affine (fractal) components in the auto-power spectrum without contribution of simple harmonicmotions. To avoid the estimation of H, the procedure canbe repeated both for h and for 1/h, and the averaged fractalpower SXXh

ðf Þ is calculated by

SXXhðf Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikSXXh

ðf Þk � kSXX1=hðf Þk

qð2Þ

where x1/h[n] is obtained by h-plicating each point of theoriginal time series.

Nevertheless, when dealing with the PSD of real electro-physiological signals (Fig. 2, first row), the presence of thebroad-band activities does not allow to obtain a good esti-mate of the fractal component of the time series, as someresiduals of the oscillatory component are left. Inspiredby this approach, we propose to compute eSXðf Þ, a modifiedaveraged fractal power that will account only for the self-similar portion of the PSD.

To do that, first we compute the cross-power spectrumbetween the two hi and 1/hi coarse grained versions of x[n]

Fig. 2. Extraction of the fractal and harmonic spectral characteristics.(First row) PSD of the signal recorded from the CPU of one representativeanimal (note the log–log units). (Second row) Family of coarse-grained/fractal-like PSD’s (in colors) superimposed over the real PSD (in black);some residuals from the harmonic component remain in the fractal-likePSD’s. (Third row) Mean fractal-component (blue trace) and linear fit (redtrace) for the real PSD (in black). (Fourth row) Iterative gaussiandecomposition of the relative spectrum (harmonic component) computedby canceling the fractal component from the real PSD. (For interpretationof the references to color in this figure legend, the reader is referred to theweb version of this article.)

Fig. 3. Boxplot representation of the two parameters that define the PLC. Parameters were grouped according to the four brain locations sampled and to thetype of drug dispensed. The scaling exponent b (upper axis) is obtained by computing the slope of the linear fit adjusted to the fractal characteristic of thePLC while the A0 parameter (lower axis) defines the intercept of the linear fit with the power axis at log10(f/1 Hz) = 0.

M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628 623

for a range of values of hi = h1 . . .hN. As a result, a family offractal-like PSD with some residuals of the oscillatoryfrequency bands are obtained (Fig. 2, second row).

By computing the Tukey-biweigth average of this familyof curves [25], a robust statistic (not affected by outliers) ofthe mean fractal component of the PSD is obtained (Fig. 2,third row).

eSXðf Þ ¼ TifkSXhiX1=hiðf Þkg with hi ¼ h1 . . . hN ð3Þ

where Ti stands for the Tukey-biweigth average of thefamily of cross-spectrums kSXhi

X1=hiðf Þk, computed from

the hi and 1/hi coarse-grained versions of the signal.Finally, a linear least-squares fit of eSXðf Þ is computed,

giving the two parameters that characterize the PLCaccording to log (PSD) = A0 � blog (f); where scaling expo-nent b is the slope of the linear fit and A0, the intersectionwith the y-axis at log10(f/1 Hz) = 0.

3.2. Gaussian decomposition of the harmonic component

The harmonic component is obtained by removing thelinear fit of the PLC from the original PSD. This characteris-tic shows a polymodal shape composed by a series ofgaussian-like bumps that correspond to the oscillatorymodes or frequency bands of the PSD (see Fig. 2, fourthrow). These gaussian-like bumps were extracted by succes-sively fitting to number of gaussian distributions accordingto the equation:

Gðf Þ ¼X

i

aie� f�fi

wi=2

� �2

ð4Þ

where f is the frequency, i is the number of Gaussians, ai isthe maximum spectral power of the ith Gaussian (ithfrequency band), fi is the peak central frequency for theith band and wi represents the peak bandwidth (thedistance from center to 2% of full height).

Fig. 4. Modulation of the PLC around its fulcrum point. (Upper axis)Boxplot representation of the ensemble of recordings at motor cortexgrouped according to the drug administered (blue: saline, red: apomor-phine, green: haloperidol). Note that lines trend to have a minimumdeviation and to cross at frequencies in a point in the b range (�20 Hz).(Lower axis) Location of the fulcrum point obtained by computing a kerneldensity estimate of the number of crossing points per log (f) � log (PSD)unit (see text). Data from the four structures were taken into account. Themaximum is located at [log (f) = 1.37, log (PSD) = �1.08]. (For interpre-tation of the references to color in this figure legend, the reader is referredto the web version of this article.)

624 M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628

In the fitting procedure new Gaussians are successivelyadded using the maximum residual point as the new centerpoint guess. Firstly, Gaussians are least-squares fittedaccording to the formula described above, i.e. the centerpoint is fitted as a continuous floating point number.Secondly, when an optimal Gaussian is found the fitting isrepeated using a penalty function forcing the initial guess

of the center point to become integral. The curve fitting ofthe polymodal distribution profiles was carried out usinga Simplex algorithm [26] for the non-linear parameters fi

and wi combined with a least squares fit of the linear ai

parameters inside the gauss function evaluation call.Although Gaussian decomposition is an inherently non-robust approach, the algorithm described above proved toexhibit fairly robust convergence behavior and to provideoptimal and stable solutions. However, in few cases it wasnecessary to supervise some of the adjusted spectrums.

4. Results

4.1. Dopaminergic modulation of the fractal characteristic

Fig. 3 shows the slope b, and the y-axis intercept A0 (i.e.,at log10(f/1 Hz) = 0) for the PLC computed according to themodified CGSA procedure described above. Linear least-squares fits of the PLC were estimated in the 12–200 Hzrange with h varying from 1 to 4 in steps of 0.1.

Qualitatively, results reveal that dopaminergic drugscause an effective modulation in the two parameters thatcharacterize the PLC. Related to the values estimated forthe saline condition, apomorphine administration inducesa decrease in both parameters, b and A0 while on thecontrary, haloperidol increases them. Roughly, both param-eters, b and A0 trend to show values that are sightly higherin the motor cortex than in the subcortical structures.

Significance of the changes induced in the b and A0

parameters were assessed by means of a two-way MANO-VA with two factors, drug and structure. Statistical analysisreveals that dopaminergic modulation induce significantchanges in the PLC across the four structures. OverallMANOVA revealed a significant effect on both parametersfor the drug (saline, apomorphine or haloperidol: F4,270 =20.20, p < 0.0001), and structure factors (Cx, CPU, STN orSNr: F6,270 = 15.26, p < 0.0001). No significant interactionwas detected (F12,270 = 0.13,p = 1).

Tukey’s HSD post hoc test showed that the scale expo-nent and y-axes intercept values were significantly differ-ent after the administration of saline and the two drugs(apomorphine or haloperidol). Complementary, differencesin location factor revealed that b and A0 values were signif-icantly higher in the motor cortex when compared to theother three nuclei. CPU values were also higher than sub-thalamic ones.

It is interesting to note how increases in the b exponentare accompanied by increases in the y-axis intercept. Thiswould suggest the presence of a fulcrum point for the mod-ulation of the spectral component. To further investigatethis issue, we analyzed the dispersion of the PLC computedfrom the b and A0 parameters. Fig. 4 (top), shows the box-plot representation of these estimations grouped accordingto the substance injected, for the motor cortex recordings.Linear fits belonging to records obtained under apomor-phine effects (red) begin at power values that are lowerthan those of the saline (blue) or haloperidol injections(green). Haloperidol recordings present the largest valuesat low frequencies, but decrease faster than in the salineand apomorphine conditions, so they reach low power lev-

Fig. 5. Oscillatory modes of the harmonic component of the PSD under saline (upper), apomorphine (center) and haloperidol (bottom) effects. Axes showthe distribution of the peak locations (relative amplitude vs. log10(f)) for the gaussian decomposition of the harmonic component of the PSD. Colorbarsrepresent the kernel density estimation of the number of peaks per unit of log10(f) found by the decomposition. Note the existence of a series of frequencysegments with high probability of hosting an oscillatory mode. In contrast, other regions in the spectra show a low probability of hosting peaks (define theborders of the different frequency bands).

M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628 625

els for high frequencies. Under saline effects, powers arealways in-between of those recorded during the adminis-tration of the dopaminergic drugs. This kind of compensa-tion effect between the b and A0 parameters makes the PLCto coalesce in a frequency range close to f � 20 Hz.

Actually, we observe that most of the intersection pointsare located around a unique and well defined maximum.This was confirmed by computing three intersection pointsfor each animal individually: namely, the intersection ofthe PLC under the saline vs. haloperidol conditions, the

saline vs. apomorphine condition and finally, the apomor-phine vs. haloperidol condition. Then a kernel densityestimate [27] of the number of intersection points per log(f) � log (PSD) unit was computed (see Fig. 4, bottom).

4.2. Dopaminergic modulation of the oscillatory component

The harmonic component of the PSD was decomposedinto a series of gaussian curves with three parameters,namely their amplitude ai, bandwidth wi, and central

626 M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628

frequency fi. This allowed the characterization of the har-monic component of the PSD according to a series of oscil-latory modes or peaks that account for the harmonicproperties of the PSD.

Fig. 5 shows a representation where the amplitude ai ofall the peaks has been plotted against the log10 of the cen-tral frequency value fi. It is easy to observe that the oscilla-tory modes trend to shape groups around well-definedfrequency portions. There are some frequency rangeswhere the probability of finding peaks is high while in oth-ers, no modes are detected. This is actually confirmed bythe computation of the kernel density estimate [27] ofthe number of peaks per frequency unit (color traces).

According to that, it is possible to find clear regions thatroughly match up to some bands of the classical division ofbrain rhythms: namely, near-DC (0.3 � 1 Hz), d (1 � 4 Hz), h(4 � 8 Hz), a (8 � 12 Hz), low-b (12 � 20 Hz), high-b (20 �30 Hz), low-c (30 � 60 Hz), high-c (60 � 100 Hz) and highfrequency oscillations (HFO, >100 Hz).

As observed in Fig. 5, five of these nine regions pre-sented peaks in all conditions: d, h, high/low-c and HFO.Neither near-DC nor a ranges showed a significant numberof peaks across all the animals and conditions. Interest-ingly, in the b range we found a different behavior depend-ing on the drug factor: while in saline and haloperidolconditions there was a higher number of peaks in thelow-b than in the high-b range, after apomorphine admin-istration, the number of peaks in the high-b range clearlyexceeded those of the low-b band.

Differences in the amplitude and frequency of the oscil-latory activities at the five bands with peaks in all condi-tions were assessed by means of a two-way ANOVA withtwo factors, drug and location followed by a Tukey’s HSDpost hoc test.

In terms of the central frequency of the peaks fi, activi-ties did not show differences except in the low-c band.Drug factor was significant (F(2,101) = 8.015,p < 0.0001)while no location effect (F(3,101) = 1.0991,p = 0.3532) norinteraction were detected (F(6,101) = 1.3884, p = 0.2265).Post-hoc analyses revealed that under apomorphine ef-fects, low-c peaks had frequencies that were significantlylower than those of saline or haloperidol conditions.

For the amplitude of the peaks ai, significant differenceswere found for all of these 5 bands except for d. In the hrange significant effects were found for drug (F(2,92) =9.3512, p < 0.0001), location (F(3,92) = 7.7132,p < 0.0001)and interaction (F(6,92) = 2.8294,p = 0.0142). Post-hoc testrevealed that the power in this band was higher under apo-morphine effect than in saline or haloperidol conditions.Additionally, motor cortex presented stronger values ofpower, compared with those of the basal ganglia struc-tures. Interaction revealed that the increase of powerunder apomorphine effect was larger in the motor cortexlocation. Low-c band was characterized by significant ef-fects in the drug (F(2,101) = 6.4545, p = 0.0023) and locationfactors (F(3,101 = 20.2496,p < 0.0001). No interaction effectwas detected for this band (F(6,101) = 1.0506, p = 0.3974).Post-hoc tests showed that after apomorphine administra-tion the power at this frequency band was significantlybigger than in the other conditions. The effect of locationshowed that cortex had the largest values of power,

followed by CPU, both significantly higher than those ofSTN and SNr. In the high-c range, drug factor was signifi-cant (F(2,120) = 9.7961,p < 0.0001) while location (F(3,120) =2.1931,p = 0.0924) and interaction (F(6,120) = 0.1989,p =0.9765) factors were not. Post-hoc test again revealed thatpower in this band was higher after apomorphine injectionthan in the two other conditions. Only location effect wassignificant in the HFO band (F(3,120) = 10.2971,p < 0.0001).No significant drug (F(2,120) = 2.6198,p = 0.0770) nor inter-action (F(6,120) = 1.5188,p = 0.1777) effects were detectedin this band. Post-hoc test showed that power in motorcortex and CPU were larger than those of STN and SNr.

5. Conclusion

Although traditional analysis of the oscillatory activityhave been limited to measurements related to peaks inthe frequency spectrum, other PSD characteristics like thescale-free feature have received attention more recently[4,8,7,13,14,28]. Here we have shown that both the har-monic component and the fractal characteristics of thebrain activity can be effectively modulated by dopaminer-gic manipulation. Nevertheless, the differences betweenrecordings can be explained better by the modulation ofwidely distributed PLC than by narrow peak activities inparticular frequency ranges.

To obtain the fractal characteristic of the brain activitywe have proposed here a slight modification of the CGSAalgorithm [23]. While the original method relies on thehypothesis that oscillatory signals are harmonic compo-nents (i.e. sinusoids), it is well know that oscillatory activ-ity in brain signals cannot be approximated by harmonicpeaks. Our version is able to efficiently deal with signalscomposed by the combination of a fractal component to-gether with a non-harmonic – but oscillatory – component,allowing us to separate the harmonic/oscillatory from thescale-free/fractal components of the brain signals.

Although the functional role of this power-law distribu-tion remains unknown, it is evident that dopaminergicmodulation affects the properties of the PLC, suggesting afunctional significance of this characteristic in the brain.PLC presents task performance modulation and regionalvariations, with the scaling exponent b being larger in de-fault network and visual cortex and smaller in hippocam-pus and cerebellum [6]. Our findings confirm and extendthese results. We observe a topological dependence inthe value of the scaling exponent: the value of the scalingexponent is larger in the motor cortex compared withthose in the basal ganglia. Although this effect could beattributed to differences between the recording electrodes(micro-electrodes could emphasize local, high frequencyactivity, more than screws at motor cortex, correspondingto activities over larger areas that would show more lowfrequency activity), we also find differences in the PLCparameters across basal ganglia structures, ruling out thepossibility of this confound.

All these results are consistent with previous theoreti-cal studies showing that brain in the SOC state shows highsensitivity to environmental changes [5,30]. Respect tobasal conditions (saline injection), the administration of a

M. Valencia et al. / Chaos, Solitons & Fractals 45 (2012) 619–628 627

dopaminergic agonist (apomorphine) causes in the PLC anopposing effect to that observed when using a dopaminer-gic antagonist (haloperidol). This constitutes a relevant re-sult in that it demonstrates that drugs with inverse effectsover the nervous system, cause opposite effects in the PLC.

Our analysis also determines the existence of a fulcrumpoint for modulation of the PLC around 20 Hz. Interest-ingly, this feature has already been detected in a previouswork devoted to analyze the human perceptual perfor-mance [29]. Using a different methodological approach,authors detected that the PLC swinged around 13 Hz, mod-ulated by the execution of correct and incorrect behavioralresponses. Nevertheless, further research must be per-formed to understand the reason for these specific values,across species or related to different pathological brainstates.

We also observe remarkable modulations in the ampli-tude of the harmonic oscillations at some frequencyranges. By first detecting and then analyzing the oscillatorymodes of brain signals, we were able to detect the fre-quency ranges where effective harmonic oscillations arepresent (without need of a priori assumptions). Moreover,canceling the fractal component from the PSD makes theharmonic component to become a relative measure ofstrength of oscillatory modes over the background activityrelated to the fractal component. This results in a kind ofnormalization of the oscillatory component that allows todirectly compare the strength of the oscillatory modesacross electrodes or specimens. The gaussian decomposi-tion of this residual, provides a natural method to decom-pose the harmonic component into different frequencybands that are roughly coincident with those of the classi-cal neurophysiology.

It has been widely explored that, in the rat cortex andbasal ganglia nuclei, prominent local field potential oscilla-tions occur in several frequency bands. These include h(4–8 Hz) [31,32], c (30–100 Hz) [33] and high frequencyoscillations (HFO > 100 Hz) [34,35]. Consistent with ourfindings, these studies show that the properties of theseactivities are modified by the administration of dopamineagonists (i.e. apomorphine, quinpirole), which induce anincrease in the power of both h and c bands [36,37]. Theacute administration of haloperidol (dopamine antagonist)does not change the spectral profile of the power spectrum,at least in terms of its oscillatory modes [38]. Interestingly,here we have found that the acute administration ofhaloperidol does change the PLC of the spectrum.

To our knowledge, this is the first study in using andconfirming the reverse effects of two opposing drugs(dopaminergic agonist/antagonist) over the fractal charac-teristics of the oscillatory activity. Unveiling the effects ofpharmacological modulation is an active area of researchin neuroscience. It needs of robust indexes and approachesto evaluate the impact of these manipulations. We thinkthat our approach provides a tool to account for the effec-tive modulation of the PLC, resulting in a tool to explorehow DA manipulation effectively modifies brain dynamics.

All these results should motivate further research intothe analysis of the form that harmonic activities areinlayed into the universal 1/fb characteristic of the powerspectrum. It remains a challenge to understand not only

the role of the PLC and its significance, but also to differen-tiate the effects of harmonic activities on the PLC andviceversa. Future empirical and theoretical work must bedevoted to connect this scale-free property of the brainactivity with the mainstream of the -classical- electrophys-iological research. This will help to understand how brainoscillations, event-related potentials, and intrinsic networkactivity gives rise to the mechanisms involved in normalpsychology and brain disorders.

Acknowledgement

This work has been supported by a grant by the Fondode Investigaciones Sanitarias (FIS 070034) and by the UTEProyecto CIMA. Miguel Valencia acknowledges financialsupport from the Spanish Ministry of Science and Innova-tion, Juan de la Cierva Programme Ref. JCI-2010-07876.

The funders had no role in study design, data collectionand analysis, decision to publish, or preparation of themanuscript.

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