IN DEGREE PROJECT MEDICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2017

Dopamine replacement therapy reduces beta band burst duration in Parkinson’s disease

ALESSANDRO MECCONI

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF TECHNOLOGY AND HEALTH

Dopamine replacement therapy reduces beta band burst duration inParkinson’s disease

Dopaminersattningsbehandling forkortar aktivitetsutbrott i betabandet vidParkinsons sjukdom

Alessandro Mecconi

Date: June 2017Supervisor: Arvind KumarReviewer: Tobias Nyberg

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Abstract

One of the main characteristics of Parkinson’s disease (PD) is an exaggeratedoscillatory activity in the beta band (12-30 Hz). This activity has been linkedto the rise of symptoms such as bradykinesia and akinesia. Even if dopaminereplacement therapy (oral intake of dopamine pro-drug levodopa) reverses thesesymptoms, the effect of the treatment on the beta band activity has still notbeen completely understood. Therefore, here the temporal dynamics of betaband activity in human patients affected by PD were characterized with andwithout levodopa treatment. Local-field-potential (LFP) recordings from fivepatients undergoing dopamine replacement therapy were used. From the LFPs,the extracted beta epochs with significantly higher power than expected froma comparable noisy signal were analyzed. This analysis showed that beta bandactivity occurred in bursts meaning that high amplitude oscillation alternatedwith silenced periods. The pathological state also distinguished itself for longerepochs and with power that increased with the length of the epoch. The admin-istration of levodopa reduced the duration of bursts and decreased the overallmean power of the beta band activity. Finally, epochs with the same number ofcycles were compared. The Coefficient of Variation prior such epochs suggestedthat the ongoing activity might lock into a synchronization process prior theburst. These results provide important information to better understand howlevodopa alleviates some of the symptoms of PD and pave the way to developbetter computational models for the emergence of beta oscillations.

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Acknowledgments

During my thesis I was given the opportunity to constantly learn about com-putational neuroscience, a field that I had very little knowledge about. I wouldlike to thank Arvind Kumar, my supervisor, for the precious feedback, supportand new ideas; my reviewer Tobias Nyberg and all the people from CST thathelped me with their valuable advice. I would also like to thank Prof. PeterBrown for giving me the opportunity of working on such valuable data. I wouldlike to thank all my friends here in Stockholm and back home that had to bearme when the only thing I would talk about was Parkinson’s Disease. A veryspecial thank you goes to my family and to Madlen: even if you were far away,your caring support made me feel you were close.

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Contents

1 Introduction 1

2 Materials and methods 22.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Fitting raw data . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Signal filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.4 Cycle by cycle analysis . . . . . . . . . . . . . . . . . . . . . . . . 42.5 Cycle by cycle threshold and pathological beta epochs . . . . . . 52.6 Generation of surrogate signals, CDF and CV . . . . . . . . . . . 5

3 Results 73.1 Beta band activity . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Power in beta band epochs . . . . . . . . . . . . . . . . . . . . . 73.3 Cumulative distribution of cycle occurrences . . . . . . . . . . . . 103.4 Variability decrease prior and after the burst . . . . . . . . . . . 10

4 Discussion 134.1 Thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Characterization of beta band bursts . . . . . . . . . . . . . . . . 134.3 Mechanisms regulating bursty activity . . . . . . . . . . . . . . . 144.4 Possible synchronization prior and during the burst . . . . . . . . 15

5 Conclusion 16

Appendix A State of the art 1

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1 Introduction

Parkinson’s Disease is a neurodegenerative disorder characterized by the loss ofdopaminergic neurons in the substantia nigra pars compacta (SNc) projectingto the striatum, one of the main components and input of the basal ganglia.Distinctive motor symptoms of PD are limb tremor at rest, slowness and rigidityof movement (bradykinesia) and impairment of muscle movement (akinesia) [7].A recurrent feature of PD is an exaggerated persistence of beta band (12-30 Hz)oscillations in local-field-potentials. These disruptive oscillations are primarilyobserved in the cortical-basal ganglia loop and are likely to be generated inthe subthalamo-pallidal (STN-GPe) network [9]. Indeed, spectral estimationsof LFPs recorded in the subthalomo-pallidal network show a prominent peak inthe beta band that is normally not found in healthy animals or under dopaminereplacement therapy [20]. This oscillation persistence has been linked to someof the motor disorders distinctive in PD: akinesia and bradykinesia [11].In both the healthy and the pathological state, beta band activity is not con-stantly present over time, but rather occurs in bursts (a sudden and brief highamplitude activity). In healthy rats and non-human primates beta band burstsare only a few cycles long and were observed to occur spontaneously and inprecise stages of movement tasks or after sensory cues [10, 5]. In a parkinsonianstate, on the other hand, beta bursts are characterized by a longer duration thatmight have deleterious effects by disturbing network dynamics [5]. Furthermore,it has been observed that longer beta epochs (the occurrence of an exaggeratedbeta band activity, that is a burst) have higher amplitudes [21]. The mecha-nisms of how a lack of dopamine leads to such exaggerated beta band activityare still poorly understood.Levodopa, oral intake of dopamine, is the first stage of non-invasive therapyto tackle PD symptoms [7]. It increases dopamine concentration levels in thestriatum leading to the suppression of exaggerated beta band activity in thebasal ganglia. When patients stop responding to levodopa, deep brain stimu-lation (DBS) is used as a last resort treatment in advanced states of PD. DBSelectrodes are surgically implanted in the STN or the GPi and deliver a contin-uous high frequency stimulation (≈130 Hz). These electrodes can also be usedto record LFPs of the ongoing activity.The main objective of this thesis is to characterize the temporal dynamics of betaband oscillations in PD patients on and off levodopa medication. The recordingswere obtained from implanted electrodes in humans undergoing DBS surgery.Beta band activity was classified and analyzed depending on its power, durationand number of cycles in order to have an understanding of the mechanismsunderlying PD and symptom treatment.

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2 Materials and methods

This section introduces the origin of the used data and will present the employedanalytical methods necessary to characterize beta band epochs and extract de-sired properties.

2.1 Data

The LFP data used in the thesis was provided by Prof. Peter Brown (OxfordUniversity, UK). Five patient gave their informed consent and the original studywas approved by the ethics committee. Patients underwent the implantation ofDBS electrodes in both the STN and GPi. The electrodes were permanentand quadripolar having four platinum-iridium cylindrical surfaces (MedtronicNeurologic Division, models 3387 and 3389), for a total of three contact pairs(channels). From 3 to 6 days after surgery, recordings were performed. Thedata was acquired in two states. Patients stopped their daily dosage medicationovernight (Table 1) and were seated on a bed while the first recording took place(OFF state). Afterwards, the patients were administered 200 mg of levodpa andafter approximately an hour, the recording took place again (ON). The acquiredsignals were amplified, band-passed between 1 Hz and 300 Hz and re-sampled toa common sampling rate of 1 kHz (all data has been previously analyzed andpublished by [4]).

Table 1: Patient details, modified from [4].Patient Age and Gender Disease Duration Levodopa Daily Dose

1 39/M 7 years 200 mg 1300 mg3 64/M 9 years 200 mg 1000 mg4 49/M 17 years 200 mg 1500 mg5 37/M 10 years 200 mg 150 mg

Only STN recordings were considered as the subthalamo-pallidal (GPe-STN)network is the most important component for sustaining oscillations. Record-ings from the same patient before and after intake of dopamine had differentduration. So, the duration of the recording in the ON state was normalized withthe duration of the recording in the OFF state. Patient 2 was not consideredas beta band activity was not present. Every signal was processed offline usingMatlab R© R2015a (The MathWorks Inc. Natick, Massachusetts).

2.2 Fitting raw data

For every channel in both the OFF and ON state, a unique threshold wasdefined that depended only on the dynamics of such channel. The score of theraw unfiltered LFP signal was standardized (see Appendix A). A 50 Hz band-stop filter was implemented in order to eliminate the power-line interference (seeAppendix A). Next, a small two-second time window was created and the signal

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Figure 1: The blue line represents the spectral estimation and the red linerepresents the fitting function. It can be seen how higher beta power drives thefitting function towards higher powers for lower frequencies as it overestimatesestimation’s trend.

inside this window was extracted. A spectral estimation was performed using aFast Fourier Transform (FFT) and both power and frequency information wasacquired. Successively, the time window was shifted by one second, the newportion of signal was extracted and spectral estimate information was acquiredagain. This process was repeated for the whole length of the signal. Finally,the mean value of both power and frequency from every segment were used torecover the spectral estimate of the entire signal.As briefly mentioned before, population signals recorded from different cerebralregions show a typical shape of the power spectrum which can be described asa power law (Equation 1),

Pexp(f) =γ

fα(1)

where Pexp(f) is the power of the signal at a frequency f , α is the exponentthat describes how rapidly power changes as a function of frequency, and γis amplitude scaling factor. Here, this function was used to estimate a powerthreshold in order to determine whether a given beta cycle is a pathologicaloscillatory wave or part of the ongoing colored noise. The fitting was performedin a frequency band between 5 Hz and 100 Hz and α and γ were estimated. Thus,using the estimated values of α the expected power value at any given frequencycan be derived. A distribution of threshold values (one for every frequency) wereextracted by fitting the eq. 1 to the spectrum of the LFP (Figure 1).

2.3 Signal filtering

Once the thresholds were created, the LFPs from every channel were character-ized. The raw data from every channel were standardized and filtered with asecond order IIR band-pass filter centered in each beta band power peak with

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cutting frequencies ±3 Hz from the center of band. As every patient had adifferent recorded power spectrum, the band-pass filter was manually centeredon the beta band peak for every channel.

Figure 2: Zero-crossings are defined as every intersection between the thickorange line and the filtered LFP in blue. In this way it was possible to isolateevery single cycle and calculate its instantaneous power, the black line.

2.4 Cycle by cycle analysis

Later, the band-passed signal was transformed into a square wave simply bysetting every positive value equal to +1 and every negative value equal to -1.In order to identify the zero-crossings, the signal was differentiated. In thisway, a positive value was obtained in the zero-crossing whenever the squarewave was ascending and a negative one when it was descending (Figure 2).This was necessary in order to divide the signal into single period cycles. Twoconsecutive positive-derivative values from the above mentioned process wouldbe the pointers that identify the beginning and the end of a single cycle. Fromevery cycle, frequency and instantaneous power were calculated, the latter usingParseval’s theorem. It states that the power, Pinst, obtained by integration ofthe spectral components is equal to the square of the signal integrated over thetime domain (Equation 2),

Pinst =1

2T

∫ T

−T|s(t)|2dt (2)

where s(t) is the cycle amplitude and T the period of the given cycle. Asthe power was extracted from the human data, for simplicity it will be calledrecorded power.

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2.5 Cycle by cycle threshold and pathological beta epochs

It is important now to identify and mark where significant beta activity oc-curs. To do so, the recorded power of every band-passed cycle was comparedwith the distribution of expected power values obtained in the fitting (Section2.2). Recorded power was determined to be significant, that is originating froma pathological state, if its value would differentiate more than two standarddeviations from the expected power distribution.

Figure 3: Beta epochs are marked with a black square line over the filtered LFPin blue.

After the power classification was performed on every cycle for the whole lengthon the signal, the method was corrected in order to improve beta activity identi-fication. In a cycle by cycle approach there is a risk of obtaining false negatives,that is cycles that are not classified as beta activity, but could be consideredas such as i.e. is occurring in a burst. To overcome this issue, a correctionin two steps was performed. First, every cycle that was classified as non-beta,which was in the middle of two cycles that were originating from a pathologicalstate, was re-classified as beta pathological activity. Secondly, the re-classifiedbeta cycle must have had real power that differentiated more than one standarddeviation from the expected value distribution.Beta epochs were defined as a set of single cycles that have instantaneousrecorded power levels significantly higher than the threshold (Figure 3). This is anew method for the characterization of beta epochs. To the author’s knowledge,literature does not suggest any similar method in order to identify exaggeratedbeta band activity. Finally, information on both time duration and number ofcycles for every epoch and for the total length of the beta activity (sum of everyepoch) was acquired.

2.6 Generation of surrogate signals, CDF and CV

For every channel, 500 surrogate signals were generated by randomly shufflingthe LFP’s single period cycles. In this way number of beta activity cycles,

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frequency distribution and amplitudes were preserved in the surrogate signal.Each surrogate signal was later characterized for the same above mentioned pa-rameters (such surrogate data will be used in section 3.3 in order to compare theON and the OFF levodopa states with a random activity with same dynamics).A cumulative distribution function (CDF) expresses how much epochs with agiven number of cycles account for the total sum of cycles (Figure 7). The usedmethod (see section 2.4) allowed to classify the epochs based on their numberof cycles. This allowed to account the weight of every epoch duration in anongoing activity.The coefficient of variation (CV) indicates how much the standard deviation ofa given signal differs from its mean value (see Appendix A). Here, every epochwith the same number of cycles was overlapped at onset, that is the beginning ofsuch epoch. The ratio between the standard deviation of the set of overlappingepochs and its mean was calculated in order to extract common epoch properties(Section 3.4).

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3 Results

The following section will present the results of the temporal dynamics analysisof the beta band activity in both the ON and the OFF state.

3.1 Beta band activity

The signal was filtered in the beta band and divided into single cycles. An epochwas defined as a set of oscillation cycles that exceeded a given threshold (seeMaterials and Methods). LFPs showed a bursty behaviour and the duration ofbeta oscillations epochs varied from one cycle up to about thirty cycles (depend-ing on patient), alternated with moments of silence. Both the occurrence andthe length of the burst depended on the threshold decided in section 2.5 (i.e.by lowering the threshold, a higher number of epoch would be detected). Theduration of beta activity above threshold in relationship with the total durationof the signal was calculated for every channel in both the ON state and the OFFstate. There were differences between the two states and among every patient(Table 2).

Table 2: The table lists the overall relative duration of beta band activity torecorded time depending on patient, levodopa administration (ON state or OFFstate) and channel.

Patient 1 Patient 3 Patient 4 Patient 5Cond. ON OFF ON OFF ON OFF ON OFFSTN01 0.58 0.69 0.66 0.74 0.30 0.62 0.45 0.50STN12 0.57 0.57 0.61 0.71 0.75 0.57 0.41 0.62STN23 0.42 0.69 0.61 0.77 0.61 0.56 0.57 0.73

3.2 Power in beta band epochs

Figure 4.A illustrates the distribution of the mean power of every epoch inrelation with its duration in an OFF state. In this way it was possible tocompare power variation in same length epochs and power variation dependingon the length of the epoch. In an OFF state there was an increase in power as afunction of the duration of beta band epochs. In an ON state this phenomenonis not as prominent. Long beta band epochs were pinned down, but the powerdid not increase in the same fashion of the OFF state while increasing the lengthof the epoch. It maintained values close to the total mean power value of thesignal (Figure 5A). In summary, the OFF state showed an overall higher meanpower in respect of the ON state and a higher number of longer bursts.Figures 4.B and 5.B illustrate the mean power density distribution, that is howmany epochs with a certain duration have a specific power value. In both the

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Figure 4: (A) illustrates the power of the epoch given its length in the OFFstate. It can be noticed how with increasing the length of the epoch the powerincreases. (B) illustrates a power colour density plot, that is how many epochswith the same power have the same duration. On the right, the colour bar, fromblue to yellow, represents the number of epochs with the same power.

Figure 5: (A) illustrates the power of the epoch given its length in the ONstate. It can be noticed how with increasing the length of the epoch the powerincreases less in respect to the OFF state. (B) illustrates a power colour densityplot, that is how many epochs with the same power have the same duration. Onthe right, the colour bar, from blue to yellow, represents the number of epochswith the same power. It can be noticed how there is a high number of epochswith low duration.

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ON and the OFF state it appears that in the first 250 ms epochs tend to groupin discrete intervals.Figure 6 is a collection of histograms from the STN of patient 5. It is clearfrom the histograms that both the ON and the OFF state differentiate in countdistribution for every interval: the ON state has a lower count of longer epochsand a higher for single cycles. In the OFF state the histogram highlights howepochs tend to have set duration and a higher count of long duration epochs.Lastly, in the OFF state epochs tend to group in specific time intervals for lowerduration.

Figure 6: (A)(C)(E) count distribution histograms for the ON state. (B)(D)(F)count distribution histograms for the OFF state. Bursts manifest in discretetime intervals in both states. The x-axis represents the epoch duration and they-axis the total epoch count with a given duration. It can be seen how the OFFstate has a higher number of long duration epochs.

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3.3 Cumulative distribution of cycle occurrences

Once the histograms of the OFF state were obtained, the cumulative distributionfunction (CDF) of cycle occurrences was calculated.A two-sample Kolmogorov-Smirnov test with a significance level set at 5% (α =0.05) was exploited in order to evaluate if two CDFs differentiated significantlyone from the other. In every case the ON state (green) and the OFF state (blue)were significantly different. In every case, except for patient 4, the OFF statewas significantly different from the surrogate data set (red). Furthermore, theON state CDFs for patients 1,3 and 5 are strongly comparable to the ones ofthe surrogate data.The auto-correlation function of the epoch duration distribution was imple-mented in order to identify possible patterns in epoch occurrences. The auto-correlation function for both the ON and the OFF state returned values < 0.2for every channel.

Figure 7: The ON state CDF, the OFF state CDF and the surrogate data CDFof all patients are represented respectively in green, blue and red.

3.4 Variability decrease prior and after the burst

Every epoch with the same number of cycles was overlapped one another atthe onset (the beginning of an epoch) for the OFF state (Figure 8.A and 8.B).The mean of the overlapped epochs in figures 8.A and 8.B appear to have asteady decrease of the oscillation rather than an abrupt end. The Coefficientof Variation (CV) was calculated on an interval starting 300 ms before onsetto 500 ms after. The CV considerably starts decreasing 200 ms before onset,it progressively increases during the burst and it finally drops again at the

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offset (the end of an epoch). Finally, CV returns to values similar to the onesantecedent the first decrease (Figure 8.D and 8.E).

Figure 8: Bursts of two and four cycles from the OFF state are considered.All the epochs are aligned at onset (0 ms). (A)(B) show the overlapped timewindows with the mean of the two cycle burst in red and the mean of the fourcycle burst in blue. (C) compares the two means. (D)(E) are the CV of the twoand four cycle burst respectively. (F) compares the two CVs.

In the ON state it can be seen that the overall behaviour does not change (Figure9). There is still higher CV during the burst and a lower one before onset andafter offset. The value of CV, though, in the ON state is lower in respect to theOFF state. It can be noticed how also the amplitude of the LFP recording islower in the ON state in respect to the OFF state.

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Figure 9: Bursts of two and four cycles from the ON state are considered. All theepochs are aligned at onset (0 ms). (A)(B) show the overlapped time windowswith the mean of the two cycle burst in red and the mean of the four cycle burstin blue. (C) compares the two means. (D)(E) are the CV of the two and fourcycle burst respectively. (F) compares the two CVs.

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4 Discussion

4.1 Thresholding

One of the main characteristics of PD is the existence of an excessive betaband activity. However, it is not obvious beyond what threshold beta bandoscillations can be considered pathological as: (1) even healthy state animalsshow transient beta oscillations [10], (2) in statistical terms, brain LFP is similarto a colored noise whose power decreases with frequency [13]. That is, evenwhen there is no obvious oscillation, the LFP will have a non-zero beta bandactivity. So, it is important to set a meaningful threshold in order to differentiatesignificant pathological activity from activity that could statistically occur giventhe system’s dynamics. Here, such threshold was created by fitting the function(Equation 1) that represents the ideal coloured noise dynamics of a recording tothe spectral estimate of such recording. In this way the threshold was definedas the expected power value that would change in function of frequency (Figure1).As there were exaggerated beta band oscillations, the expected power value inthis band was overestimated by a small factor (compared to an ideal spectrumin which there is no peak). This can be seen in the fitting: higher beta bandpower will ”push” the fitting function towards higher values for low frequencies.Nevertheless, this increase would be limited as the beta band is very smallin band compared with the whole spectrum. This overestimation can be seenas a stricter condition in order to identify a pathological activity because thethreshold will have higher values. The mean power of the activity in the ONstate could have been chosen, but that would have been biased as beta activity isnot always necessarily expected in the same way and beta power is an unreliablebio-marker (see Appendix A).

4.2 Characterization of beta band bursts

In order to compare results between the ON and the OFF state, the durationof each ON state channel was normalized in respect to its respective OFF state.This was necessary as recordings from the same patient do not have same du-ration in the two states. Indeed, for longer LFP recordings it is safe to assumethat a higher number of beta band activity epochs will occur.It has been previously reported that in healthy non-human primates and ratsbeta band oscillation bursts occur in specific stages of movement tasks and havea duration of a few cycles [5, 10]. A parkinsonian condition distinguishes itselffor having both longer duration epochs and higher power in long epochs. Therelationship between a high epoch power and the duration of such epoch (Figure4.A) has been recently reported in [21]. In this thesis, it emerged how the powerin the ON state does not increase in the same fashion as the OFF state (withincreasing epoch duration) and has an overall lower mean power (Figure 5.A).So, dopamine replacement appears to reduce the power, and consequently theamplitude (see Equation 2), of the LFP recordings. The change in amplitude

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can be specifically seen by comparing the epoch profile in Figure 8.C with Figure9.C.Also, it was of interest to investigate how epochs would distribute themselvesin time and if there was any differences between the ON and the OFF state. Acount histogram was constructed and it emerged how epochs tend to group indiscrete time intervals (Figure 6), especially for epochs with a small number ofcycles (less than five). Such discreetness is due to the fact that these oscillationshave been obtained by filtering the LFP in a narrow band. In this way theepochs have a combination of cycles with slightly different frequencies that willminimally effect their duration (epochs with the same number of cycles will havea similar duration). It is important to note that in [21] epochs below 100 ms werenot considered, to limit the changes in amplitude due to noise fluctuations. Inthis thesis these smaller epochs were considered in order to see if there were anydifferences between the ON state and the OFF state for such epochs. Indeed, itemerged how the ON state has a significantly higher number of short durationepochs in respect of the OFF state. So, dopamine replacement therapy appearsto also quench long duration epochs and increase short duration ones.

4.3 Mechanisms regulating bursty activity

As healthy human data is not available, the pathological state was comparedwith surrogate data that derived from the recorded activity. The generatedsurrogate data has the same number of beta cycles, frequency distribution andamplitude. This was done in order to assess if longer epochs occurring in theOFF state can also be obtained by a random process with the same dynamicsof the beta band activity or are particular of a pathological state. By randomlyshuffling every cycle of the recorded LFP, a test signal is created in which itis possible to check if a random activity with the same properties of PD couldproduce sustained beta bursts. For Figure 7 channels with a medium relativeduration were considered. This was done as for long relative duration, theshuffling of the cycles for the surrogate data would have been less effective: if arelative duration is high, the possibility of having different cycle combinationsis low. So, the surrogate signal would have very similar composition to thereal signal. This is very clear in patient 4 where the OFF state CDF andthe surrogate data CDF coincide. Furthermore, a long relative duration wouldsuggest that the beta band activity is more persistent and less bursty.The obtained CDFs might suggest that there could be two mechanisms modu-lating the bursty activity of the beta band in PD. The first one is a stochasticprocess that triggers a burst: the ON state and the surrogate duration dis-tribution are comparable. Indeed, a stochastic behaviour was also observedby performing the auto-correlation function of the epoch duration distribution.This was done in order to evaluate any pattern in epoch duration occurrence (i.e.if after a three cycle epoch a five cycle would be expected). The auto-correlationfunction for every channel in both states returned values < 0.2 implying thatepoch occurrence cannot be predicted. The second mechanism, instead, ap-pears to sustain the triggered burst in time: the count of longer epochs are

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significantly higher in the OFF state in respect of both the ON state and thesurrogate data, whereas the count of short epochs are significantly lower. Thismight suggest that such sustaining mechanism is not stochastic, but modulatedby an other process, i.e a possible synchronization prior and during the burst.In the OFF state such mechanism might be strong enough to sustain the burstfor a long period of time and dopamine replacement therapy might specificallyinteract with the strength of such mechanism quenching burst duration.

4.4 Possible synchronization prior and during the burst

The variability at onset is necessarily equal to zero as it is an imposed conditionfor the epoch overlapping. The increase of variability during the burst couldbe caused by the frequency jitter in the beta band. The raw signal was filteredusing a band pass filter having passing band length of 7 Hz (see section 2.2). So,even if the epochs might have the same number of cycles it will not necessarilyhave exactly the same duration. A decrease of variability was expected to occurjust before the onset: if the signal is divided in single cycles, the variability willdecrease in the last part of the period (Figure 8 and Figure 9). A decrease ofCV 200 ms before onset probably represents the silenced period between twoconsecutive bursts (Figure 8). The network might be steadily going througha synchronization process before and during the burst occurrence. Indeed, themore neural populations are locked in synchronicity the longer the bursts andthe higher the amplitude of the LFP recording [4, 21]. Even if the results mightbe consistent with the previous findings, Figures 8 and 9 are not informativeenough as the 200 ms silenced period before onset could also only represent thetail of the previous burst. So, it is hard to detect with certainty an occurringsynchronization process in the silenced period in such figures. Finally, the dif-ference in CV value between the OFF state and the ON state is due to thedifference in amplitude of the signals.

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5 Conclusion

Levodopa may reduce PD symptoms in patients by quenching beta band epochduration and the overall mean power level. Here, it has been seen that sus-tained and high power beta band epochs in LFP recordings from the STN arecharacteristic of a parkinsonian condition. More specifically, there could be twomechanisms responsible for PD bursty activity. The first one is a stochasticprocess that triggers the burst. The second one, which could be a possible syn-chronization process, is responsible for sustaining burst duration. Dopaminereplacement therapy might specifically interact with such mechanism by weak-ening the capability of sustaining a burst. Finally, the decrease of the CV beforethe onset was identified to possibly be the silenced period in which the burst’stail is present and a synchronization process is taking place (the CV is noteffective in order to detect neural population synchronization).

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[19] D James Surmeier, Weixing Shen, Michelle Day, Tracy Gertler, Savio Chan,Xianyong Tian, and Joshua L Plotkin. The role of dopamine in modulatingthe structure and function of striatal circuits. Progress in brain research,183:148–167, 2010.

[20] Yoshihisa Tachibana, Hirokazu Iwamuro, Hitoshi Kita, Masahiko Takada,and Atsushi Nambu. Subthalamo-pallidal interactions underlying parkin-sonian neuronal oscillations in the primate basal ganglia. European Journalof Neuroscience, 34(9):1470–1484, 2011.

[21] Gerd Tinkhauser, Alek Pogosyan, Simon Little, Martijn Beudel, Damian MHerz, Huiling Tan, and Peter Brown. The modulatory effect of adap-tive deep brain stimulation on beta bursts in parkinson’s disease. Brain,140(4):1053, 2017.

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A State of the art

Parkinson’s disease is a motor disorder correlated to the malfunctioning of thebasal ganglia in processing motor cortical inputs. The basal ganglia consists ofa set of interconnected nuclei creating a network. It is consequently importantto have a good understanding of the basal ganglia’s network functional organi-zation, of how this network is perturbed during Parkinson’s disease and finallywhat existing tools tackle Parkinson’s disease’s symptoms nowadays.

Basal ganglia’s network description

The basal ganglia is a fundamental component of the cerebrum located in boththe midbrain and the forebrain. It consists of a set of subcortical nuclei inter-connected by either inhibitory or excitatory projection neurons. A projectionneuron can be broadly defined as a neuron whose axons stretch from the cellbody to another region in the brain. The main nuclei are the corpus striatum,the substantia nigra, which consists of substantia nigra pars compacta (SNc)and substantia nigra pars reticulata (SNr), and the subthalamic nucleus (STN).The corpus striatum can be further divided in striatum and pallidum, the latterformed by the globus pallidus internus (GPi) and the globus pallidus externus(GPe) (Figure 10).The basal ganglia receives projections from the cortex and projects to manyother areas of the brain, especially back to the cortex through the thalamus.This is generally known as the basal ganglia-cortical loop. One of the manyfunctions of the thalamus is to convey basal ganglia information back to themotor cortex. Although the exact motor function of the basal ganglia is stilllargely debated, it is known that it is involved in regulation and fine control ofmovement.

Figure 10: Coronal section of the basal ganglia. Figureby Andrew Gillies (User:Anaru)-Own work, CC BY-SA 3.0,https://commons.wikimedia.org/w/index.php?curid=506222

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Projections can be either excitatory or inhibitory. In the brain the major in-hibitory projections are called GABAergic as the neurotransmitter γ-aminobutyricacid (GABA) is released on specific synaptic targets in order to compete withexcitatory actions. Instead excitatory projections are called glutamatergic asthe released neurotransmitter is glutamate. It is important that inhibition andexcitation must be present and balanced in a network in order to have neuraldynamics that lead to proper temporal information transfer. This informationtransfer is important i.e. to initiate and control motor actions.The network connectivity of the basal ganglia-cortical loop is given in Figure11. It is remarked in [7] and [2] how specific portions of the striatum receiveglutamatergic projections from the cortex. The striatum has GABAergic out-put projections both to the GPi and to the GPe. The GPe has an inhibitoryprojection to the STN that, in turn, has an excitatory projection to the GPi.This is known as the indirect pathway. The STN excites the GPe back througha glutamatergic projection. The direct pathway is known as the excitatory pro-jection from the striatum to the GPi. The STN can also be directly excited bythe cortex through the hyperdirect pathway. The GPi is considered the overalloutput of the basal ganglia that projects to the thalamus. Lastly, the dopamin-ergic projections from the SNc to the striatum help to shape the strength of thestriatal output. How dopamine does so, though, is still a matter of debate [19].

Figure 11: Schematic representation of the basal ganglia-cortical loop network.Red arrows are glutamatergic projections, black arrows are GABAergic projec-tions and blue arrows are dopaminergic projections. (i) is the indirect pathway,(d) the direct pathway and (h) the hyperdirect pathway.

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Parkinson’s disease

Parkinson’s disease (PD) is a neurodegenerative disorder that primarily hitsthe central nervous system and compromises the motor system. The exactcauses are still unknown. On the other hand, there is large consensus that thehallmark of Parkinson’s disease is the denervation (or loss) of the dopaminergicneurons in the SNc that project to the striatum [3, 6, 7, 14, 20]. PD’s mainsymptoms are rest tremor, bradykinesia and akinesia. Rest tremor consists in ashaking movement that occurs when the person is an a rest state, i.e sitting ona chair. Normally rest tremor disappears when the patient initiates an action.Bradykinesia consists in movement slowness and stiffness while performing anytype of motor activity. Akinesia is the loss of normal motor functioning resultingin an impairment of muscle movement.

The cortex entrains the basal ganglia in Parkinson’s disease

As previously mentioned, the main characteristic of PD is the denervation of thedopaminergic neurons in the SNc that project to the striatum. This is generallyconsidered to be the key concept in order to understand the strengthening thatoccurs between the cortex and the basal ganglia [3, 7, 9, 14, 16, 20]. The roleof dopamine in the basal ganglia is important as it regulates the STN’s and thestriatum’s abilitiy in reading cortical inputs. In dopamine depleted states thecortex manages to entrain both the STN and the striatum.The striatum is considered to be the input nucleus of the basal ganglia. It is com-posed by 90% of GABAergic projection neurons called medium-spiny-neurons(MSNs) that provide the sole striatal output. MSNs have two states, up anddown. In an healthy basal ganglia, MSNs in the down state are silent while inthe up state they increase their activity only when the synaptic cortical inputsare of sufficient strength and duration over time. This configuration assures thatMSNs seldom fire when excited by the cortex: they shape their input-output re-lationship in order to filter out uncorrelated cortical glutamatergic inputs [7]. Itis also remarked by [7] how some theoretical models have proposed that the over-all computational goal of basal ganglia is to decorrelate cortical inputs throughdopamine. Furthermore, MSNs can be divided in those which express D1-classdopamine receptors that project directly to the GPi and D2-class dopaminereceptors that project to the GPe. Note that these are respectively the abovementioned direct and indirect pathways.It is reported in [3, 7, 9, 20] that MSNs in dopamine depleted state alter theircortical input reading, that is they lose the ability of filtering uncorrelated corti-cal inputs and consequently increase their activity. The dopamine depleted statealso leads to the suppression of the striato-GPi direct pathway and enhancementof the striato-GPe indirect pathway. As striatal projections are GABAergic, theenhancement of the indirect pathway leads to a suppression of the GPe that un-leashes the STN from inhibition. Unlike the striatum, the STN faithfully readscortical inputs coming from the hyperdirect pathway. Some remarks have beenmade on how in a parkinsonian basal ganglia there is an imbalance of neural

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processing to the output (GPi) caused by the enhancement of the hyperdirectpathway and inhibition of the indirect one [20].

Oscillations in the basal ganglia and Local-Field-Potentials

The combination of STN cortical entrainment and GPe inhibition leads to STN-GPe coupling. In this configuration the exchange of inputs between STN andGPe is enhanced as they engage in an oscillatory activity. Some studies, suchas [9, 20], have suggested that the STN and GPe increase their activity in abursty fashion. The STN excites the GPe until the GPe manages to overcomethe inhibition from the striatum and project a GABAergic input back to theSTN. This resets the STN activity and the whole process restarts creating andoscillation. So, the oscillation in the GPe-STN network are altering reverbera-tions of excitations and inhibitions maintained by a both continuous inhibitionof the GPe and excitation of the STN [9].Local-Field-Potentials (LFPs) are necessary in order to appreciate the oscilla-tory behaviour of the GPe and the STN as they record the activity of a smallneuron population. LFP result from a complex interaction of synaptic andcellular mechanisms, major driving influence appear to originate from slow sub-threshold currents [3]. These are currents that do not manage to change themembrane potential in a way to trigger an action potential. Note that an actionpotential is a signal the neuron generates when it sends information to otherneurons. It is an all-or-none signal with a very brief duration generated as re-sponse to certain inputs. LFP are closely related to the activity of individualneurons, even though they represent a population-based behaviour [12]. Thisis exactly why LFP are chosen to study oscillatory behaviour in the STN-GPenetwork: a population-based metric is superior to a single cell recording as manystates, especially in Parkinson’s disease, are represented across populations [12].It is a general practice to record LFP in the STN or GPi using implantablemicroelectrodes. Indeed, the GPi is the output of the basal ganglia and theSTN is a structure in which a whole set of information conveys from the motorcortex and the GPe.

Basal ganglia beta band

In the parkinsonian basal ganglia, oscillations initiated by STN-GPe couplingare considered to have a broad frequency band of 13-30 Hz [3, 7, 9, 12, 20]. Thisband is known as the basal ganglia beta band and emerges in LFP recordingsin both the STN and the GPi. There is an interest in exploring this band as inrecordings of a pathological state there is a power peak in the spectrum of suchband. Whereas, in healthy animals or in patients ongoing treatment, such peakis not present [7, 20] (Figure 12).Beta band activity is normally associated with bradykinesia and akinesia, butnot with rest tremor which has a characteristic oscillation frequency of 5 Hz[8]. This could suggest that the mechanisms regulating tremor in Parkinsondisease’s are different from the ones regulating bradykinesia and akinesia.

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Figure 12: On the left a spectral estimation of a LFP recorded in the STN ofa patient undergoing levodopa treatment. On the right a spectral estimation ofthe same patient without the treatment. The beta band power peak is noticeableat 18 Hz. The peak at 5 Hz is the tremor frequency.

It is remarked in [7] how neuronal discharges in the STN are locked to LFP oscil-latory activity in the beta band. As previously mentioned, the STN unleashedfrom GPe inhibition has an irregular or bursty activity modulated by low fre-quency inputs (rhythms) descending from the cortex. The exaggerated couplingbetween STN and GPe is usually indirectly measured as the average power ofthe beta band activity recorded in the LFP [11]. As a consequence, beta be-comes an important biomarker as its changes could correlate with changes inthe clinical state of a patient. Unsurprisingly, there is not one biomarker inParkinson’s disease that can be directly linked to all the symptoms, but just tosome [12].Such increased coupling between STN and GPe in a parkinsonian basal gangliais thought to occur when there is a synchronous phase locking between the twonuclei. This prolonged phase locking leads to an increasing amplification of thebeta band. Interestingly, [4] has shown that the amplitude increase abruptlyends after a certain time interval. This sudden amplitude change is correlatedto an instantaneous phase slip that brakes the synchronicity between STN andGPe (Figure 13).Slowly the phase re-locks and the amplitude increases. The reason why thisphenomenon occurs is still unknown ([4] suggests that it could depend on theinactivation of T-type calcium channels in the STN caused by dopamine’s tran-sient depolarization or by a cortex re-synchronization). In a healthy state, thebasal ganglia is in the middle between phase-lock and non-synchronous dynam-ical activity, in an unhealthy state there is a shifting towards synchronization[17].Other than knowing that the beta activity is present, it is interesting to know

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Figure 13: In time STN and GPe become more synchronous and the amplitudeof the beta band increases. This amplitude abruptly changes when a phase-slipbreaks the synchrony. Reprinted with permission from [4]

Figure 14: It is noticeable how beta activity changes in time (left), yellowindicates high spectral power. The mean power, though, is concentrated in thebeta activity band (right).

how the beta band behaves in time. More specifically it is interesting to knowhow stable it is in a temporal interval. In fact, a beta band recording waxesand wanes in time (Figure 14). The temporal stability of the amplitude can beassessed with the coefficient of variation (CV) that is the standard deviation ofthe time varying beta amplitude divided by its mean [11] (Figure 15). The CVis inversely correlated to the degree of akinesia and bradykinesia of parkinsonianpatients. It was shown in [11] to be a reliable cross-patient marker index due tothe fact that low CV translated in high motor impairment.The decrease of beta band activity (and consequently of bradykinesia and aki-nesia) that occurs with dopamine administration shows how such activity highlydepends on dopaminergic inputs. it has been observed in [3, 4, 20] that witha systematic dopamine administration, abnormal beta band oscillation have a

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Figure 15: (A) filtered LFP showing beta oscillation. (B) Instantaneous ampli-tude in red with the mean amplitude as the thick dashed line. The standarddeviation is marked with thin dashed lines. Reprinted with permission from[11].

tendency to decrease in amplitude. The same thing is seen in [9, 12] for DBStreatment. Problems arise in considering beta band activity as a solid biomarker.As a matter of fact, prior to and during movement and during sleep oscillatorybeta band activity is reduced. On top of that, not everyone affected by Parkin-son’s disease expresses a prominent beta band activity. In some rare cases, thereis even no difference in beta band activity before and after treatment [3, 12].

Symptom treatment

Today, the golden standard for PD symptom treatment is dopamine replacementtherapy that consists in the administration of levodopa, a dopamine precursordrug. levodopa manages to cross the blood-brain barrier and increase dopamineconcentration levels in the brain. Dopamine concentration also increases in thestriatum leading to a suppression of the beta band activity in the basal ganglia.Motor impairments such as akinesia and bradykinesia consequently decrease[20]. In the long term (five to ten years) levodopa loses its effectiveness due todrug resistance. It has also been associated to the development of further motordisorders in 80% of patients [7].Another treatment is the lesioning of the STN through an invasive surgical

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intervention. This leads to the complete suppression of the STN overdrivenactivity and decrease of motor symptoms in the patient.Deep Brain Stimulation (DBS) consists in surgically implanting a battery-poweredneurostimulator that through electrodes stimulates specific target areas of thebrain. DBS was first tested and the end of the 80s and was FDA approvedfor Parkinson’s disease in 1997 [1]. Electrodes are placed in the STN and theneurostimulator below the collarbone under the skin.Although DBS is used to treat Parkinson’s disease symptoms, it is still unclearhow it works [7, 8, 9, 14]. Nevertheless, [9] suggests that DBS quenches betaband oscillations by inhibiting the STN (Figure 16). This is probably why motorimpairment improves. When stimulated, STN’s activity decreases and is moreregular. It was also seen how GPe irregular activity does not change [9, 20].

Figure 16: Schematic representation of DBS interacting with STN-GPe.

Stimulation parameters are decided by the physician that manually tunes themafter evaluating the patient’s response to stimulation. Generally a neurostimu-lator is set to deliver high frequency stimulation at around 130 Hz, an amplitudeof 1-4 V and pulse width of 60 ms [8]. It is also remarked that such parametertuning highly depends on the physiological properties of the tissue and on thegeometric configuration of the electrode. Unfortunately, different patients reactdifferently to DBS, some even showing very small or no improvement in Parkin-son’s disease motor symptoms. This can also be partly explained by the factthat only patients in an advanced state of the disease receive DBS treatment(the basal ganglia efficiency is already highly compromised) [12].DBS electrodes can be also used to record the ongoing activity in the basalganglia in patients undergoing levodopa treatment. Once the patients haveundergone the implantation of the leads, they can be withdrawn from medicationin order to acquire a pathological beta band activity. Later, levodopa can be

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administered again and a recording from a condition under medication can beacquired. An example can be seen in [4].

Signal Analysis

This section treats some basic tools in order to properly analyze LFP signals.

Digital Filters

Every digital filter performs a set of mathematical operations on a discrete timeseries in order to pull out certain properties. The z transform decomposes agiven signal with an integer number n that is exponent of a complex number, z.In the z domain, in a linear time invariant (LTI) system (Figure 17), the transferfunction H(z) can be written as the ratio of two polynomials in function of z.This kind of expression is valid for every type of digital filter as every digitalfilter is characterized by its transfer function (which is always the ratio betweentwo polynomials) [15].

H(z) =Y (z)

X(z)=b(0) + b(1)z−1 + ...+ b(q)z−q

1 + a(1)z−1 + ...+ a(p)z−p(3)

The numerator of Equation 3 is composed by coefficients b that go from b(0)to b(q) multiplied by a set of coefficients with an exponent that goes from 0to q that represents the number of input elements. Note that q is the numberof elements for which the input is delayed before reaching the output (discretetime series). The denominator has the same properties, but is composed bycoefficients a and they go from 1 to a(p). By choosing the correct vectors fora and b, and the number of input elements, every type of digital filter can beconstructed. The numerator is a polynomial in function of z, with z that variesfrom z0 = 1 to z−q that is the order of the polynomial that defines the numberof zeros. In the denominator, instead, the order of the polynomial defines thenumber of poles. Indeed, knowing the number of poles and zeros it is possibleto reconstruct the transfer function of the system.Digital filters can be of two types having either a finite impulse response (FIR)or an infinite impulse response (IIR). The main difference is how the system isbuilt: the z transfer function contains a denominator (the a vector) that indicatethe feedback values. In this way IIR is said to be recursive (FIR has a = 0).

Figure 17: Linear time invariant system. X(z) is the input, Y(z) the output,H(z) the transfer function, a(i) and b(j) respectively the i and j number ofelements of the numerator’s and denominator’s polynomials.

The main advantage of using IIR filters is managing to meet the wanted specifi-cations of a filter with a smaller function order in respect of FIR (computation

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advantage). The drawback is that IIR filters do not have a linear phase responseas the filter introduces a phase distortion after being applied. This is a problemfor real time filtering. On offline analysis this can be solved using anticausal fil-ters that restore the phase distortion by filtering the signal twice after reversingthe time axis.

Spectral Estimates

A biological signal is a representation of an ongoing physiological activity. Wedefine a signal to be WSS (wide sense stationary) if its mean and correlationfunction do not change in time, but only in function of the lag [18]. Biologicalsignals are generally not WSS as they adapt to a given conditions over time.What can be done is to consider the biological signal to be WSS in a given timeinterval. Such signals are generally more informative in the frequency domainrather than the temporal one [18]. A spectral estimate is an estimation of thetheoretical spectrum of the signal. In real cases the definition of spectrum of asignal, the square of the absolute value of the Fourier transform, is not applicableas recorded signals have a limited duration. Working with time limited signalsintroduces a set of errors, so that is why only an estimation of the theoreticalspectrum can be done.By extracting the spectral estimation, information on how the power of thesignal distributes itself on the frequencies is obtained. This is generally definedas power spectrum density (PSD). If the signal is WSS, then the spectrum issymmetric, real and positive. This means that the magnitude of a real power isobtained. As a biological signal is always assumed to be WSS in a time interval,for every finite real signal an implicit windowing occurs. Indeed, a signal x0[n]of finite length can be considered as a signal of infinite length multiplied by asquare window of height 1.

x0[n] = x[n]rect[n] (4)

Where x0[n] is a finite signal in discrete time domain, x[n] is an infinite lengthsignal and rect[n] is a rectangular window of height 1. As stated, the wayto calculate the spectrum is to use the square of the absolute of the Fouriertransform, so in frequency domain equation 4 can be written as

X0(f) = X(f) ∗DN (f) (5)

where X0(f) is the finite Fourier transform of the signal, X(f) is the Fouriertransform of the signal with infinite length and Dn(f) is Dirichlet’s kernel thatcan be expressed as

DN (f) = Te−j2πfT (N−1) sin(πfTN)

sin(πfT )(6)

once the length of the rectangular is known. N is the total number of elementsof the rectangular window and T is the sampling interval.

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So the Fourier transform of a window is an oscillating function. For example, theFourier transform of a signal that is a single sine wave is a Dirac delta centeredin the sine’s frequency. If such wave was to be truncated, after the convolutionwith the window’s Fourier transform, X0 will be proportional to a functionsin(f)f centered in every delta. In the ideal case the power is concentrated

in the Dirac delta, whereas the in the real case the power is distributed onevery frequency. This phenomena is called power leakage and it is inevitable.Nevertheless, signals with mean different from zero are more affected by suchphenomena. Normally, the mean of a signal is removed prior estimating thespectrum in order to have a better estimation.If the signal is composed by more sine wave with different frequencies, the lobesoverlap and the spectrum becomes “less correct”. This is why it is called spectralestimation: it is impossible to recover the real spectrum, but just an estimationof it.

Standard Score

A standard score (or z-score) allows to convert the scores of a given distributionin z-scores in what becomes a standard normal distribution. A score is definedas a random variable of a distribution. This allows to compare elements fromtwo distributions (i.e. LFP signals) that are different from each other. A z-scorecan be calculated as:

z =X − µσ

where X is the original score, µ the mean and σ the standard deviation. So,through a z-score the mean of the distribution is subtracted to the score and itis normalized by the standard deviation. This is why two z-scores from differentdistributions can now be compared.

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