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

Transcription

1 DEGREE PROJECT IN 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 TECHNOLOGY SCHOOL OF TECHNOLOGY AND HEALTH

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3 Dopamine replacement therapy reduces beta band burst duration in Parkinson s disease Dopaminersättningsbehandling förkortar aktivitetsutbrott i betabandet vid Parkinsons sjukdom Alessandro Mecconi Date: June 2017 Supervisor: Arvind Kumar Reviewer: Tobias Nyberg i

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5 Abstract One of the main characteristics of Parkinson s disease (PD) is an exaggerated oscillatory activity in the beta band (12-30 Hz). This activity has been linked to the rise of symptoms such as bradykinesia and akinesia. Even if dopamine replacement therapy (oral intake of dopamine pro-drug levodopa) reverses these symptoms, the effect of the treatment on the beta band activity has still not been completely understood. Therefore, here the temporal dynamics of beta band activity in human patients affected by PD were characterized with and without levodopa treatment. Local-field-potential (LFP) recordings from five patients undergoing dopamine replacement therapy were used. From the LFPs, the extracted beta epochs with significantly higher power than expected from a comparable noisy signal were analyzed. This analysis showed that beta band activity occurred in bursts meaning that high amplitude oscillation alternated with silenced periods. The pathological state also distinguished itself for longer epochs and with power that increased with the length of the epoch. The administration of levodopa reduced the duration of bursts and decreased the overall mean power of the beta band activity. Finally, epochs with the same number of cycles were compared. The Coefficient of Variation prior such epochs suggested that the ongoing activity might lock into a synchronization process prior the burst. These results provide important information to better understand how levodopa alleviates some of the symptoms of PD and pave the way to develop better computational models for the emergence of beta oscillations. iii

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

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9 Contents 1 Introduction 1 2 Materials and methods Data Fitting raw data Signal filtering Cycle by cycle analysis Cycle by cycle threshold and pathological beta epochs Generation of surrogate signals, CDF and CV Results Beta band activity Power in beta band epochs Cumulative distribution of cycle occurrences Variability decrease prior and after the burst Discussion Thresholding Characterization of beta band bursts Mechanisms regulating bursty activity Possible synchronization prior and during the burst Conclusion 16 Appendix A State of the art 1 vii

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11 1 Introduction Parkinson s Disease is a neurodegenerative disorder characterized by the loss of dopaminergic neurons in the substantia nigra pars compacta (SNc) projecting to 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 rigidity of 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 primarily observed in the cortical-basal ganglia loop and are likely to be generated in the subthalamo-pallidal (STN-GPe) network [9]. Indeed, spectral estimations of LFPs recorded in the subthalomo-pallidal network show a prominent peak in the beta band that is normally not found in healthy animals or under dopamine replacement therapy [20]. This oscillation persistence has been linked to some of the motor disorders distinctive in PD: akinesia and bradykinesia [11]. In both the healthy and the pathological state, beta band activity is not constantly present over time, but rather occurs in bursts (a sudden and brief high amplitude activity). In healthy rats and non-human primates beta band bursts are only a few cycles long and were observed to occur spontaneously and in precise stages of movement tasks or after sensory cues [10, 5]. In a parkinsonian state, on the other hand, beta bursts are characterized by a longer duration that might have deleterious effects by disturbing network dynamics [5]. Furthermore, it has been observed that longer beta epochs (the occurrence of an exaggerated beta band activity, that is a burst) have higher amplitudes [21]. The mechanisms of how a lack of dopamine leads to such exaggerated beta band activity are still poorly understood. Levodopa, oral intake of dopamine, is the first stage of non-invasive therapy to tackle PD symptoms [7]. It increases dopamine concentration levels in the striatum leading to the suppression of exaggerated beta band activity in the basal ganglia. When patients stop responding to levodopa, deep brain stimulation (DBS) is used as a last resort treatment in advanced states of PD. DBS electrodes are surgically implanted in the STN or the GPi and deliver a continuous high frequency stimulation ( 130 Hz). These electrodes can also be used to record LFPs of the ongoing activity. The main objective of this thesis is to characterize the temporal dynamics of beta band oscillations in PD patients on and off levodopa medication. The recordings were obtained from implanted electrodes in humans undergoing DBS surgery. Beta band activity was classified and analyzed depending on its power, duration and number of cycles in order to have an understanding of the mechanisms underlying PD and symptom treatment. 1

12 2 Materials and methods This section introduces the origin of the used data and will present the employed analytical methods necessary to characterize beta band epochs and extract desired properties. 2.1 Data The LFP data used in the thesis was provided by Prof. Peter Brown (Oxford University, UK). Five patient gave their informed consent and the original study was approved by the ethics committee. Patients underwent the implantation of DBS electrodes in both the STN and GPi. The electrodes were permanent and quadripolar having four platinum-iridium cylindrical surfaces (Medtronic Neurologic Division, models 3387 and 3389), for a total of three contact pairs (channels). From 3 to 6 days after surgery, recordings were performed. The data was acquired in two states. Patients stopped their daily dosage medication overnight (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 and after approximately an hour, the recording took place again (ON). The acquired signals were amplified, band-passed between 1 Hz and 300 Hz and re-sampled to a common sampling rate of 1 khz (all data has been previously analyzed and published 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 mg 3 64/M 9 years 200 mg 1000 mg 4 49/M 17 years 200 mg 1500 mg 5 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. Recordings from the same patient before and after intake of dopamine had different duration. So, the duration of the recording in the ON state was normalized with the duration of the recording in the OFF state. Patient 2 was not considered as beta band activity was not present. Every signal was processed offline using Matlab 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 was defined that depended only on the dynamics of such channel. The score of the raw unfiltered LFP signal was standardized (see Appendix A). A 50 Hz bandstop filter was implemented in order to eliminate the power-line interference (see Appendix A). Next, a small two-second time window was created and the signal 2

13 Figure 1: The blue line represents the spectral estimation and the red line represents the fitting function. It can be seen how higher beta power drives the fitting function towards higher powers for lower frequencies as it overestimates estimation s trend. inside this window was extracted. A spectral estimation was performed using a Fast Fourier Transform (FFT) and both power and frequency information was acquired. Successively, the time window was shifted by one second, the new portion of signal was extracted and spectral estimate information was acquired again. 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 to recover the spectral estimate of the entire signal. As briefly mentioned before, population signals recorded from different cerebral regions show a typical shape of the power spectrum which can be described as a power law (Equation 1), P exp (f) = γ f α (1) where P exp (f) is the power of the signal at a frequency f, α is the exponent that describes how rapidly power changes as a function of frequency, and γ is amplitude scaling factor. Here, this function was used to estimate a power threshold in order to determine whether a given beta cycle is a pathological oscillatory wave or part of the ongoing colored noise. The fitting was performed in 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 frequency can be derived. A distribution of threshold values (one for every frequency) were extracted 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 characterized. The raw data from every channel were standardized and filtered with a second order IIR band-pass filter centered in each beta band power peak with 3

14 cutting frequencies ±3 Hz from the center of band. As every patient had a different recorded power spectrum, the band-pass filter was manually centered on the beta band peak for every channel. Figure 2: Zero-crossings are defined as every intersection between the thick orange line and the filtered LFP in blue. In this way it was possible to isolate every 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 by setting 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 this way, a positive value was obtained in the zero-crossing whenever the square wave 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. Two consecutive positive-derivative values from the above mentioned process would be the pointers that identify the beginning and the end of a single cycle. From every cycle, frequency and instantaneous power were calculated, the latter using Parseval s theorem. It states that the power, P inst, obtained by integration of the spectral components is equal to the square of the signal integrated over the time domain (Equation 2), P inst = 1 T s(t) 2 dt (2) 2T T where s(t) is the cycle amplitude and T the period of the given cycle. As the power was extracted from the human data, for simplicity it will be called recorded power. 4

15 2.5 Cycle by cycle threshold and pathological beta epochs It is important now to identify and mark where significant beta activity occurs. To do so, the recorded power of every band-passed cycle was compared with the distribution of expected power values obtained in the fitting (Section 2.2). Recorded power was determined to be significant, that is originating from a pathological state, if its value would differentiate more than two standard deviations from the expected power distribution. Figure 3: Beta epochs are marked with a black square line over the filtered LFP in blue. After the power classification was performed on every cycle for the whole length on the signal, the method was corrected in order to improve beta activity identification. 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 considered as such as i.e. is occurring in a burst. To overcome this issue, a correction in 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 pathological state, was re-classified as beta pathological activity. Secondly, the re-classified beta cycle must have had real power that differentiated more than one standard deviation from the expected value distribution. Beta epochs were defined as a set of single cycles that have instantaneous recorded power levels significantly higher than the threshold (Figure 3). This is a new method for the characterization of beta epochs. To the author s knowledge, literature does not suggest any similar method in order to identify exaggerated beta band activity. Finally, information on both time duration and number of cycles for every epoch and for the total length of the beta activity (sum of every epoch) was acquired. 2.6 Generation of surrogate signals, CDF and CV For every channel, 500 surrogate signals were generated by randomly shuffling the LFP s single period cycles. In this way number of beta activity cycles, 5

16 frequency distribution and amplitudes were preserved in the surrogate signal. Each surrogate signal was later characterized for the same above mentioned parameters (such surrogate data will be used in section 3.3 in order to compare the ON and the OFF levodopa states with a random activity with same dynamics). A cumulative distribution function (CDF) expresses how much epochs with a given number of cycles account for the total sum of cycles (Figure 7). The used method (see section 2.4) allowed to classify the epochs based on their number of cycles. This allowed to account the weight of every epoch duration in an ongoing activity. The coefficient of variation (CV) indicates how much the standard deviation of a given signal differs from its mean value (see Appendix A). Here, every epoch with the same number of cycles was overlapped at onset, that is the beginning of such epoch. The ratio between the standard deviation of the set of overlapping epochs and its mean was calculated in order to extract common epoch properties (Section 3.4). 6

17 3 Results The following section will present the results of the temporal dynamics analysis of 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 epoch was defined as a set of oscillation cycles that exceeded a given threshold (see Materials and Methods). LFPs showed a bursty behaviour and the duration of beta oscillations epochs varied from one cycle up to about thirty cycles (depending on patient), alternated with moments of silence. Both the occurrence and the 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). The duration of beta activity above threshold in relationship with the total duration of the signal was calculated for every channel in both the ON state and the OFF state. 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 to recorded time depending on patient, levodopa administration (ON state or OFF state) and channel. Patient 1 Patient 3 Patient 4 Patient 5 Cond. ON OFF ON OFF ON OFF ON OFF STN STN STN Power in beta band epochs Figure 4.A illustrates the distribution of the mean power of every epoch in relation with its duration in an OFF state. In this way it was possible to compare power variation in same length epochs and power variation depending on the length of the epoch. In an OFF state there was an increase in power as a function of the duration of beta band epochs. In an ON state this phenomenon is not as prominent. Long beta band epochs were pinned down, but the power did not increase in the same fashion of the OFF state while increasing the length of the epoch. It maintained values close to the total mean power value of the signal (Figure 5A). In summary, the OFF state showed an overall higher mean power 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 how many epochs with a certain duration have a specific power value. In both the 7

18 Figure 4: (A) illustrates the power of the epoch given its length in the OFF state. It can be noticed how with increasing the length of the epoch the power increases. (B) illustrates a power colour density plot, that is how many epochs with the same power have the same duration. On the right, the colour bar, from blue 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 ON state. It can be noticed how with increasing the length of the epoch the power increases less in respect to the OFF state. (B) illustrates a power colour density plot, that is how many epochs with the same power have the same duration. On the right, the colour bar, from blue to yellow, represents the number of epochs with the same power. It can be noticed how there is a high number of epochs with low duration. 8

19 ON and the OFF state it appears that in the first 250 ms epochs tend to group in discrete intervals. Figure 6 is a collection of histograms from the STN of patient 5. It is clear from the histograms that both the ON and the OFF state differentiate in count distribution for every interval: the ON state has a lower count of longer epochs and a higher for single cycles. In the OFF state the histogram highlights how epochs 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 lower duration. 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 discrete time intervals in both states. The x-axis represents the epoch duration and the y-axis the total epoch count with a given duration. It can be seen how the OFF state has a higher number of long duration epochs. 9

20 3.3 Cumulative distribution of cycle occurrences Once the histograms of the OFF state were obtained, the cumulative distribution function (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 significantly one 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 state was significantly different from the surrogate data set (red). Furthermore, the ON state CDFs for patients 1,3 and 5 are strongly comparable to the ones of the surrogate data. The auto-correlation function of the epoch duration distribution was implemented in order to identify possible patterns in epoch occurrences. The autocorrelation function for both the ON and the OFF state returned values < 0.2 for every channel. Figure 7: The ON state CDF, the OFF state CDF and the surrogate data CDF of 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 at the 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 a steady decrease of the oscillation rather than an abrupt end. The Coefficient of Variation (CV) was calculated on an interval starting 300 ms before onset to 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 10

21 offset (the end of an epoch). Finally, CV returns to values similar to the ones antecedent 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 time windows with the mean of the two cycle burst in red and the mean of the four cycle burst in blue. (C) compares the two means. (D)(E) are the CV of the two and four cycle burst respectively. (F) compares the two CVs. In the ON state it can be seen that the overall behaviour does not change (Figure 9). There is still higher CV during the burst and a lower one before onset and after offset. The value of CV, though, in the ON state is lower in respect to the OFF state. It can be noticed how also the amplitude of the LFP recording is lower in the ON state in respect to the OFF state. 11

22 Figure 9: Bursts of two and four cycles from the ON state are considered. All the epochs are aligned at onset (0 ms). (A)(B) show the overlapped time windows with the mean of the two cycle burst in red and the mean of the four cycle burst in blue. (C) compares the two means. (D)(E) are the CV of the two and four cycle burst respectively. (F) compares the two CVs. 12

23 4 Discussion 4.1 Thresholding One of the main characteristics of PD is the existence of an excessive beta band activity. However, it is not obvious beyond what threshold beta band oscillations can be considered pathological as: (1) even healthy state animals show transient beta oscillations [10], (2) in statistical terms, brain LFP is similar to a colored noise whose power decreases with frequency [13]. That is, even when there is no obvious oscillation, the LFP will have a non-zero beta band activity. So, it is important to set a meaningful threshold in order to differentiate significant pathological activity from activity that could statistically occur given the system s dynamics. Here, such threshold was created by fitting the function (Equation 1) that represents the ideal coloured noise dynamics of a recording to the spectral estimate of such recording. In this way the threshold was defined as the expected power value that would change in function of frequency (Figure 1). As there were exaggerated beta band oscillations, the expected power value in this band was overestimated by a small factor (compared to an ideal spectrum in which there is no peak). This can be seen in the fitting: higher beta band power will push the fitting function towards higher values for low frequencies. Nevertheless, this increase would be limited as the beta band is very small in band compared with the whole spectrum. This overestimation can be seen as a stricter condition in order to identify a pathological activity because the threshold will have higher values. The mean power of the activity in the ON state could have been chosen, but that would have been biased as beta activity is not always necessarily expected in the same way and beta power is an unreliable bio-marker (see Appendix A). 4.2 Characterization of beta band bursts In order to compare results between the ON and the OFF state, the duration of 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 duration in the two states. Indeed, for longer LFP recordings it is safe to assume that a higher number of beta band activity epochs will occur. It has been previously reported that in healthy non-human primates and rats beta band oscillation bursts occur in specific stages of movement tasks and have a duration of a few cycles [5, 10]. A parkinsonian condition distinguishes itself for having both longer duration epochs and higher power in long epochs. The relationship between a high epoch power and the duration of such epoch (Figure 4.A) has been recently reported in [21]. In this thesis, it emerged how the power in the ON state does not increase in the same fashion as the OFF state (with increasing epoch duration) and has an overall lower mean power (Figure 5.A). So, dopamine replacement appears to reduce the power, and consequently the amplitude (see Equation 2), of the LFP recordings. The change in amplitude 13

24 can be specifically seen by comparing the epoch profile in Figure 8.C with Figure 9.C. Also, it was of interest to investigate how epochs would distribute themselves in time and if there was any differences between the ON and the OFF state. A count histogram was constructed and it emerged how epochs tend to group in discrete time intervals (Figure 6), especially for epochs with a small number of cycles (less than five). Such discreetness is due to the fact that these oscillations have been obtained by filtering the LFP in a narrow band. In this way the epochs have a combination of cycles with slightly different frequencies that will minimally effect their duration (epochs with the same number of cycles will have a similar duration). It is important to note that in [21] epochs below 100 ms were not considered, to limit the changes in amplitude due to noise fluctuations. In this thesis these smaller epochs were considered in order to see if there were any differences between the ON state and the OFF state for such epochs. Indeed, it emerged how the ON state has a significantly higher number of short duration epochs in respect of the OFF state. So, dopamine replacement therapy appears to 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 compared with surrogate data that derived from the recorded activity. The generated surrogate data has the same number of beta cycles, frequency distribution and amplitude. This was done in order to assess if longer epochs occurring in the OFF state can also be obtained by a random process with the same dynamics of the beta band activity or are particular of a pathological state. By randomly shuffling every cycle of the recorded LFP, a test signal is created in which it is possible to check if a random activity with the same properties of PD could produce sustained beta bursts. For Figure 7 channels with a medium relative duration were considered. This was done as for long relative duration, the shuffling of the cycles for the surrogate data would have been less effective: if a relative duration is high, the possibility of having different cycle combinations is low. So, the surrogate signal would have very similar composition to the real signal. This is very clear in patient 4 where the OFF state CDF and the surrogate data CDF coincide. Furthermore, a long relative duration would suggest that the beta band activity is more persistent and less bursty. The obtained CDFs might suggest that there could be two mechanisms modulating the bursty activity of the beta band in PD. The first one is a stochastic process that triggers a burst: the ON state and the surrogate duration distribution are comparable. Indeed, a stochastic behaviour was also observed by 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-correlation function for every channel in both states returned values < 0.2 implying that epoch occurrence cannot be predicted. The second mechanism, instead, appears to sustain the triggered burst in time: the count of longer epochs are 14

25 significantly higher in the OFF state in respect of both the ON state and the surrogate data, whereas the count of short epochs are significantly lower. This might suggest that such sustaining mechanism is not stochastic, but modulated by 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 burst for a long period of time and dopamine replacement therapy might specifically interact 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 condition for the epoch overlapping. The increase of variability during the burst could be caused by the frequency jitter in the beta band. The raw signal was filtered using 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 necessarily have exactly the same duration. A decrease of variability was expected to occur just before the onset: if the signal is divided in single cycles, the variability will decrease in the last part of the period (Figure 8 and Figure 9). A decrease of CV 200 ms before onset probably represents the silenced period between two consecutive bursts (Figure 8). The network might be steadily going through a synchronization process before and during the burst occurrence. Indeed, the more neural populations are locked in synchronicity the longer the bursts and the higher the amplitude of the LFP recording [4, 21]. Even if the results might be consistent with the previous findings, Figures 8 and 9 are not informative enough as the 200 ms silenced period before onset could also only represent the tail of the previous burst. So, it is hard to detect with certainty an occurring synchronization process in the silenced period in such figures. Finally, the difference in CV value between the OFF state and the ON state is due to the difference in amplitude of the signals. 15

26 5 Conclusion Levodopa may reduce PD symptoms in patients by quenching beta band epoch duration and the overall mean power level. Here, it has been seen that sustained and high power beta band epochs in LFP recordings from the STN are characteristic of a parkinsonian condition. More specifically, there could be two mechanisms responsible for PD bursty activity. The first one is a stochastic process that triggers the burst. The second one, which could be a possible synchronization process, is responsible for sustaining burst duration. Dopamine replacement therapy might specifically interact with such mechanism by weakening the capability of sustaining a burst. Finally, the decrease of the CV before the onset was identified to possibly be the silenced period in which the burst s tail is present and a synchronization process is taking place (the CV is not effective in order to detect neural population synchronization). 16

27 References [1] Fda approves brain implant to help reduce parkinson s disease and essential tremor symptoms, [2] Garrett E Alexander and Michael D Crutcher. Functional architecture of basal ganglia circuits: neural substrates of parallel processing. Trends in neurosciences, 13(7): , [3] John-Stuart Brittain and Peter Brown. Oscillations and the basal ganglia: motor control and beyond. Neuroimage, 85: , [4] Hayriye Cagnan, Eugene Paul Duff, and Peter Brown. The relative phases of basal ganglia activities dynamically shape effective connectivity in parkinson s disease. Brain, 138(6): , [5] Joseph Feingold, Daniel J Gibson, Brian DePasquale, and Ann M Graybiel. Bursts of beta oscillation differentiate postperformance activity in the striatum and motor cortex of monkeys performing movement tasks. Proceedings of the National Academy of Sciences, 112(44): , [6] Viviana Gradinaru, Murtaza Mogri, Kimberly R Thompson, Jaimie M Henderson, and Karl Deisseroth. Optical deconstruction of parkinsonian neural circuitry. science, 324(5925): , [7] Constance Hammond, Hagai Bergman, and Peter Brown. Pathological synchronization in parkinson s disease: networks, models and treatments. Trends in neurosciences, 30(7): , [8] Morten L Kringelbach, Ned Jenkinson, Sarah LF Owen, and Tipu Z Aziz. Translational principles of deep brain stimulation. Nature Reviews Neuroscience, 8(8): , [9] Arvind Kumar, Stefano Cardanobile, Stefan Rotter, and Ad Aertsen. The role of inhibition in generating and controlling parkinson s disease oscillations in the basal ganglia. Frontiers in Systems Neuroscience, 5:86, [10] Daniel K Leventhal, Gregory J Gage, Robert Schmidt, Jeffrey R Pettibone, Alaina C Case, and Joshua D Berke. Basal ganglia beta oscillations accompany cue utilization. Neuron, 73(3): , [11] S Little, A Pogosyan, AA Kuhn, and P Brown. Beta band stability over time correlates with parkinsonian rigidity and bradykinesia. Experimental neurology, 236(2): , [12] Simon Little and Peter Brown. What brain signals are suitable for feedback control of deep brain stimulation in parkinson s disease? Annals of the New York Academy of Sciences, 1265(1):9 24,

28 [13] Joshua Milstein, Florian Mormann, Itzhak Fried, and Christof Koch. Neuronal shot noise and brownian 1/f 2 behavior in the local field potential. PloS one, 4(2):e4338, [14] Anan Moran, Edward Stein, Hadass Tischler, Katya Belelovsky, and Izhar Bar-Gad. Dynamic stereotypic responses of basal ganglia neurons to subthalamic nucleus high-frequency stimulation in the parkinsonian primate. Front. Syst. Neurosci, 5(21), [15] A.V. Oppenheim, A.S. Willsky, and S.H. Nawab. Signals and Systems. Prentice-Hall signal processing series. Prentice Hall, [16] Boris Rosin, Maya Slovik, Rea Mitelman, Michal Rivlin-Etzion, Suzanne N Haber, Zvi Israel, Eilon Vaadia, and Hagai Bergman. Closed-loop deep brain stimulation is superior in ameliorating parkinsonism. Neuron, 72(2): , [17] Leonid L Rubchinsky, Choongseok Park, and Robert M Worth. Intermittent neural synchronization in parkinson s disease. Nonlinear dynamics, 68(3): , [18] Leif Sörnmo and Pablo Laguna. Bioelectrical signal processing in cardiac and neurological applications, volume 8. Academic Press, [19] D James Surmeier, Weixing Shen, Michelle Day, Tracy Gertler, Savio Chan, Xianyong Tian, and Joshua L Plotkin. The role of dopamine in modulating the structure and function of striatal circuits. Progress in brain research, 183: , [20] Yoshihisa Tachibana, Hirokazu Iwamuro, Hitoshi Kita, Masahiko Takada, and Atsushi Nambu. Subthalamo-pallidal interactions underlying parkinsonian neuronal oscillations in the primate basal ganglia. European Journal of Neuroscience, 34(9): , [21] Gerd Tinkhauser, Alek Pogosyan, Simon Little, Martijn Beudel, Damian M Herz, Huiling Tan, and Peter Brown. The modulatory effect of adaptive deep brain stimulation on beta bursts in parkinson s disease. Brain, 140(4):1053,

29 A State of the art Parkinson s disease is a motor disorder correlated to the malfunctioning of the basal ganglia in processing motor cortical inputs. The basal ganglia consists of a set of interconnected nuclei creating a network. It is consequently important to have a good understanding of the basal ganglia s network functional organization, of how this network is perturbed during Parkinson s disease and finally what 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 both the midbrain and the forebrain. It consists of a set of subcortical nuclei interconnected by either inhibitory or excitatory projection neurons. A projection neuron can be broadly defined as a neuron whose axons stretch from the cell body 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 latter formed 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 many other 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 many functions of the thalamus is to convey basal ganglia information back to the motor cortex. Although the exact motor function of the basal ganglia is still largely debated, it is known that it is involved in regulation and fine control of movement. Figure 10: Coronal section of the basal ganglia. Figure by Andrew Gillies (User:Anaru)-Own work, CC BY-SA 3.0, 1

30 Projections can be either excitatory or inhibitory. In the brain the major inhibitory projections are called GABAergic as the neurotransmitter γ-aminobutyric acid (GABA) is released on specific synaptic targets in order to compete with excitatory actions. Instead excitatory projections are called glutamatergic as the released neurotransmitter is glutamate. It is important that inhibition and excitation must be present and balanced in a network in order to have neural dynamics that lead to proper temporal information transfer. This information transfer is important i.e. to initiate and control motor actions. The network connectivity of the basal ganglia-cortical loop is given in Figure 11. It is remarked in [7] and [2] how specific portions of the striatum receive glutamatergic projections from the cortex. The striatum has GABAergic output projections both to the GPi and to the GPe. The GPe has an inhibitory projection 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 through a glutamatergic projection. The direct pathway is known as the excitatory projection from the striatum to the GPi. The STN can also be directly excited by the cortex through the hyperdirect pathway. The GPi is considered the overall output of the basal ganglia that projects to the thalamus. Lastly, the dopaminergic projections from the SNc to the striatum help to shape the strength of the striatal 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 projections and blue arrows are dopaminergic projections. (i) is the indirect pathway, (d) the direct pathway and (h) the hyperdirect pathway. 2

31 Parkinson s disease Parkinson s disease (PD) is a neurodegenerative disorder that primarily hits the central nervous system and compromises the motor system. The exact causes are still unknown. On the other hand, there is large consensus that the hallmark of Parkinson s disease is the denervation (or loss) of the dopaminergic neurons in the SNc that project to the striatum [3, 6, 7, 14, 20]. PD s main symptoms are rest tremor, bradykinesia and akinesia. Rest tremor consists in a shaking movement that occurs when the person is an a rest state, i.e sitting on a chair. Normally rest tremor disappears when the patient initiates an action. Bradykinesia consists in movement slowness and stiffness while performing any type of motor activity. Akinesia is the loss of normal motor functioning resulting in 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 the dopaminergic neurons in the SNc that project to the striatum. This is generally considered to be the key concept in order to understand the strengthening that occurs between the cortex and the basal ganglia [3, 7, 9, 14, 16, 20]. The role of dopamine in the basal ganglia is important as it regulates the STN s and the striatum s abilitiy in reading cortical inputs. In dopamine depleted states the cortex manages to entrain both the STN and the striatum. The striatum is considered to be the input nucleus of the basal ganglia. It is composed by 90% of GABAergic projection neurons called medium-spiny-neurons (MSNs) that provide the sole striatal output. MSNs have two states, up and down. In an healthy basal ganglia, MSNs in the down state are silent while in the up state they increase their activity only when the synaptic cortical inputs are of sufficient strength and duration over time. This configuration assures that MSNs seldom fire when excited by the cortex: they shape their input-output relationship in order to filter out uncorrelated cortical glutamatergic inputs [7]. It is also remarked by [7] how some theoretical models have proposed that the overall computational goal of basal ganglia is to decorrelate cortical inputs through dopamine. Furthermore, MSNs can be divided in those which express D1-class dopamine receptors that project directly to the GPi and D2-class dopamine receptors that project to the GPe. Note that these are respectively the above mentioned direct and indirect pathways. It is reported in [3, 7, 9, 20] that MSNs in dopamine depleted state alter their cortical input reading, that is they lose the ability of filtering uncorrelated cortical inputs and consequently increase their activity. The dopamine depleted state also leads to the suppression of the striato-gpi direct pathway and enhancement of the striato-gpe indirect pathway. As striatal projections are GABAergic, the enhancement of the indirect pathway leads to a suppression of the GPe that unleashes the STN from inhibition. Unlike the striatum, the STN faithfully reads cortical inputs coming from the hyperdirect pathway. Some remarks have been made on how in a parkinsonian basal ganglia there is an imbalance of neural 3

32 processing to the output (GPi) caused by the enhancement of the hyperdirect pathway 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 and GPe is enhanced as they engage in an oscillatory activity. Some studies, such as [9, 20], have suggested that the STN and GPe increase their activity in a bursty fashion. The STN excites the GPe until the GPe manages to overcome the inhibition from the striatum and project a GABAergic input back to the STN. This resets the STN activity and the whole process restarts creating and oscillation. So, the oscillation in the GPe-STN network are altering reverberations of excitations and inhibitions maintained by a both continuous inhibition of the GPe and excitation of the STN [9]. Local-Field-Potentials (LFPs) are necessary in order to appreciate the oscillatory behaviour of the GPe and the STN as they record the activity of a small neuron population. LFP result from a complex interaction of synaptic and cellular mechanisms, major driving influence appear to originate from slow subthreshold currents [3]. These are currents that do not manage to change the membrane potential in a way to trigger an action potential. Note that an action potential is a signal the neuron generates when it sends information to other neurons. It is an all-or-none signal with a very brief duration generated as response to certain inputs. LFP are closely related to the activity of individual neurons, even though they represent a population-based behaviour [12]. This is exactly why LFP are chosen to study oscillatory behaviour in the STN-GPe network: a population-based metric is superior to a single cell recording as many states, especially in Parkinson s disease, are represented across populations [12]. It is a general practice to record LFP in the STN or GPi using implantable microelectrodes. Indeed, the GPi is the output of the basal ganglia and the STN is a structure in which a whole set of information conveys from the motor cortex and the GPe. Basal ganglia beta band In the parkinsonian basal ganglia, oscillations initiated by STN-GPe coupling are considered to have a broad frequency band of Hz [3, 7, 9, 12, 20]. This band is known as the basal ganglia beta band and emerges in LFP recordings in both the STN and the GPi. There is an interest in exploring this band as in recordings of a pathological state there is a power peak in the spectrum of such band. Whereas, in healthy animals or in patients ongoing treatment, such peak is not present [7, 20] (Figure 12). Beta band activity is normally associated with bradykinesia and akinesia, but not with rest tremor which has a characteristic oscillation frequency of 5 Hz [8]. This could suggest that the mechanisms regulating tremor in Parkinson disease s are different from the ones regulating bradykinesia and akinesia. 4

33 Figure 12: On the left a spectral estimation of a LFP recorded in the STN of a patient undergoing levodopa treatment. On the right a spectral estimation of the same patient without the treatment. The beta band power peak is noticeable at 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 oscillatory activity in the beta band. As previously mentioned, the STN unleashed from GPe inhibition has an irregular or bursty activity modulated by low frequency inputs (rhythms) descending from the cortex. The exaggerated coupling between STN and GPe is usually indirectly measured as the average power of the beta band activity recorded in the LFP [11]. As a consequence, beta becomes an important biomarker as its changes could correlate with changes in the clinical state of a patient. Unsurprisingly, there is not one biomarker in Parkinson s disease that can be directly linked to all the symptoms, but just to some [12]. Such increased coupling between STN and GPe in a parkinsonian basal ganglia is thought to occur when there is a synchronous phase locking between the two nuclei. This prolonged phase locking leads to an increasing amplification of the beta band. Interestingly, [4] has shown that the amplitude increase abruptly ends after a certain time interval. This sudden amplitude change is correlated to an instantaneous phase slip that brakes the synchronicity between STN and GPe (Figure 13). Slowly the phase re-locks and the amplitude increases. The reason why this phenomenon occurs is still unknown ([4] suggests that it could depend on the inactivation of T-type calcium channels in the STN caused by dopamine s transient depolarization or by a cortex re-synchronization). In a healthy state, the basal ganglia is in the middle between phase-lock and non-synchronous dynamical 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 5

34 Figure 13: In time STN and GPe become more synchronous and the amplitude of the beta band increases. This amplitude abruptly changes when a phase-slip breaks the synchrony. Reprinted with permission from [4] Figure 14: It is noticeable how beta activity changes in time (left), yellow indicates high spectral power. The mean power, though, is concentrated in the beta activity band (right). how the beta band behaves in time. More specifically it is interesting to know how stable it is in a temporal interval. In fact, a beta band recording waxes and wanes in time (Figure 14). The temporal stability of the amplitude can be assessed with the coefficient of variation (CV) that is the standard deviation of the time varying beta amplitude divided by its mean [11] (Figure 15). The CV is inversely correlated to the degree of akinesia and bradykinesia of parkinsonian patients. It was shown in [11] to be a reliable cross-patient marker index due to the fact that low CV translated in high motor impairment. The decrease of beta band activity (and consequently of bradykinesia and akinesia) that occurs with dopamine administration shows how such activity highly depends on dopaminergic inputs. it has been observed in [3, 4, 20] that with a systematic dopamine administration, abnormal beta band oscillation have a 6

35 Figure 15: (A) filtered LFP showing beta oscillation. (B) Instantaneous amplitude in red with the mean amplitude as the thick dashed line. The standard deviation 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 DBS treatment. Problems arise in considering beta band activity as a solid biomarker. As a matter of fact, prior to and during movement and during sleep oscillatory beta band activity is reduced. On top of that, not everyone affected by Parkinson s disease expresses a prominent beta band activity. In some rare cases, there is 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 replacement therapy that consists in the administration of levodopa, a dopamine precursor drug. levodopa manages to cross the blood-brain barrier and increase dopamine concentration levels in the brain. Dopamine concentration also increases in the striatum 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 to drug resistance. It has also been associated to the development of further motor disorders in 80% of patients [7]. Another treatment is the lesioning of the STN through an invasive surgical 7

36 intervention. This leads to the complete suppression of the STN overdriven activity and decrease of motor symptoms in the patient. Deep Brain Stimulation (DBS) consists in surgically implanting a battery-powered neurostimulator that through electrodes stimulates specific target areas of the brain. DBS was first tested and the end of the 80s and was FDA approved for Parkinson s disease in 1997 [1]. Electrodes are placed in the STN and the neurostimulator below the collarbone under the skin. Although DBS is used to treat Parkinson s disease symptoms, it is still unclear how it works [7, 8, 9, 14]. Nevertheless, [9] suggests that DBS quenches beta band oscillations by inhibiting the STN (Figure 16). This is probably why motor impairment improves. When stimulated, STN s activity decreases and is more regular. 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 them after evaluating the patient s response to stimulation. Generally a neurostimulator is set to deliver high frequency stimulation at around 130 Hz, an amplitude of 1-4 V and pulse width of 60 ms [8]. It is also remarked that such parameter tuning highly depends on the physiological properties of the tissue and on the geometric configuration of the electrode. Unfortunately, different patients react differently to DBS, some even showing very small or no improvement in Parkinson s disease motor symptoms. This can also be partly explained by the fact that 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 basal ganglia in patients undergoing levodopa treatment. Once the patients have undergone the implantation of the leads, they can be withdrawn from medication in order to acquire a pathological beta band activity. Later, levodopa can be 8

37 administered again and a recording from a condition under medication can be acquired. 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 time series in order to pull out certain properties. The z transform decomposes a given 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 transfer function 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 digital filter is characterized by its transfer function (which is always the ratio between two polynomials) [15]. H(z) = Y (z) X(z) = b(0) + b(1)z b(q)z q 1 + a(1)z 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 0 to q that represents the number of input elements. Note that q is the number of elements for which the input is delayed before reaching the output (discrete time series). The denominator has the same properties, but is composed by coefficients a and they go from 1 to a(p). By choosing the correct vectors for a and b, and the number of input elements, every type of digital filter can be constructed. The numerator is a polynomial in function of z, with z that varies from z 0 = 1 to z q that is the order of the polynomial that defines the number of zeros. In the denominator, instead, the order of the polynomial defines the number of poles. Indeed, knowing the number of poles and zeros it is possible to 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 is built: the z transfer function contains a denominator (the a vector) that indicate the 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 of elements of the numerator s and denominator s polynomials. The main advantage of using IIR filters is managing to meet the wanted specifications of a filter with a smaller function order in respect of FIR (computation 9