Characterization of Scale-free Properties of Human … P… · EESD Path: targets maximum state...
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EESD Path: targets maximum state discriminatory power, selecting the best single frequency range from (A) with which to distinguish Awake vs. SWS brain states Characterization of Scale-free Properties of Human Electrocorticography in Awake and Slow Wave Sleep States John M. Zempel 1,2 , David Politte 3 , Matthew Kelsey 3 , Ryan Verner 3,4 , Tracy S. Nolan 3 , Abbas Babajani-Feremi 5 , Fred Prior 3 and Linda J. Larson-Prior 1,3 Departments of Neurology 1 , Pediatrics 2 , Radiology 3 , Biomedical Engineering 4 , Anatomy and Neurobiology 5 , Washington University School of Medicine, St. Louis, MO, USA Like many complex dynamic systems, the brain exhibits scale-free dynamics that follow power law scaling. Broadband power spectral density (PSD) of brain electrical activity exhibits state-dependent power law scaling with a log frequency exponent that varies across frequency ranges. Widely divergent naturally occurring neural states, awake and slow wave sleep (SWS) periods, were used evaluate the nature of changes in scale-free indices. We demonstrate two analytic approaches to characterizing electrocorticographic (ECoG) data obtained during Awake and SWS states. A data driven approach was used, characterizing all available frequency ranges. Using an Equal Error State Discriminator (EESD), a single frequency range did not best characterize state across data from all six subjects, though the ability to distinguish awake and SWS states in individual subjects was excellent. Multisegment piecewise linear fits were used to characterize scale-free slopes across the entire frequency range (0.2-200 Hz). These scale-free slopes differed between Awake and SWS states across subjects, particularly at frequencies below 10 Hz and showed little difference at frequencies above 70 Hz. A Multivariate Maximum Likelihood Analysis (MMLA) method using the multisegment slope indices successfully categorized ECoG data in most subjects, though individual variation was seen. The ECoG spectrum is not well characterized by a single linear fit across a defined set of frequencies, but is best described by a set of discrete linear fits across the full range of available frequencies. With increasing computational tractability, the use of scale-free slope values to characterize EEG data will have practical value in clinical and research EEG studies. REFERENCES 1. Freeman, W.J. and Zhai, J. (2009) ‘Simulated power spectral density (PSD) of background electrocorticogram (ECoG)’. Cogn Neurodyn, vol. 3, pp. 97-103. 2. He, B.J., Zempel, J.M. Snyder, A.Z., Raichle, M.E. (2010) ‘The temporal structures and functional significance of scale-free brain activity’ Neuron, vol. 66, pp. 353-369. 3. Iber C, Ancoli-Israel S, Chesson A, Quan SF. The AASM manual for the scoring of sleep and associated events: rules, terminology, and technical specifications, 1st ed. Westchester, IL: American Academy of Sleep Medicine; 2007. Our analysis of scale-free properties of human ECoG has provided several new insights into the characteristic of this property when the brain changes its state between awake and asleep. By choosing to allow the data to define the regions over which linear slopes could be fit to log-log plots of signal power by frequency, we show that EEG spectrum is not well characterized by a single linear fit across a defined set of frequencies, but is best described by a set of discrete linear fits across the full range of frequencies available. Further, we show that when the data defines the frequency range of the log-log data, slope changes taken from global averages of all sensors show differences from those previously reported (Freeman and Zhai, 2009;He et al., 2010). In agreement with others (Miller et al., 2009a), we find an abrupt slope change at about 75 Hz in most subjects at which point the slope shifts to more negative values near -4. While we report data computed over 30 sec intervals in this report, we also examined changes in shorter (10 second) intervals, finding similar behaviors and lending credence to the characterization of human brain activity as scale-free. Several interesting features of this analysis emerge. First, with increasing frequency, the slopes of the segments increased, from positive to slightly negative in segment one up to more than negative four at the highest frequency segment. Second, the slopes of the highest frequency range, segment four (generally above 70 Hz), show little difference between awake and asleep neural states. Modulation of high frequencies (gamma, high gamma) has been implicated in many studies to be associated with cognitive processing, but gamma frequency power is still high in sleep. Despite expected organization of gamma frequency activity in awake states with ongoing behavior, no systematic differences in slope were present. The largest differences between Awake and SWS were seen in segments one and two, the two lowest frequency ranges. At the lowest frequency values, the interaction of the hardware filter and the presence of up-down activity in the lowest frequency range actually flipped the expected negative segment one slope to a positive value in many electrodes. Indeed, including frequency ranges beyond 1-100 Hz provided a superior ability to distinguish between ECOG from awake and SWS states, indicating the importance of partitioning this frequency range. Interestingly, the very highest frequency data used in this study (up to 200 Hz) was not particularly helpful in distinguishing awake and asleep ECOG. These characteristics are illustrated by the PSD and line fit plots, shown below for four subjects. Red and blue lines correspond to the average value of the PSD over all time intervals and sensors. The green, heavily clustered, lines each show the least error line fit for a single channel, time interval and spectrum segment. Subjects. Following informed consent under a protocol approved by the Institutional Review Board of Washington University, eight pediatric subjects (4-18 years, 3m/5f) undergoing invasive monitoring for the surgical treatment of intractable epilepsy provided awake and asleep data across 1-7 days, uncontrolled for behavior. Data were collected using a research EEG amplifier (2 subjects, 64 sensors, Synamps/2™, Compumedics Neuroscan, 1kHz, DC-200 Hz) or using the clinical amplifier for long term and broader coverage (6 subjects, 72-116 sensors, Pro Amp, LaMont Medical, 500 Hz, 0.1-200 Hz). Sensor Arrays. Arrays varied in their placement, number and configuration, with two subjects additionally implanted with depth electrodes. Depth electrode and strip data were excluded from these analyses, which focus on sensor grids. Grid arrays consisted of 20-64 sensors in three configurations, shown above right. Electrode data were segmented from CT and co-registered onto MRI volume rendering of the brain for each subject (8x8, Subject 2 shown). SWS Wake 4X5 Grid Layouts 4X8 8X8 Preprocessing. Bad channels and artifact-filled time periods were identified and removed from further processing. Five minute continuous segments were identified using standard criteria 3 for wake, N2, N3 (slow wave sleep: SWS) and REM sleep episodes. Data were further partitioned into uniform 30-second intervals. METHODS Spectral Partitioning. The power spectral densities (PSDs) of the scroll data were computed for each time interval for each channel in each ECoG grid. Then, for each PSD, 183 frequency ranges were considered, including the "classical EEG" bands (up/down, 0.5-1 Hz; delta, 0.2-4 Hz; theta, 4-8 Hz; alpha 8-12 Hz; low alpha, 8-10 Hz; high alpha 10- 12 Hz; beta, 16-30 Hz; low beta 12-15 Hz, intermediate beta, 15-8 Hz; high beta, 18-30 Hz; gamma 30-100 Hz). The frequencies varied from 0.2 Hz to 250 Hz and were approximately equally spaced in log-frequency. Figure A below represents the set of spectral partitions, with each horizontal line spanning the band of an individual range. For each frequency range, a least-squares linear fit to the PSD was computed in log-frequency versus log-PSD coordinates. The slopes of these best-fit lines are the quantities of interest. Figure B shows an example of best-fit lines in the 1-100Hz band for an average PSD. EESD Sample slope value distributions and their respective Gaussian models are shown in (C). Given these Gaussian models for each frequency partition, an EESD threshold slope x* is readily calculated. The computed probability of correct state classification is illustrated in (D) below. The horizontal lines extend over the frequency ranges used to calculate PSDs and the slopes of PSDs. These values represent the maximum discriminating power achievable using power-law signature slopes. Note that the maximally discriminative frequency ranges vary from subject to subject. MMLA The MMLA method utilizes multivariate analysis with a Bayesian classifier to include slope data from multiple slope segments, adding higher dimensionality to the classifier. The best performing classifier to distinguish between Awake and SWS data for the six subjects utilized segment two and segment three slope data. Each point in (E) represents a 30 second interval from a single electrode. The data clusters are shown partitioned with the classifier’s decision boundary. The MMLA classifier performance was affected by the data from subject six, which was different than the rest of the subject data, highlighted in (F). Analysis Paths. The slopes of computed best-fit PSD line segments are analyzed using two complementary methods: Equal Error State Discriminator (EESD) and Multivariate Maximum Likelihood Analysis (MMLA). For defined brain states A and SWS, calculate µ and σ of slopes for each frequency range For each frequency range, calculate x* and probability of correct classification Pick frequency range from (A) with largest probability of correct classification of A and SWS data. MMLA Path: is focused on categorizing brain states using least- error piecewise linear representations of the appropriate PSD. For brain states A and SWS, use data from selected time interval to perform optimized multisegment piecewise fit of entire frequency range to normalized PSD data to minimize total fit error, E p , across all electrodes where Characterize A and SWS data by selecting N segment linear fit based on error in fit, E p , to normalized PSD data. Use Bayesian quadratic classifier to partition slope features of A verses SWS data in a least error sense given the piecewise characterization. Calculate µ and Σ of slopes for each linear segment. RESULTS A B CONCLUSIONS C D E F Awake SWS McD03 McD04 McD05 McD06 Class decision boundary is defined where
Transcript of Characterization of Scale-free Properties of Human … P… · EESD Path: targets maximum state...
EESD Path: targets maximum state discriminatory power, selecting the best single frequency range from (A) with which to distinguish Awake vs. SWS brain states
Characterization of Scale-free Properties of Human Electrocorticography in Awake and Slow Wave Sleep States
John M. Zempel1,2, David Politte3, Matthew Kelsey3, Ryan Verner3,4, Tracy S. Nolan3, Abbas Babajani-Feremi5, Fred Prior3 and Linda J. Larson-Prior1,3
Departments of Neurology1, Pediatrics2, Radiology3, Biomedical Engineering4, Anatomy and Neurobiology5, Washington University School of Medicine, St. Louis, MO, USA
Like many complex dynamic systems, the brain exhibits scale-free dynamics that follow power law scaling. Broadband power spectral density (PSD) of brain electrical activity exhibits state-dependent power law scaling with a log frequency exponent that varies across frequency ranges. Widely divergent naturally occurring neural states, awake and slow wave sleep (SWS) periods, were used evaluate the nature of changes in scale-free indices. We demonstrate two analytic approaches to characterizing electrocorticographic (ECoG) data obtained during Awake and SWS states. A data driven approach was used, characterizing all available frequency ranges. Using an Equal Error State Discriminator (EESD), a single frequency range did not best characterize state across data from all six subjects, though the ability to distinguish awake and SWS states in individual subjects was excellent. Multisegment piecewise linear fits were used to characterize scale-free slopes across the entire frequency range (0.2-200 Hz). These scale-free slopes differed between Awake and SWS states across subjects, particularly at frequencies below 10 Hz and showed little difference at frequencies above 70 Hz. A Multivariate Maximum Likelihood Analysis (MMLA) method using the multisegment slope indices successfully categorized ECoG data in most subjects, though individual variation was seen. The ECoG spectrum is not well characterized by a single linear fit across a defined set of frequencies, but is best described by a set of discrete linear fits across the full range of available frequencies. With increasing computational tractability, the use of scale-free slope values to characterize EEG data will have practical value in clinical and research EEG studies.
REFERENCES 1. Freeman, W.J. and Zhai, J. (2009) ‘Simulated power spectral density (PSD) of background electrocorticogram (ECoG)’. Cogn Neurodyn, vol. 3, pp. 97-103. 2. He, B.J., Zempel, J.M. Snyder, A.Z., Raichle, M.E. (2010) ‘The temporal structures and functional significance of scale-free brain activity’ Neuron, vol. 66, pp. 353-369. 3. Iber C, Ancoli-Israel S, Chesson A, Quan SF. The AASM manual for the scoring of sleep and associated events: rules, terminology, and technical specifications, 1st ed. Westchester, IL: American Academy of Sleep Medicine; 2007.
Our analysis of scale-free properties of human ECoG has provided several new insights into the characteristic of this property when the brain changes its state between awake and asleep. By choosing to allow the data to define the regions over which linear slopes could be fit to log-log plots of signal power by frequency, we show that EEG spectrum is not well characterized by a single linear fit across a defined set of frequencies, but is best described by a set of discrete linear fits across the full range of frequencies available. Further, we show that when the data defines the frequency range of the log-log data, slope changes taken from global averages of all sensors show differences from those previously reported (Freeman and Zhai, 2009;He et al., 2010). In agreement with others (Miller et al., 2009a), we find an abrupt slope change at about 75 Hz in most subjects at which point the slope shifts to more negative values near -4. While we report data computed over 30 sec intervals in this report, we also examined changes in shorter (10 second) intervals, finding similar behaviors and lending credence to the characterization of human brain activity as scale-free.
Several interesting features of this analysis emerge. First, with increasing frequency, the slopes of the segments increased, from positive to slightly negative in segment one up to more than negative four at the highest frequency segment. Second, the slopes of the highest frequency range, segment four (generally above 70 Hz), show little difference between awake and asleep neural states. Modulation of high frequencies (gamma, high gamma) has been implicated in many studies to be associated with cognitive processing, but gamma frequency power is still high in sleep. Despite expected organization of gamma frequency activity in awake states with ongoing behavior, no systematic differences in slope were present. The largest differences between Awake and SWS were seen in segments one and two, the two lowest frequency ranges. At the lowest frequency values, the interaction of the hardware filter and the presence of up-down activity in the lowest frequency range actually flipped the expected negative segment one slope to a positive value in many electrodes. Indeed, including frequency ranges beyond 1-100 Hz provided a superior ability to distinguish between ECOG from awake and SWS states, indicating the importance of partitioning this frequency range. Interestingly, the very highest frequency data used in this study (up to 200 Hz) was not particularly helpful in distinguishing awake and asleep ECOG. These characteristics are illustrated by the PSD and line fit plots, shown below for four subjects. Red and blue lines correspond to the average value of the PSD over all time intervals and sensors. The green, heavily clustered, lines each show the least error line fit for a single channel, time interval and spectrum segment.
Subjects. Following informed consent under a protocol approved by the Institutional Review Board of Washington University, eight pediatric subjects (4-18 years, 3m/5f) undergoing invasive monitoring for the surgical treatment of intractable epilepsy provided awake and asleep data across 1-7 days, uncontrolled for behavior. Data were collected using a research EEG amplifier (2 subjects, 64 sensors, Synamps/2™, Compumedics Neuroscan, 1kHz, DC-200 Hz) or using the clinical amplifier for long term and broader coverage (6 subjects, 72-116 sensors, Pro Amp, LaMont Medical, 500 Hz, 0.1-200 Hz).
Sensor Arrays. Arrays varied in their placement, number and configuration, with two subjects additionally implanted with depth electrodes. Depth electrode and strip data were excluded from these analyses, which focus on sensor grids. Grid arrays consisted of 20-64 sensors in three configurations, shown above right. Electrode data were segmented from CT and co-registered onto MRI volume rendering of the brain for each subject (8x8, Subject 2 shown).
SWS
Wake
4X5 Grid Layouts
4X8
8X8
Preprocessing. Bad channels and artifact-filled time periods were identified and removed from further processing. Five minute continuous segments were identified using standard criteria3 for wake, N2, N3 (slow wave sleep: SWS) and REM sleep episodes. Data were further partitioned into uniform 30-second intervals.
METHODS
Spectral Partitioning. The power spectral densities (PSDs) of the scroll data were computed for each time interval for each channel in each ECoG grid. Then, for each PSD, 183 frequency ranges were considered, including the "classical EEG" bands (up/down, 0.5-1 Hz; delta, 0.2-4 Hz; theta, 4-8 Hz; alpha 8-12 Hz; low alpha, 8-10 Hz; high alpha 10-12 Hz; beta, 16-30 Hz; low beta 12-15 Hz, intermediate beta, 15-8 Hz; high beta, 18-30 Hz; gamma 30-100 Hz). The frequencies varied from 0.2 Hz to 250 Hz and were approximately equally spaced in log-frequency. Figure A below represents the set of spectral partitions, with each horizontal line spanning the band of an individual range. For each frequency range, a least-squares linear fit to the PSD was computed in log-frequency versus log-PSD coordinates. The slopes of these best-fit lines are the quantities of interest. Figure B shows an example of best-fit lines in the 1-100Hz band for an average PSD.
EESD Sample slope value distributions and their respective Gaussian models are shown in (C). Given these Gaussian models for each frequency partition, an EESD threshold slope x* is readily calculated. The computed probability of correct state classification is illustrated in (D) below. The horizontal lines extend over the frequency ranges used to calculate PSDs and the slopes of PSDs. These values represent the maximum discriminating power achievable using power-law signature slopes. Note that the maximally discriminative frequency ranges vary from subject to subject.
MMLA The MMLA method utilizes multivariate analysis with a Bayesian classifier to include slope data from multiple slope segments, adding higher dimensionality to the classifier. The best performing classifier to distinguish between Awake and SWS data for the six subjects utilized segment two and segment three slope data. Each point in (E) represents a 30 second interval from a single electrode. The data clusters are shown partitioned with the classifier’s decision boundary. The MMLA classifier performance was affected by the data from subject six, which was different than the rest of the subject data, highlighted in (F).
Analysis Paths. The slopes of computed best-fit PSD line segments are analyzed using two complementary methods: Equal Error State Discriminator (EESD) and Multivariate Maximum Likelihood Analysis (MMLA).
For defined brain states A and SWS, calculate µ and σ of slopes for each frequency range
For each frequency range, calculate x* and probability of correct classification
Pick frequency range from (A) with largest probability of correct classification of A and SWS data.
MMLA Path: is focused on categorizing brain states using least-error piecewise linear representations of the appropriate PSD.
For brain states A and SWS, use data from selected time interval to perform optimized multisegment piecewise fit of entire frequency
range to normalized PSD data to minimize total fit error, Ep, across all electrodes where
Characterize A and SWS data by selecting N segment linear fit based on error in fit, Ep, to normalized PSD data.
Use Bayesian quadratic classifier to partition slope features of A verses SWS data in a least error sense given the piecewise
characterization.
Calculate µ and Σ of slopes for each linear segment.
RESULTS A B
CONCLUSIONS
C D
E F
Aw
ake
SWS
McD03 McD04 McD05 McD06
Class decision boundary is defined where
