Automated Subject-Specific Peak Identification
 and Ballistocardiographic Artifact Correction
                 in EEG-fMRI...
The secret dream of a neuroscientist
           is to map the human brain: WHERE and WHEN

                               ...
Brain mapping has useful applications

       Pathologies
       • Dyslexia                    • Epilepsy
         (5% sch...
Nowadays we have reliable means
           to localize brain functions

                  EEG exam               fMRI exam...
What an ElectroEncephaloGram (EEG) is

                                   100 billion



                               (1...
EEG exam

                                         EEG electrode
                      Signal amplitude
                  ...
EEG exam:
           Event Related Potentials (ERP)
                      Signal amplitude
                               ...
Information in EEG and ERP
           The latency of peaks , i.e. the time interval between the
           stimulus and th...
Basics of Magnetic Resonance Imaging (MRI)

           Up to 70 % of body weight is made up by water


                   ...
MRI exam


                                   MR-scanner


       strong
       magnet                                   S...
MRI exam:                                MR-scanner
            functional MRI




Activity:
            on            on ...
Do we have everything we need?

              personality
                                           We have the means:
  ...
Temporal resolution

           The smaller the interval the higher the temporal resolution

    μV                       ...
Spatial resolution

           The finer the grid the higher the spatial resolution




                   EEG-ERP (cm)   ...
EEG-fMRI achieves high temporal and spatial resolution


                                                                 ...
What do we need for EEG-fMRI?

           • MR-compatible EEG equipment

                                             Ampl...
EEG-fMRI exam


                            Scanner room                          Control room
                           ...
Some examples




                18
How we approach the problem of
           cerebral localization of brain functions
                                       ...
How we approach the problem of
           cerebral localization of brain functions
                                       ...
The quantification of amplitudes and latencies
           in ERPs may be challenging

                PRE-LEXICAL         ...
Features of peak quantification approaches

            Reliability
            Reproducibility, over subjects and over ...
Method 1: Peak-picking is a search for extrema
           in predefined time intervals

                                  ...
Method 2: Dynamic time warping (DTW) is a
           nonlinear mapping of two signals
           The ERP is compared with ...
We proposed a method (ppDTW) that integrates
           peack-picking and Dynamic Time Warping


        Compared by means...
The reference signal must contain
           all the peaks of interest
           We computed the reference by interpolati...
Case study
           (Assecondi et al., Clinical Neurophysiology 2009)


           • Normal children and children diagno...
Performance of the methods
           on normal and dyslexic subjects
                 normal                             ...
We evaluate the methods by comparing
           the automated scoring with the visual scoring
           C   =    correct ...
Conclusion

           We developed an automated peak detection method that
           takes into account the inter-subjec...
How we approach the problem of
           cerebral localization of brain functions
                                       ...
EEG-fMRI achieves high temporal and spatial resolution


                                                                 ...
An artifact is a contamination
           of the data of interest
           Suppose you want to listen to the radio while...
Two main artifacts affect EEG-fMRI recordings

   • Image acquisition artifact
     caused by the RF-waves
     and time-v...
The BallistoCardioGraphic artifact (BCGa)
                                  R    R    R    R    R     R    R   R
         ...
Distribution of scalp arteries




                                                                 Adapted from Gray, 191...
The BCG artifact can be removed
           if an additive model is assumed


                                             ...
Intra-subject variability of the BCGa


                            Heart beat




                     -0.2       0      ...
Inter-subject variability of the BCGa
                       S1       S2         S3         S4         S5   S6
           ...
The BCG artifact removal algorithms must take the
           inter- and intra-subject variability into account

       Gro...
Blind Source Separation identifies the sources
             generating the recorded signal

                              ...
We proposed a BSS method that uses Canonical
           Correlation Analysis to identify the sources

        Step 1: Iden...
Case study
           (Assecondi et al., Physics in Medicine and Biology 2009)


           • Patients affected by epileps...
Comparison of cleaned and raw EEG




                                                                 BSS-CCA
           ...
Comparison of cleaned and raw EEG




                                                                 BSS-CCA
           ...
Conclusion

           The BCG artifact has an intrinsic inter- and intra-subject
           variability that make the per...
How we approach the problem of
           cerebral localization of brain functions
                                       ...
The methodologies of analysis of ERPs and EEG
           are intrinsically different




    s          s          s      ...
The proposed method is adapted to ERPs

        Step 1: Identification of sources         Step 2: Selection of artifact so...
Case study
           (Assecondi et al., submitted to Clinical Neurophysiology)


           • Healthy volunteers
        ...
Three different types of stimuli were used

               Detection                    GoNogo                 Motor
     ...
In most cases both methods are able to recover
           ERP time series
                                     Detection t...
BSS-CCA seems more effective to recover small
           amplitude low frequency components

                             ...
How we approach the problem of
           cerebral localization of brain functions
                                       ...
Do the very different environments in which the data are
           recorded have an effect on the physiological process u...
To disentangle effects of factors affecting EEG-fMRI
           data, different situations must be compared


            ...
Case study
           (Assecondi et al., submitted to Clinical Neurophysiology)


           • Healthy volunteers
        ...
We found differences between
           0T, 3T and cleaned data
           •   Amplitude decrease in 3T
           •   Lat...
Reaction time: rt@3T-rt@0T
                                                                                       ***
    ...
Conclusion

           The quality of average ERP is less sensitive to the method
           used to remove the BCG. Howev...
How we approach the problem of
           cerebral localization of brain functions
                                       ...
Overall considerations and future prospects

           • The localization of brain functions can be improved by taking in...
Automated Subject-Specific Peak Identification
 and Ballistocardiographic Artifact Correction
                 in EEG-fMRI...
Related publications

• S. Assecondi, et al. Effect of the static magnetic field of the MR-
  scanner on ERPs: evaluation ...
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  1. 1. Automated Subject-Specific Peak Identification and Ballistocardiographic Artifact Correction in EEG-fMRI Sara Assecondi Dep. Electronics and Information Systems MEDISIP, Ghent University Promotors: Prof. Dr. Ir. S. Staelens, Prof. Dr. P. Boon
  2. 2. The secret dream of a neuroscientist is to map the human brain: WHERE and WHEN personality sensory emotions problem solving reasoning hearing language speech vision bla…. bla…. bla…. Introduction: general background 2
  3. 3. Brain mapping has useful applications Pathologies • Dyslexia • Epilepsy (5% school aged children) (0.5-1 % of the population) EL DYS XIA Cognition • mind, reasoning, … • perception, … • intelligence, learning… Introduction: general background 3
  4. 4. Nowadays we have reliable means to localize brain functions EEG exam fMRI exam Take an image of the brain- fMRI Introduction: general background 4
  5. 5. What an ElectroEncephaloGram (EEG) is 100 billion (100000000000) Neurons communicate by means of electrical impulses: the brain is characterized by an electrical activity that can be measured in μV Signal amplitude (μV) Time (ms) Introduction: general background 5
  6. 6. EEG exam EEG electrode Signal amplitude (μV) Time (ms) Introduction: general background 6
  7. 7. EEG exam: Event Related Potentials (ERP) Signal amplitude μV ERP (μV) STIMULUS - electric, - auditory - visual Time ms (ms) - cognitive... Introduction: general background 7
  8. 8. Information in EEG and ERP The latency of peaks , i.e. the time interval between the stimulus and the occurrence of a peak, gives temporal information about the sequence of events in the brain μV perception decoding comprehension μV . . . ms stimulus ms stimulus latency Each peak is related to a specific stage Scalp of the information process, through its map latency Introduction: general background 8
  9. 9. Basics of Magnetic Resonance Imaging (MRI) Up to 70 % of body weight is made up by water 70% O N H H H 1H nucleus ≈ S Water has a spin molecule and a magnetic moment By making use of the magnetic properties in brain tissues, an image of the brain can be reconstructed Introduction: general background 9
  10. 10. MRI exam MR-scanner strong magnet Sagittal view Radio-frequency waves and time-varying magnetic fields Axial view Introduction: general background 10
  11. 11. MRI exam: MR-scanner functional MRI Activity: on on on off off off off time Activity: • Endogenous (epileptic spikes) • Exogenous (external stimuli) Introduction: general background 11
  12. 12. Do we have everything we need? personality We have the means: sensory emotions • EEG μV problem solving reasoning hearing language ms speech vision • fMRI Two new important concepts: • Temporal resolution • Spatial resolution Introduction: general background 12
  13. 13. Temporal resolution The smaller the interval the higher the temporal resolution μV μV μV ms ms ms EEG-ERP (ms) fMRI (s) μV ms Introduction: general background 13
  14. 14. Spatial resolution The finer the grid the higher the spatial resolution EEG-ERP (cm) fMRI (mm) Scalp map Introduction: general background 14
  15. 15. EEG-fMRI achieves high temporal and spatial resolution Invasive 0 Brain PET -1 EEG+ERP Map -2 fMRI NIRS Log size (m) -3 Column Layer -4 Adapted from Cohen and Bookheimer, 1994 Neuron -5 Non-invasive -3 -2 -1 0 1 2 3 4 5 Log time (s) Take the advantage of both EEG and fMRI to have, at the same time, high temporal and high spatial resolution Introduction: general background 15
  16. 16. What do we need for EEG-fMRI? • MR-compatible EEG equipment Amplifier syncbox Power pack Galvanic isolation • MR scanner Introduction: general background 16
  17. 17. EEG-fMRI exam Scanner room Control room EEG electrode EEG wires PC amplifier Activity: on on on off off off off Adapted from Bénar, PhD thesis Introduction: general background 17
  18. 18. Some examples 18
  19. 19. How we approach the problem of cerebral localization of brain functions Integration of EEG and fMRI Time domain Time and spatial domain Improving the temporal Data quality of simultaneous localization of brain functions EEG-fMRI recordings Quantitative and automated identification of ERP peaks Data quality of simultaneous ERP-fMRI recordings Data interpretation Effect of different recording environments on the process under investigation Overview 19
  20. 20. How we approach the problem of cerebral localization of brain functions Integration of EEG and fMRI Time domain Time and spatial domain Improving the temporal Data quality of simultaneous localization of brain functions EEG-fMRI recordings Quantitative and automated identification of ERP peaks Data quality of simultaneous ERP-fMRI recordings Data interpretation Effect of different recording environments on the process under investigation Overview 20
  21. 21. The quantification of amplitudes and latencies in ERPs may be challenging PRE-LEXICAL LEXICAL POST-LEXICAL N3 N4 N0 N1 N2 P0 P1 P4 P600 P2b P2a 0ms 160ms 420ms 800ms • Challenges • Information to retrieve – Number of peaks – Latency of each peak – Labelling – Amplitude of each peak – Inter-subject variability – Label of each peak Time domain: Automatic identification of ERP peaks 21
  22. 22. Features of peak quantification approaches  Reliability  Reproducibility, over subjects and over time  Objectivity Gold standard: expert clinician Automated methods: Peak-picking, • Time consuming Dynamic Time Warping • subjective • Fast • Objective N1 N1 μV  μV   P2  P2 stimulus ms stimulus ms Time domain: Automatic identification of ERP peaks 22
  23. 23. Method 1: Peak-picking is a search for extrema in predefined time intervals N3 N4 N0 N1 N2 P0 P1 P4 P600 P2b P2a Predifined time interval Example: Looking for the N3 peak Drawbacks • Define the time interval • Highly dependent on the • N3 is a negative peak: defined intervals search for a minimum • Does not take into account • Assign the N3 label the inter-subject variability to the minimum found Time domain: Automatic identification of ERP peaks 23
  24. 24. Method 2: Dynamic time warping (DTW) is a nonlinear mapping of two signals The ERP is compared with a reference signal containing the peaks of interest Linear alignment Dynamic Time Warping reference reference subject subject Time (ms) Time (ms)     Drawback A peak is always found: it may not be a peak Time domain: Automatic identification of ERP peaks 24
  25. 25. We proposed a method (ppDTW) that integrates peack-picking and Dynamic Time Warping Compared by means of DTW REFERENCE SUBJECT Sequence of candidate peaks Peak-picking in a time interval centered at the candidate peak Measured latencies and amplitudes Time domain: Automatic identification of ERP peaks 25
  26. 26. The reference signal must contain all the peaks of interest We computed the reference by interpolating mean amplitudes and latencies derived from a normal population Peak variability derived Reference from a normal population Time domain: Automatic identification of ERP peaks 26
  27. 27. Case study (Assecondi et al., Clinical Neurophysiology 2009) • Normal children and children diagnosed with developmental dyslexia • Reading related ERP • Latencies automatically determined: – Peak picking – ppDTW • Validation – Comparison with the visual scoring of an expert clinician Time domain: Automatic identification of ERP peaks 27
  28. 28. Performance of the methods on normal and dyslexic subjects normal dyslexic N0 N2 N3 N4 N1N2 N3 N4 P1 P2b P4 P2b P4 P600 ppdtw ppdtw visual scoring visual scoring peak picking peak picking Time domain: Automatic identification of ERP peaks 28
  29. 29. We evaluate the methods by comparing the automated scoring with the visual scoring C = correct identifications S = substitutions C S D I D = deletions expert     I = insertions method     N1 precision recall F-score Latency N1 1 C C 1 1 C S I C S D 2P 2R Peak-picking 93% 80% 85% PP-DTW 93% 86% 89% Time domain: Automatic identification of ERP peaks 29
  30. 30. Conclusion We developed an automated peak detection method that takes into account the inter-subject variability and a-priori knowledge about the ERP (in the reference) A-priori knowledge may be derived from literature, hypothesis about the ERP experiment, expertise of the clinician The method is valuable with different ERPs, when huge databases have to be measured or when the same subject must be examined during a therapy or rehabilitation Time domain: Automatic identification of ERP peaks 30
  31. 31. How we approach the problem of cerebral localization of brain functions Integration of EEG and fMRI Time domain Time and spatial domain Improving the temporal Data quality of simultaneous localization of brain functions EEG-fMRI recordings Quantitative and automated identification of ERP peaks Data quality of simultaneous ERP-fMRI recordings Data interpretation Effect of different recording environments on the process under investigation Overview 31
  32. 32. EEG-fMRI achieves high temporal and spatial resolution Invasive 0 Brain PET -1 EEG+ERP Map -2 fMRI NIRS Log size (m) -3 Column Layer -4 Adapted from Cohen and Bookheimer, 1994 Neuron -5 Non-invasive -3 -2 -1 0 1 2 3 4 5 Log time (s) EEG - fMRI implies the interaction of different physical and physiological systems ARTIFACTS (human being, EEG system, MR scanner) Time and spatial domain: Data quality of simultaneous EEG-fMRI 32
  33. 33. An artifact is a contamination of the data of interest Suppose you want to listen to the radio while a bell is ringing din don Source of noise o Data of interest l i d e ? i a i s s n i n d s i i Time and spatial domain: Data quality of simultaneous EEG-fMRI 33
  34. 34. Two main artifacts affect EEG-fMRI recordings • Image acquisition artifact caused by the RF-waves and time-varying gradients ~0.5 s Very deterministic BCG-peak • Ballistocardiographic artifact is a blood related effect due to the high static magnetic field R-peak Only QUASI-deterministic ~1 s Time and spatial domain: Data quality of simultaneous EEG-fMRI 34
  35. 35. The BallistoCardioGraphic artifact (BCGa) R R R R R R R R 100 µV 10 seconds • It depends on the proximity of the EEG electrodes to blood vessels • It is synchronous to the heart beat and spread throughout the heart beat and all over the scalp Time and spatial domain: Data quality of simultaneous EEG-fMRI 35
  36. 36. Distribution of scalp arteries Adapted from Gray, 1918 Time and spatial domain: Data quality of simultaneous EEG-fMRI 36
  37. 37. The BCG artifact can be removed if an additive model is assumed Noise and Recorded other non-MR signal = EEG + BCGa + related artifacts Estimate of the BCGa that depends on the algorithm used subtraction BCGa model Time and spatial domain: Data quality of simultaneous EEG-fMRI 37
  38. 38. Intra-subject variability of the BCGa Heart beat -0.2 0 0.2 0.4 0.6 seconds Time and spatial domain: Data quality of simultaneous EEG-fMRI 38
  39. 39. Inter-subject variability of the BCGa S1 S2 S3 S4 S5 S6 channels seconds Time and spatial domain: Data quality of simultaneous EEG-fMRI 39
  40. 40. The BCG artifact removal algorithms must take the inter- and intra-subject variability into account Group 1: methods based on Average Artifact Subtraction  Moving Average  Weighted Average  Selective Averaging based on clustering Group 2: methods based on Blind Source Separation  Optimal Basis Set (OBS)  Independent Component Analysis (ICA)  Canonical Correlation Analysis (CCA) Time and spatial domain: Data quality of simultaneous EEG-fMRI 40
  41. 41. Blind Source Separation identifies the sources generating the recorded signal s1 Blind Cerebral Source s2 sources Separation s3 (BSS) Non-cerebral x2 x3 X s4 sources x1 x4 constraints s1 s2 s3 s4 BSS as an artifact removal technique is twofold: • Step 1: Identification of sources • Step 2: Selection of sources (brain signal or artifact) Time and spatial domain: Data quality of simultaneous EEG-fMRI 41
  42. 42. We proposed a BSS method that uses Canonical Correlation Analysis to identify the sources Step 1: Identification of sources Step 2: Selection of artifact sources EEG epoch 1 EEG epoch 2 Criteria have to be met simultaneously: - correlation of sources common to two consecutive EEG epochs - Sources must not be sinusoidal EEG rhythms Sources or Canonical BSS-CCA variates time . . . . . . Time and spatial domain: Data quality of simultaneous EEG-fMRI 42
  43. 43. Case study (Assecondi et al., Physics in Medicine and Biology 2009) • Patients affected by epilepsy • Recording of 20 minutes of simultaneous EEG-fMRI • Artifact removal – AAS – CCA • Validation – Frequency content at the harmonics of the ECG – Global Field Power – Signal Envelope Time and spatial domain: Data quality of simultaneous EEG-fMRI 43
  44. 44. Comparison of cleaned and raw EEG BSS-CCA AAS RAW Time and spatial domain: Data quality of simultaneous EEG-fMRI 44
  45. 45. Comparison of cleaned and raw EEG BSS-CCA AAS RAW Time and spatial domain: Data quality of simultaneous EEG-fMRI 45
  46. 46. Conclusion The BCG artifact has an intrinsic inter- and intra-subject variability that make the performance of artifact removal algorithms subject-dependent We proposed a method to remove the BCG artifact that deals with the intra- and inter-subject variability The proposed method is an added value especially in those cases where the AAS fails, because of the excessive intra- subject variability of the artifact Time and spatial domain: Data quality of simultaneous EEG-fMRI 46
  47. 47. How we approach the problem of cerebral localization of brain functions Integration of EEG and fMRI Time domain Time and spatial domain Improving the temporal Data quality of simultaneous localization of brain functions EEG-fMRI recordings Quantitative and automated identification of ERP peaks Data quality of simultaneous ERP-fMRI recordings Data interpretation Effect of different recording environments on the process under investigation Overview 47
  48. 48. The methodologies of analysis of ERPs and EEG are intrinsically different s s s s s • Smaller amplitude • Involve additional averaging • Different signal-to-noise ratio The method to remove the BCG artifact needs modifications to select the non-cerebral sources Time and spatial domain: Data quality of simultaneous ERP-fMRI 48
  49. 49. The proposed method is adapted to ERPs Step 1: Identification of sources Step 2: Selection of artifact sources Average BCG EEG epoch Criteria have to be met simultaneously: - correlation of sources extracted from the average BCG and the EEG epoch - Sources that maximally contribute at the same time to the artifact and to the EEG Sources or Canonical BSS-CCA Sources important for the EEG but not variates for the artifact are not removed . . . . . . Time and spatial domain: Data quality of simultaneous ERP-fMRI 49
  50. 50. Case study (Assecondi et al., submitted to Clinical Neurophysiology) • Healthy volunteers • Three tasks: – Visual: Visual detection task (5 subjects) – Cognitive: Go-nogo task (5 subjects) – Motor: Motor task (7 subjects) • In two situations: – Outside the MR-scanner room (0T) – Inside the MR-scanner, without scanning (3T) • BCG artifact removal – AAS (Average Artifact Subtraction) – CCA (Canonical Correlation Analysis) Time and spatial domain: Data quality of simultaneous ERP-fMRI 50
  51. 51. Three different types of stimuli were used Detection GoNogo Motor Left visual field No Go Left keypress Central visual field Go Withhold Right visual field Right keypress Time and spatial domain: Data quality of simultaneous ERP-fMRI 51
  52. 52. In most cases both methods are able to recover ERP time series Detection task 0T 3T Time and spatial domain: Data quality of simultaneous ERP-fMRI 52
  53. 53. BSS-CCA seems more effective to recover small amplitude low frequency components Motor task AAS BSS-CCA 0T 3T Time and spatial domain: Data quality of simultaneous ERP-fMRI 53
  54. 54. How we approach the problem of cerebral localization of brain functions Integration of EEG and fMRI Time domain Time and spatial domain Improving the temporal Data quality of simultaneous localization of brain functions EEG-fMRI recordings Quantitative and automated identification of ERP peaks Data quality of simultaneous ERP-fMRI recordings Data interpretation Effect of different recording environments on the process under investigation Overview 54
  55. 55. Do the very different environments in which the data are recorded have an effect on the physiological process under investigation? ERP lab MR scanner position sitting laying Light dimmed dimmed Noise no yes Screen orientation In front mirrors Magnetic fields no yes Time and spatial domain: Effect of different environments 55
  56. 56. To disentangle effects of factors affecting EEG-fMRI data, different situations must be compared Effect of the static field +position Static 0T field No MR-related artifacts BCG artifact Time and spatial domain: Effect of different environments 56
  57. 57. Case study (Assecondi et al., submitted to Clinical Neurophysiology) • Healthy volunteers • Three tasks: – Visual: Visual detection task (5 subjects) – Cognitive: Go-nogo task (5 subjects) – Motor: Motor task (7 subjects) • In two situations: – Outside the MR-scanner room (0T) – Inside the MR-scanner, without scanning (3T) • BCG artifact removal – AAS (Average Artifact Subtraction) – CCA (Canonical Correlation Analysis) Time and spatial domain: Effect of different environments 57
  58. 58. We found differences between 0T, 3T and cleaned data • Amplitude decrease in 3T • Latency increase in 3T • Strong contamination of the data due to the artifact • Difference in the scalp distribution 0T 3T After BCG removal goP3 GoNogo task Ipsi N1 Detection task Time and spatial domain: Effect of different environments 58
  59. 59. Reaction time: rt@3T-rt@0T *** *** *** 50 *** *** *** *** ** * * ** * 0 - - ms - subject - ** *** -50 - p>0.05 * p<0.05 *** *** ** p<0.01 *** p<0.001 -100 Leuven -150 *** Detection Go-Nogo Motor Time and spatial domain: Effect of different environments 59
  60. 60. Conclusion The quality of average ERP is less sensitive to the method used to remove the BCG. However, BSS-CCA seems to be more effective with low frequency low amplitude components and when less trials are available Differences are found between different environment. More subjects are needed to obtain robust results Different situations must also be taken into account (dummy scanner, actual fMRI acquisition) Time and spatial domain: Effect of different environments 60
  61. 61. How we approach the problem of cerebral localization of brain functions Integration of EEG and fMRI Time domain Time and spatial domain Improving the temporal Data quality of simultaneous localization of brain functions EEG-fMRI recordings Quantitative and automated identification of ERP peaks Data quality of simultaneous ERP-fMRI recordings Data interpretation Effect of different recording environments on the process under investigation Overview 61
  62. 62. Overall considerations and future prospects • The localization of brain functions can be improved by taking into account a-priori knowledge of the process and the inter- and intra- subject variability • New multimodal approaches, e.g. EEG-fMRI, offer a deeper insight into how the brain works (great help by the availability of commercial MR-compatible EEG systems) Fundamental research Development of methods • to understand the relation between • to improve the integration of EEG and fMRI the two modalities and to • to comprehend the effect of the actually benefit by the different very different environments on EEG information extracted by data different modalities Overall considerations and future prospects 62
  63. 63. Automated Subject-Specific Peak Identification and Ballistocardiographic Artifact Correction in EEG-fMRI Sara Assecondi Dep. Electronics and Information Systems MEDISIP, Ghent University Promotors: Prof. Dr. Ir. S. Staelens, Prof. Dr. P. Boon Thank you!
  64. 64. Related publications • S. Assecondi, et al. Effect of the static magnetic field of the MR- scanner on ERPs: evaluation of visual, cognitive and motor potentials Submitted. • S. Assecondi, et al. Automated identification of ERP peaks through Dynamic Time Warping: an application to developmental dyslexia Clinical Neurophysiology, DOI: 10.1016/j.clinph.2009.06.023. • S. Assecondi, et al. Removal of the ballistocardiographic artifact from EEG-fMRI data: a canonical correlation approach Physics in Medicine and Biology. Vol. 54 (2). 2009. pp. 1673-1689 64

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