Beamformer Source Analysis in MEG

Transcription

1 Beamformer Source Analysis in MEG Douglas Cheyne, PhD Program in Neurosciences and Mental Health Hospital for Sick Children Research Institute & Department of Medical Imaging University of Toronto CCD Macquarie University, March, 2017

2 Source Imaging using MEG Inverse Problem (Helmholtz, 1853) Sensors To determine the underlying current sources in head from the measured external potentials or fields Sources Sources Solutions are non-unique May be highly underdetermined Solution: Construct forward models of the sources and fit models to data

3 Inverse solutions in MEG Main approaches to source modeling in MEG: Dipole fitting (parametric) methods overdetermined solution, well understood need to know number of independent sources difficult to combine results across subjects Linear inverse (minimum-norm estimates) no need to specify number of sources can model distributed sources model based - requires pseudoinverse of large matrices (regularization) requires artifact-free data Spatial filtering (beamforming) adaptive ( data-driven ) stable solutions suppresses artifacts in data automatically performance degrades for highly synchronous sources

4 Spatial filtering methods A spatial filter is the weighted output of the MEG sensor array that reflects activity at a specific brain location over time Signal Space Projection (SSP) W(r) source virtual sensor d(t) = W T M(t) source strength time W(r) = L(r) = forward model (lead field) of source

5 Spatial filtering methods A spatial filter is the weighted output of the MEG sensor array that reflects activity at a specific brain location over time Signal Space Projection (SSP) noise sources source W(r) virtual sensor d(t) = W T M(t) source strength time W(r) = L(r) = forward model (lead field) of source

6 Spatial filtering methods A spatial filter is the weighted output of the MEG sensor array that reflects activity at a specific brain location over time Signal Space Projection (SSP) noise sources source W(r) virtual sensor d(t) = W T M(t) source strength time W(r) = L(r) = forward model (lead field) of source Adaptive Beamformer W(r) noise sources source source strength time W(r) = L (r) C m -1 / L (r) C m -1 L (r)

7 Spatial filtering methods Source images can be produced by generating beamformer weights at each voxel throughout brain volume at arbitrary resolution and plotting source amplitude or power Vector beamformers orthogonal current sources at each voxel* Scalar beamformers compute optimal current direction at each voxel *for EEG # directions = 3, for MEG spherical model, # directions = 2

8 Introduction of Beamforming Methods in EEG/MEG Linearly Constrained Minimum-Variance (LCMV) beamformer (Van Veen et al., 1997) first application of beamformer method to EEG/MEG inverse problem, EEG only Synthetic Aperture Magnetometry (SAM) (Robinson & Vrba, 1999) introduction of scalar beamformer and differential imaging Dynamic Imaging of Coherent Sources (DICS) (Gross et al., 2001) frequency domain beamformer, coherence analysis Eigenspace / spatiotemporal beamformer (Sekihara et al., 2001, 2002; Dalal et al., 2004) eigenspace beamformer (averaged data), NutMEG toolbox Event-related SAM (ersam) (Cheyne et al., 2004, 2006) adapted SAM algorithm to image evoked responses SAMerf (Robinson, 2004) SAM algorithm modified for short time windows and averaging ( not same as ersam ) Event-related beamformer (ERB) (Cheyne et al., 2008) ersam with optimized orientation calculation 5-D beamformer (Dalal et al., 2010) computes beamformer over separate frequency bands and time windows

9 Differential imaging using the SAM beamformer T trials Single trial data Compute beamformer Compute Source Power M channels M x M Active Covariance matrix (C A ) M x M Baseline Covariance matrix (C B ) compute beamformer weights W(r) = C -1 B/B T C -1 B Pseudo-T = W(r) T C A W(r) W(r) T C B W(r) baseline active N samples Forward solution (B) for source r source 3.0 pseudo-t 1.0 Narrow-band Filter (e.g., Hz) and segment into active and control windows repeat for all voxels SAM = Synthetic Aperture Magnetometry (Robinson & Vrba, 1999) Alternatively, compute pseudo-f = F - 1 if F > 1. = 1-1/F if F < 1.0 where F = W(r) T C A W(r) / W(r) T C B W(r)

10 SAM versus Event-related Beamformer

11 Event-related (spatiotemporal) beamformer T trials Single trial data Compute beamformer source activity for voxel j S(j,t) = W(j) x m(t) M channels M x M Covariance matrix (C) compute beamformer weights W(j) = C -1 B/B T C -1 B N samples Forward solution (B) for source j source t = 20 ms Bandpass filter (e.g., 1 50 Hz) Take absolute value and repeat for all voxels Map power at latency of evoked response 3.0 pseudo-z 1.0

12 Beamformer localization of premovement motor field (MF) Time course at peak (virtual sensor) DC-15 Hz button press Self-paced right index finger movement Recording time 10 min ( movements) ERB image in MRIViewer (t = -40 ms, threshold = FWHM)

13 Introduction to Beamformers Beamformer Units and Weight Normalization: Beamformer filter can only suppress noise sources that are correlated across sensors Uncorrelated noise (e.g., random system noise) will be amplified by the weights in a non-uniform manner, with increasing distortion with increasing distance from the sensors This gain error must be removed from image data

14 Spatial filtering methods weight normalization virtual sensor at peak (na-m) s(r,t) = w(r) T m(t) Source location Non-normalized (units = na-m) virtual sensor at peak (pseudo-z) Source activity (peak= 20 nam) + Gaussian noise s(r,t) = wn(r) T m(t) Normalized (units = pseudo-z)

15 Spatial filtering methods weight normalization The non-uniform distortion of beamformer images can be removed by normalizing the weight vector for each voxel w(r), to have unit length ( unit-gain or Borgiatti-Kaplan beamformer) wn M ( ( )) 2 ( r) = w(r) wi r i=0 Units of w(r) = A-m / Tesla (output of beamformer is A-m) Units of w n (r) are arbitrary units (output of beamformer in arbitrary units) The neural activity index (Van Veen, 1997) and pseudo-z (Robinson and Vrba, 1999) include an additional scaling of the unit-gain beamformer to units of specified noise n w wn ( ) 2 ( r) = w(r) wi( r)n w M i=0 Output of beamformer is scaled to units of noise variance. Robinson termed this pseudo-z

16 Introduction to Beamformers Interpreting the spatial extent of activity peaks in beamformer images Do bigger blobs mean more (stronger) activation?

17 Effect of SNR on beamformer resolution Simulated bilateral auditory cortex sources X = 0.0 cm Y = 5.5 and -5.5 cm Z = 6.0 cm + Gaussian noise Q= 60 na-m Q= 40 na-m Q= 20 na-m Stronger source (higher SNR) = more focal source in image

18 Introduction to Beamformers Beamformer solutions depend on: 1) Accuracy of forward solution (L) 2) Ability to obtain stable inverse of covariance matrix (C m ) W(r) = L (r) C m -1 / L (r) C m -1 L (r) Depends on: condition number of covariance matrix (ratio of max / min eigenvalues) number of channels (less is better?) bandwidth of data (smaller bandwidth increases covariance error) number of time samples in data (about 30 s recommended) From: Brookes M. et al., (2008) Optimizing experimental design for MEG beamformer imaging. NeuroImage 39:

19 How much data is required? Decrease in FWHM of beamformer peaks / increase in pseudo-z power with increasing amount of data used to compute covariance matrix (from Brookes et al., 2008)

20 Covariance Matrix Regularization: Beamformers - Regularization In cases where data covariance is rank deficient (e.g., PCA or SSS has been applied to the raw data) or ill-conditioned (e.g., too few samples, averaged data) regularization of covariance matrix may be required [ ] 1 L θ L T θ ( C + µσ) 1 L θ W θ = C + µσ # $ % & 1 Diagonal regularization As µ à As µ à 0 W θ = L θ! " L T θ L θ # $ 1 W θ = C 1 L θ " # L T θ C 1 L θ $ % 1 (minimum noise sensitivity) (maximum spatial resolution) L q = forward solution for target location C = data covariance matrix µ = regularization parameter S = diagonal matrix of sensor noise Σ = σ 11 σ 22 0 σ σ MM

21 Introduction to Beamformers Do I need to clean my data? Advantages: reduces amount of noise sources beamformer has to suppress may be required if noise sources are large, close to brain sources Disadvantages: noise reduction techniques will reduce rank of covariance matrix requiring regularization (reduces spatial resolution)

22 Beamformer suppression of eye-movement artifacts adult performing self-paced movements (KIT-Macquarie MEG 160) Sensor data (all channels) (0 15 Hz) During fixation During visual scanning Motor cortex activation (t = -75 ms) Motor cortex time-course 40 BJ_rightIndex_voxel_0.0_3.0_9.0_(0.944_ 0.264_0.198) with fixation with eye movement 10 Moment (nam) Scanning Fixating Time (sec)

23 Suppression of ferromagnetic artifacts Motor Field (MF) localization in adult subject with metal retainer Average (frontal sensors) 200 ft ERB source image (2 mm) t =- 40 ms (DC 15 Hz) Right index finger movement L R

24 Limitations of beamforming methods The Source Correlation Problem: Beamformers will fail to detect highly synchronous (zero-phase correlated) sources

25 Spatial filtering methods effects of source correlation Simulation (3 sources) Source power Source power Source activity Source power Source power

26 Spatial filtering methods effects of source correlation Simulation (auditory evoked fields) Source 1 (0, 5.5, 6.0) Source 2 (0, -5.5, 6.0) Gaussian noise (10-20 ft / Hz 1/2 ) 150 trials Beamformer source reconstruction left right Right hemisphere source jittered trial-by-trial by 6 ms Average (all sensors) Trial-by-trial latency jitter of 6 ms reduces effect of correlation

27 Spatial filtering methods effects of source correlation From: Cheyne D., Bostan AC., Gaetz W, Pang EW. (2007) Event-related beamforming: A robust method for presurgical functional mapping using MEG Clinical Neurophysiology, Vol 118 pp

28 (a) Whole-Array Beamforming (b) Half-Array Beamforming pseudo Z pseudo Z pseudo Z (c) Left Hemisphere 4 3 N1m P1m -4 P2m Time (ms) Right Hemisphere Whole Array Half Array Time (ms) From Herdman A. and Cheyne D. A Practical Guide to MEG and Beamforming. In: T. Handy (Ed) Brain Signal Analysis: Advances in Neuroelectric and Neuromagnetic Methods. MIT Press, Massachusetts pp

29 Correcting for correlations in beamformer solutions Coherent Source Region Suppression method (Dalal et al., 2006) identify region where correlated source is know to exist can be done iteratively to image (e.g., left and right hemisphere sources) suppression ROI Image 1 (RH suppression) Image 2 (RH suppression) corrected image = max(image1,image2)

30 Limitations of beamforming methods Source Polarity Problem: Scalar beamformer gives optimal current direction but true polarity of the source is unknown, since beamformer weights derived from source power (covariance) This means source polarity can flip randomly form voxel to voxel Solutions: plot absolute power (LCMV, ERB imaging) flip source waveforms to have uniform polarity across subjects constrain source orientation to cortical surface

31 Adaptive (Minimum-variance) Beamforming Source Polarity Problem: Source waveforms (virtual sensors) in brainwave can be rectified or flipped Alternatively vector (LCMV) beamformer can be used waveforms will be rectified!

32 Some recent publications using BrainWave Mersov A., Jobst C., Cheyne D., De Nil, L. (2016) Sensorimotor oscillations prior to speech onset reflect altered motor networks in adults who stutter. Frontiers in Human Neuroscience 10: 443. Pu Y., Cornwell BR., Cheyne D., Johnson BW. (2016) The functional role of human right hippocampal theta rhythm in environmental encoding during spatial navigation. Human Brain Mapping 38: Isabella S., Ferrari P., Jobst, C., Cheyne JA., Cheyne D. (2015) Complementary roles of cortical oscillations in automatic and controlled processing during a rapid serial task. NeuroImage 118:

33 The BrainWave Toolbox What it does: computes event-related (evoked) and SAM beamformer source images computes source activity time courses ( virtual sensors ) average or time-frequency plots volumetric source images in MEG or MNI space (latter requires SPM8 or SPM12 installed) warping of template MRI to head shapes (if MRI not available, requires SPM) surface based images using Freesurfer or CIVET cortical meshes group analysis with contrasts and permutation test group averaging of source activity waveforms or their time-frequency transformations built-in 4D viewers for volumes or surfaces

34 The BrainWave Toolbox Software requirements requires MATLAB w/ standard toolboxes runs on Linux, Mac OS X or Windows platforms optimized using multi-threaded compiled C++ mex functions (more cores = faster ) supports CTF, Yokogawa-KIT, Elekta-Neuromag MEG data import and co-register DICOM MRI fit spherical models to MRI surfaces (requires FSL, Mac and Linux versions)

35 Sample Datasets: CTF_adult: self-paced motor responses (left and right) in adult subject 151-channel CTF MEG system MRI and co-registered Freesurfer and CIVET surfaces KIT_child: motor responses (left and right) in preschooler 112 channel Yokogawa-KIT Child MEG No MRI CTF_group: 8 subjects performing motor task (left and right) 151-channel CTF MEG system pre-calculated group images (volume and surface) Elekta_SEF: right median-nerve stimulation in adult subject 306-channel VectorView MEG system no-sss preprocessing

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37 BrainWave: Data Organization and Preprocessing Steps 1. Import and epoch MEG data epoch continuous datasets into one dataset per condition, should be same length (e.g., for comparing time courses) each dataset name must begin with <subjectid> code followed by underscore

38 Suggested Reading Beamforming Methods: Barnes, G.R., Hillebrand, A., Statistical flattening of beamformer images. Hum. Brain Mapp. 18, Brookes M., Vrba J., Robinson S., Stevenson C., Peters A., Barnes A., Morris P. (2008) Optimising experimental design for MEG beamformer imaging. NeuroImage 39: Cheyne D., Bakhtazad L. and Gaetz W. (2006) Spatiotemporal mapping of cortical activity accompanying voluntary movements using an event-related beamforming approach Human Brain Mapping 27: Cheyne D., Bostan AC., Gaetz W, Pang EW. (2007) Event-related beamforming: A robust method for presurgical functional mapping using MEG Clinical Neurophysiology, Vol 118 pp Gross, J., Kujala, J., Hamalainen, M., Timmermann, L., Schnitzler, A., Salmelin, R., Dynamic imaging of coherent sources: studying neural interactions in the human brain. Proc. Natl. Acad. Sci. U. S. A. 98 (2), Herdman A., Cheyne D. (2009) A practical guide for MEG and Beamforming. In. Handy T. Brain Signal Analysis MIT Press pp Hillebrand, A., Singh, K.D., Holliday, I.E., Furlong, P.L., Barnes, G.R., A new approach to neuroimaging with magnetoencephalography. Hum. Brain Mapp. 25, Hillebrand, A., Barnes, G.R., The use of anatomical constraints with MEG beamformers. NeuroImage 20, Robinson, S. and Vrba J. (1999). Functional neuroimaging by synthetic aperture magnetometry. Nenonen J, Ilmoniemi RJ, Katila T, editors. Proceedings of Biomag 2000 Conference. p Sekihara, K., Nagarajan, S.S., Poeppel, D., Marantz, A., Miyashita, Y. (2001) Reconstructing spatio-temporal activities of neural sources using an MEG vector beamformer technique. IEEE Trans Biomed Eng 48, Van Veen, B.D., van Drongelen, W., Yuchtman, M., Suzuki, A., (1997) Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 44,