Chapter 22 Surface Laplacian - jallen.faculty.arizona.edu · Chapter 22 John JB Allen. ... Exercise...
Transcript of Chapter 22 Surface Laplacian - jallen.faculty.arizona.edu · Chapter 22 John JB Allen. ... Exercise...
Surface Laplacian Transform
Is a Spatial FilterIn fact, is the second spatial derivative of the potentials (change in acceleration over space)
Increases topographical specificityFilters out spatially broad features (shared among electrodes)
Thus a high-pass spatial filter (attenuating low spatial-frequency signals)
Caveats:Only for EEG, not MEG dataBest for 64+ electrodes
Surface Laplacian Transform
Spatially-broad features are likely:Volume conducted from distal sourcesDistributed but highly coherent sources
Estimates potentials at the duraEspecially important for connectivity analyses
Surface Laplacian Transform
AKA CSD or SCDCurrent Source DensityCurrent Scalp DensitySurface Current Density
BUT … not brain sourcesSources and sinks of electrical activity at the level of the skullPreferred term: Surface Laplacian
Identifies the mathematical transform usedOther methods available (e.g., Hjorth)
Surface Laplacian TransformAdvantages
Improves Topographical localizationMinimizes volume-conduction effects (important for connectivity analyses)A reference-independent approach!Requires few parameters or assumptions
No head model required (and assumptions about conductivity of layers)No assumptions about source locations
Surface Laplacian TransformCaveats
More sensitive to radial than tangential dipoles.Thus sources in sulci will be minimized
DisadvantageSpatially-broad activities attenuated or eliminated (e.g., P3b)
ImplicationsResults stem from relatively local and superficial sourcesDo not use surface Laplacian if you expect deep sourcesDo not use if you expect widely-distributed coherent sources
Surface Laplacian TransformImplementation
Apply SL to time-domain signalsPerform frequency-domain transformations subsequentlyFor ERPs, applying SL to single trials equivalent to applying it averageMike sayz… Must apply to all conditions, all subjects
Units are now Units influenced by smoothing parametersBut not relevant if using baseline normalization in time-frequency analyses (dB, percent, Z)
Surface Laplacian TransformComputation
Hjorth: subtract from each electrode the average of neighbors’ activity
SimpleComputationally fastBUT…
Not elegantVolume conduction does not affect all neighbors equally
Instead, compute 3D second-spatial derivative
Surface Laplacian Transform3D second-spatial derivative (spherical derivative)Several methods:
Deblurring methods with realistic head modelsSpherical Spline interpolations that make no assumptions about conductivity
Spherical spline method of Perrin et al. (1987, 1989) widely used
Surface Laplacian TransformSpherical spline method requires computation of G and H (weighting) matrices
Where:i, j are electrodesm is constant positive integer for smoothness (2-6; higher number
filters our more low spatial frequencies)P is Legendre polynomial for spherical coordinate distancesn is order term for P (Figure 22.2)
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More is better?
No, more is sometimes just more..
“With 64 electrodes, order values above 10 mean that the spatial frequency precision of the Laplacian exceeds the spatial resolution of the EEG cap…”
“…as the order becomes large, only very high spatial frequencies can pass through the filter. This may impede cross-subject averaging and comparisons.”
Surface Laplacian Transform
Where:i, j are electrodesm is constant positive integer for smoothness (2-6; higher number
filters our more low spatial frequencies)P is Legendre polynomial for spherical coordinate distancesn is order term for P (Figure 22.2)cosdist is cosine distance among all pairs of electrodes assuming unit
sphere:
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Surface Laplacian TransformNow, armed with G & H, compute the Laplacian!
Wherelapi is Laplacian for electrode i and one time point, j is each other
electrodeHij is H Matrix corresponding to electrodes i and jC is data!!!!
λ is smoothing parameter added to diagonal elements of G matrix (suggested value of 10-5)
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λ
Surface Laplacian TransformCan use functions or toolboxes
laplacian_perrinX.mCSD Toolbox Hjorth
Jürgen Kayser
Surface Laplacian TransformConnectivity – volume-conducted activity will increase connectivity across wide distances
Surface Laplacian TransformConnectivity – volume-conducted activity will increase connectivity across wide distances
Surface Laplacian TransformTool for cleaning noise?
Not only a low-pass spatial filter – it is a band-pass spatial filter’
Removes very low and very high frequenciesBut need many electrodes to see impact on high spatial frequencies
Surface Laplacian TransformTool for cleaning noise?
Not only a low-pass spatial filter – it is a band-pass spatial filter’
Removes very low and very high frequenciesBut need many electrodes to see impact on high spatial frequencies
BUT … it is no substitute for good clean data!Besides … who has 256 channels?
Good Practices in ReportingState the purpose of applying the LaplacianTransform
Increase topographical localizationFacilitate electrode-level connectivity analysesAttenuate volume-conducted features that might overshadow local effects of primary interest
If examined raw and Laplacian, state how results changedBe clear about which algorithm was used
And specify any parameters that were changed from default values (and WHY!)