Surface Laplacian. Chapter 22 John JB Allen

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1 Surface Laplacian Chapter 22 John JB Allen

2 Is a Spatial Filter In fact, is the second spatial derivative of the potentials (change in acceleration over space) Increases topographical specificity Filters out spatially broad features (shared among electrodes) Thus a high-pass spatial filter (attenuating low spatial-frequency signals) Caveats: Only for EEG, not MEG data Best for 64+ electrodes

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4 Spatially-broad features are likely: Volume conducted from distal sources Distributed but highly coherent sources Estimates potentials at the dura Especially important for connectivity analyses

5 AKA CSD or SCD Current Source Density Current Scalp Density Surface Current Density BUT not brain sources Sources and sinks of electrical activity at the level of the skull Preferred term: Surface Laplacian Identifies the mathematical transform used Other methods available (e.g., Hjorth)

6 Advantages Improves Topographical localization Minimizes 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

7 Caveats More sensitive to radial than tangential dipoles. Thus sources in sulci will be minimized Disadvantage Spatially-broad activities attenuated or eliminated (e.g., P3b) Implications Results stem from relatively local and superficial sources Do not use surface Laplacian if you expect deep sources Do not use if you expect widely-distributed coherent sources

8 Implementation Apply SL to time-domain signals Perform frequency-domain transformations subsequently For ERPs, applying SL to single trials equivalent to applying it average Mike sayz Must apply to all conditions, all subjects Units are now Units influenced by smoothing parameters But not relevant if using baseline normalization in time-frequency analyses (db, percent, Z)

9 Computation Hjorth: subtract from each electrode the average of neighbors activity Simple Computationally fast BUT Not elegant Volume conduction does not affect all neighbors equally Instead, compute 3D second-spatial derivative

10 3D second-spatial derivative Easy to visualize in 2D form: Exercise 22.1

11 3D second-spatial derivative (spherical derivative) Several methods: Deblurring methods with realistic head models Spherical Spline interpolations that make no assumptions about conductivity Spherical spline method of Perrin et al. (1987, 1989) widely used

12 Spherical spline method requires computation of G and H (weighting) matrices Where: i, j are electrodes m is constant positive integer for smoothness (2-6; higher number filters our more low spatial frequencies) P is Legendre polynomial for spherical coordinate distances n is order term for P (Figure 22.2)

13 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.

14 Where: i, j are electrodes m is constant positive integer for smoothness (2-6; higher number filters our more low spatial frequencies) P is Legendre polynomial for spherical coordinate distances n is order term for P (Figure 22.2) cosdist is cosine distance among all pairs of electrodes assuming unit sphere: 1 2

15 Figure 22.3 (and helpful auxiliary figure)

16 Now, armed with G & H, compute the Laplacian! Where lap i is Laplacian for electrode i and one time point, j is each other electrode H ij is H Matrix corresponding to electrodes i and j C is data!!!! λ λ is smoothing parameter added to diagonal elements of G matrix (suggested value of 10-5 )

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18 Can use functions or toolboxes laplacian_perrinx.m

19 Can use functions or toolboxes laplacian_perrinx.m CSD Toolbox Hjorth Jürgen Kayser

20 Simulated data (Figure 22.4)

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22 Nunez vs Perrin! Spatial correlation =.9798

23 Connectivity volume-conducted activity will increase connectivity across wide distances

24 Connectivity volume-conducted activity will increase connectivity across wide distances

25 Tool for cleaning noise? Not only a low-pass spatial filter it is a bandpass spatial filter Removes very low and very high frequencies But need many electrodes to see impact on high spatial frequencies

26 Tool for cleaning noise? Not only a low-pass spatial filter it is a bandpass spatial filter Removes very low and very high frequencies But need many electrodes to see impact on high spatial frequencies BUT it is no substitute for good clean data! Besides who has 256 channels?

27 Good Practices in Reporting State the purpose of applying the Laplacian Transform

28 AR Reference Effects CSD Resting Eyes Closed Alpha Power LM Cz

29 Good Practices in Reporting State the purpose of applying the Laplacian Transform Increase topographical localization Facilitate electrode-level connectivity analyses Attenuate volume-conducted features that might overshadow local effects of primary interest If examined raw and Laplacian, state how results changed Be clear about which algorithm was used And specify any parameters that were changed from default values (and WHY!)