Transcript Document
We show how a parameterization of the strongly folded boundary between the gray and white matter can be used as constraints for a beamformer in order to estimate local activations inside the brain during a certain task on a time scale of milliseconds. Each pair (ψ,φ) on the sphere corresponds to a location in 3-d space described by its cartesian coordinates (x,y,z). Color codes below are the values of these coordinates as functions of the angles in rectangular and polar plots. Contour lines at constant values of x, y and z define the boundary lines between the gray and white matter in corresponding sagittal, coronal and axial slices, respectively. ψ x-coordinate z-coordinate φ -6.6cm 0 6.6cm -7.6cm 0 7.6cm -9.8cm 0 9.8cm Applying the beamformer allows us to estimate the source power at locations posterior and anterior of the central sulcus. Going top to bottom in the plots below means moving left to right along the sulcus. Each row exhibits the forward solution, the beamformer pattern and two time series. Dotted blues lines show the time course from a single MEG sensor as a reference. The red curves represent the time dependence of local activity for a time span of 480ms with the vertical black line at maximum finger flexion. From bottom to top activation shifts from a time point prior to peak flexion to a time thereafter, representing traveling waves from right to left along both walls of the central sulcus. φ y An MRI scan is transformed into a coordinate system defined by the nasion, and the left and right preauricular points on the subject’s head. y-coordinate The sensitivity of EEG and MEG to sources on the gray-white matter boundary is quite different. For MEG the orientation is most important and regions of high sensitivity (indicated in yellow for MEG and EEG) are located in the walls of the fissures where the current flow is tangential with respect to the surface defined by the sensors. For EEG distance from the electrodes is more important than orientation. The plot on the right shows the differences of normalized sensitivities with red/yellow indicating regions where MEG is more sensitive, plotted in blue shades are areas of higher sensitivity for EEG. The gray-white matter boundary defines the locations and directions of the primary currents in the cortex and can be used as an anatomical constraint for various kinds of beamforming algorithms [4]. Here we show results using an extension of the algorithm known as SAM (synthetic aperture magnetometry) [5] which can be applied to averaged data. A beamforming filter HΘ is calculated by minimizing the power from all locations and directions while keeping the signal constant from a location and direction of interest Θ =Θ(x,y,z,ψ,φ). In general the beamformer and the power at Θ are given by ψ x Freesurfer [1,2] is used to extract the surface which defines the gray-white matter boundary and to inflate it into a sphere. Sagittal Coronal Axial That way, we have a quasi-continuous representation of the brain surface and can sample and tessellate it at any desired accuracy. The transformation into a sphere is unique and invertible, i.e. every point on the gray-white matter boundary corresponds to a single point on the sphere and vice versa because both surfaces are singly connected and therefore topologically equivalent [3]. The spherical coordinate system of latitude ψ and longitude φ can now be mapped onto the brain surface. The vectors perpendicular to this surface are of particular interest because due to the columnar organization of the cortex, the primary currents are oriented in these directions. 1 C 1Gθ 2 1 Hθ and S G C G θ θ θ 1 Gθ C Gθ where C represents the covariance matrix of the data and GΘ is the forward solution from Θ. For averaged data C cannot be inverted and the procedure has to be restricted to the signal subspace by expanding GΘ and HΘ into the eigenvectors υ(k) of C. The expansion coefficients hk for the beamformer and the source power can then be expressed in terms of gl and the eigenvalues λl of C. gk hk = λk l=1 λl M 2 gl -1 and 2 Sθ -1 = . l=1 λl M 2 gl References [1] Dale A.M., Fischl B.,Sereno M.I., Neuroimage 9: 179-194 (1999) [2] Fischl B., Sereno M.I., Dale A.M,, Neuroimage 9: 195-207 (1999) [3] Fischl B., Sereno M.I., Tootell R.B.M., Human Brain Mapping 8: 272-285 (1999) Comparison of fMRI and MEG activity recorded during an experiment where subjects were asked to synchronize with an external metronome. Left: Signal intensity masked with a correlation threshold of 0.5. Middle:Signal intensity at locations along the gray-white matter boundary. Right: Global power calculated from the beamformer using MEG data recorded from the same subject performing the same task. [4] Dale A.M., Sereno M.I., Journal of Cognitive Neuroscience 5/2: 162-176 (1993) [5] Robinson S.E., Vrba J., in: Recent Advances in Biomagnetism, Tohoku University Press, Sendai (1999) Acknowledgement Work supported by NINDS (grant NS39845), NIMH (grant MH42900) and the Human Frontier Science Program.