Bruce FischlMGH NMR CenterComputational Neuroanatomy.CollaboratorsAnders M. Dale MGHAndre van der Kouwe MGHMarty Sereno UCSDDavid Salat MGHChristophe Destrieux ToursThanks also to Randy Buckner, Bruce Rosen, Eric Halgren, MarilynAlbert, Gina Kuperberg, Ron Killiany, Diana Rosas, David Kennedy,Nikos Makris, Verne Caviness, Paul Raines, Chad Wissler, Roger Tootell,Doug Greve, Sean Marrett, Janine Mendola, Rahul Desikan, Kevin Teich,Chris Moore, Christian Haselgrove, Tony Harris, Evelina Busa, MaureenGlessner, and Nouchine HadjikhaniDefinition 1: The manner in which the neuroanatomical structure of thebrain facilitates or carries out computations.Computational Neuroanatomy:Definition 2: The application of computational techniques to modelneuroanatomical structures.Definition 1: The manner in which the neuroanatomical structure of thebrain facilitates or carries out computations.Computational Neuroanatomy:Definition 2: The application of computational techniques to modelneuroanatomical structures.Definition 1: The manner in which the neuroanatomical structure of thebrain facilitates or carries out computations.Computational Neuroanatomy:Definition 2: The application of computational techniques to modelneuroanatomical structures.Warning!There are no textbooks on computational neuroanatomy:Much of what you hear in this lecture will be opinion!Talk Outline• The Spatial Structure of Retinotopic Cortex.• Cortical Analysis.• Subcortical Analysis.Talk Outline• The Spatial Structure of Retinotopic Cortex.• Cortical Analysis.• Subcortical Analysis.How is the Visual Field Representedin Mammalian Cortex?*(Physically Flattened Macaque V1)Stimulus2-DG map of V1*thanks to Eric Schwartz for this slideWhat is the form of the retino-cortical map function?First insight: Burkhardt Fischer (1970):If retinal cell density/length is 1/rThen several possible optic tract exist maps,one of which is (z=retina, w=cortex):221(,)(,)log()log()tan/wuxyivxyzxyiyxzxiy−=+==++=+Problems With Log(z)Hypothesis• In cat, V1 not really log polar.• Retinal cell density doesn’t necessarilydetermine the cortical map. This point stilluncertain in both monkey and cat!• Log(z) has a singularity at the origin – themost important place!Add a small constant, and map eachhemifield separately: W=log(z+a)Removal of the Foveal SingularityEccentricityàPolar Angleà*thanks to Eric Schwartz for this slideConformal Maps• A map function is said to be conformal if- It preserves local angles (equivalent to…)- The jacobian of the map function is non-singular• Riemann map theorem: a conformal map is uniquelydetermined by one point correspondence, one angle, andboundary of the two domains (retina and cortex).• Log(z) is not conformal, but Log(z+a) is.• Can only meaningfully talk about magnification functionif the map is conformal!Riemann fit to V1Includes eye position regression andgeodesic brain flattening*thanks to Eric Schwartz for this slideWhat Do Images Look Like inCortex?Original image “Retinal” image “Cortical” image*thanks to Eric Schwartz for this slideSummary of CurrentKnowledge of Spatial Maps• They exist and are strongly space-variant incat, owl, monkey, human etc.• They are approximately conformal (V1).• We don’t know if they are “functional” ornot.• We don’t know how to do visual computationon SV maps in biology or in computers.Talk Outline• The Spatial Structure of Retinotopic Cortex.• Cortical Analysis.• Subcortical Analysis.Talk Outline• The Spatial Structure of Retinotopic Cortex.• Cortical Analysis.• Subcortical Analysis.None of the preceding analysis of the spatialstructure of the representation of the visualfield in V1 could have been done withoutknowing the position and orientation of thecortex.Why Is a Model of theCortical Surface Useful?Why Is a Model of theCortical Surface Useful?Local functional organization of cortex is largely 2-dimensional!From (Sereno et al, 1995, Science).Flat Map of Monkey Visual AreasD.J. Felleman and D.C. Van Essen, CC, 1991Why Is Constructing aModel of The CorticalSurface Difficult?The cortex is highly folded!• Partial voluming.• Subject motion.• Susceptibility artifacts.• Bias field.• Tissue inhomogeneities.Intensity of a tissueclass varies as afunction of spatiallocationSources of within-classintensity variation• Partial voluming – a single voxel may contain more than one tissue type.• Bias field – effective flip angle or sensitivity of receive coil may vary across space.• Tissue inhomogeneities – even within tissue type (e.g. cortical gray matter), intrinsic properties such as T1, PD can vary (up to 20%).Contrast-to-Noise RatioHigher CNR values imply the class distributions overlap less.All the previous effects reduce the CNR.( )222BABACNR+−=For two classes, A and B, the contrast-to-noise ratio (CNR) isgiven by (one possible definition):Assigning tissue classes to voxels can be difficultT1 weighted MR volumeGoal: Reconstruction of theCortical SurfaceGenerate a geometrically accurate and topologicallycorrect model of the cerebral cortex.Uses of the surface reconstruction include:• Visualization of functional and structural neuroimaging data.• Calculation of morphometric properties of the cortex.• High-resolution averaging of cortical data across subjects.• Increasing spatial resolution of EEG/MEG data.Which Surface toReconstruct?Pial surface is ultimate goal, but pretty much impossibleto directly generate a representation of from MRI images(many have tried!).Alternative: construct an interim representation of theinterface between gray matter and white matter, and useit to infer the location of the true cortical surface (Daleand Sereno, 1993).Skull Stripping and building ofBoundary Element ModelsConductivity Boundaries for BEMInner Skull Outer Skull Outer SkinMRI Segmentation and SurfaceReconstructionSurface RepresentationsTwo Choices:• Lagrangian – generate an explicit representation ofthe surface through a tessellation. Surfacedeformations are then carried out by computing themovement of points (vertices) on the surface.• Eulerian – represent the surface by embedding it in ahigher-dimensional space. The surface is representedimplicitly as the set of points with constant value in thehigher dimensional function (the “level-set” approach ofOsher and Sethian).TessellationTessellation - a covering of a space with