COMPUTATIONAL (NEURO)ANATOMY

Transcription

1 COMPUTATIONAL (NEURO)ANATOMY Duygu Tosun-Turgut, Ph.D. Center for Imaging of Neurodegenerative Diseases Department of Radiology and Biomedical Imaging

2 Computational anatomy Computational Anatomy's goal is to define methods for the quantization of shape within biological structures. Origins of Computational Anatomy (CA) may be found in the central thesis of Sir D'Arcy Wentworth Thompson s 1917 book entitled On Growth and Form. D'Arcy believed that biologists of his day over emphasized the role of evolution, and under emphasized the roles of physical laws and mechanics, as determinants of the form and structure of living organisms.

3 Scientific goal HUMAN NEUROANATOMY Correlations Associations CLINICAL PRACTICE Disease Cognitive function Treatment effect

4 Quantitative neuroanatomy Traditional volumetrics Tissue volumes Measures from manually/automatically delineated region-ofinterests (ROIs) Voxel-based morphometry (VBM) Tensor-based / deformation-based morphometry (TBM / DBM) Surface-based morphometry (e.g., FreeSurfer)

5 Tissue-type volumetrics T1-weighted MRI Gray matter volume White matter volume CSF volume GLOBAL MEASURES!

6 Lobar ROIs Frontal Lobe intelligence, behavior motor control Parietal Lobe sensory perception language Temporal Lobe hearing, smell language Occipital Lobe vision

7 Basal ganglia voluntary motor control, procedural learning relating to routine behaviors or "habits"

8 Thalamus relaying sensory and motor signals to the cerebral cortex, regulating consciousness, sleep, and alertness

9 Hippocampus consolidation of information from short-term memory to long-term memory and spatial navigation [Frank Gaillard Designs]

10 Manual anatomical delineation ~29-30 slices High intra- and inter-rater reliability requires rigorous training Enormous investment of time Prone to error

11 Semi-automated hippocampal delination 4 marks are placed on 5 slices along its length representing the width of the hippocampus (medial, inferior, lateral, superior)

12 Automatic anatomical delineation Identify structures on template brain Warp template to new subject using gray scale images, sometimes landmark assisted Apply resultant transformation to template ROIs

13 Semi-automated vs automated hippocampal segmentation Surgical Navigation Technologies (SNT) FreeSurfer Method Amygdala Hippo GM Fimbria / Alveus Intralimbic Gyrus Parahippo Gyrus SNT No Yes No No No Freesurfer Partial Yes Yes Yes Partial

14 Comparison of hippocampal volume The error bars show the standard deviation. The numbers at the base of the bars indicate the adjusted hippocampal volume in mm 3

15 PTSD effect on hippocampal subfields Volume in mm3 corrected for ICV Control PTSD % ERC Sub CA1 CA1-2 transition CA3&DG * [Wang et al. Arch Gen Psychiatry 2010, 67: ]

16 Not limited to structural MRI Probabilistic maps for 11 tract-of-interests (TOIs) [Huan et al. 2008]

17 Auto Tract-of-Interest Measurement DARTEL Create Template DARTEL Individual FA Averaged Template DARTEL Register to Template Susumu s ICBM FA Template with Fibers (22 TOIs) DARTEL Inverse Warping DARTEL Warp Images Individual FA+TOI Jacobian Determinant FA+TOI in common space

18 Anterior thalamic radiation 5% 20%

19 Neurodegeneration on cingulum bundle in AD contiuum CN (n=32) MCI (n=30) amci (n=15) AD (n=30) MCI<CN p amci<cn p AD<CN p L. t.cg FA 0.36 (0.02) 0.36 (0.02) 0.35 (0.02) 0.33 (0.03) n.s. n.s. <0.001 R. t.cg FA 0.37 (0.03) 0.37 (0.02) 0.37 (0.02) 0.34 (0.03) n.s. n.s. <0.001 L. t.cg Vol [ ] 0.98 (0.15) 0.91 (0.13) 0.88 (0.12) 0.77 (0.15) <0.001 R. t.cg Vol [ ] 1.10 (0.21) 1.04 (0.14) 1.02 (0.12) 0.84 (0.17) n.s. n.s. <0.001 CN MCI

20 Limitations of traditional volumetrics A priori selection of ROIs is required. Disease pathology and cognitive involvement may not be confined in anatomical boundaries. Effect may be localized; obscured by ROI Common ROIs are affected by variety of diseases (low specificity). Suggested solutions: Look at smaller ROIs (limit is single voxel) Identify spatial pattern of effects (statistical ROI)

21 Voxel-wise morphometry Suited for discerning patterns of structural change Explore location and extent of variation Use nonlinear registration or warping of images Automated within subject to capture changes in brain over time between subject to measure deviation from a reference between subject to relate anatomy to clinical/functional scores Independently estimated statistics at each voxel Multiple comparison Low statistical power

22 Voxel-based morphometry (VBM) A voxel by voxel statistical analysis is used to detect regional differences in the amount of grey matter between populations to identify correlations with age, cognitive-scores etc. Original image Spatially normalised Segmented grey matter Smoothed The data are pre-processed to sensitize the tests to regional tissue volumes, usually grey or white matter. [SPM, FSL, HAMMER, ]

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24 Preprocessing Standard Protocol Optimized Protocol Involves segmenting images before normalizing, so as to normalize gray matter / white matter / CSF separately

25 VBM example: Aging Significant grey matter volume loss with age superior parietal pre and post central insula cingulate

26 VBM example: Sex differences Females > Males Males > Females L superior temporal sulcus R middle temporal gyrus intraparietal sulci mesial temporal temporal pole anterior cerebellar

27 VBM example: brain asymmetry Right frontal and left occipital petalia

28 Function of preprocessing To shape the data in such a way that makes statistical analysis sensitive for local changes in tissue composition. 3 general steps for preprocessing a T1 image for standard/optimized VBM segmentation spatially normalization smoothing The optimized procedure also involves modulating the data to yield volume information. [Good et. al., A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (2001)]

29 Segmentation Segmentation is the process to label/ identify voxels in native T1 space as Gray matter White matter CSF Other (skull, dura, fat, background, etc ) Intensity histogram fit by multi-gaussians. Segmentation is an automated process that separates tissue types with mixture model cluster analysis based on 1. Voxel intensities 2. A priori knowledge of the location of gray matter, white matter, CSF, and other tissues in normal brains [Good et. al., A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (2001)]

30 Spatial normalization: Why? Inter-subject averaging extrapolate findings to the population as a whole increase statistical power above that obtained from single subject Reporting of significances/activations as coordinates within a standard stereotactic space e.g. the space described by Talairach & Tournoux e.g. a tissue-specific template created by the investigator from study-specific subject data [Good et. al., A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains (2001)] [Mechelli et. al., Voxel-Based Morphometry of the Human Brain: Methods and Applications (2005)] [Ashburner and Friston, Why Voxel-Based Morphometry Should Be Used (2001)]

31 Spatial normalization Determine transformation that minimizes the dissimilarity / maximizes the similarity between an image and a (combination of) template image(s) Two stages: 1. affine registration to match size and position of the images 2. non-linear warping to match the detailed brain shape brain masks can be applied (e.g. for lesions) Bayesian constraints A mask weights the normalization to brain instead of nonbrain

32 Bayesian constraints Algorithm simultaneously minimizes: Sum of squared difference between template and subject Squared distance between the parameters and their expectation Empirically generated priors Bayesian constraints applied to both: affine transformation based on empirical prior ranges nonlinear deformation based on smoothness constraint (minimizing membrane energy)

33 With & Without the Bayesian formulation Template image Affine Registration (χ 2 = 472.1) Non-linear registration with regularisation (χ2 = 302.7) Non-linear registration without regularisation (χ2 = 287.3)

34 Smoothing: Why? Potentially increase signal to noise (matched filter theorem) Inter-subject averaging (allowing for residual differences after normalization) Increase validity of statistics (more likely that errors distributed normally) Data must be normally distributed as a Gaussian field model is used for statistical analysis Smoothing with an isotropic Gaussian kernel inherently makes the data more normally distributed by the central limit theorem Central Limit Theorem: the summation of many variables which have a finite variance will produce a sum that is approximately normally distributed

35 Smoothing Convolution Result of applying a weighted average Kernel defined in terms of FWHM (full width at half maximum) of filter ~16-20mm (PET) ~6-8mm (fmri) Ultimate smoothness ~ applied smoothing + intrinsic image smoothness ( resels : RESolvable Elements) FWHM Gaussian smoothing kern Before convolution Convolved with a circle Convolved with a Gaussian

36 Preprocessed data for four subjects Warped, modulated grey matter 12mm FWHM smoothed

37 Optimized versus Standard VBM Nonlinear spatial normalization during preprocessing causes brain regions to differentially experience a change in volume Optimized VBM removes the mis-segmentation that is sometimes seen in standard VBM through the second segmentation step Optimized VBM also employs a modulation step Modulation = (voxel values) x (Jacobian determinants) = (reestablishing volume information) Outputs: No information on absolute volume size Standard VBM: tissue concentration, or in other words, the proportion of the type of tissue to the proportion of all other tissue types in the given region Optimized VBM: information about percentage of brain volume

38 Final step to create statistical parametric maps.

39 Some explanations of the differences Mis-classify Mis-register Folding Thickening Thinning Mis-register Mis-classify

40 Limitations of VBM Confuses tissue volume loss and displacement Relies on the automated segmentation of images Regions of abnormal WM may be incorrectly classified as GM Segmentation of subcortical structures can be problematic due to mixing of GM and WM Apparent loss of grey matter in this individual as less tissue falls inside model region Disease Effect Grey matter displaced outside expected region appears as loss White Matter Loss

41 It s more than a spatial normalization! Original image Spatially normalized Spatial Normalisation Template image Deformation field

42 Morphometry on deformation fields Deformation-based morphometry looks at absolute displacements Tensor-based morphometry looks at local shapes Vector field Tensor field

43 Comparing VBM to deformation morphometry Coarse non-rigid transformation Compare regional stats: e.g. Gray Matter density Fine+Accurate Nonlinear transformation Transformation describes all differences Voxel-based morphometry Deformation or tensorbased morphometry

44 Deformation field Original Warped Template & x' # $ y'! $! $ % z'!" = & t $ t $ $ % t (x, y,z) # (x, y,z)!! (x, y,z)!"

45 Jacobian Matrix Jacobian the pointwise volume change at each point! # J = # # "# j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33! $ # & # & = # & # %& # # " x' x x' y x' z y' x y' y y' z z' x z' y z' z $ & & & & & & % J = j 11 ( j 22 j 33 j 23 j 32 ) j 21 ( j 12 j 33 j 13 j 32 )+ j 31 ( j 12 j 23 j 13 j 22 )

46 Jacobian Matrix of partial derivatives When moving in a path across one anatomy, how quickly are we moving in each axis in the other anatomy? X y=t(x) Y x=(x1,x2) y=(y1,y2) x=t -1 (y) J(x 1, y 1, z 1 ) = V 2 V 1 >1, voxel expansion J(x 1, y 1, z 1 ) = V 2 V 1 <1, voxel shrinkage

47 Relative volumes Deformation-based morphometry (DBM)

48 Graphical flowchart of the analysis procedure used to compute the growth rate maps and identify regions with significant accelerations or decelerations. Rajagopalan V et al. J. Neurosci. 2011;31:

49 Local tissue growth rate patterns relative to cerebral growth rate, overlaid on the average brain. Rajagopalan V et al. J. Neurosci. 2011;31:

50 Deformation distance summary Deformations can be considered within a small or large deformation setting Small deformation setting is a linear approximation Large deformation setting accounts for the nonlinear nature of deformations Uses Lie Group Theory

51 Strain tensor J: original Jacobian matrix J = RU R: an orthonormal rotation matrix U: a symmetric matrix containing only zooms and shears. Tensor-based morphometry (TBM)

52 Detecting brain growth patterns in normal children using tensor based morphometry

53 References Friston et al (1995): Spatial registration and normalisation of images. Human Brain Mapping 3(3): Ashburner & Friston (1997): Multimodal image coregistration and partitioning - a unified framework. NeuroImage 6(3): Collignon et al (1995): Automated multi-modality image registration based on information theory. IPMI 95 pp Ashburner et al (1997): Incorporating prior knowledge into image registration. NeuroImage 6(4): Ashburner et al (1999): Nonlinear spatial normalisation using basis functions. Human Brain Mapping 7(4): Ashburner & Friston (2000): Voxel-based morphometry - the methods. NeuroImage 11: I. C. Wright et al. A Voxel-Based Method for the Statistical Analysis of Gray and White Matter Density Applied to Schizophrenia. NeuroImage 2: (1995). I. C. Wright et al. Mapping of Grey Matter Changes in Schizophrenia. Schizophrenia Research 35:1-14 (1999). J. Ashburner & K. J. Friston. Voxel-Based Morphometry - The Methods. NeuroImage 11: (2000). J. Ashburner & K. J. Friston. Why Voxel-Based Morphometry Should Be Used. NeuroImage 14: (2001). C. D. Good et al. Automatic Differentiation of Anatomical Patterns in the Human Brain: Validation with Studies of Degenerative Dementias. NeuroImage 17:29-46 (2002). Bookstein FL. "Voxel-Based Morphometry" Should Not Be Used with Imperfectly Registered Images. NeuroImage 14: (2001). W.R. Crum, L.D. Griffin, D.L.G. Hill & D.J. Hawkes. Zen and the art of medical image registration: correspondence, homology, and quality. NeuroImage 20: (2003). N.A. Thacker. Tutorial: A Critical Analysis of Voxel-Based Morphometry. Miller, Trouvé, Younes On the Metrics and Euler-Lagrange Equations of Computational Anatomy. Annual Review of Biomedical Engineering, 4: (2003) plus supplement Beg, Miller, Trouvé, L. Younes. Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms. Int. J. Comp. Vision, 61: (2005)

54 Nonlinear registration software Only listing public software that can (probably) estimate detailed warps suitable for longitudinal analysis. HAMMER MNI_ANIMAL Software Package SPM VTK CISG Registration Toolkit there is much more software that is less readily available...

55 Need for surface-based morphometry Anatomical analysis is not like functional analysis it is completely stereotyped. Registration to a template (e.g. MNI/Talairach) doesn t account for individual anatomy. Even if you don t care about the anatomy, anatomical models allow functional analysis not otherwise possible. Function has surface-based organization. Inter-subject registration: anatomy, not intensity Cortical parcellation: Automatically generated ROI tuned to each subject individually Intrinsic smoothing (i.e., Like 3D, but 2D) Intrinsic clustering Visualization: Inflation/Flattening Cortical morphometric measures

56 Voxel versus surface voxel surface

57 Surface-based inter-subject registration Gray matter-to-gray matter (it s all gray matter!) Gyrus-to-gyrus and sulcus-to-sulcus Some minor folding patterns won t line up Fully automated or landmark-based Atlas registration is probabilistic, most variable regions get less weight

58 Volume-based Smoothing 14mm FWHM 7mm FWHM Smoothing is averaging of nearby voxels

59 Volume-based Smoothing 14mm FWHM 5 mm apart in 3D 25 mm apart on surface! Kernel much larger Averaging with other tissue types (WM, CSF) Averaging with other functional areas

60 Why additional volume analysis? Surface-based coordinate system/registration appropriate for cortex but not for thalamus, ventricular system, basal ganglia, etc

61 Surface-based morphometry resources Some example references B. Fischl & A.M. Dale. Measuring Thickness of the Human Cerebral Cortex from Magnetic Resonance Images. PNAS 97(20): (2000). S.E. Jones, B.R. Buchbinder & I. Aharon. Three-dimensional mapping of cortical thickness using Laplace's equation. Human Brain Mapping 11 (1): (2000). J.P. Lerch et al. Focal Decline of Cortical Thickness in Alzheimer s Disease Identified by Computational Neuroanatomy. Cereb Cortex (2004). Narr et al. Mapping Cortical Thickness and Gray Matter Concentration in First Episode Schizophrenia. Cerebral Cortex (2005). Thompson et al. Abnormal Cortical Complexity and Thickness Profiles Mapped in Williams Syndrome. Journal of Neuroscience 25(16): (2005). J.-F. Mangin, D. Rivière, A. Cachia, E. Duchesnay, Y. Cointepas, D. Papadopoulos- Orfanos, D. L. Collins, A. C. Evans, and J. Régis. Object-Based Morphometry of the Cerebral Cortex. IEEE Trans. Medical Imaging 23(8): (2004).

62 What FreeSurfer does FreeSurfer creates computerized models of the brain from MRI. Volumes Surfaces Surface Overlays ROI Summaries Input: T1-weighted (MPRAGE,SPGR) (.dcm/.nii) Output: Segmented & parcellated conformed volume (.mgz)

63 Structural MRI Acquisition Methods for Brain: PD, T1, T2 and T2* weighting Which is best for brain morphometry/freesurfer? PD-weighting (proton/spin density) + T1-weighting (gray/white contrast) + T2-weighting (bright CSF/tumor) FLASH 5 FLASH 30 T2-SPACE

64 MPRAGE (FLASH with inversion) has the best contrast for FreeSurfer because FLASH 30 MPRAGE MPRAGE parameters chosen for optimal gray/white/csf contrast FreeSurfer statistics (priors) based on MPRAGE

65 Motion correction and averaging 001.mgz + rawavg.mgz 002.mgz Usually only need one. Does not change native resolution.

66 Conform orig.mgz rawavg.mgz Changes to image volume with 1mm 3 voxel dimensions. All volumes will be conformed.

67 Talairach transform Computes 12 DOF transform matrix Does NOT resample MNI305 template Mostly used to report coordinates

68 Intensity bias Left side of the image much brighter than right side Worse in multi-coil system Makes gray/white segmentation difficult Nonparametric nonuniformity normalization (N3) algorithm

69 Intensity normalization Most WM = 110 intensity Allows for atlas-based tissue segmentation

70 70 Skull stripping Removes all non-brain image voxels Skull, eyes, neck, dura An atlas-based approach Input image volume Brain image volume [mri/brainmask.mgz]

71 71 Automatic volume labeling Fill in subcortical structures to create subcortical mass Various atlases e.g. RB_all_ White Matter Cortex Lateral Ventricle Thalamus Useful in ROI-based morphometry Caudate Pallidum Putamen Amygdala Hippocampus Segmented image volume [mri/aseg.mgz]

72 72 White matter segmentation Separates white matter from everything else Uses segmented image volume to fill in subcortical structures WM image volume [mri/wm.mgz] Removes cerebellum, but keeps brain stem intact

73 Surfaces: White and Pial

74 Subcortical mass Includes all white matter Includes subcortical structures Includes ventricles Excludes brain stem and cerebellum Hemispheres separated Connected (no islands)

75 Radiological or neurological convention? Right Left

76 Tessellation Mosaic of triangles tessellation vertex Errors: Donut holes, handles Due: Imaging noise, errors in previous processing steps

77 77 Topological defects Fornix hippocampus Pallidum and Putamen Cortical Defects Ventricles and Caudate Holes Handles Automatically Fixed

78 Topological defects Nudge original surface Follow T1 intensity gradients Smoothness constraint Vertex identity preserved

79 Pial surface Nudge white surface Follow T1 intensity gradients Vertex identity preserved

80 Non-cortical areas of surface Amygdala, Putamen, Hippocampus, Caudate, Ventricles, CC [surf/?h.cortex.label]

81 81 Surface mapping Mesh ( Finite Element ) Vertex = point of triangles Neighborhood XYZ at each vertex Triangles/Faces ~ 150,000 Area, Distance Curvature, Thickness Moveable

82 Cortical thickness Distance between white and pial surfaces One value per vertex In mm Surface-based more accurate than volume-based [surf/?h.thickness]

83 Curvature (Radial) Maximal circle tangent to surface at each vertex Curvature measure ~ 1/radius of circle One value per vertex Signed (sulcus/gyrus) Actually use Gaussian curvature [surf/?h.curv]

84 84 Surface inflation Nudge vertices No intensity constraint See inside sulci Used for sphere

85 Sulcal depth [surv/?h.sulc]

86 A surface-based coordinate system

87 Parcellation vs. segmentation (cortical) parcellation (subcortical) segmentation [mri/aparc+aseg.mgz]

88 Why not just register to an ROI Atlas? 12 DOF (Affine) ICBM Atlas

89 Problems with affine (12 DOF) registration Subject 1

90 Automatic surface segmentation Precentral Gyrus Postcentral Gyrus Superior Temporal Gyrus Based on individual s folding pattern

91 Borrowed from (Halgren et al., 1999)

92 Rosas et al., 2002 Sailer et al., 2003 Kuperberg et al., 2003 Fischl et al., 2000 Gold et al., 2005 Salat et al., 2004 Rauch et al., 2004

93 Gyral white matter segmentation + + Nearest cortical label to point in white matter

94 Endless possibilities!? Longitudinal modeling Multimodal integration! 1. fmri 2. FDG-PET 3. DTI 4. ASL 5. Amyloid PET 6..