Deformation Morphometry: Basics and Applications

Transcription

1 Deformation Morphometry: Basics and Applications Valerie Cardenas Nicolson, Ph.D. Assistant Adjunct Professor NCIRE, UCSF, SFVA Center for Imaging of Neurodegenerative Diseases VA

2 Challenge Clinical studies aim to describe effect of disease/treatment on brain Where to look for effects? Anatomic variability Manual methods: time consuming, rater error Goal: automatically measure differences, look everywhere, account for anatomic variability, high power

3 Deformation Morphometry Automated Suited for discerning patterns of structural change Explore location and extent of variation Use nonlinear registration or warping of images Within: capture changes in brain over time Between: measure deviation from atlas brain relate anatomy to clinical/functional variables Low power

4 Using Between Subject Registration: Computational Morphometry Reference Anatomy Individual Coarse Non-Rigid Transformation Compare Regional Stats: e.g. Gray Matter Density Voxel Morphometry Fine+Accurate Nonlinear Transformation Transformation Describes All Differences Deformation or Tensor Morphometry

5 Deformation Morphometry Models Univariate single modality Statistics on scalar summary measures of the Jacobian matrix (e.g., determinant, trace, geodesic anisotropy) Multivariate single modality Statistics on deformation tensors, 3D displacements Univariate multimodality Covary scalar deformation map with other imaging map May account for variability if maps are related (e.g., longitudinal and baseline atrophy related) Multivariate multimodality Dependent variables are deformation maps and other imaging map (e.g., FA) Sensitivity to effects may increase if dependent variables are related (e.g., GM perfusion and GM atrophy) X x=(x1,x2) Reference y=t(x) x=t -1 (y) Slide: 5 Y Target y=(y1,y2) When moving in a path across one anatomy, how quickly are we moving in each axis in the other anatomy? Summarized by the Jacobian Matrix of partial derivatives

6 Images in Clinical Study Map 1; diagnosis 0 age 65 score 16 Map 2; diagnosis 1 age 68 score 8 Map n; diagnosis 1 age 73 score 4 Deformation tensor map z 11 z 12 z 21 z 22 z n1 z n2 Jacobian map z 13 z 14 z 23 z 24 z n3 z n4 y 11 y 12 y 21 y 22 y n1 y n2 FA map y 13 y 14 y 23 y 24 y n3 y n4

7 Univariate Single Modality y 11 y 12 y 13 y 14 Map 1; diagnosis 0 age 65 score 16 y 21 y 22 y 23 y 24 Map 2; diagnosis 1 age 68 score 8 y n1 y n3 y n2 y n4 Map n; diagnosis 1 age 73 score 4 y y y y y y n n β β β diag1 age1 score1 β β β β int1 diag 2 age2 score2 β int 2 diag1 disg2 coefficient maps for each variable t diag1 t diag2 statistic maps for each variable diag3 diag4 t diag3 t diag4

8 Jacobian Determinant V 1 T(x 1,y 1,z 1 ) V 2 J =0.9, 10% tissue loss J =1.1, 10% tissue gain

9 Jacobian or log Jacobian? 0 J ; log transform normalizes distribution J Count Count Count Jac_AC Jac_LHip Jac_WM log 10 J Count Count Count Equal probabilities to expansions and shrinkages that are reciprocals, i.e Log10Jac_AC log10jac_lhip J =0.5, log 10 J =-0.3 J =2.0, log 10 J = log10jac_wm 32 controls; all distributions pass tests for normality

10 Age -map J Log 10 J Age T-map J Log 10 J If your data are normal, choice of J or log 10 J matter of preference.

11 Bibliography: Univariate Single Modality Cardenas et al. 2009, J Neurovirol. Jun 4:1-10. Pieperhoff et al. 2008, J Neurosci 28(4): Kim et al. 2008, NeuroImage 39(3): Cardenas et al., Arch Neurol 64(6): Leow et al. 2009, NeuroImage 45(3): Aljabar et al. 2008, NeuroImage 39(1):

12 Limitation of Jacobian Determinant Information about shape change largely lost Orientation specific characteristics lost 2D Example: shape change no volume change Possible solution: examine deformation tensors, full Jacobian matrix, displacement fields

13 Multivariate single modality Map 1; diagnosis 0 age 65 score 16 Map 2; diagnosis 1 age 68 score 8 Map n; diagnosis 1 age 73 score 4

14 Example 1: Deformation tensors in HIV Lepore et al., 2008 IEEE TMI, 27(1): S is positive definite symmetric; statistics on 6-vector 2D Corpus Callosum Example: green shows p<0.05 3D: p-value maps Multivariate shows comparable patterns of atrophy with greater sensitivity log 10 J log 10 J Log(S) Log(S) Note there is not complete overlap between methods; univariate and multivariate single modality analyses can be complementary!

15 Example 2: Deformation tensors in alcohol recovery Studholme and Cardenas., 2007 MICCAI LNCS, 4792: Statistics on 9-vector; all elements from Jacobian matrix encoding longitudinal change in reference coordinates F-map full Jacobian F-map J Effect maps: directional patterns of volume change revealed in deep WM and subcortical nuclei J J

16 Bibliography: Multivariate Single Modality Gaser et al. 1999, NeuroImage 10: Gaser et al. 2001, NeuroImage 13: Thompson and Toga 1997, Medical Image Analysis 1: Worsley et al. 1998, Human Brain Mapping 6:

17 Univariate Multimodality: Imaging covariate y 12 y 12 y 11 y 11 y 22 y 22 y 21 y 21 y n1 y n1 y n2 y n2 y 13 y 13 y 14 y 14 y 23 y 23 y 24 y 24 y n3 y n3 y n4 y n4 Map 1; diagnosis 0 age 65 score 16 Map 2; diagnosis 1 age 68 score 8 Map n; diagnosis 1 age 73 score 4 diag1 disg2 coefficient maps for each variable t diag1 t diag2 statistic maps for each variable diag3 diag4 t diag3 t diag4

18 Covarying longitudinal deformation with baseline deformation Cardenas and Studholme, 2004 MICCAI LNCS, 3217: SD vs Controls SD vs Controls; w/ atrophy state Idea: Rate of tissue loss increases with progression of disease, therefore baseline brain atrophy is related to longitudinal brain atrophy.

19 Multivariate Multimodality y 12 y 12 y 11 y 11 y 22 y 22 y 21 y 21 y n1 y n1 y n2 y n2 y 13 y 13 y 14 y 14 y 23 y 23 y 24 y 24 y n3 y n3 y n4 y n4 Map 1; diagnosis 0 age 65 score 16 Map 2; diagnosis 1 age 68 score 8 Map n; diagnosis 1 age 73 score 4 y,diag1 y,diag2 t y,diag1 t y,diag2 diag1 diag2 y,diag3 y,diag4 t y,diag3 t y,diag4 diag3 diag4

20 Few published examples of voxel-wise multivariate multimodality focus of workshop! Co-analysis of DTI and Structural Imaging in Alzheimer s Disease poster presentation ISMRM 2010

21 Motivation for Co-Analysis Our current implementation of nonlinear registration of structural images uses only T1; no information for alignment of within white matter DTI provides good imaging of white matter Deformation morphometry co-analysis with DTI may reveal more disease-related brain abnormalities than either modality alone Is whole greater than sum of parts?

22 Voxel-wise Statistical Models Univariate single modality FA = group + age J =group + age Univariate multimodality J = group + age + FA Multivariate multimodality J FA = group + age

23 Univariate Single Modality T-statistic Maps for Group p<0.05, uncorrected FA = group + age; group effect J = group + age; group effect Red shows regions of FA or JAC in AD; blue show regions of FA or J in AD

24 Univariate multimodality T-statistic maps for group p<0.05, uncorrected J = group + age + FA; group effect J = group + age; group effect

25 Multivariate multimodality Overlay Group T-statistic maps, p<0.05, uncorrected J FA = group + age; overall group effect Group on FA Overlay group effect; FA = group + age Overlay group effect; J = group + age Red: overall group effect only; Green: group effect on FA or J alone; Yellow: group effect either single modality OR multivariate

26 Discussion of Co-analysis of DTI and Structure in AD Co-analysis of structural images and DTI did not reveal significantly more AD-related brain abnormalities than a voxel-wise analysis of structural images alone. However, the value of co-analysis may vary across different stages of the disease, especially in early AD. Univariate analysis of FA images revealed few AD-related abnormalities. Other metrics of diffusion, such as full diffusion tensor or kurtosis, could be more sensitive measures than FA

27 Bibliography: Multivariate multimodality Friese et al. 2010, J Alzheimers Dis 20(2): Avants et al. 2008, Acad Radiol 15(11):

28 Overall Summary Choice of using deformation tensors or scalar Hypothesis, shape change or atrophy? Could be complementary Multimodality Benefits of additional modalities may differ by disease May be limited applications of voxel-wise analysis disease-affected regions in DTI may be related to different regions in structure

29 Multivariate Analysis Tool Most examples in this presentation created with valmap : partially supported by RR Advantages Matlab license not required Can incorporate a spatially varying independent variable Can use spatially invariant independent variable Can use multiple dependent variables (multivariate); maps or spatially invariant