1. STATISTICAL SHAPE ANALYSIS OF BRAIN STRUCTURES USING SPHERICAL WAVELETS
D Nain1, M Styner3, M Niethammer4, J J Levitt4,
M E Shenton4, G Gerig3, A Bobick1, A Tannenbaum2
1 College of Computing, 2 Schools of Electrical & Computer and Biomedical Engineering, Georgia Tech, Atlanta, USA
3 Department of Computer Science and Department of Psychiatry, UNC, Chapel Hill, USA
4 Department of Psychiatry, VAMC-Brockton, Harvard Medical School, Boston, USA

2. Motivation
The aim of our work is to investigate whether there exists morphological differences of selected brain structures between groups of neuropsychiatric patients with neuroanatomic abnormalities and a group of healthy controls.
To reach this aim, we compare structures extracted from MRI images of different subjects using statistical tests.

3. Background
Morphometric analysis of brain structures provides new information which is not available by conventional volumetric measurements
Many shape representation are used
Dense sampled point representation (PDM)
Medial axis
Surface parameterization using expansion into a series (i.e. spherical harmonics basis functions)
Combined, these representations provide new complementary measurement tools to answer clinical research questions.

4. Our Contribution
We propose to use a spherical wavelet shape representation
Each coefficient describes a portion of the surface and the size of that portion depends on the scale of the coefficient
Potential Advantages:
Coefficients are not as localized as points in a PDM representation (can capture shape characteristics of different spatial extent, i.e a bending of a portion of the shape)
Coefficients have both a scale and space interpretation over Fourier or spherical harmonic coefficients that only have a scale interpretation

5. Method – Step 1: Pre-Processing
Binary segmentations are pre-processed with UNC Shape Analysis Pipeline
Guarantee spherical topology, extract surface
Compute spherical parameterization and align surfaces for correspondence
Output are triangulated SPHARM-PDM surfaces

6. Method – Step 2: Spherical Wavelet Coefficient (SWC) Representation
A spherical wavelet description is computed for each SPHARM-PDM surface using the spherical parameterization
Each shape is then represented by a series of 3D spherical wavelet coefficients (SWC)
Each 3D coefficient is associated with a spherical wavelet function that describes the shape at a specific scale and spatial region

7. SWC Region of Influence Visualization
SCALE 1
Main region of influence of
a 3D coefficient at scale 1
on the sphere
Main region of influence of
a 3D coefficient at scale 1
on SPHARM-PDM surface
Main region of influence of
another 3D coefficient at scale 1
on the sphere
Main region of influence of
another 3D coefficient at scale 1
on SPHARM-PDM surface

8. SWC Region of Influence Visualization
SCALE 2
Main region of influence of
a 3D coefficient at scale 2
on the sphere
Main region of influence of
a 3D coefficient at scale 2
on SPHARM-PDM surface
Main region of influence of
another 3D coefficient at scale 2
on the sphere
Main region of influence of
another 3D coefficient at scale 2
on SPHARM-PDM surface

9. SWC Region of Influence Visualization
SCALE 3
Main region of influence of
a 3D coefficient at scale 3
on the sphere
Main region of influence of
a 3D coefficient at scale 3
on SPHARM-PDM surface
Main region of influence of
another 3D coefficient at scale 3
on the sphere
Main region of influence of
another 3D coefficient at scale 3
on SPHARM-PDM surface

10. Method – Step 3: Statistics
We use the UNC statistical test toolbox that analyzes differences between two groups of surfaces described by a set of features.
The group differences are computed locally for every feature using the standard robust Hotelling T^2 two sample metric.
Statistical p-values, both raw and corrected for multiple comparisons are given as output.
The toolbox outputs a global average P-value for all features, as well as a raw and corrected P-value for each feature.

11. Experiments Two schizophrenia case studies on brain structures
We use two types of features:
3D coordinates of SPHARM-PDM
3D spherical wavelet coefficients
We visualize:
Average statistic (whether 2 groups are different)
Local statistics (where on the surface those differences are)

12. Experiment1: Hippocampus Data
Data acquired by UNC (Stanley Foundation)
Schizophrenia study on the hippocampus brain structure in male adult
56 schizophrenia subjects and 26 healthy control subjects
The structures were corrected for difference in head size (ICV)
Reference:
M. Styner, J. Lieberman, D. Pantazis, and G. Gerig, “Boundary and medial shape analysis of the hippocampus in schizophrenia,” Medical Image Analysis, vol. 8, no. 3, pp. 197–203, 2004.

13. Average statistic across surface Left Hippocampus
Shape feature
SPHARM-PDM
SWC
Level 1
Levels 1-2
Levels 1-3
P-value of average statistic across surface
0.285
0.008**
0.0358* *
P-value of 95 percentile statistic across surface
0.0384* *
0.0432*
* Indicates statistical difference between groups at significance level 0.05
** Indicates statistical difference between groups at significance level 0.01

14. SPHARM-PDM Significance Maps
Left Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

15. SWC Significance Maps, Level 1
Left Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

16. SWC Significance Maps, Levels 1-2
Left Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

17. SWC Significance Maps, Levels 1-3
Left Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

18. Average statistic across surface Right Hippocampus
Shape feature
SPHARM-PDM
SWC
Level 1
Levels 1-2
Levels 1-3
P-value of average statistic across surface ** **
0.002 ** **
P-value of 95 percentile statistic across surface
0.004 **
5e-05 ** **
* Indicates statistical difference between groups at significance level 0.05
** Indicates statistical difference between groups at significance level 0.01

19. SPHARM-PDM Significance Maps
Right Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

20. SWC Significance Maps, Level 1
Right Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

21. SWC Significance Maps, Levels 1-2
Right Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

22. SWC Significance Maps, Levels 1-3
Right Hippocampus
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

23. Experiment 2: Caudate Data
Data acquired by Harvard PNL (Stanley Foundation)
Schizo-typal personality disorder (SPD) in female adult patients
32 SPD subjects and 29 healthy control subjects were analyzed
The structures were corrected for difference in head size (ICV)
Reference:
Koo MS, Levitt JJ, McCarley RW, Seidman LJ, Dickey CC, Niznikiewicz MA, Voglmaier MM, Zamani P andLong KL, Kim SS, and Shenton ME., “Reduction of caudate volume in neuroleptic-naive female subjects with schizotypal personality disorder,” Biol Psychiatry 2006, vol. 1, no. 60, pp. 40–48

24. Average statistic across surface Left Caudate
Shape feature
SPHARM-PDM
SWC
Level 1
Levels 1-2
Levels 1-3
P-value of average statistic across surface
0.0441*
0.1955 * *
P-value of 95 percentile statistic across surface * * *
* Indicates statistical difference between groups at significance level 0.05
** Indicates statistical difference between groups at significance level 0.01

25. SPHARM-PDM Significance Maps
Left Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

26. SWC Significance Maps, Level 1
Left Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

27. SWC Significance Maps, Levels 1-2
Left Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

28. SWC Significance Maps, Levels 1-3
Left Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

29. Average statistic across surface Right Caudate
Shape feature
SPHARM-PDM
SWC
Level 1
Levels 1-2
Levels 1-3
P-value of average statistic across surface
0.0041** **
0.0014** **
P-value of 95 percentile statistic across surface **
0.0034**
0.0048** **
* Indicates statistical difference between groups at significance level 0.05
** Indicates statistical difference between groups at significance level 0.01

30. SPHARM-PDM Significance Maps
Right Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

31. SWC Significance Maps, Level 1
Right Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

32. SWC Significance Maps, Levels 1-2
Right Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

33. SWC Significance Maps, Levels 1-3
Right Caudate
Lateral View
Medial View
Raw
FDR
P > 0.05
P = 0.05
P = 0

34. Conclusions
The scale-space decomposition of the SWC provides shape features that describe group differences at a variety of scales and spatial locations, providing additional information in addition to local features such as PDM.
The results show that the SWC representation nicely complements the PDM results by correlating with areas of significance for the right caudate and hippocampus and indicating new areas of significance preserved under the FDR correction for both the left caudate nucleus and left hippocampus.
Further studies providing correction for age and medication will be needed to draw clinical conclusions.