FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics

Hongtu Zhu, Ph.D. Department of Biostatistics and

Biomedical Research Imaging Center, University of North Carolina at Chapel Hill


Outline

Motivation

Multivariate Varying Coefficient Models Simulation Studies

Real Data Analysis


Motivation

Functional Connectivity

Structural Connectivity

Anatomical MRI, DTI (HARDI)

group 1group 2

EEG, fMRI, resting fMRI


Neonatal Brain Development

Knickmeyer RC, et al. J Neurosci, 2008 28: 12176-12182.

Motivation

PI: John H. Gilmore.

www.google.com


Early Brain Development

Knickmeyer RC, et al. J Neurosci, 2008 28: 12176-12182.

Motivation

2 week 1 year 2 year


Diffusion Tensor Tract Statistics

Motivation

2 week 1 year 2 year 2 week 1 year 2 year

FA Tensor


Motivation

Casey, B.J. et al. TRENDS in Cognitive Sciences, 2005 9(3): 104-110.

Macaque Brain Development PI: Martin Styner& Marc Niethammer.


Motivation



Motivation



(e)

Functional Analysis of Diffusion Tensor Tract Statistics

Data

Yi(s j ) (y i,1(s j ),L ,y i,m (s j ))T

• Diffusion properties (e.g., FA, RA)

{s1,L ,snG}• Grids

• Covariates (e.g., age, gender, diagnostic)

x1,L ,xn

FA

MD

1

2

3


FADTTS


Multivariate Varying Coefficient Model

y i,k (s) x iT Bk (s) i,k (s) i,k (s)

i,k () ~ SP(0, )

i,k () ~ SP(0, ),

(s,s') (s,s)1(s s')

y (s,s') (s,s') (s,s)1(s s')

x1,L , xn

Low Frequency Signal High Frequency NoiseVarying Coefficients

Decomposition:

Covariance operator:


Weighted Least Squares Estimate

minBk (s)j1

nG

Kh (s s j )[i1

n

y i,k (s j ) x iT Bk (s j )]

2

n{vec( ˆ B (s) B(s) 0.5O(H 2)) : s [0,L0]} L G(0, (s,s') X 1)

Low Frequency SignalKey Advantage


Smooth individual functions

min i ,k (s) Kh (s j s)[y i,k (s j ) x iT ˆ B k (s j ) i,k (s j )]

2

j1

nG

ˆ (s,t) ˆ i(s) ˆ i(t)T

i1

n

{( ˆ k,l , ˆ k,l (s)) : l 1,L ,}

Functional Principal Component Analysis

Estimated covariance operator

Estimated eigenfunctions


Statistical Inferences

Testing Linear Hypotheses

Local Test Statistics

Global Test Statistics

Sn (s j ) nd(s j )T [C( (s j,s j ) X

1)CT ] 1d(s j )

Sn (s j ) k2(m) and Sn wkk

2(1)k1

K

,

H0 : Cvec(B(s)) = b0(s) versus H1 : Cvec(B(s)) b0(s)

Sn n d(s)T [C( (s,s) X 1)CT ] 1d(s)ds

0

L0

Grid Point Whole Tract


Asymptotics

Confidence Band

( ˆ b k,l (s) -Ck,l ()

n, ˆ b k,l (s) +

Ck,l ()n

)

n[ ˆ b k,l (s) - bk,l (s) - bias( ˆ b k,l (s))] Gk,l ()

Confidence band

Critical point

P(sups[0,L0 ] | Gk,l (s) |Ck,l ()) =1-


Pros

• Directly smooth varying coefficient functions• Explicitly account for functional nature of tract statistics• Characterize low frequency signal • Drop high frequency noise• Increase statistical power

Cons

• Complicated asymptotic results• Computationally intensive

Comparisons


Simulation Studies

Model

))(ˆ),(ˆ())(),(( 23132313 sscss Setting


Simulation Studies

Testing )0,0())(),((: 23130 ssH


Power Comparison between GLM and FADTTS

n 64, 0.05

n 64, 0.01

n 128, 0.01

n 128, 0.05


Real Data Analysis


Early Brain Development

•


Real Data Analysis

128 subjects

Splenium

Diffusion properties = Gender + Gestational age

1

2

3

FA

MD


Real Data Analysis


Local P-values

FA

MD


Confidence Bands

FA

MD

1

2

3

Gender AgeIntercept


Functional Principal Component Analysis

FA MD

1

2

3

Eigenvalues


FADTTS GUI Toolbox


FADTTS GUI Toolbox

Input: Raw data and test data.• Raw data include tract data, design data and diffusion

data. • Test data include test matrix and vector.• All data is in .mat format.Output: Basic plots and P-value plots• Basic plots include diffusion plot, coefficient plot,

eigenvalue and eigenfunction plot, confidence band plot.• P-value plot include local p-value (in –log10 scale) plot

with global p-value. Download: FADTTS GUI Toolbox with related documents and

sample data is free to download from http://www.nitrc.org/projects/fadtts/


Summary

• From the statistical end, we have developed a new functional analysis pipeline for delineating the structure of the variability of multiple diffusion properties along major white matter fiber bundles and their association with a set of covariates of interest.

• From the application end, FADTTS is demonstrated in a clinical study of neurodevelopment for revealing the complex inhomogeneous spatiotemporal maturation patterns as the apparent changes in fiber bundle diffusion properties.

• We developed a GUI Tool box to facilitate the application of FADTTS.


Future Research

• extend FADTTS to the analysis of high angular resolution diffusion image (HARDI).

• extend FADTTS to principal directions and full diffusion tensors on fiber bundles.

• extend to more complex fiber structures, such as the medial manifolds of fiber tracts.

• extend FADTTS to longitudinal studies and family studies.


References• Zhu, H.T., Kong, L.L., Li, R.Z., Styner, M., Gerig, G., Lin, W.L., Gilmore, J. H.

(2011). FADTTS: Functional Analysis of Diffiusion Tensor Tract Statistics varying coefficient models for DTI tract statistics. Neuroimage, in press.

• Zhu, H.T., Li, R. Z., Kong, L.L. (2011). Multivariate varying coefficient models for functional responses. Submitted.

• Zhu, H., Styner, M., Li, Y., Kong, L., Shi, Y., Lin, W., Coe, C., and Gilmore, J. (2010). Multivariate varying coefficient models for DTI tract statistics. In Jiang, T., Navab, N., Pluim, J., and Viergever, M., editors, Medical Image Computing and Computer-Assisted Intervention MICCAI 2010, volume 6361 of Lecture Notes in Computer Science, pages 690-697. Springer Berlin / Heidelberg.

• NICTR Toolbox (2011). FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics. http://www.nitrc.org/projects/fadtts/

Documents

FADTTS: Functional Analysis of Diffusion Tensor Tract Statistics