Mapping White Matter Connections in the Brain using Diffusion-Weighted Imaging and Tractography Andy Alexander Waisman Center Departments of Medical Physics and Psychiatry University of Wisconsin - Madison

Overview Streamline Tractography Probabilistic Tractography Global Tractography

Diffusion Models Diffusion Tensor Imaging (Basser et al. 1994) HARDI (High Angular Resolution Diffusion Imaging) –Single Shell of Diffusion Weighting –SHD of ADC (Frank et al. 2002, Alexander 2002) –Q-Ball (Tuch 2004) Diffusion Spectrum (q-Space) Imaging –qSI (Callaghan 1991; Assaf et al. 2000) –DSI (Wedeen et al. 2005) – Cartesian q-space –HYDI (Wu and Alexander 2007) – Multiple Shells Orientation Distribution Function - ODF –(Tuch et al. 2003; Wedeen et al. 2005) Fiber ODF –(Tournier et al. 2004; Descoteaux et al. 2007)

Diffusion Models Diffusion Tensor Imaging (Basser et al. 1994) HARDI (High Angular Resolution Diffusion Imaging) –Single Shell of Diffusion Weighting –SHD of ADC (Frank et al. 2002, Alexander 2002) –Q-Ball (Tuch 2004) Diffusion Spectrum (q-Space) Imaging –qSI (Callaghan 1991; Assaf et al. 2000) –DSI (Wedeen et al. 2005) – Cartesian q-space –HYDI (Wu and Alexander 2007) – Multiple Shells Orientation Distribution Function - ODF –(Tuch et al. 2003; Wedeen et al. 2005) Fiber ODF –(Tournier et al. 2004; Descoteaux et al. 2007)

Diffusion Tensor Imaging DW images

Courtesy G Kindlmann

White Matter Tractography

Tract Construction

Figure 1

Streamline Methods Steering or Propagation: Streamlines (Mori 1999; Conturo 1999; Basser 2000) Tensor Deflection (Westin 2002; Lazar 2003) Tensorlines (Weinstein 1999; Lazar 2003) Tract Integration: FACT (Mori 1999) Euler (Conturo 1999) Runge Kutta (Basser 2000)

DT-MRI Alexander Pretty Pictures M Lazar

PreopPostop Lazar et al. AJNR 2006

Corpus Callosum Abnormalities in Autism 24 y.o. autistic male26 y.o. male

cience S AAAS Brain Disconnectivity In Autism 12 July 2004 Vol 299 No Pages $10

Not-so Pretty Pictures 24 y.o. autistic male26 y.o. autistic male

Tractography Errors Error Sources/Factors: Anything that affects DTI accuracy: Tractography Errors are Cumulative Tensor Fields are Heterogeneous (Branches, Crossing, Adjacent WM Tracts) False Branching & Termination Visually Apparent DTI Artifacts => Tractography Error Look at Raw Image Data! SMALL ERRORS CAN HAVE CATASTROPHIC RESULTS!

Comparison of Tractography Algorithms Tensorlines (Weinstein et al. 1999): V out = f e 1 + (1 - f )((1 - g)v in + gD. v in ) f = 1 g = 0 streamlines f = 0 g = 1 deflection f = 0 g = 0.3 stiff deflection

How to Interpret Pretty Pictures? If Tractograms Look Realistic – Are They? Tractograms Usually Look Realistic

DT-MRI Alexander SLF CR CC CING Partial Volume Effects on Anisotropy

Catani

Tract Dispersion y x y’ x’ S x’ S y’

Tract Dispersion: Model Lazar & Alexander Neuroimage 2003

Estimating Tract Confidence Models: Lazar & Alexander Neuroimage (2003); Probabilistic Tractography: Behrens et al. MRM (2003); Parker et al. JMRI (2003) Bootstrap Tractography: Lazar & Alexander Neuroimage (2005); Jones et al. ISMRM (2004) Multisubject Tractography Analysis: Mori et al. MRM 2002; Toosy et al. 2004; Thottakara et al. 2006

DT-MRI Alexander Probabilistic Tractography Small angular perturbations are added at each ‘step’ – PICo (Parker JMRI 2003); FSL (Behrens et al. 2003) Our approach: RAVE (Random Vector) Perturbation -from a single seed multiple pathways are generated by calculating a perturbed eigenvector direction at discrete points along the trajectory (e.g., Monte Carlo Tractography) Lazar & Alexander ISMRM 2002

RAVE perturbation algorithm y’ x’ z’ 11 y’ x’ z’ 11  - degree of perturbation Lazar & Alexander ISMRM 2002

Streamline Solution  = 0.2 RAVE Solution Lazar & Alexander ISMRM 2002

Bootstrap Tractography BOOT-TRAC Bootstrap: Non-parametric distribution estimation method - iterative resampling with replacement - Efron (1979) - DTI: Pajevic & Basser (2003); Jones (2003); Hasan et al. (2004) * Resample raw DW images Boot-Trac: Requires 2+ DTI data sets from same session - tractography repeated from seed location with random resampling (Lazar & Alexander 2005, Jones 2005)) No Model Assumed – describes actual variations in data Wild Bootstrap, Residual Bootstrap – Chung 2006; Jones 2008

BOOT-TRAC Lazar & Alexander Neuroimage 2005

Multisubject Tractography Analysis Parcelatewhole-brain tracts using cortical template Co-register binarized tractography connection data between subjects Thottakara et al. Neuroimage 2006

Diffusion MRI - Alexander Average Connectivity Patterns (16 subjects) Area 4 Area 6 Area 8 ROIs Thottakara et al. Neuroimage 2006

Diffusion MRI - Alexander Composite Map – Highest Connection Probability Thottakara et al. Neuroimage 2006

Anatomical and Functional Parcellation Freesurfer Parcellation Maps 2005 Previously Available 2009 Now Using

Framework of modeling human connectome using dMRI [Zalesky et. al., 2010]

Human Connectome Average connectivity matrix for 33 participants Cortex: Left HemisphereCortex: Right Hemisphere Left Subcortical Right Subcortical Cortex: Left Hemisphere Cortex: Right Hemisphere Left Subcortical Right Subcortical

Diffusion MRI - Alexander Nonhuman Primate DTI Template 238 Macaques

Nonhuman Primate Inferior Frontal-Occipital Fasciculus top left Single Subject Average Population

Global Tractography Considerable ambiguities of tract solutions for complex fiber architecture Fiber ODF helps but ambiguities remain Global Tractography –Find ‘optimal’ tractography solutions that are consistent with regional or global measurements

Global Tractography Algorithms Graph Theory Tractography –Iturria-Medina 2007; Lifshits 2009; Zalesky 2009; Sotiropoulos 2010; Collins 2010 Min Energy Solution – 2 regions –Fletcher 2007;Cheng 2006 Particle Filtering - Zhang 2009 Gibbs Tracking – Kreher 2007 Spin Glass Model – Fillard 2009

Gibbs Tracking (Kreher, Mader and Kiselev, MRM 2007) DWI signals  Tract Model Build ‘fiber’ configurations using small line pieces Use fiber geometry to generate synthetic DW data Synthetic data compared against measured DW data and fiber configuration is adjusted to obtain new solution Iterative optimization methods are used to maximize consistency between measured data and tracts

Gibbs Tracking (Kreher, Mader and Kiselev, MRM 2007)

Complex Optimization Problem Computationally Demanding! Whole brain ~ one month Potential Payoff is High – Accurate reconstruction

Validation Critical problem – How do we know what is real? – How accurate? Synthetic & Phantom Data ‘Known’ Neuroanatomy Comparison with Tracer Studies

DT-MRI Alexander Dyrby et al. Neuroimage 2008

Alexander Lab - Funding: NIH, Dana Foundation