MaxEnt 2007 Saratoga Springs, NY

Computing the ProbabilityOf Brain Connectivity with Diffusion Tensor MRI

JS ShimonyAA EpsteinGL Bretthorst

Neuroradiology SectionNIL and BMRL

Part 1: Diffusion Tensor (DT) MRI(Brain Connectivity later)

• Diffusion MR images can measure water proton displacements at the cellular level

• Probing motion at microscopic scale (m), orders of magnitude smaller than macroscopic MR resolution (mm)

• This has found numerous research and clinical applications

Diffusion: Left MCA stroke

Standard Spin Echo

Mz

90 180 echo

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Gz

RF/RO

Diffusion Spin Echo

Mz

90 180 echo

Mxy

M=Mxyexp(-bD)

Gz

RF/RO

Diffusion: Pulse Sequence

RF

Gss

Gro

Gpe

90 180

EPI Readout

Echo Train

Anisotropic Diffusion in WM Fibers

Diffusion: Single Direction

Diffusion Tensor Imaging Model

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Basser et al., JMR, 1994 (103) 247Uses 8 parameters (D ≠ data)

How Diffusion is Measured by MRI

Diffusion Sensitization (q)S

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Image courtesy: C. Kroenke

Diffusion Anisotropy

Diffusion Sensitization (q)

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Image courtesy: C. Kroenke

Mean Diffusivitiy

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DT

• Mean Diffusivity is the average of the diffusion in the different directions

Diffusion Anisotropy• Anisotropy is normalized

standard deviation of diffusion measurements in different directions

• FA and RA most common• Range from 0 to 1

RA=0

RA<1 MD

MDMDMDRA

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22

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Baseline image / Anisotropy

Color Diffusion

Part 2: Brain Connectivity

•DT data provides a directional tensor field in the brain, used to map neuronal fibers

•Detailed WM anatomy used in:–Pre-surgical planning–Neuroscience interest in functional networks

•Previously could only be done using cadavers or invasive studies in primates

•Termed DT Tractography (DTT)

3D Diffusion Tensor Field

Example of Streamline Tracking

Streamline DTT

• Advantages:– Conceptually and computationally simple– Was the first to be developed

• Disadvantages:– Limited to high anisotropy, high signal areas– Can only produce one track – Can’t handle track splitting – Has the greatest difficulty with crossing fibers

Applications: Anatomy

Jellison AJNR 25:356

DTT and Crossing Fibers

• Major limitation of current methods of DTT

• Difficult to resolve with current methods and SNR

• Volume averaging effects• Known areas in the brain• Decrease sensitivity and

specificity, distorts connection probabilities

Crossing Fibers Locations

Probabilistic DTT

• Behrens et al. MRM 2003 50:1077-1088• Advantages:

– Better accounts for experimental errors – More robust tracking results– Better deals with crossing fibers, low SNR

• Disadvantages:– Computationally intense – Probabilities will be modified by crossing

fibers

Probabilistic Tractography

• Since each pixel is independent in this model the probability for the DT parameters given the data D can be factored:

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• Express DT parameters for pixel i

Utilize Angular Error Estimations

Cone of angularuncertainty

Angularpdf

Low Anisotropy High Anisotropy

Probabilistic Tracking

Startzone

Endzone

Example Probabilistic DTT

Part 3: Methods and Results

• Use prior information!!!• Assumption of pixel independence is

non_biological • Nerve fiber bundles can travel over long

distances in the brain and cross many pixels

• Incorporate this into the model via a: “Nearest Neighbor Connectivity Parameter”

Adding the Connectivity Parameter

• No independence between the pixels• Each pixel depends on its neighbors via

the prior of its connectivity

IPIDPDIP iii

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• Add nearest neighbor connectivity parameter

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Connectivity Parameter Prior

Adding Connectivity Parameter

• The preference for connectivity is indicated by the prior for ij

• Express this as the probability that a water molecule will diffuse from pixel i to j

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Parallel Processing Details• Connection between

neighboring pixels complicates the calculations

• When processing on a parallel computer, the values of the neighbors cannot change

• Example in 1D and 2D

Method: 3x3x3 Simulation

Results: Connectivity Parameter

Coronal Section in Crossing Fiber area

Anatomy Comparison

Results: Connectivity Parameter

Summary• DT imaging provides accurate estimation of

the tensor field of the WM in the brain• Accurate estimation of the connectivity

between different brain regions is of great clinical and research interest

• Prior work has assumed independent pixels• Prior information on local connectivity may

provide a more accurate representation of the underlying tissue structure

• Acknowledgements: NIH K23 HD053212, NMSS PP1262, and Chris Kroenke