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**MaxEnt 2007 Saratoga Springs, NY**

Computing the Probability Of Brain Connectivity with Diffusion Tensor MRI JS Shimony AA Epstein GL Bretthorst Neuroradiology Section NIL and BMRL

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**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 (mm), orders of magnitude smaller than macroscopic MR resolution (mm) This has found numerous research and clinical applications Short introduction

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**Diffusion: Left MCA stroke**

Clinical use

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Standard Spin Echo Mz Mxy Mxy echo 90 180 RF/RO Gz

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Diffusion Spin Echo M=Mxyexp(-bD) Mz Mxy echo 90 180 RF/RO Gz D

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**Diffusion: Pulse Sequence**

90 180 Echo Train RF Gss EPI Readout Gro Multi directional Gpe

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**Anisotropic Diffusion in WM Fibers**

Fibers give anisotropy

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**Diffusion: Single Direction**

Example of anisotropy

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**Diffusion Tensor Imaging Model**

Basser et al., JMR, 1994 (103) 247 Uses 8 parameters (D ≠ data) λ1 λ2 λ3 The basic model

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**How Diffusion is Measured by MRI**

Signal Amplitude Example of signal decay with gradients Diffusion Sensitization (q) Image courtesy: C. Kroenke

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**Image courtesy: C. Kroenke**

Diffusion Anisotropy Signal Amplitude Example of anisotropy Diffusion Sensitization (q) Image courtesy: C. Kroenke

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Mean Diffusivitiy λ1 λ2 λ3 Key parameters MD Mean Diffusivity is the average of the diffusion in the different directions

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**Diffusion Anisotropy RA=0 RA<1**

Anisotropy is normalized standard deviation of diffusion measurements in different directions FA and RA most common Range from 0 to 1 RA=0 Key parameters - anisotropy RA<1

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**Baseline image / Anisotropy**

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Color Diffusion

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**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)

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**3D Diffusion Tensor Field**

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**Example of Streamline Tracking**

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**Streamline DTT Advantages: Disadvantages:**

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

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**Applications: Anatomy**

Jellison AJNR 25:356

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**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

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**Crossing Fibers Locations**

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**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

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**Probabilistic Tractography**

Express DT parameters for pixel i 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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**Utilize Angular Error Estimations**

pdf Cone of angular uncertainty Low Anisotropy High Anisotropy

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**Probabilistic Tracking**

End zone Start zone

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**Example Probabilistic DTT**

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**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”

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**Adding the Connectivity Parameter**

Add nearest neighbor connectivity parameter No independence between the pixels Each pixel depends on its neighbors via the prior of its connectivity

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**Connectivity Parameter Prior**

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**Adding Connectivity Parameter**

The preference for connectivity is indicated by the prior for Lij 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

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Method: 3x3x3 Simulation

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**Results: Connectivity Parameter**

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**Coronal Section in Crossing Fiber area**

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Anatomy Comparison

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**Results: Connectivity Parameter**

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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

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