# Imaging Translational Water Diffusion with Magnetic Resonance for Fiber Mapping in the Central Nervous System

Tuesday, January 10, 2006 - 2:30pm - 3:00pm

EE/CS 3-180

Thomas Mareci (University of Florida)

Work in collaboration with Evren Ozarslan of the National Institutes of Health and Baba Vemuri of the University of Florida.

Magnetic resonance can be used to measure the rate and direction of molecular translational diffusion. Combining this diffusion measurement with magnetic resonance imaging methods allows the visualization of 3D motion of molecules in structured environments, like biological tissue. In its simplest form, the 3D measure of diffusion can be modeled as a real, symmetry rank-2 tensor of diffusion rate and direction at each image voxel. At a minimum, this model requires seven unique measurements of diffusion to fit the model (Basser, et al., J Magn Reson 1994;B:247–254). The resulting rank-2 tensor can be used to visualize diffusion as an ellipsoid at each voxel and fiber connections can be inferred by connecting the path, defined by the long axis (principle eigenvector) of the ellipse, passing through each voxel.

However, the rank-2 model of diffusion fails to accurately represent diffusion in complex structured environments, like nervous tissue with many crossing fibers. This limitation can be overcome by extending the angular resolution of diffusion measurements (Tuch, et al., Proceedings of the 7

Magnetic resonance can be used to measure the rate and direction of molecular translational diffusion. Combining this diffusion measurement with magnetic resonance imaging methods allows the visualization of 3D motion of molecules in structured environments, like biological tissue. In its simplest form, the 3D measure of diffusion can be modeled as a real, symmetry rank-2 tensor of diffusion rate and direction at each image voxel. At a minimum, this model requires seven unique measurements of diffusion to fit the model (Basser, et al., J Magn Reson 1994;B:247–254). The resulting rank-2 tensor can be used to visualize diffusion as an ellipsoid at each voxel and fiber connections can be inferred by connecting the path, defined by the long axis (principle eigenvector) of the ellipse, passing through each voxel.

However, the rank-2 model of diffusion fails to accurately represent diffusion in complex structured environments, like nervous tissue with many crossing fibers. This limitation can be overcome by extending the angular resolution of diffusion measurements (Tuch, et al., Proceedings of the 7

^{th}Annual Meeting of Inter Soc Magn Reson Med, Philadelphia, 1999. p 321.) and by modeling the diffusion with higher rank tensors (Ozarslan et al., Magn. Reson. Med. 2003; 50:955-965 & Magn. Reson. Med. 2005;53;866-876). At each voxel in this more complete model, the 3D diffusion is represented by an orientation distribution function (ODF) indicating the probability of diffusion rate and direction. The diffusion ODF can be used to infer fiber connectivity but the issue of probable path selection remains a challenge. Plus the chosen procedure for path selection will influence with the level of resolution required for the measurements. In this presentation, methods of diffusion measurement and examples of diffusion-weighted magnetic resonance images from brain and spinal cord will be presented to illustrate the potential and challenges for path selecting leading to fiber mapping in the central nervous system.MSC Code:

92B20

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