Hageman:NAMICFluidMechDTITractography

Fluid Mechanics Based DTI Tractography

Overview

In this paper, we present a novel method modeled on the dynamics of a viscous fluid described by the second order non-linear Navier-Stokes equations, an extension of previous work by our group \cite{hageman-toga:2006} The Navier-Stokes equations govern flow for a viscous Newtonian fluid, a fluid whose internal stress forces are linearly related to its strain forces \cite{versteeg}. However, even though these equations are most commonly seen in the context of fluid mechanics, they have been shown to be successful in modeling a large number of diverse physical phenomena. Our second order nonlinear-based approach is an extension of previous linear PDE methods. We hypothesize that our method will have a better performance than competing tractography methods in the presence of noise and it will not require a white matter mask, commonly used by other PDE-based methods. This is because our model contains a viscous force not present in previous methods, represented as an additional convection term in the PDE. We model local viscosity of the fluid as a function of the local intervoxel and intravoxel anisotropy in the corresponding DTI image volume. The incorporation of this convection term in our flow field calculation allows us to closely couple the magnitude of the fluid velocity to the magnitude of the underlying anisotropy of the DTI tensor field, providing a dampening force in background areas, such as gray matter and CSF. This eliminates the need for the white matter mask used by other PDE-based methods to prevent the model from entering these areas. To compute an estimate of the most likely connection path between two regions in the brain, we simulate the flow of an artificial fluid between those two points through a volume whose dimensions, pressure, and local viscosity are derived from the underlying DTI data. We then numerically solve for the fluid velocity vector field. The estimated connection path is then computed by finding the optimal path through the fluid velocity that simultaneously maximizes both the fluid velocity and its gradient. We apply our method to DTI volumes from normal human subjects and to computer-generated DTI phantoms to validate our approach.

Description

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Key Investigators

• UCLA: Nathan Hageman
• UCLA: Arthur Toga, Ph.D

Publications

In Print

• NA-MIC Publications Database.

In Submission

• Hageman NS, Toga AW, Narr K, Shattuck DW (2008). A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics. IEEE Trans. in Medicial Imaging, In Submission.
• Hamilton L, Nuechterlein K, Hageman NS, Woods R, Asarnow R, Alger J, Gaser C, Toga AW, Narr K (2008). Mean Diffusivity and Fractional Anisotropy as Indicators of Schizophrenia and Genetic Vulnerability, Neuroimage, In Submission.

Links

• Hageman NS, Shattuck DW, Narr K, Toga AW (2006). A diffusion tensor imaging tractography method based on Navier-Stokes fluid mechanics. Proceedings of the 2006 IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI 2006), Arlington, VA, USA, 6-9 April 2006. p. 798-801 (PDF)
• LONI Website

Project Week Results:  2008 Winter