A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics

We introduce a method for estimating regional connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) based on a fluid mechanics model. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow. The velocity vector field of this fluid construct is then used as a connectivity metric. We generate probable connection paths by maximizing the fluid velocity along a path between two regions of interest while constraining its bending energy. Our method is based on a second-order nonlinear partial differential equation (PDE) and incorporates local anisotropy and similarity measurements into a viscosity term, which extends previous linear first-order methods. We tested our algorithm on a digital DTI phantom. Our method was able to correctly segment the structure of the phantom with various levels of noise, despite local distortion of the image pattern. We applied our method to DTI volumes from a normal human subject. Seed points were chosen along the corticospinal tracts, white matter regions with well-known connectivity. Our method produced paths that were consistent with both known anatomy and directionally encoded color (DEC) images of the DTI volumes. Applying our method to a digital phantom that simulates discrete white matter lesions, we also demonstrate that the fluid velocity field around areas of simulated localized white matter disruption becomes dampened and turbulent compared to the heat flow field from a first order PDE method. This provides a means for identifying lesion position from the fluid velocity field