In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and underand overshoots. For an interior penalty discontinuous Galerkin (DG) discretization, we present a h-adaptive refinement strategy and, alternatively, a new e...

NI-13. RESOLVING THE CHALLENGES OF PERITUMORAL EDEMA IN TRACING ARCUATE FASCICULUS FOR SURGICAL PLANNING USING TWO-TENSOR UNSCENTED KALMAN FILTER TRACTOGRAPHY Zhenrui Chen1,4, Yanmei Tie1, Lauren O’Donnell1,2, Laura Rigolo1, Alireza Mehrtash1,2, Olutayo Olubiyi1, Isaiah Norton1, Ofer Pasternak3, Yogesh Rathi3, and Alexandra Golby1,2; Department of Neurosurgery, Brigham and Women’s Hospital, Har...

Streamline similarity comparison has become an active research topic recently. We present a novel streamline similarity comparison method inspired by the bag-of-features idea from computer vision. Our approach computes a feature vector, spatially sensitive bag-of-features, for each streamline as its signature. This feature vector not only encodes the statistical distribution of combined feature...

In this paper, we build upon a new model, describing the random motion of water molecules in fibrous tissues, to develop a multifiber deterministic tractography algorithm. We apply this algorithm to track the corticospinal tract of the human brain, in both controls and patients with tumors.

The stability and accuracy of a streamline diffusion finite element method (SDFEM) on arbitrary grids applied to a linear 1-d singularly perturbed problem are studied in this paper. With a special choice of the stabilization quadratic bubble function, the SDFEM is shown to have an optimal second order in the sense that ‖u − uh‖∞ ≤ C infvh∈V h ‖u − vh‖∞, where uh is the SDFEM approximation of th...

Diffusion MRI tractography is increasingly used in pre-operative neurosurgical planning to visualize critical fiber tracts. However, a major challenge for conventional tractography, especially in patients with brain tumors, is tracing fiber tracts that are affected by vasogenic edema, which increases water content in the tissue and lowers diffusion anisotropy. One strategy for improving fiber t...

Euler’s equation expresses the relationship between the velocity and the pressure fields in inviscid flow. Written in terms of streamline coordinates, this equation gives information about not only about the pressure-velocity relationship along a streamline (Bernoulli’s equation), but also about how these quantities are related as one moves in the direction transverse to the streamlines. The tr...

From observations of direct numerical simulations (DNS) of twodimensional turbulence with inverse energy cascade, two physical pictures of particle pair diffusion are proposed based on persistent streamline topology associated with stagnation points. One picture describes the step-by-step separation process of individual pairs in a local frame moving with them, whereas the other serves as a sta...

MRI tractography is the mapping of neural fiber pathways based on diffusion MRI of tissue diffusion anisotropy. Tractography based on diffusion tensor imaging (DTI) cannot directly image multiple fiber orientations within a single voxel. To address this limitation, diffusion spectrum MRI (DSI) and related methods were developed to image complex distributions of intravoxel fiber orientation. Her...

We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the numerical solution of such optimal control problems. In the discretize-then-optimize approach the optimal control problem is first discretized, using the SUPG met...