TY - JOUR

T1 - Multivalued geodesic ray-tracing for computing brain connections using diffusion tensor imaging

AU - Sepasian, N.

AU - Thije Boonkkamp, ten, J.H.M.

AU - Haar Romenij, ter, B.M.

AU - Vilanova, A.

PY - 2012

Y1 - 2012

N2 - Diffusion tensor imaging (DTI) is a magnetic resonance technique used to explore anatomical fibrous structures, like brain white matter. Fiber-tracking methods use the diffusion tensor (DT) field to reconstruct the corresponding fibrous structure. A group of fiber-tracking methods trace geodesics on a Riemannian manifold whose metric is defined as a function of the DT. These methods are more robust to noise than more commonly used methods where just the main eigenvector of the DT is considered. Until now, geodesic-based methods were not able to resolve all geodesics, since they solved the Eikonal equation, and therefore were not able to deal with multivalued solutions. Our algorithm computes multivalued solutions using an Euler–Lagrange form of the geodesic equations. The multivalued solutions become relevant in regions with sharp anisotropy and complex geometries, or when the first arrival time does not describe the geodesic close to the anatomical fibrous structure. In this paper, we compare our algorithm with the commonly used Hamilton–Jacobi (HJ) equation approach. We describe and analyze the characteristics of both methods. In the analysis we show that in cases where, e.g., U-shaped bundles appear, our algorithm can capture the underlying fiber structure, while other approaches will fail. A feasibility study with results for synthetic and real data is shown.

AB - Diffusion tensor imaging (DTI) is a magnetic resonance technique used to explore anatomical fibrous structures, like brain white matter. Fiber-tracking methods use the diffusion tensor (DT) field to reconstruct the corresponding fibrous structure. A group of fiber-tracking methods trace geodesics on a Riemannian manifold whose metric is defined as a function of the DT. These methods are more robust to noise than more commonly used methods where just the main eigenvector of the DT is considered. Until now, geodesic-based methods were not able to resolve all geodesics, since they solved the Eikonal equation, and therefore were not able to deal with multivalued solutions. Our algorithm computes multivalued solutions using an Euler–Lagrange form of the geodesic equations. The multivalued solutions become relevant in regions with sharp anisotropy and complex geometries, or when the first arrival time does not describe the geodesic close to the anatomical fibrous structure. In this paper, we compare our algorithm with the commonly used Hamilton–Jacobi (HJ) equation approach. We describe and analyze the characteristics of both methods. In the analysis we show that in cases where, e.g., U-shaped bundles appear, our algorithm can capture the underlying fiber structure, while other approaches will fail. A feasibility study with results for synthetic and real data is shown.

U2 - 10.1137/110824395

DO - 10.1137/110824395

M3 - Article

VL - 5

SP - 483

EP - 504

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 2

ER -