Improved algorithm for generating evenly-spaced streamlines from an orientation field on a triangulated surface

Abstract

Background:Vector fields such as cardiac fiber orientation can be visualized on a surface using streamlines. The application of evenly-spaced streamline generation to the construction of interconnected cable structure for cardiac propagation models has more stringent requirements imperfectly fulfilled by current algorithms. Method:We developed an open-source C++/python package for the placement of evenly-spaced streamlines on a triangulated surface. The new algorithm improves upon previous works by more accurately handling streamline extremities, U-turns and limit cycles, by providing stronger geometrical guarantees on inter-streamline minimal distance, particularly when a high density of streamlines (up to 10μm spacing) is desired, and by making a more efficient parallel implementation available. The approach requires finding intersections between geometrical capsules and triangles to update an occupancy mask defined on the triangles. This enables fast streamline integration from thousands of seed points to identify optimal streamline placement. Results:The algorithm was assessed qualitatively on different left atrial models of fiber orientation with varying mesh resolutions (up to 375k triangles) and quantitatively by measuring streamline lengths and distribution of inter-streamline minimal distance. The complexity and the computational performance of the algorithm were studied as a function of streamline spacing in relation to triangular mesh resolution. Conclusion:More accurate geometrical computations, attention to details and fine-tuning led to an algorithm more amenable to applications that require precise positioning of streamlines.