2017 Slicer Western Week/Laplace equation solver

From VASST Wiki

Key Investigators

  • Jordan Dekraker (Robarts Research Institute)
  • Jess Rodgers (Robarts Research Institute)

Project Description

Objective Approach and Plan Progress and Next Steps
  • Currently implementation first initializes using volumetric fast marching from source and sink, then weights and combines the two.
  • Next, we use iterative finite-differences approach to obtain better solution settings, by using a 26-neighbour average to compute the updated potential field, and terminating when the potential field change is below a specified threshold (sum of changes < 0.001%) or a maximum iteration is reached.
  • MATLAB code found at https://github.com/jordandekraker/HippUnfolding.

Background and References

  • Relevant paper for using Laplace in cortical laminar profiles: http://www.sciencedirect.com/science/article/pii/S1053811913003480.
  • The Laplace equation is can be useful for indexing within a volume, and provides a level of smoothness that is suitable for most applications in biology.
  • It is often used to index cortical laminae and streams can be generated across the gradient for determining cortical thickness.
  • In our work we also use it to compute the perpendicular gradients across the hippocampus to index its proximal-distal and longitudinal extents.