Knowing that glioma cells preferentially spread along nerve fibers, we propose the use of a geodesic distance on the Riemannian manifold of brain diffusion tensors to replace the Euclidean distance used in the clinical practice and to correctly identify the tumor invasion margin. This mathematical model results in a first-order PDE that can be numerically solved in a stable and consistent way with.
To compute the geodesic distance, we use actual Diffusion Weighted Imaging (DWI) data from 11 patients with glioma and compare our predicted growth with follow-up MRI scans. Results show improvement in predicting the invasion margin when using the geodesic distance as opposed to the 2 cm conventional Euclidean distance.
Since the method of data collection from individual biomolecules is analogous to that from individual animals, we propose to use methods from ecology to provide spatial insight. Ecologists regularly quantify animal movement using the concepts of correlated random walk, net squared displacement, and first-passage time. In this talk, we will demonstrate the applicability of these methods in the context of cell biology. In particular, we will show how we can distinguish biomolecule trajectories undergoing a correlated random walk from those that do not, and how we can identify the presence of transient confinement zones in molecular diffusion.