A PDE approach for measuring tissue thickness
We outline an Eulerian framework for computing the thickness of tissues between two simply connected boundaries. Thickness is defined as the length of trajectories which follow a smooth vector field constructed in the region between the boundaries. A pair of partial differential equations (PDEs) are then solved and combined to yield length without requiring the explicit construction of the trajectories. An efficient, stable, and computationally fast solution to these PDEs is found by careful selection of finite differences according to an upwinding condition. The behavior and performance of the method is demonstrated on two simulations and two magnetic resonance imaging data sets in two and three dimensions. These experiments reveal very good performance and show strong potential for application in tissue thickness visualization and quantification.