Modifications to the Viscous Fluid Registration Model

The fluid PDE is summarised by

$$\nabla \cdot \bar{\bar{ \sigma}} + \vec{f} = 0$$ (2)

where $\vec{f}$ is the driving force and $\bar{\bar{\sigma}}$ is the stress tensor, given by

$$\bar{\bar{\sigma}} = -p\bar{\bar{I}} + \mu \left( \nabla \vec{v} + ( \nabla \vec{v})^T \right)$$ (3)

where $\vec{v}$ is the velocity field, p is a pressure term and $\mu$ is the viscosity parameter.

We now describe methods of introducing inhomogeneities into the application of the fluid algorithm [7] such that deformation is reduced or prohibited in areas specified as passive, motionless or weakly deformable. They are intended for use with prior estimates of the rigidity or cross-population variability of different tissue structures identified in a rough initial segmentation.