Diffuse domain method for needle insertion simulations

We present a new strategy for needle insertion simulations without the necessity of meshing. A diffuse domain approach on a regular grid is applied to overcome the need for an explicit representation of organ boundaries. A phase field function captures the transition of tissue parameters and boundary conditions are imposed implicitly. Uncertainties of a volume segmentation are translated in the width of the phase field, an approach that is novel and overcomes the problem of defining an accurate segmentation boundary. We perform a convergence analysis of the diffuse elastic equation for decreasing phase field width, compare our results to deformation fields received from conforming mesh simulations and analyze the diffuse linear elastic equation for different widths of material interfaces. Then, the approach is applied to computed tomography data of a patient with liver tumors. A three-class U-Net is used to automatically generate tissue probability maps serving as phase field functions for the transition of elastic parameters between different tissues. The needle tissue interaction forces are approximated by the absolute gradient of a phase field function, which eliminates the need for explicit boundary parameterization and collision detection at the needle-tissue interface. The results show that the deformation field of the diffuse domain approach is comparable to the deformation of a conforming mesh simulation. Uncertainties of tissue boundaries are included in the model and the simulation can be directly performed on the automatically generated voxel-based probability maps. Thus, it is possible to perform easily implementable patient-specific elastomechanical simulations directly on voxel data.