3D simulation of needle-tissue interaction with application to prostate brachytherapy

This paper presents a needle-tissue interaction model that is a 3D extension of prior work based on needle and tissue models discretized using the Finite Element Method. The use of flexible needles necessitates remeshing the tissue during insertion, since simple mesh-node snapping to the tip can be detrimental to the simulation. In this paper, node repositioning and node addition are the two methods of mesh modification examined for coarse meshes. Our focus is on numerical approaches for fast implementation of these techniques. Although the two approaches compared, namely the Woodbury formula (matrix inversion lemma) and the boundary condition switches, have the same computational complexity, the Woodbury formula is shown to perform faster due to its cache-efficient order of operations. Furthermore, node addition is applied in constant time for both approaches, whereas node repositioning requires longer and variable computational times. A method for rendering the needle forces during simulated insertions into a 3D prostate model has been implemented. Combined with a detailed anatomical segmentation, this will be useful in teaching the practice of prostate brachytherapy. Issues related to discretization of such coupled (e.g., needle-tissue) models are also discussed.