  In this paper, we propose to train deep neural networks with biomechanical
simulations, to predict the prostate motion encountered during
ultrasound-guided interventions. In this application, unstructured points are
sampled from segmented pre-operative MR images to represent the anatomical
regions of interest. The point sets are then assigned with point-specific
material properties and displacement loads, forming the un-ordered input
feature vectors. An adapted PointNet can be trained to predict the nodal
displacements, using finite element (FE) simulations as ground-truth data.
Furthermore, a versatile bootstrap aggregating mechanism is validated to
accommodate the variable number of feature vectors due to different patient
geometries, comprised of a training-time bootstrap sampling and a model
averaging inference. This results in a fast and accurate approximation to the
FE solutions without requiring subject-specific solid meshing. Based on 160,000
nonlinear FE simulations on clinical imaging data from 320 patients, we
demonstrate that the trained networks generalise to unstructured point sets
sampled directly from holdout patient segmentation, yielding a near real-time
inference and an expected error of 0.017 mm in predicted nodal displacement.
