High-order 3D FEM of prostate needle insertion forces

The long term goal of this project is to predict the deformation brachytherapy needle insertion using a 3D finite element model (FEM). Our FEM was based on a realistic prostate geometry obtained from ultrasound images from a human patient subject, including the geometry of the urethra and prostate capsule. The model was used to investigate pin cushion deformation that occurs during brachytherapy just prior to puncture of the capsule. A 2D FEM was used previously to validate the approach. The 2D FEM employed non-linear element basis functions and the model predictions were compared to those reported in the literature. The current study employed a 3D FEM model with code developed in Matlab and using linear combinations of cubic Hermite finite element basis functions. The material properties for the prostate were those obtained from the literature. The base mesh was defined as an ellipsoidal prostate and capsule, with 48 nodes defining the prostate surface. The urethra was modelled as a paraboloid running through the prostate. The nodal parameters of the prostate base mesh were then optimized to match the unique anatomy of the representative human prostate under investigation. The surface fitting error after optimization was 1.4 mm. Finally, a 10 N axial force was applied to an apical capsule node and the deformed mesh satisfying force balance equilibrium was converged to in approximately 1 hour. A 8% reduction was found for the overall axial displacement of the node at which the force was applied when the results using the encapsulated prostate model was compared to previous results where the capsule was not included. This finding suggests that the capsule plays a prominent mechanical role in brachytherapy needle insertion and warrants a more in-depth study of capsule mechanical properties.