Sparse Grids for quantifying motion uncertainties in biomechanical models of radiotherapy patients

Abstract

Quantifying the uncertainties in biomedical simulations has strong potential in medical software systems. It allows us to improve objective confidence levels for numerical predictions. The Stochastic Collocation (SC) method is a promising way to create the link between existing simulation codes and advanced Uncertainty Quantification (UQ) methods, as it does not require modifying the original source code and meanwhile has better convergence rate comparing with traditional stochastic approaches. We describe the implementation of the Stochastic Collocation method with an adaptive sparse grid numerical integration, and apply it in the context of radiotherapy treatment planning of patients with head and neck cancer. In this case, the statistical sampling of most probable postures of patient specific anatomy of the neck region is used to estimate deformations of the tumor region in order to find a suitable safety margin around target volumes.
Especially, in highly flexible body areas, like the neck and upper thorax regions, the number of degrees of freedom of motion patterns can be quite large. The fast and stable prediction of most probable motion patterns, derived from previous cohorts, influences the ability to incorporate uncertainties caused by motion into the treatment planning process. The optimal number of samples not only reduces the number of simulations needed to generate an individually fitted internal target volume as a starting point for a standardized planning target volume, but also promises to minimize computational demands in robust planning scenarios, where plans are challenged by different possible motion scenarios.