MaThRad Workshop discussion: Bayesian update model

On the 9th and 10th of February, the first MaThRad Clinical Workshop was held in London, where dozens of academics, from numerous disciplines, gathered to exchange ideas, learn about each other’s fields, and develop collaborative projects which MaThRad could undertake.

The second area of interdisciplinary projects is focused on a Bayesian Statistical model for particle detection.

Updating Beam

We wish to construct a hypothetical Bayesian model that updates the beam position and intensity given the patients position. This would incorporate topics mentioned in the previous post, in particular the detection of gamma rays. As we would use external measurements of gamma rays to derive the location of the emission and use that to infer the proton dose delivery.

Analysis

We will mathematically explore methods for applying perturbations to a given treatment plan, and then compare the perturbed treatment plan to a re-optimised plan. The goal of such a project would be to answer the question “Can the treatment be adapted to changes of the day without re-calculating everything?” A preliminary mathematical study has already been conducted by Jasmine Lewis, who performed sensitivity analysis of Bortfeld’s model of the Bragg curve, the details of which may be found here.

Simulator for Patient Movement

In most current forms of robust optimisation the uncertainty in the positions of the internal organs of the patient are assumed to follow a uniform distribution. However, this significantly increases the number of degrees of freedom which the model contains, which in turn increases the number of simulations required for a “robust” optimisation. A potential project would be to develop a simulation for the internal organs motion and deformations of a patient. The applications of this project would be to consider distributions are better fitted to the body of a patient, which would in turn reduce the number of degrees of freedom and thus speed up the optimisation process. Additionally, this work could feed into a four dimensional model of the treatment allowing to accurately simulate the patient dose as the internal components fluctuate.