MaThRad Workshop discussion: Robust Optimisation

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 third area of interdisciplinary projects is focused on Robust Optimisation of the Boltzmann equation from multiple perspectives.

Multi-Objective Functionals

Presently most models only account for dose delivered when optimising beam position and intensity; however, they do not account for Linear Energy Transfer (LET), , the rate at which energy is lost by the particle along its track. When substantial amounts of energy is deposited locally this leads to increased biological damage to the surrounding tissue. This damage to the tissue may result in secondary cancers, and thus accounting for biological damage in the objective functional may reduce this risk. One potential method would be to introduce a term which minimises the proximal and distal parts of the Bragg peak.

Alternate Heavy Ion Therapies

Presently MaThRad is focused on the proton radiation therapy; however, as the mathematical framework is similar, this work can be extended to other heavy ion therapies, such as Helium or Carbon ions. Whilst the biological damage caused by these therapies is greater, they may have a reduced risk of secondary tumours, as the biological damage is greater than the cells capacity to repair itself, and thus there is a reduced probability of mutation. Another potential avenue would be to combine external beam therapy and internal radiation sources in the context of Boron-Neutron capture therapy.

Robustness vs Optimality

We aim to answer the question “Does robust optimisation result in a sub-optimal plan being selected?” We wish to understand the trade off between robustness and the nominal plan quality. To answer this question we shall conduct sensitivity analysis of the biological and beam parameters to estimate their significance, and understand how uncertainty impacts the delivered dose. One potential method would be to use perturbations with knowledge of uncertainties to estimate the delivered dose. Such methods may be computationally expensive, so fast algorithms must be developed if this route is considered.

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