Dynamic fluence map sequencing using piecewise linear leaf position functions

Abstract

Within the setting of intensity modulated radiation therapy (IMRT) and the fully continuous version of IMRT called volumetric modulated radiation therapy (VMAT), we consider the problem of matching a given fluence map as well as possible in limited time by the use of a linear accelerator (linac) with a multi-leaf collimator (MLC). We introduce two modeling strategies to manage the nonconvexity and the associated local minima of this problem. The first is the use of linear splines to model the MLC leaf positions as functions of time. The second is a progressively controllable smooth model (instead of a step function) of how the leaves block the fluence radiation.We propose a two part solution: an outer loop that optimizes the dose rate pattern over time, and an inner loop that given a dose rate pattern optimizes the leaf trajectories.

Technical Note: Improving VMAT delivery efficiency by optimizing the dynamic collimator trajectory

“…Another time savings measure for sliding window VMAT is to not enforce that the leaves start and stop closed at the field edges. This type of fluence map delivery however presents a difficult non‐convex optimization problem and since computing the optimal solution is not tractable, we cannot compute the field delivery time. However, the basic notion that there are preferred collimator angles by aligning the MLC leaves to avoid orthogonally traversing humps in the fluence map still holds true in this delivery style, and thus, the usage of the SPG according (Eq. )…”

Resource allocation problems with expensive function evaluations

“…If sufficient time is allocated to all treatment arcs, all fluence maps can be perfectly replicated. However, such long treatments are undesirable as the expected inaccuracy caused by patient movement increases, and put a strain on hospital facilities (Kelly et al, 2019). It is common to aim for treatments with a low delivery time, e.g., at most T total per patient.…”