Dependence of fluence errors in dynamic IMRT on leaf-positional errors varying with time and leaf number

In d-MLC based IMRT, leaves move along a trajectory that lies within a user-defined tolerance (TOL) about the ideal trajectory specified in a d-MLC sequence file. The MLC controller measures leaf positions multiple times per second and corrects them if they deviate from ideal positions by a value greater than TOL. The magnitude of leaf-positional errors resulting from finite mechanical precision depends on the performance of the MLC motors executing leaf motions and is generally larger if leaves are forced to move at higher speeds. The maximum value of leaf-positional errors can be limited by decreasing TOL. However, due to the inherent time delay in the MLC controller, this may not happen at all times. Furthermore, decreasing the leaf tolerance results in a larger number of beam hold-offs, which, in turn leads, to a longer delivery time and, paradoxically, to higher chances of leaf-positional errors (≤TOL). On the other end, the magnitude of leaf-positional errors depends on the complexity of the fluence map to be delivered. Recently, it has been shown that it is possible to determine the actual distribution of leaf-positional errors either by the imaging of moving MLC apertures with a digital imager or by analysis of a MLC log file saved by a MLC controller. This leads next to an important question: What is the relation between the distribution of leaf-positional errors and fluence errors. In this work, we introduce an analytical method to determine this relation in dynamic IMRT delivery. We model MLC errors as Random-Leaf Positional (RLP) errors described by a truncated normal distribution defined by two characteristic parameters: a standard deviation σ and a cut-off value Δx₀ (Δx ₀∼TOL). We quantify fluence errors for two cases: (i) Δx₀≫σ (unrestricted normal distribution) and (ii) Δx₀≪σ (Δx₀-limited normal distribution). We show that an average fluence error of an IMRT field is proportional to (i) σ/ALPO and (ii) Δx₀/ALPO, respectively, where ALPO is an Average Leaf Pair Opening (the concept of ALPO was previously introduced by us in Med. Phys. 28, 2220-2226 (2001). Therefore, dose errors associated with RLP errors are larger for fields requiring small leaf gaps. For an N-field IMRT plan, we demonstrate that the total fluence error (if we neglect inhomogeneities and scatter) is proportional to 1/√N, where N is the number of fields, which slightly reduces the impact of RLP errors of individual fields on the total fluence error. We tested and applied the analytical apparatus in the context of commercial inverse treatment planning systems used in our clinics (Helios^™ and BrainScan^™). We determined the actual distribution of leaf-positional errors by studying MLC controller (Varian Mark II and Brainlab Novalis MLCs) log files created by the controller after each field delivery. The analytically derived relationship between fluence error and RLP errors was confirmed by numerical simulations. The equivalence of relative fluence error to relative dose error was verified by a direct dose calculation. We also experimentally verified the truthfulness of fluences derived from the log file data by comparing them to film data.