Homogenized blocked arcs for multicriteria optimization of radiotherapy: analytical and numerical solutions.
OBJECTIVE
Homogenized blocked arcs are intuitively appealing as basis functions for multicriteria optimization of rotational radiotherapy. Such arcs avoid an organ-at-risk (OAR), spread dose out well over the rest-of-body (ROB), and deliver homogeneous doses to a planning target volume (PTV) using intensity modulated fluence profiles, obtainable either from closed-form solutions or iterative numerical calculations. Here, the analytic and iterative arcs are compared.


METHODS
Dose-distributions have been calculated for nondivergent beams, both including and excluding scatter, beam penumbra, and attenuation effects, which are left out of the derivation of the analytic arcs. The most straightforward analytic arc is created by truncating the well-known Brahme, Roos, and Lax (BRL) solution, cutting its uniform dose region down from an annulus to a smaller nonconcave region lying beyond the OAR. However, the truncation leaves behind high dose hot-spots immediately on either side of the OAR, generated by very high BRL fluence levels just beyond the OAR. These hot-spots can be eliminated using alternative analytical solutions "C" and "L," which, respectively, deliver constant and linearly rising fluences in the gap region between the OAR and PTV (before truncation).


RESULTS
Measured in terms of PTV dose homogeneity, ROB dose-spread, and OAR avoidance, C solutions generate better arc dose-distributions than L when scatter, penumbra, and attenuation are left out of the dose modeling. Including these factors, L becomes the best analytical solution. However, the iterative approach generates better dose-distributions than any of the analytical solutions because it can account and compensate for penumbra and scatter effects. Using the analytical solutions as starting points for the iterative methodology, dose-distributions almost as good as those obtained using the conventional iterative approach can be calculated very rapidly.


CONCLUSIONS
The iterative methodology is appropriate and useful for computing homogenized blocked arcs, as it produces better dose-distributions than the analytic approaches and their obvious extensions, and can more straightforwardly be used to generate homogenized arcs for concave OARs. However, the analytical solutions provide promising starting points for the iterative algorithm, leading to fast convergence.
Fenwick
John D
JD
Department of Physics, Clatterbridge Centre for Oncology, Clatterbridge Road, Wirral CH63 4JY, United Kingdom. john.fenwick@ccotrust.nhs.uk
Pardo-Montero
Juan
J
D008962:Models, Theoretical; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*; D012542:Scattering, Radiation