The idea of IMRT is to treat a patient using beams of non-uniform fluences from a number of different directions (or a continuous arc) to plan and deliver a dose distribution to enable conformal high dose to target volumes and acceptably low dose to the OARs (A simple example was shown in Figure 2, page 3.) IMRT is an advanced form of three-dimensional conformal radiotherapy (3D-CRT). As Figure 5 illustrates, both 3D-CRT and IMRT require the planner to set the beam arrangement (beam angle, energy, and etc.). In 3D-CRT, the planner also has to decide how to use beam shapers to shapes the resulting radiation. In IMRT, the planner only needs to specify the treatment criteria (such as what minimum dose delivered to target volumes) so that the radiation is inversely optimized by TPS. Each beam is automatically shaped by an MLC and divided into non-equi-weighted segments. The non-uniform beam fluence is inversely optimized by the objective function algorithm imbedded in TPS to optimally meet all the treatment criteria. With direct machine parameter optimization, MLC settings are produced
19
directly during the optimization process without post process like conversion or filtering which may degrade the plan quality during dose delivery. Conventionally, the objective functions used in IMRT are (static) dose-volume based.
COP is an IMRT process that uses probabilistic (stochastic) dose-volume-based pDVH objective functions to adjust the beam fluence intensity profiles. Denote Dv the dose delivered to
volume v of an ROI. In contrast to the static Dv in basic criteria/objective functions, COP
computes and optimizes Dv at a specified coverage probability — the probability that a realized
target or OAR dose metric Dv exceeds the dose of interest (Rx, tolerance or other dose) when the
modeled treatment planning and delivery uncertainties are taken into account. COP seeks an optimized dose distribution for a patient to i.e., maximally achieve targets and OARs coverage probability to overcome the degraded dosimetric effect due to GUs.
The procedure of COP optimization on the patient-specific coverage probability with incorporated GUs of known PDFs is graphically illustrated in Figure 6. The deviations introduced by GUs may include shifting effects (due to systematic setup errors), blurring effects (due to random setup errors) and re-arranging dose with respect to the voxels (due to organ deformation). Different probable treatment courses (one treatment course = delivery of the
20
prescription dose in nfrac fractions) can yield different dose distribution and different patient
responses. To evaluate dose incorporating uncertainties, one way is to mimic dose delivery to one of thousands of possible virtual treatment courses, each with nfrac fractions. Each fraction of
each treatment course is associated with different GUs dependent on the parameters sampled from the known PDF(s). Dose shift invariance (Sharma et al. 2012) is assumed here so that dose distribution remains unchanged regardless of geometric changes of ROIs. Dose of each displaced voxel in the ROIs is calculated and accumulated over nfrac fractions. The consequent
accumulative DVHs of each ROI for all the treatment courses can be obtained and converted into a dose volume coverage map (DVCM) – a 2D grid with many small grid squares that contain percentile values of DVHs on their Dv locations. (See section 3.2.1 for details) These percentile
values, also called coverage probability, are associated each Dv on the DVCM. A pDVH of q
(Gordon et al. 2010) is a virtual DVH created by connecting all Dv with coverage probability q.
A pDVH criterion for q is Dv corresponding to q for a target/an OAR.
Figure 6. Workflow of how a pDVH of coverage probability q are determined (a–c) and how COP performs optimization (a-d) based on pDVH criteria by simulating ntx virtual treatment courses, each with nfrac
fractions. (a) For each fraction of a virtual treatment course, find the total offset (black arrow) for all the GUs of each voxel in the ROI (black thick circle) and get the dose for the displaced voxel, assuming shift- invariance for dose distribution (illustrated as grey thin solid isodose lines). (b) Get ntx accumulative ROI
DVHs over all the fractions. (c) The ntx DVH samples are converted into a dose volume coverage map
(DVCM), as a 2D grid built with many small grid squares. Each grid square will be assigned a probability value equivalent to the percentile value of DVHs that lie left to this grid squares, according to the distribution of DVH samples. A virtual DVH of a certain percentile value (i.e., coverage) q, namely pDVH of q, can be determined on this map. (d) pDVH criteria (such as Pr[Dv ≥d] ≥q) are used to optimize the dose
21
Note that the concept of pDVH is not unique. A similar metric called dose–volume population histogram (DVPH) related to the patient-specific coverage probability was independently and simultaneously developed before (Nguyen et al. 2009). With known SDs of the systematic and random errors for deformation-free/rotation-free structures, DVPH was the consequence of the distribution of systematic and random errors being incorporated into DVH display. Compared to DVPH, the usage of pDVH in this dissertation has been extended to plan optimization to account for GUs for both rigid and deformable structures.