Example of three γ evaluations; Zero (1), moderate (2), and steep (3) dose gradients. The angle that the γ vector makes to the dose axis is θ. For steep dose gradients, the value of θ is assumed to be sufficiently close to 90° that the evaluation is essentially entirely along the distance axis (e.g., equivalent to the distance-to-agreement test).
Examples of the γ vector for two different sets of dose difference and distance to agreement (DTA) criteria. The evaluated dose distribution gradient is 1% mm−1 in both cases. In case 1, the dose and DTA criteria are 3% and 2 mm, respectively, while in case 2, the dose and DTA criteria are 2% and 3 mm, respectively. θ are 34° and 56° for cases 1 and 2, respectively.
Example showing that the γ evaluation vector is always normal to the evaluated distribution and, therefore, the γ angle θ is a function only of the evaluated dose renormalized dose gradient.
Typical (a) prostate and (b) PTV histograms showing the relationship between dose and normalized dose gradient (as described by sin2θ). These angles were based on α = 1%/mm, corresponding to 3%, 3 mm dose difference and distance to agreement criteria, respectively.
Example dose and gradient histogram of the rectum for a prostate cancer treatment plan. (a) These angles were based on α = 1%/mm, corresponding to 3%, 3 mm dose difference and distance to agreement criteria, respectively. (b) These angles were based on α = 1.5%/mm, corresponding to 3%, 2 mm dose difference and distance to agreement criteria, respectively. (c) These angles were based on α = 0.67%/mm, corresponding to 2%, 3 mm dose difference and distance to agreement criteria, respectively.
Histogram of the maximum sin2θ, based on α = 1%/mm, for the rectum for prostate cancer patients.
Relative frequency, presented proportional to the marker area, of dose difference and DTA criteria for published studies that used the γ dose distribution comparison technique. The most common set of criteria were 3% and 3 mm, but dose differences as large as 20% (off scale) and DTA agreements as large as 7 mm were also used. The smallest value of α was 0.17%/ mm, although most comparisons employed α ⩾ 1%/mm.
sin2θ as a function of α. For example, for a comparison where sin2θ = 0.95 with α = 1%/mm, representing the cases studied in this paper, the same comparison would have sin2θ = 0.82 if α = 0.5%/mm.
Characteristics of the dose distributions used in the evaluation.
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