Computational Methods

The following sections demonstrate the algorithms used for computing field comparison metrics of the ViewRay Field Uniformity-Timing Check application.

Gamma Computation

Gamma analysis is performed based on the formalism presented by D. A. Low et. al., A technique for the quantitative evaluation of dose distributions., Med Phys. 1998 May; 25(5): 656-61. In this formalism, the Gamma quality index γ is defined as follows for each point along the measured profile R_m given the reference profile R_c:

γ = min{Γ(R_m,R_c}∀{R_c}

where:

Γ = √ (r^2(R_m,R_c)/Δd_M^2 + δ^2(R_m,R_c)/ΔD_M^2),

r(R_m,R_c) = | R_c - R_m |,

δ(R_m,R_c) = Dc(R_c) - D_m(R_m),

D_c(R_c) and D_m(R_m) represent the reference and measured signal at each R_c and R_m, respectively, and

Δd_M and ΔD_M represent the absolute and Distance To Agreement Gamma criterion (by default 2%/1mm), respectively.

The absolute criterion is typically given in percent and can refer to a percent of the maximum dose (commonly called the global method) or a percentage of the voxel R_m being evaluated (commonly called the local method). The application is capable of computing gamma using either approach, and can be set when calling CalcGamma by passing a boolean value of 1 (for local) or 0 (for global). By default, the global method (0) is used.

The computation applied in this application is the 1D algorithm, in that the distance to agreement criterion is evaluated only along the dimension of the reference profile when determining min{Γ(R_m,R_c}∀{R_c}. To accomplish this, the reference profile is shifted relative to the measured profile using linear 1D GPU (when available) interpolation. For each shift, Γ(R_m,R_c} is computed, and the minimum value γ is determined.

To improve computation efficiency, the computation space ∀{R_c} is limited to twice the distance to agreement parameter. Thus, the maximum "real" Gamma index returned by the application is 2.