Table 2.

Results for the 3-dimensional γ-index for the PBS test case in Fig. 4a. The comparison uses δd₀ = 3 mm, δD₀ = 3%, and region of interest denned by 20% of the maximum dose. The depths d₁, d₂, and d₃ are 54 mm, 108 mm, and 162 mm of polystyrene, respectively. At each depth, 1024 measured points in a plane are compared to 562 × 10³ voxels from treatment planning. Method A is used as the “gold standard” for determining the accuracy of the other methods. The accuracy of Method B shows that linear interpolation introduces ~ 1% error. Method E is the fastest method with ~ 1% accuracy. Method I is slower than than Method E by a factor of 10, but it can be used to check the magnitude of 2^nd-order terms. Method G is only slightly slower than the 2^nd-order methods and has accuracy better than 0.2%.

	Pγ≤1 [%]	Depth d1 Accuracy [%]	Calc. time [s]	Pγ≤1 [%]	Depth d2 Accuracy [%]	Calc. time [s]	Pγ≤1 [%]	Depth d3 Accuracy [%]	Calc. time [s]
A	94.38	-	88.2	99.46	-	2.3	96.46	-	8.1
B	93.25	1.2	1.3	99.46	0.0	1.2	95.63	0.9	5.3
C	52.72	44	0.0016	68.93	31	0.0015	62.82	35	0.0017
D	93.45	1.0	0.14	98.39	1.1	0.14	96.26	0.2	0.14
E	93.25	1.2	0.018	99.29	0.2	0.019	96.46	0.0	0.018
F	92.88	1.6	0.13	99.11	0.4	0.14	98.03	1.6	0.13
G	94.38	0.0	0.28	99.28	0.2	0.29	96.46	0.0	0.28
H	94.01	0.4	0.17	99.28	0.2	0.17	96.46	0.0	0.17
I	93.26	1.2	0.16	99.46	0.0	0.17	96.46	0.0	0.16