An Empirical Model for Describing the Small Field Penumbra in Radiation Therapy

Table 1

The coplanar penetration depth (ϖ) and e^−μϖ on the right-side penumbra after double exposures.

Distance from central axis of point d on the x axis (cm)	Gantry angles
	0°		30°		45°		60°		90°
		e^−μϖ		e^−μϖ		e^−μϖ		e^−μϖ		e^−μϖ
0	11.00	0.95223^#	11.00	0.95223	11.00	0.95223	11.00	0.95223	11.00	0.95223
0.1	11.00	0.95223	10.95	0.95233	10.93	0.95238	10.91	0.95241	10.90	0.95244
0.2	11.00	0.95223	10.90	0.95244	10.86	0.95253	10.83	0.95260	10.80	0.95265
0.3	11.00	0.95223	10.85	0.95255	10.79	0.95268	10.74	0.95278	10.70	0.95286
0.4	10.99	0.95223	10.80	0.95266	10.71	0.95283	10.65	0.95296	10.60	0.95308
0.5	10.99	0.95223	10.74	0.95277	10.64	0.95298	10.56	0.95315	10.50	0.95329
0.6	10.99	0.95223	10.69	0.95287	10.57	0.95313	10.48	0.95333	10.40	0.95350
0.7	10.98	0.95223	10.64	0.95298	10.50	0.95329	10.39	0.95352	10.30	0.95371
0.8	10.98	0.95223	10.58	0.95309	10.42	0.95344	10.30	0.95370	10.20	0.95393
0.9	10.97	0.95223	10.53	0.95321	10.35	0.95359	10.21	0.95389	10.10	0.95414
1	10.96	0.95223	10.47	0.95332	10.27	0.95375	10.12	0.95407	10.00	0.95435
1.1	10.96	0.95223	10.42	0.95343	10.20	0.95390	10.04	0.95426	9.90	0.95456
1.2	10.95	0.95223	10.36	0.95354	10.13	0.95406	9.95	0.95445	9.80	0.95477
1.3	10.94	0.95223	10.30	0.95365	10.05	0.95421	9.86	0.95463	9.70	0.95499
1.4	10.93	0.95223	10.25	0.95377	9.97	0.95437	9.77	0.95482	9.60	0.95520
1.5	10.92	0.95223	10.19	0.95388	9.90	0.95452	9.68	0.95501	9.50	0.95541
1.6	10.91	0.95223	10.13	0.95400	9.82	0.95468	9.59	0.95519	9.40	0.95562
1.7	10.90	0.95223	10.07	0.95411	9.75	0.95483	9.50	0.95538	9.30	0.95584

^#Data are calculated from () by using e^−μϖ, μ = 0.00494 cm⁻¹ at 6 MV in water.