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

Figure 2

(a) The calculation of the length at a gantry angle of θ on by geometric method after double exposures with a larger and a smaller field. The larger field was 6 × 4 cm² and the smaller field was 4 × 2 cm² field, respectively. S represents the linear accelerator radiation source position with a gantry angle of 0°, and S′ denotes the source position after a gantry rotation of θ degrees. o is the rotational isocenter; d is the field edge of the small field delivered at 0° at the 4 cm side of the 4 × 2 cm² field; a indicates the field edge of the larger field at the 6 cm side of the 6 × 4 cm² field when the gantry rotates to the angle of θ. is the half-field size of the smaller field on the 4 cm side of the 4 × 2 cm² field while is the half-field size of the larger field on the 6 cm side of the 6 × 4 cm² field. denotes the half-field size on the 4 cm side of the 4 × 2 cm² field () and denotes the half-field size on the 6 cm side of the 6 × 4 cm² field (). (b) This figure shows the geometric derivation of . is the key factor controlling the dose distribution from the larger field onto the penumbra region of the smaller field along  =  −  − , where , and  = . For details, please refer to Appendix B.

(a)

(b)