Lateral dose profile characterization in scanning particle therapy

Abstract

The trade-off between flatness, quantization error, and robustness on the one side and penumbra width on the other side can be described analytically for equally weighted spots. Treatment planning systems often perform a least-squares optimization of the individual spot weights which results in smaller lateral penumbras and smaller quantization errors than for uniform discrete scanning. However, the benefit of this weight optimization decreases with increasing lambda (in the regime lambda > sigma(b)). The spot spacing, which is obtained from the scenario that the optimization objective is met by uniform discrete scanning, poses a sharp upper limit for the spot spacing lambda in weight optimization methods.

A Monte Carlo study on the collimation of pencil beam scanning proton therapy beams

“…The smaller spot spacing used for the spherical target was to reduce the edge quantization effect described by Ref. 7 which was not an issue for the cubic target. Energy layers were spaced 2.0 MeV apart.…”

“…This is due to the aforementioned edge quantization effect. 7 Addition of a rind pushes the quantization away from the target and into the rind, greatly reducing its impact on the target volume. As a consequence, lateral coverage is also improved with the addition of a rind, although coverage in the longitudinal direction is unaffected, as shown by the 1D dose profiles along the central axis in Fig.…”

“…5,6 In pencil beam scanning (PBS) proton therapy systems, the lateral edge (also termed penumbra here and elsewhere) depends on the in-air spot size, the spot spacing, energy layering, and optimization of the relative spot weights. PBS plans typically use 1000 or more pencil beams superimposed to produce a dose plateau, and careful optimization can produce a lateral penumbra almost as sharp as an individual pencil beam: Baumer and Farr 7 showed that for the 1D case, the lateral penumbra generally lies between 1.13σ and 1.68σ, where σ is the standard deviation of the lateral dose profile of a single spot. Improvements in beam focusing can potentially sharpen the penumbra by decreasing the spot size.…”

Fundamental radiological and geometric performance of two types of proton beam modulated discrete scanning systems

“…As reported previously, there is a direct relationship between spot size and scanned penumbra. 7 For evenly spaced spots of equal fluence the penumbra is typically 1.4 times the standard deviation of the beam spot profile, taken to be sigma of the Gaussian distribution in this case. This relationship holds closely within the observed data ( Fig.…”

Treatment planning aspects and Monte Carlo methods in proton therapy

“…In the case where the individual pristine Bragg peaks are optimized in terms of weight and position throughout the lateral direction, it is possible to achieve a homogeneous dose profile with a penumbra close to the penumbra of a single pencil beam, whereas equally weighted pristine Bragg peaks lead to a wider penumbra of the still homogeneous dose profile. 48 To further improve the lateral penumbra an aperture can be used also for scanning delivery systems, 49 since then the large angle scatter from the treatment head is reduced. Thus, scanning techniques are able to conformingly irradiate the target volume in the lateral and distal directions and further reduce the dose in the proximal direction when compared with the scattering proton delivery method.…”