Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling

Gebäck, Tobias; Asadzadeh, Mohammad

doi:10.1080/00411450.2012.671207

Cited by 3 publications

(2 citation statements)

References 9 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To model the 6-dimensional proton phase-space density in the patient the integro-differential Linear Boltzmann equation, which all MC methods are based on, is simplified using physics based approximations. The approximations employed, namely the continuous slowing down approximation, the energy-loss straggling approximation, the small-angle Fokker-Planck (FP) approximation, together with the separation of the proton phase-space density (Gebäck and Asadzadeh 2012)…”

Section: Algorithm Componentsmentioning

confidence: 99%

See 1 more Smart Citation

Yet anOther Dose Algorithm (YODA) for independent computations of dose and dose changes due to anatomical changes

Burlacu,

Lathouwers,

Perkó

2024

Phys. Med. Biol.

View full text Add to dashboard Cite

Objective: To assess the viability of a physics-based, deterministic and adjoint-capable algorithm for performing treatment planning system independent dose calculations and for computing dosimetric differences caused by anatomical changes.Approach: A semi-numerical approach is employed to solve two partial differential equations for the proton phase-space density which determines the deposited dose. Lateral hetereogeneities are accounted for by an optimized (Gaussian) beam splitting scheme. Adjoint theory is applied to approximate the change in the deposited dose caused by a new underlying patient anatomy.Main results: The quality of the dose engine was benchmarked through three-dimensional gamma index comparisons against Monte Carlo simulations done in TOPAS. The worst passing rate for the gamma index with (1 mm, 1 %, 10 % dose cut-off) criteria is 94.55 %. The effect of delivering treatment plans on repeat CTs was also tested. For a non-robustly optimized plan the adjoint component was accurate to 5.7 % while for a robustly optimized plan it was accurate to 4.8 %.Significance: YODA is capable of accurate dose computations in both single and multi spot irradiations when compared to TOPAS. Moreover, it is able to compute dosimetric differences due to anatomical changes with small to moderate errors thereby facilitating its use for patient-specific quality assurance in online adaptive proton therapy.

show abstract

Section: Algorithm Componentsmentioning

confidence: 99%

“…The advantage of the FE equation ( 3) is its analytical solution via Fourier transforms (Gebäck and Asadzadeh 2012), namely…”

Section: The Fe Equationmentioning

confidence: 99%