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Dose distributions for proton therapy treatments are almost exclusively calculated using pencil beam algorithms. An essential input to these algorithms is the patient model, derived from x-ray computed tomography (CT), which is used to estimate proton stopping power along the pencil beam paths. This study highlights a potential inaccuracy in the mapping between mass density and proton stopping power used by a clinical pencil beam algorithm in materials less dense than water. It proposes an alternative physically-motivated function (the mass average, or MA, formula) for use in this region. Comparisons are made between dose-depth curves calculated by the pencil beam method and those calculated by the Monte Carlo particle transport code MCNPX in a one-dimensional lung model. Proton range differences of up to 3% are observed between the methods, reduced to  <1% when using the MA function. The impact of these range errors on clinical dose distributions is demonstrated using treatment plans for a non-small cell lung cancer patient. The change in stopping power calculation methodology results in relatively minor differences in dose when plans use three fields, but differences are observed at the 2%-2 mm level when a single field uniform dose technique is adopted. It is therefore suggested that the MA formula is adopted by users of the pencil beam algorithm for optimal dose calculation in lung, and that a similar approach is considered when beams traverse other low density regions such as the paranasal sinuses and mastoid process.

Original publication




Journal article


Phys Med Biol

Publication Date





4243 - 4261


Algorithms, Calibration, Carcinoma, Non-Small-Cell Lung, Humans, Lung Neoplasms, Monte Carlo Method, Phantoms, Imaging, Proton Therapy, Radiotherapy Dosage, Radiotherapy Planning, Computer-Assisted, Tomography, X-Ray Computed