Inter-comparison of relative stopping power estimation models for proton therapy

Abstract

Theoretical stopping power values were inter-compared for the Bichsel, Janni, ICRU and Schneider relative stopping power (RSP) estimation models, for a variety of tissues and tissue substitute materials taken from the literature. The RSPs of eleven plastic tissue substitutes were measured using Bragg peak shift measurements in water in order to establish a gold standard of RSP values specific to our centre's proton beam characteristics. The theoretical tissue substitute RSP values were computed based on literature compositions to assess the four different computation approaches. The Bichsel/Janni/ICRU approaches led to mean errors in the RSP of -0.1/+0.7/-0.8%, respectively. Errors when using the Schneider approach, with I-values from the Bichsel, Janni and ICRU sources, followed the same pattern but were generally larger. Following this, the mean elemental ionisation energies were optimized until the differences between theoretical RSP values matched measurements. Failing to use optimized I-values when applying the Schneider technique to 72 human tissues could introduce errors in the RSP of up to -1.7/+1.1/-0.4% when using Bichsel/Janni/ICRU I-values, respectively. As such, it may be necessary to introduce an additional step in the current stoichiometric calibration procedure in which tissue insert RSPs are measured in a proton beam. Elemental I-values can then optimized to match these measurements, reducing the uncertainty when calculating human tissue RSPs.

The impact of secondary fragments on the image quality of helium ion imaging

“…To maximize the treatment accuracy, knowledge of the position of the Bragg-peak distal fall-off within the patient is crucial. The distance from beam entry to a specified relative dose point on the distal slope of the fall-off (e.g., 90% of the peak dose) which is related to the range of the ions can be obtained from the Bethe-Bloch stopping power formula (Bethe & Ashkin 1953, Doolan et al 2016). In current clinical practice, the stopping power information within the patient is retrieved by converting Hounsfield Units (HUs) from a X-ray planning CT to relative stopping power (RSP) (Schneider et al 1996), defined as the stopping power of a material relative to that of water.…”

Deriving the mean excitation energy map from dual-energy and proton computed tomography

“…At present, there is no clear consensus on which SPR expression is the most appropriate for computing the theoretical SPR values [26,27]. In this study, we calculated the theoretical SPR using the equation proposed by Schneider et al [23], which neglects shell, density, Barkas and Bloch correction terms and energy dependency.…”

“…This approximation of the Bethe-Bloch theory [28,29] has been proven to be valid and is widely used in proton therapy to compute the stopping power of human tissues [23]. Bethe-Bloch theory is not valid for proton energies below 1 MeV but it was found to have a negligible clinical impact [27]. Ödén et al [26] compared Schneider's approach with the SRIM software [30], which incorporates all mentioned corrections, and concluded that Bethe's equation without correction terms could safely be used because SPR errors below 0.1% were obtained across 72 biological tissues.…”

“…Ödén et al [26] compared Schneider's approach with the SRIM software [30], which incorporates all mentioned corrections, and concluded that Bethe's equation without correction terms could safely be used because SPR errors below 0.1% were obtained across 72 biological tissues. In a recent work, Doolan et al [27] did an inter-comparison of four existing SPR models for proton therapy: Bichsel's [31], Janni's [32] and ICRU's formulas [1] to compute the absolute stopping power of tissues, and Schneider's [23] to compute the relative stopping power. The SPR value of eleven plastic materials was experimentally determined and it was compared against the four theoretical approaches.…”

High accuracy proton relative stopping power measurement

“…This value of 〈 〉 I w is in the range of values from the literature 67-82 eV [37,38]. Recently, Doolan et al [39] derived a set of optimized Table 2 The measured thickness t m ( ± 1 standard deviation) of the 32 sample materials. Experimental relative stopping powers (RSP Exp) determined with an uncertainty < 0.4% at an initial proton energy of 149 MeV compared to RSPs derived from the Bethe-Bloch approximation with Bragg additivity rule (BB), with mean excitation energy for water set to 78 eV (BB(78)) and from Geant4 simulations (RSP Geant4).…”