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Technical Note: On the calculation of stopping‐power ratio for stoichiometric calibration in proton therapy
Author(s) -
Ödén Jakob,
Zimmerman Jens,
Bujila Robert,
Nowik Patrik,
Poludniowski Gavin
Publication year - 2015
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.4928399
Subject(s) - stopping power , calibration , bragg peak , value (mathematics) , additive function , proton , stoichiometry , proton therapy , physics , nuclear medicine , mathematics , computational physics , chemistry , statistics , optics , mathematical analysis , nuclear physics , medicine , organic chemistry , detector
Purpose: The quantitative effects of assumptions made in the calculation of stopping‐power ratios (SPRs) are investigated, for stoichiometric CT calibration in proton therapy. The assumptions investigated include the use of the Bethe formula without correction terms, Bragg additivity, the choice of I ‐value for water, and the data source for elemental I ‐values. Methods: The predictions of the Bethe formula for SPR (no correction terms) were validated against more sophisticated calculations using the srim software package for 72 human tissues. A stoichiometric calibration was then performed at our hospital. SPR was calculated for the human tissues using either the assumption of simple Bragg additivity or the Seltzer‐Berger rule (as used in ICRU Reports 37 and 49). In each case, the calculation was performed twice: First, by assuming the I ‐value of water was an experimentally based value of 78 eV (value proposed in Errata and Addenda for ICRU Report 73) and second, by recalculating the I ‐value theoretically. The discrepancy between predictions using ICRU elemental I ‐values and the commonly used tables of Janni was also investigated. Results: Errors due to neglecting the correction terms to the Bethe formula were calculated at less than 0.1% for biological tissues. Discrepancies greater than 1%, however, were estimated due to departures from simple Bragg additivity when a fixed I ‐value for water was imposed. When the I ‐value for water was calculated in a consistent manner to that for tissue, this disagreement was substantially reduced. The difference between SPR predictions when using Janni's or ICRU tables for I ‐values was up to 1.6%. Experimental data used for materials of relevance to proton therapy suggest that the ICRU‐derived values provide somewhat more accurate results (root‐mean‐square‐error: 0.8% versus 1.6%). Conclusions: The conclusions from this study are that (1) the Bethe formula can be safely used for SPR calculations without correction terms; (2) simple Bragg additivity can be reasonably assumed for compound materials; (3) if simple Bragg additivity is assumed, then the I ‐value for water should be calculated in a consistent manner to that of the tissue of interest (rather than using an experimentally derived value); (4) the ICRU Report 37 I ‐values may provide a better agreement with experiment than Janni's tables.