Technical Note: On the calculation of stopping-power ratio for stoichiometric calibration in proton therapy.
OBJECTIVE
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.
Department of Medical Physics, Karolinska University Hospital, Stockholm SE-17176, Sweden and Department of Medical Radiation Physics, Stockholm University and Karolinska Institutet, Stockholm SE-17176, Sweden.
Jakob
J
Ödén
Department of Medical Physics, Karolinska University Hospital, Stockholm SE-17176, Sweden.
Jens
J
Zimmerman
Department of Medical Physics, Karolinska University Hospital, Stockholm SE-17176, Sweden and Department of Physics, Royal Institute of Technology, Stockholm SE-10691, Sweden.
Robert
R
Bujila
Department of Medical Physics, Karolinska University Hospital, Stockholm SE-17176, Sweden.
Patrik
P
Nowik
Department of Medical Physics, Karolinska University Hospital, Stockholm SE-17176, Sweden.
Gavin
G
Poludniowski
D002138:Calibration; D006801:Humans; D061766:Proton Therapy / Q000379:methods*; D014057:Tomography, X-Ray Computed