The breakdown of Molière's multiple-scattering theory for short pathlengths occurring dur... more The breakdown of Molière's multiple-scattering theory for short pathlengths occurring during Monte Carlo simulations with charged particles is demonstrated. It has been found that in certain conditions where the theory is assumed to be valid, significant distortions of the angular distribution occur that make the sampling of the polar angle questionable in numerous steps of Monte Carlo simulations. The limits of the theory have been investigated, both using a large number of terms in the Molière's series and using steps of Molière's theory where 1/B expansions are not involved. At B = 4.5 the commonly accepted 3-term series expansion yields differences up to +/- 6% compared with the evaluation of the complete Molière angular distribution, and up to 7 terms in the series are needed in order to achieve agreement within +/- 2%. One percent agreement requires B = 10. Numerical values of the full distribution are given in terms of Molière's parameters B and reduced angle theta. By using the general dependence of the distribution results are valid for both electron and proton Monte Carlo simulations in any material.
Objective. To review the currently available data on beam quality correction factors, k Q , for i... more Objective. To review the currently available data on beam quality correction factors, k Q , for ionization chambers in clinical proton beams and derive their current best estimates for the updated recommendations of the IAEA TRS-398 Code of Practice. Approach. The reviewed data come from 20 publications from which k Q values can be derived either directly from calorimeter measurements, indirectly from comparison with other chambers or from Monte Carlo calculated overall chamber factors, f Q . For cylindrical ionization chambers, a distinction is made between data obtained in the centre of a spread-out Bragg peak and those obtained in the plateau region of single-energy fields. For the latter, the effect of depth dose gradients has to be considered. To this end an empirical model for previously published displacement correction factors for single-layer scanned beams was established, while for unmodulated scattered beams experimental data were used. From all the data, chamber factors, f Q , and chamber perturbation correction factors, p Q , were then derived and analysed. Main results. The analysis showed that except for the beam quality dependence of the water-to-air mass stopping power ratio and, for cylindrical ionization chambers in unmodulated beams, of the displacement correction factor, there is no remaining beam quality dependence of the chamber perturbation correction factors p Q . Based on this approach, average values of the beam quality independent part of the perturbation factors were derived to calculate k Q values consistent with the data in the literature. Significance. The resulting data from this analysis are current best estimates of k Q values for modulated scattered beams and single-layer scanned beams used in proton therapy. Based on this, a single set of harmonized values is derived to be recommended in the update of IAEA TRS-398.
In order to give the correct dose to a patient, the monitor chamber for a proton scanning system ... more In order to give the correct dose to a patient, the monitor chamber for a proton scanning system has to be calibrated. As recombination of ion pairs occurs in the monitor chamber, the relation between the number of particles traversing it per time unit and the ionization chamber signal is not linear. A method developed for a scanned pulsed proton beam taking the nonlinear monitor signal into account is described. A vital part of the reference dosimetry procedure is to determine the absorbed dose under reference conditions, which is recommended to be done with an ionization chamber. For a scanned pulsed proton beam, the recombination in the ionization chamber is not negligible and the signal from the ionization chamber has to be corrected. In this work, it is shown that although the pulse length is comparable to the ion transit time the beam can be considered as continuously scanned if the applied high voltage is not too small. Also shown is that the two-voltage formula for a continuous beam is under some conditions applicable for a continuous scanned beam as well.
The properties of silicon diode detectors, used for dosimetry in clinical proton beams, were inve... more The properties of silicon diode detectors, used for dosimetry in clinical proton beams, were investigated with special regard to the measurement of relative dose distributions in water. Different types of silicon diode detector were studied, and the resulting distributions of detector signal versus depth in the water phantom were compared with the corresponding distributions obtained with a plane-parallel NACP ionization chamber. The measurements were performed in a proton beam with an initial energy of 173 MeV. It is shown that the Hi-p silicon detector gives a signal which is proportional to the ionization density in the silicon crystal in all parts of the Bragg curve, and for all levels of accumulated dose to the detector. This is in contrast to detectors based on n-type silicon, or on low resistivity p-type silicon. After pre-irradiation, these latter detectors show a stopping-power dependent recombination, yielding an increase in the detector signal per unit dose with increasing LET. This effect leads to an over-response in the Bragg peak, which increases gradually with the accumulated detector dose. Using the Hi-p silicon diode detector, the depth ionization distribution was found to be equal to the distribution obtained with the plane-parallel NACP ionization chamber at all pre-irradiation levels, within the experimental accuracy. This implies that the quotient between the ionization in the detector and the absorbed dose to the surrounding water is equal for these detectors.
There is a need for tools that in a simple way can be used for the evaluation of image quality re... more There is a need for tools that in a simple way can be used for the evaluation of image quality related to clinical requirements in mammography. The aim of this work was to adjust the present European image quality criteria to be relevant also for digital mammography images, and to use as simple and as few criteria as possible. A pilot evaluation of the new set of criteria was made with mammograms of 28 women from a General Electric Senographe 2000D full-field digital mammography system. One breast was exposed using the standard automatic exposure mode, the other using about half of that absorbed dose. Three experienced radiologists evaluated the images using visual grading analysis technique. The results indicate that the new quality criteria can be used for the evaluation of image quality related to clinical requirements in digital mammography in a simple way. The results also suggest that absorbed doses for the mammography system used may be substantially reduced.
The formalism and data in the two most recent dosimetry recommendations for clinical proton beams... more The formalism and data in the two most recent dosimetry recommendations for clinical proton beams, ICRU Report 59 and the forthcoming IAEA Code of Practice, are compared. Chamber calibrations in terms of air kerma and absorbed dose to water are considered, including five different cylindrical ionization chamber types commonly used in proton beam dosimetry. The methodology for both types of calibration for ionization chambers is described in ICRU Report 59. The procedure based on air kerma calibrations is compared with an alternative formalism based on IAEA Codes of Practice (TRS-277, TRS-381), modified for proton beams. The new IAEA Code of Practice is exclusively based on calibrations in terms of absorbed dose to water and a direct comparison with ICRU Report 59 recommendations is made. Common to the two formalisms are the fundamental quantities Wair and w(air) and their atmospheric conditions of applicability. The difference in the recommended values of the ratio w(air)/Wair (protons to 60Co) is as large as 2.3%. The use of Wair and w(air) values for dry air (IAEA) and for ambient air (ICRU) is a contribution to the discrepancy, and the ICRU usage is questioned. For air kerma based chamber calibrations, ICRU Report 59 does not take into account the effect of different compositions of the build-up cap and chamber wall on the calibration beam quality. For the chamber types included in the study, this introduces discrepancies of up to 1.1%. Combined with differences in the recommended basic data, discrepancies in absorbed dose determination in proton beams of up to 2.1% are found. For the absorbed dose to water based formalism, differences in the formalism, notably the omission of perturbation factors for 60Co in ICRU 59, and data yield discrepancies in calculated kQ factors, and in absorbed dose determinations, between -1.5% and +2.6%, depending on the chamber type and the proton beam quality.
Calculations of stopping power ratios, water to air, for the determination of absorbed dose to wa... more Calculations of stopping power ratios, water to air, for the determination of absorbed dose to water in clinical proton beams using ionization chamber measurements have been undertaken using the Monte Carlo method. A computer code to simulate the transport of protons in water (PETRA) has been used to calculate sw.air-data under different degrees of complexity, ranging from values based on primary protons only to data including secondary electrons and high-energy secondary protons produced in nonelastic nuclear collisions. All numerical data are based on ICRU 49 proton stopping powers. Calculations using primary protons have been compared to the simple continuous slowing-down approximation (c.s.d.a.) analytical technique used in proton dosimetry protocols, not finding significant differences that justify elaborate Monte Carlo simulations except beyond the mean range of the protons (the far side of the Bragg peak). The influence of nuclear nonelastic processes, through the detailed generation and transport of secondary protons, on the calculated stopping-power ratios has been found to be negligible. The effect of alpha particles has also been analysed, finding differences smaller than 0.1% from the results excluding them. Discrepancies of up to 0.6% in the plateau region have been found, however, when the production and transport of secondary electrons are taken into account. The large influence of nonelastic nuclear interactions on proton depth-dose distributions shows that the removal of primary protons from the incident beam decreases the peak-to-plateau ratio by a large factor, up to 40% at 250 MeV. It is therefore emphasized that nonelastic nuclear reactions should be included in Monte Carlo simulations of proton beam depth-dose distributions.
The breakdown of Molière's multiple-scattering theory for short pathlengths occurring dur... more The breakdown of Molière's multiple-scattering theory for short pathlengths occurring during Monte Carlo simulations with charged particles is demonstrated. It has been found that in certain conditions where the theory is assumed to be valid, significant distortions of the angular distribution occur that make the sampling of the polar angle questionable in numerous steps of Monte Carlo simulations. The limits of the theory have been investigated, both using a large number of terms in the Molière's series and using steps of Molière's theory where 1/B expansions are not involved. At B = 4.5 the commonly accepted 3-term series expansion yields differences up to +/- 6% compared with the evaluation of the complete Molière angular distribution, and up to 7 terms in the series are needed in order to achieve agreement within +/- 2%. One percent agreement requires B = 10. Numerical values of the full distribution are given in terms of Molière's parameters B and reduced angle theta. By using the general dependence of the distribution results are valid for both electron and proton Monte Carlo simulations in any material.
Objective. To review the currently available data on beam quality correction factors, k Q , for i... more Objective. To review the currently available data on beam quality correction factors, k Q , for ionization chambers in clinical proton beams and derive their current best estimates for the updated recommendations of the IAEA TRS-398 Code of Practice. Approach. The reviewed data come from 20 publications from which k Q values can be derived either directly from calorimeter measurements, indirectly from comparison with other chambers or from Monte Carlo calculated overall chamber factors, f Q . For cylindrical ionization chambers, a distinction is made between data obtained in the centre of a spread-out Bragg peak and those obtained in the plateau region of single-energy fields. For the latter, the effect of depth dose gradients has to be considered. To this end an empirical model for previously published displacement correction factors for single-layer scanned beams was established, while for unmodulated scattered beams experimental data were used. From all the data, chamber factors, f Q , and chamber perturbation correction factors, p Q , were then derived and analysed. Main results. The analysis showed that except for the beam quality dependence of the water-to-air mass stopping power ratio and, for cylindrical ionization chambers in unmodulated beams, of the displacement correction factor, there is no remaining beam quality dependence of the chamber perturbation correction factors p Q . Based on this approach, average values of the beam quality independent part of the perturbation factors were derived to calculate k Q values consistent with the data in the literature. Significance. The resulting data from this analysis are current best estimates of k Q values for modulated scattered beams and single-layer scanned beams used in proton therapy. Based on this, a single set of harmonized values is derived to be recommended in the update of IAEA TRS-398.
In order to give the correct dose to a patient, the monitor chamber for a proton scanning system ... more In order to give the correct dose to a patient, the monitor chamber for a proton scanning system has to be calibrated. As recombination of ion pairs occurs in the monitor chamber, the relation between the number of particles traversing it per time unit and the ionization chamber signal is not linear. A method developed for a scanned pulsed proton beam taking the nonlinear monitor signal into account is described. A vital part of the reference dosimetry procedure is to determine the absorbed dose under reference conditions, which is recommended to be done with an ionization chamber. For a scanned pulsed proton beam, the recombination in the ionization chamber is not negligible and the signal from the ionization chamber has to be corrected. In this work, it is shown that although the pulse length is comparable to the ion transit time the beam can be considered as continuously scanned if the applied high voltage is not too small. Also shown is that the two-voltage formula for a continuous beam is under some conditions applicable for a continuous scanned beam as well.
The properties of silicon diode detectors, used for dosimetry in clinical proton beams, were inve... more The properties of silicon diode detectors, used for dosimetry in clinical proton beams, were investigated with special regard to the measurement of relative dose distributions in water. Different types of silicon diode detector were studied, and the resulting distributions of detector signal versus depth in the water phantom were compared with the corresponding distributions obtained with a plane-parallel NACP ionization chamber. The measurements were performed in a proton beam with an initial energy of 173 MeV. It is shown that the Hi-p silicon detector gives a signal which is proportional to the ionization density in the silicon crystal in all parts of the Bragg curve, and for all levels of accumulated dose to the detector. This is in contrast to detectors based on n-type silicon, or on low resistivity p-type silicon. After pre-irradiation, these latter detectors show a stopping-power dependent recombination, yielding an increase in the detector signal per unit dose with increasing LET. This effect leads to an over-response in the Bragg peak, which increases gradually with the accumulated detector dose. Using the Hi-p silicon diode detector, the depth ionization distribution was found to be equal to the distribution obtained with the plane-parallel NACP ionization chamber at all pre-irradiation levels, within the experimental accuracy. This implies that the quotient between the ionization in the detector and the absorbed dose to the surrounding water is equal for these detectors.
There is a need for tools that in a simple way can be used for the evaluation of image quality re... more There is a need for tools that in a simple way can be used for the evaluation of image quality related to clinical requirements in mammography. The aim of this work was to adjust the present European image quality criteria to be relevant also for digital mammography images, and to use as simple and as few criteria as possible. A pilot evaluation of the new set of criteria was made with mammograms of 28 women from a General Electric Senographe 2000D full-field digital mammography system. One breast was exposed using the standard automatic exposure mode, the other using about half of that absorbed dose. Three experienced radiologists evaluated the images using visual grading analysis technique. The results indicate that the new quality criteria can be used for the evaluation of image quality related to clinical requirements in digital mammography in a simple way. The results also suggest that absorbed doses for the mammography system used may be substantially reduced.
The formalism and data in the two most recent dosimetry recommendations for clinical proton beams... more The formalism and data in the two most recent dosimetry recommendations for clinical proton beams, ICRU Report 59 and the forthcoming IAEA Code of Practice, are compared. Chamber calibrations in terms of air kerma and absorbed dose to water are considered, including five different cylindrical ionization chamber types commonly used in proton beam dosimetry. The methodology for both types of calibration for ionization chambers is described in ICRU Report 59. The procedure based on air kerma calibrations is compared with an alternative formalism based on IAEA Codes of Practice (TRS-277, TRS-381), modified for proton beams. The new IAEA Code of Practice is exclusively based on calibrations in terms of absorbed dose to water and a direct comparison with ICRU Report 59 recommendations is made. Common to the two formalisms are the fundamental quantities Wair and w(air) and their atmospheric conditions of applicability. The difference in the recommended values of the ratio w(air)/Wair (protons to 60Co) is as large as 2.3%. The use of Wair and w(air) values for dry air (IAEA) and for ambient air (ICRU) is a contribution to the discrepancy, and the ICRU usage is questioned. For air kerma based chamber calibrations, ICRU Report 59 does not take into account the effect of different compositions of the build-up cap and chamber wall on the calibration beam quality. For the chamber types included in the study, this introduces discrepancies of up to 1.1%. Combined with differences in the recommended basic data, discrepancies in absorbed dose determination in proton beams of up to 2.1% are found. For the absorbed dose to water based formalism, differences in the formalism, notably the omission of perturbation factors for 60Co in ICRU 59, and data yield discrepancies in calculated kQ factors, and in absorbed dose determinations, between -1.5% and +2.6%, depending on the chamber type and the proton beam quality.
Calculations of stopping power ratios, water to air, for the determination of absorbed dose to wa... more Calculations of stopping power ratios, water to air, for the determination of absorbed dose to water in clinical proton beams using ionization chamber measurements have been undertaken using the Monte Carlo method. A computer code to simulate the transport of protons in water (PETRA) has been used to calculate sw.air-data under different degrees of complexity, ranging from values based on primary protons only to data including secondary electrons and high-energy secondary protons produced in nonelastic nuclear collisions. All numerical data are based on ICRU 49 proton stopping powers. Calculations using primary protons have been compared to the simple continuous slowing-down approximation (c.s.d.a.) analytical technique used in proton dosimetry protocols, not finding significant differences that justify elaborate Monte Carlo simulations except beyond the mean range of the protons (the far side of the Bragg peak). The influence of nuclear nonelastic processes, through the detailed generation and transport of secondary protons, on the calculated stopping-power ratios has been found to be negligible. The effect of alpha particles has also been analysed, finding differences smaller than 0.1% from the results excluding them. Discrepancies of up to 0.6% in the plateau region have been found, however, when the production and transport of secondary electrons are taken into account. The large influence of nonelastic nuclear interactions on proton depth-dose distributions shows that the removal of primary protons from the incident beam decreases the peak-to-plateau ratio by a large factor, up to 40% at 250 MeV. It is therefore emphasized that nonelastic nuclear reactions should be included in Monte Carlo simulations of proton beam depth-dose distributions.
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Papers by Joakim Medin