A semi-analytical procedure to determine the ion recombination correction factor in high dose-per-pulse beams.

BACKGROUND: The conventional theories and methods of determining the ion recombination correction factor, such as Boag theory and the related two voltage method and Jaffé plot extrapolation, do not seem to yield accurate results in FLASH /high dose per pulse (DPP) beams ( > $>$ 10 mGy DPP). This is due to the presence of a large free electron fraction that distorts the electric field inside the chamber sensitive volume. To understand the influence of these effects on the ion recombination correction factor and to develop new expressions for it, it is necessary to re-visit the underlying physics. PURPOSE: To present a mathematical procedure to develop an analytical expression for the ion recombination correction factor. The expression is the basis for an extrapolation method so the correction factor can be determined in a clinical setting. METHODS: A semi-analytical solution method, the homotopy perturbation method (HPM), is used to solve the partial differential equations (PDEs) describing the charge carrier physics, including space charge and free electrons. The electron velocity and attachment rate are modeled as functions of the electric field strength. An expression for the charge collection efficiency and ion recombination correction factor are developed. A fit procedure based on this expression is used to compare it to measured data from previously published articles. Another fit procedure using a general equation is also proposed and compared to the data. RESULTS: The series obtained for the charge collection efficiency and the ion recombination correction factor are determined to be asymptotic series and the optimal truncation established. The ion recombination correction factor exhibits a 1 / V 2 $1/V^2$ dependency due to the free electron presence. The fit using this expression agrees well with measured data as long as (1) the DPP is below 1 Gy for chambers with a 1 mm plate separation and (2) when the DPP is below 3 Gy for chambers with a 0.5 mm plate separation. In these DPP ranges, the deviation between measured and fit value did not exceed 6%. In both chamber cases the voltage range where the fit applies decreases as DPP increases. The general equation yielded comparable results. CONCLUSIONS: The HPM was shown to be applicable to a complex system of PDEs and generate meaningful and novel solutions, as they include both space charge and free electrons. The HPM also lends itself to other chamber geometries. The fit procedure was also shown to yield accurate results for the ion recombination correction up to the 1 Gy DPP level.

Feasibility of operating a millimeter-scale graphite calorimeter for absolute dosimetry of small-field photon beams in the clinic.

PURPOSE: To characterize and build a cylindrically layered graphite calorimeter the size of a thimble ionization chamber for absolute dosimetry of small fields. This detector has been designed in a familiar probe format to facilitate integration into the clinical workflow. The feasibility of operating this absorbed dose calorimeter in quasi-adiabatic mode is assessed for high-energy accelerator-based photon beams. METHODS: This detector, herein referred to as Aerrow MK7, is a miniaturized version of a previously validated aerogel-insulated graphite calorimeter known as Aerrow. The new model was designed and developed using numerical methods. Medium conversion factors from graphite to water, small-field output correction factors, and layer perturbation factors for this dosimeter were calculated using the EGSnrc Monte Carlo code system. A range of commercially available aerogel densities were studied for the insulating layers, and an optimal density was selected by minimizing the small-field output correction factors. Heat exchange within the detector was simulated using a five-body compartmental heat transfer model. In quasi-adiabatic mode, the sensitive volume (a 3 mm diameter cylindrical graphite core) experiences a temperature rise during irradiation on the order of 1.3 mK·Gy-1 . The absorbed dose is obtained by calculating the product of this temperature rise with the specific heat capacity of the graphite. The detector was irradiated with 6 MV ( % dd ( 10 ) x  = 63.5%) and 10 MV ( % dd ( 10 ) x  = 71.1%) flattening filter-free (FFF) photon beams for two field sizes, characterized by S clin dimensions of 2.16 and 11.0 cm. The dose readings were compared against a calibrated Exradin A1SL ionization chamber. All dose values are reported at d max in water. RESULTS: The field output correction factors for this dosimeter design were computed for field sizes ranging from S clin  = 0.54 to 11.0 cm. For all aerogel densities studied, these correction factors did not exceed 1.5%. The relative dose difference between the two dosimeters ranged between 0.3% and 0.7% for all beams and field sizes. The smallest field size experimentally investigated, S clin  = 2.16 cm, which was irradiated with the 10 MV FFF beam, produced readings of 84.4 cGy (±1.3%) in the calorimeter and 84.5 cGy (±1.3%) in the ionization chamber. CONCLUSION: The median relative difference in absorbed dose values between a calibrated A1SL ionization chamber and the proposed novel graphite calorimeter was 0.6%. This preliminary experimental validation demonstrates that Aerrow MK7 is capable of accurate and reproducible absorbed dose measurements in quasi-adiabatic mode.

Monte Carlo and water calorimetric determination of kilovoltage beam radiotherapy ionization chamber correction factors.

The in-phantom calibration method for radiotherapy kilovoltage x-ray beams requires ionization chamber correction factors. The overall ionization chamber correction factor accounts for changes in the chamber response due to the displacement of water by the chamber cavity and wall, the presence of the stem and the change in incident photon energy and angular distribution in the phantom to that in air. A waterproof sheath, if required, is accounted for in a sheath correction factor. The aim of this study is to determine chamber correction factors through Monte Carlo (MC) simulations and water calorimetry measurements. Correction factors are determined for the PTW TM30013, NE2571, IBA FC65-G, IBA FC65-P and Exradin A12 ionization chambers. They are compared to experimental values obtained at the German national metrology institute Physikalisch-Technische Bundesanstalt (PTB) with their water calorimetry-based absorbed dose to water primary standard and at other national metrological institutes. An uncertainty analysis considers the contributions to the uncertainty on the chamber correction factors from the field size, photon cross sections, photon fluence spectra and chamber wall and central electrode dimensions. The MC calculated chamber correction factors are within 2.2% of unity with a standard uncertainty of 0.3%. For the 50 kV and 100 - 140 kV radiation beam qualities, the calculated correction factors deviate from the measured correction factors (with a standard uncertainty of 1%) by up to 2.6%. The calculated chamber correction factors for the PTW TM30013 and Exradin A12 are consistent with those derived from the BIPM kilovoltage primary standard. The inconsistencies between the calculated and experimental chamber correction factors indicate the need to further investigate the accuracy of kilovoltage absorbed dose to water primary standards and the use of MC simulations to determine kilovoltage beam chamber correction factors.

Absolute dosimetry of a 1.5 T MR-guided accelerator-based high-energy photon beam in water and solid phantoms using Aerrow.

PURPOSE: In this work, the fabrication, operation, and evaluation of a probe-format graphite calorimeter - herein referred to as Aerrow - as an absolute clinical dosimeter of high-energy photon beams while in the presence of a B = 1.5 T magnetic field is described. Comparable to a cylindrical ionization chamber (IC) in terms of utility and usability, Aerrow has been developed for the purpose of accurately measuring absorbed dose to water in the clinic with a minimum disruption to the existing clinical workflow. To our knowledge, this is the first reported application of graphite calorimetry to magnetic resonance imaging (MRI)-guided radiotherapy. METHODS: Based on a previously numerically optimized and experimentally validated design, an Aerrow prototype capable of isothermal operation was constructed in-house. Graphite-to-water dose conversions as well as magnetic field perturbation factors were calculated using Monte Carlo, while heat transfer and mass impurity corrections and uncertainties were assessed analytically. Reference dose measurements were performed in the absence and presence of a B = 1.5 T magnetic field using Aerrow in the 7 MV FFF photon beam of an Elekta MRI-linac and were directly compared to the results obtained using two calibrated reference-class IC types. The feasibility of performing solid phantom-based dosimetry with Aerrow and the possible influence of clearance gaps is also investigated by performing reference-type dosimetry measurements for multiple rotational positions of the detector and comparing the results to those obtained in water. RESULTS: In the absence of the B-field, as well as in the parallel orientation while in the presence of the B-field, the absorbed dose to water measured using Aerrow was found to agree within combined uncertainties with those derived from TG-51 using calibrated reference-class ICs. Statistically significant differences on the order of (2-4)%, however, were observed when measuring absorbed dose to water using the ICs in the perpendicular orientation in the presence of the B-field. Aerrow had a peak-to-peak response of about 0.5% when rotated within the solid phantom regardless of whether the B-field was present or not. CONCLUSIONS: This work describes the successful use of Aerrow as a straightforward means of measuring absolute dose to water for large high-energy photon fields in the presence of a 1.5 T B-field to a greater accuracy than currently achievable with ICs. The detector-phantom air gap does not appear to significantly influence the response of Aerrow in absolute terms, nor does it contribute to its rotational dependence. This work suggests that the accurate use of solid phantoms for absolute point dose measurement is possible with Aerrow.

Density effects of silica aerogel insulation on the performance of a graphite probe calorimeter.

PURPOSE: With the introduction of a novel graphite probe calorimeter, called the Aerrow, various thermal insulating materials are being explored to further improve the device. Silica-based aerogels are proving to be an optimal material due to their low densities, small thermal conductivities, rigidity, and machinability. The aim of this work is to determine how various silica aerogel densities affect the Aerrow's performance. METHODS: Performance concerns three areas: heat transfer from the core, the Aerrow's beam quality dependence, and the effects of an applied magnetic field on its measurement of absorbed dose to water. A numerical heat transfer study was done to determine heat transfer time constants. The EGSnrc radiation transport toolkit was used to determine absorbed dose conversion factors which are used to quantify the Aerrow's beam quality dependence. Dose conversion factors for Cobalt-60 and two clinical photon beams (6 and 10 MV) were determined. Magnetic field perturbation factors are used to characterize the Aerrow's performance under an applied magnetic field. EGSnrc with the magnetic field transport algorithm was used to determine these perturbations for a 1.5 T MR-linac. Several aerogel densities (0.01-0.55 g  cm - 3 ) were examined for each performance area. RESULTS: Heat transfer time constants were found to vary from 52 ± 2 to 117.4 ± 0.4 s. The time constants decreased with increasing aerogel density. The Aerrow's beam quality dependence varied between 0.5% and 1%, decreasing with increasing aerogel density. Beam quality dependence was determined in the range of 60 Co to 10 MV (58.4%  ≤  % d d ( 10 ) x  ≤ 73.5%). Under an applied magnetic field, perturbations were smallest when the Aerrow was parallel to the field. Perturbations varied more so when the Aerrow was perpendicular to the magnetic field and increased with increasing aerogel density. In all cases, perturbations were less than 0.6% from unity with a relative uncertainty of 0.1%. CONCLUSION: Silica-based aerogels demonstrate an improved performance over thermal insulation used in previous iterations of the Aerrow. With it, the Aerrow has shown to be robust in several areas. If heat transfer can be properly corrected for in the dose determination and the parallel orientation is used under a magnetic field, then the high density aerogel is possibly more preferable.

Aerrow: A probe-format graphite calorimeter for absolute dosimetry of high-energy photon beams in the clinical environment.

PURPOSE: In this work, the design, operation, initial experimental evaluation, and characterization of a small-scale graphite calorimeter probe - herein referred to as the Aerrow - developed for routine use in the clinical environment, are described. Similar in size and shape to a Farmer type cylindrical ionization chamber, the Aerrow represents the first translation of calorimetry intended for direct use by clinical physicists in the radiotherapy clinic. METHODS: Based on a numerically optimized design obtained in previous work, a functioning Aerrow prototype capable of two independent modes of operation (quasi-adiabatic and isothermal) was constructed in-house. Reference dose measurements were performed using both Aerrow operation modes in a 6 MV photon beam and were directly compared to results obtained with a calibrated reference-class ionization chamber. The Aerrow was then used to quantify the absolute output of five clinical linac-based photon beams (6 MV, 6 MV FFF, 10 MV, 10 MV FFF, and 15 MV; 63.2% < %dd(10)× < 76.3%). Linearity, dose rate, and orientation dependences were also investigated. RESULTS: Compared to an ion chamber-derived dose to water of 76.3 ± 0.7 cGy, the average doses measured using the Aerrow were 75.6 ± 0.7 and 74.7 ± 0.7 cGy/MU for the quasi-adiabatic and isothermal modes, respectively. All photon beam output measurements using the Aerrow in water-equivalent phantom agreed with chamber-based clinical reference dosimetry data within combined standard uncertainties. The linearity of the Aerrow's response was characterized by an adjusted R2 value of 0.9998 in the dose range of 80 cGy to 470 cGy. For the dose-rate dependence, no statistically significant effects were observed in the range of 0.5 Gy/min to 5.4 Gy/min. A relative photon beam quality dependence of 1.7% was calculated in the range of 60 Co to 24 MV (58.4% < %dd(10)× < 86.8%) using Monte Carlo. Finally, the angular dependence (gantry stationary and detector rotated) of the Aerrow's response was found to be insignificant to within ±0.5%. CONCLUSIONS: This work demonstrates the feasibility of using an ion chamber-sized calorimeter as a practical means of measuring absolute dose to water in the radiotherapy clinic. The potential introduction of calorimetry as a mainstream device into the clinical setting is powerful, as this fundamental technique has formed the basis of absorbed dose standards in many countries for decades and could one day form the basis of a new local absorbed dose standard for clinics.