The influence of small field sizes, penumbra, spot size and measurement depth on perturbation factors for microionization chambers

Monte Carlo calculation of detector perturbation and quality correction factors in a 1.5 T magnetic resonance guided radiation therapy small photon beams

Objective.With future advances in magnetic resonance imaging-guided radiation therapy, small photon beams are expected to be included regularly in clinical treatments. This study provides physical insights on detector dose-response to multiple megavoltage photon beam sizes coupled to magnetic fields and determines optimal orientations for measurements.Approach.Monte Carlo simulations determine small-cavity detector (solid-state: PTW60012 and PTW60019, ionization chambers: PTW31010, PTW31021, and PTW31022) dose-responses in water to an Elekta Unity 7 MV FFF photon beam. Investigations are performed for field widths between 0.25 and 10 cm in four detector axis orientations with respect to the 1.5 T magnetic field and the photon beam. The magnetic field effect on the overall perturbation factor (P_MC) accounting for the extracameral components, atomic composition, and density is quantified in each orientation. The density (P_ρ) and volume averaging (P_vol) perturbation factors and quality correction factors (kQB,QfB,f) accounting for the magnetic field are also calculated in each orientation.Main results.Results show thatP_volremains the most significant perturbation both with and without magnetic fields. In most cases, the magnetic field effect onP_volis 1% or less. The magnetic field effect onP_ρis more significant on ionization chambers than on solid-state detectors. This effect increases up to 1.564 ± 0.001 with decreasing field size for chambers. On the contrary, the magnetic field effect on the extracameral perturbation factor is higher on solid-state detectors than on ionization chambers. For chambers, the magnetic field effect onP_MCis only significant for field widths <1 cm, while, for solid-state detectors, this effect exhibits different trends with orientation, indicating that the beam incident angle and geometry play a crucial role.Significance.Solid-state detectors' dose-response is strongly affected by the magnetic field in all orientations. The magnetic field impact on ionization chamber response increases with decreasing field size. In general, ionization chambers yieldkQB,QfB,fcloser to unity, especially in orientations where the chamber axis is parallel to the magnetic field.

Cema-based formalism for the determination of absorbed dose for high-energy photon beams

PURPOSE

Determination of absorbed dose is well established in many dosimetry protocols and considered to be highly reliable using ionization chambers under reference conditions. If dosimetry is performed under other conditions or using other detectors, however, open questions still remain. Such questions frequently refer to appropriate correction factors. A converted energy per mass (cema)-based approach to formulate such correction factors offers a good understanding of the specific response of a detector for dosimetry under various measuring conditions and thus an estimate of pros and cons of its application.

METHODS

Determination of absorbed dose requires the knowledge of the beam quality correction factor k_Q,Qo , where Q denotes the quality of a user beam and Qo is the quality of the radiation used for calibration. In modern Monte Carlo (MC)-based methods, k_Q,Qo is directly derived from the MC-calculated dose conversion factor, which is the ratio between the absorbed dose at a point of interest in water and the mean absorbed dose in the sensitive volume of an ion chamber. In this work, absorbed dose is approximated by the fundamental quantity cema. This approximation allows the dose conversion factor to be substituted by the cema conversion factor. Subsequently, this factor is decomposed into a product of cema ratios. They are identified as the stopping power ratio water to the material in the sensitive detector volume, and as the correction factor for the fluence perturbation of the secondary charged particles in the detector cavity caused by the presence of the detector. This correction factor is further decomposed with respect to the perturbation caused by the detector cavity and that caused by external detector properties. The cema-based formalism was subsequently tested by MC calculations of the spectral fluence of the secondary charged particles (electrons and positrons) under various conditions.

RESULTS

MC calculations demonstrate that considerable fluence perturbation may occur particularly under non-reference conditions. Cema-based correction factors to be applied in a 6-MV beam were obtained for a number of ionization chambers and for three solid-state detectors. Feasibility was shown at field sizes of 4 × 4 and 0.5 cm × 0.5 cm. Values of the cema ratios resulting from the decomposition of the dose conversion factor can be well correlated with detector response. Under the small field conditions, the internal fluence correction factor of ionization chambers is considerably dependent on volume averaging and thus on the shape and size of the cavity volume.

CONCLUSIONS

The cema approach is particularly useful at non-reference conditions including when solid-state detectors are used. Perturbation correction factors can be expressed and evaluated by cema ratios in a comprehensive manner. The cema approach can serve to understand the specific response of a detector for dosimetry to be dependent on (a) radiation quality, (b) detector properties, and (c) electron fluence changes caused by the detector. This understanding may also help to decide which detector is best suited for a specific measurement situation.

Report of AAPM Task Group 155: Megavoltage photon beam dosimetry in small fields and non-equilibrium conditions

Small-field dosimetry used in advance treatment technologies poses challenges due to loss of lateral charged particle equilibrium (LCPE), occlusion of the primary photon source, and the limited choice of suitable radiation detectors. These challenges greatly influence dosimetric accuracy. Many high-profile radiation incidents have demonstrated a poor understanding of appropriate methodology for small-field dosimetry. These incidents are a cause for concern because the use of small fields in various specialized radiation treatment techniques continues to grow rapidly. Reference and relative dosimetry in small and composite fields are the subject of the International Atomic Energy Agency (IAEA) dosimetry code of practice that has been published as TRS-483 and an AAPM summary publication (IAEA TRS 483; Dosimetry of small static fields used in external beam radiotherapy: An IAEA/AAPM International Code of Practice for reference and relative dose determination, Technical Report Series No. 483; Palmans et al., Med Phys 45(11):e1123, 2018). The charge of AAPM task group 155 (TG-155) is to summarize current knowledge on small-field dosimetry and to provide recommendations of best practices for relative dose determination in small megavoltage photon beams. An overview of the issue of LCPE and the changes in photon beam perturbations with decreasing field size is provided. Recommendations are included on appropriate detector systems and measurement methodologies. Existing published data on dosimetric parameters in small photon fields (e.g., percentage depth dose, tissue phantom ratio/tissue maximum ratio, off-axis ratios, and field output factors) together with the necessary perturbation corrections for various detectors are reviewed. A discussion on errors and an uncertainty analysis in measurements is provided. The design of beam models in treatment planning systems to simulate small fields necessitates special attention on the influence of the primary beam source and collimating devices in the computation of energy fluence and dose. The general requirements for fluence and dose calculation engines suitable for modeling dose in small fields are reviewed. Implementations in commercial treatment planning systems vary widely, and the aims of this report are to provide insight for the medical physicist and guidance to developers of beams models for radiotherapy treatment planning systems.

Portal dosimetry of small unflattened beams

We developed and validated a dedicated small field back-projection portal dosimetry model for pretreatment andin vivoverification of stereotactic plans entailing small unflattened photon beams. For this purpose an aSi-EPID was commissioned as a small field dosimeter. Small field output factors for 6 MV FFF beams were measured using the PTW microDiamond detector and the Agility 160-leaf MLC from Elekta. The back-projection algorithm developed in our department was modified to better model the small field physics. The feasibility of small field portal dosimetry was validated via absolute point dose differences w.r.t. small static beams, and 5 hypofractionated stereotactic VMAT clinical plans measured with the OCTAVIUS 1000 SRS array dosimeter and computed with the treatment planning system Pinnacle v16.2. Dose reconstructions using the currently clinically applied back-projection model were also computed for comparison. We found that the latter yields underdosage of about -8% for square beams with cross section near 10 mm x 10 mm and about -6% for VMAT treatments with PTV volumes smaller than about 2cm³. With the methods described in this work such errors can be reduced to less than the ±3.0% recommendations for clinical use. Our results indicate that aSi-EPIDs can be used as accurate small field radiation dosimeters, offering advantages over point dose detectors, the correct positioning and orientation of which is challenging for routine clinical QA.

Reference dosimetry of modulated and dynamic photon beams

In the late 1980s, a new technique was proposed that would revolutionize radiotherapy. Now referred to as intensity-modulated radiotherapy, it is at the core of state-of-the-art photon beam delivery techniques, such as helical tomotherapy and volumetric modulated arc therapy. Despite over two decades of clinical application, there are still no established guidelines on the calibration of dynamic modulated photon beams. In 2008, the IAEA-AAPM work group on nonstandard photon beam dosimetry published a formalism to support the development of a new generation of protocols applicable to nonstandard beam reference dosimetry (Alfonso et al 2008 Med. Phys. 35 5179-86). The recent IAEA Code of Practice TRS-483 was published as a result of this initiative and addresses exclusively small static beams. But the plan-class specific reference calibration route proposed by Alfonso et al (2008 Med. Phys. 35 5179-86) is a change of paradigm that is yet to be implemented in radiotherapy clinics. The main goals of this paper are to provide a literature review on the dosimetry of nonstandard photon beams, including dynamic deliveries, and to discuss anticipated benefits and challenges in a future implementation of the IAEA-AAPM formalism on dynamic photon beams.

Suitability of the microDiamond detector for experimental determination of the anisotropy function of High Dose Rate 192 Ir brachytherapy sources

PURPOSE

To investigate the suitability of the microDiamond detector (mDD) type 60019 (PTW-Freiburg, Germany) to measure the anisotropy function F(r,θ) of High Dose Rate (HDR) ¹⁹² Ir brachytherapy sources.

METHODS

The HDR ¹⁹² Ir brachytherapy source, model mHDR-v2r (Elekta AB, Sweden), was placed inside a water tank within a 4F plastic needle. Four mDDs (mDD1, mDD2, mDD3, and mDD4) were investigated. Each mDD was placed laterally with respect to the source, and measurements were performed at radial distances r = 1 cm, 3 and 5 cm, and polar angles θ from 0° to 168°. The Monte Carlo (MC) system EGSnrc was used to simulate the measurements and to calculate phantom effect, energy dependence and volume-averaging correction factors. F(r,θ) was determined according to TG-43 formalism from the detector reading corrected with the MC-based factors and compared to the consensus anisotropy function _CON F(r,θ).

RESULTS

At 1 cm, the differences between measurements and MC simulations ranged from -0.8% to +0.8% for θ = 0° and from -2.1% to + 2.3% for θ ≠ 0°. At 3 and 5 cm, the differences ranged from +1.4% to +3.9% for θ = 0°, and from -0.4% to +2.9% for θ ≠ 0°. All differences were within the uncertainties (k = 2). At small angles, the phantom effect correction was up to -1.9%. This effect was mainly caused by the air between source and needle tip. The energy correction was angle-independent everywhere. For small angles at 1 cm, the volume-averaging correction was up to -2.9% and became less important for larger angles and distances. The differences of the measured F(r,θ) corrected with the MC-based factors to _CON F(r,θ) ranged from -1.0% to +3.4% for mDD1, -2.2% to +4.2% for mDD2, -2.5% to +4.0% for mDD3, and -2.6% to +3.4% for mDD4. All differences were within the uncertainties (k = 2) except one at (3 cm, 0°). For all the mDDs, F(r,0°) was always higher than _CON F(r,0°), with average differences of +3.1% (1 cm), +3.6% (3 cm), and +1.9% (5 cm). The inter-detector variability was within 2.9% (1 cm), 1.8% (3 cm), and 3.4% (5 cm).

CONCLUSIONS

A reproducible method and experimental setup were presented for measuring and validating F(r,θ) of an HDR ¹⁹² Ir brachytherapy source in a water phantom using the mDD. The phantom effect and the volume-averaging need to be taken into account, especially for the smaller distances and angles. Good agreement to _CON F(r,θ) was obtained. The discrepancies at (1 cm, 0°), accurately predicted by the MC results, may suggest a reconsideration of _CON F(r,θ), at least for this position. The slight overestimations at (3 cm,0°) and (5 cm,0°), both in comparison to _CON F(r,θ) and MC results, may be due to an underestimation of the air volume between source and needle tip, dark current, intrinsic over-response of the mDDs, or radiation-induced charge imbalance in the detector's components. The results indicate that the mDD is a valuable tool for measurements with HDR ¹⁹² Ir brachytherapy sources and support its employment for the determination and validation of TG-43 parameters of such sources.

[Detector Based Determination of Water Absorbed Dose According to DIN 6800 Teil 1: Suggestion for an Extension of the Fundamental Formalism]

For any detector to be used for the determination of absorbed dose at the point of measurement in water a basic equation is required to convert the reading of the detector into absorbed dose in water. The German DIN 6800 part 1 provides a general formalism for that. A further differentiated formalism applicable to photon dosimetry is suggested in this work. This modified formalism presents the two following still general and at the same time fundamental properties of any dosimetry detector: a) a clear distinction of correction factors with respect to the physical processes involved during the measurement, and b) the fact that the process of energy absorption in the detector is determined by the spectral distribution of the fluence of the secondary charged particles. It is concluded that based on the modified formalism and knowing this spectral distribution within the detector a general method is available with benefits for ionization chambers as well as for any other dosimetry detector and which is applicable at reference as well as non-reference conditions without any preconditions.

Fluence-weighted average subfield size in helical TomoTherapy

INTRODUCTION

Helical TomoTherapy allows a highly conformal dose distribution to complex target geometries with a good protection of organs at risk. However, the small field sizes associated with this method are a possible source of dosimetrical uncertainties. The IAEA has published detector-specific field output correction factors for static fields of the TomoTherapy in the TRS483. This work investigates the average subfield size of helical TomoTherapy plans.

MATERIAL AND METHODS

A new parameter for helical TomoTherapy was defined - the fluence-weighted average subfield size. The subfield sizes were extracted from the leaf-opening time sinograms in the RT-plan files for 30 clinical prostate and head and neck plans and were put in relation to Delat4 Phantom+ measurement results. Additionally the influence of planning parameters on the subfield size was studied by varying the modulation factor, number of iterations and pitch in the dose optimization and calculation for three different clinical indications H&N, prostate and rectum cancer. Selected plans were dosimetrically verified by Delta4 measurements to examine the reliability in dependence of the average subfield size. Furthermore, the impact of the planning parameters on a) the dose distribution, with regard to the planning target volume and regions at risks, and b) machine characteristics such as delivery time, actual modulation factor and leaf-opening times were evaluated.

RESULTS

The average equivalent square subfield lengths (s¯_eq) of the two investigated indications did not differ significantly - prostate plans: 2.75±0.14cm and H&N plans: 2.70±0.16cm, both with a jaw width of 2.5cm. No correlation between field size and measured dose deviation was detected. The number of iterations and the modulation factor have a considerable influence on the average subfield size. The higher the planned modulation factor and the more iterations are used during optimization, the smaller is the subfield size. In our pilot study plans were calculated with field sizes s¯_eq between 4.2cm and 1.7cm, with a jaw width of 2.5cm. Again, the measurement results of Delta4 showed no significant deviation from the doses calculated by the TomoTherapy planning system for the whole range of subfield sizes, and no significant correlation between field sizes and dose deviations was found. As expected, the clinical dose distribution improved with increasing modulation factor and an increasing number of iterations. The compromise between an improved dose distribution and smaller s¯_eq was shown.

CONCLUSION

In this work, a method was presented to determine the average subfield size for helical TomoTherapy plans. The response of the Delta4 did not show any dependence on field size in the range of the field sizes covered by the studied plans. The influence of the subfield sizes on other dosimetry systems remains to be investigated.

The role of radiation-induced charge imbalance on the dose-response of a commercial synthetic diamond detector in small field dosimetry

Purpose

Discrepancy between experimental and Monte Carlo simulated dose–response of the microDiamond (mD) detector (type 60019, PTW Freiburg, Germany) at small field sizes has been reported. In this work, the radiation‐induced charge imbalance in the structural components of the detector has been investigated as the possible cause of this discrepancy.

Materials and methods

Output ratio (OR) measurements have been performed using standard and modified versions of the mD detector at nominal field sizes from 6 mm × 6 mm to 40 mm × 40 mm. In the first modified mD detector (mD_reversed), the type of charge carriers collected is reversed by connecting the opposite contact to the electrometer. In the second modified mD detector (mD_shortened), the detector's contacts have been shortened. The third modified mD detector (mD_noChip) is the same as the standard version but the diamond chip with the sensitive volume has been removed. Output correction factors were calculated from the measured OR and simulated using the EGSnrc package. An adapted Monte Carlo user‐code has been used to study the underlying mechanisms of the field size‐dependent charge imbalance and to identify the detector's structural components contributing to this effect.

Results

At the smallest field size investigated, the OR measured using the standard mD detector is >3% higher than the OR obtained using the modified mD detector with reversed contact (mD_reversed). Combining the results obtained with the different versions of the detector, the OR have been corrected for the effect of radiation imbalance. The OR obtained using the modified mD detector with shortened contacts (mD_shortened) agree with the corrected OR, all showing an over‐response of less than 2% at the field sizes investigated. The discrepancy between the experimental and simulated output correction factors has been eliminated after accounting for the effect of charge imbalance.

Discussions and conclusions

The role of radiation‐induced charge imbalance on the dose–response of mD detector in small field dosimetry has been studied and quantified. It has been demonstrated that the effect is significant at small field sizes. Multiple methods were used to quantify the effect of charge imbalance with good agreement between Monte Carlo simulations and experimental results obtained with modified detectors. When this correction is applied to the Monte Carlo data, the discrepancy from experimental data is eliminated. Based on the detailed component analysis using an adapted Monte Carlo user‐code, it has been demonstrated that the effect of charge imbalance can be minimized by modifying the design of the detector's contacts.

Cherenkov emission-based external radiotherapy dosimetry: I. Formalism and feasibility

PURPOSE

Cherenkov emission (CE)-based external beam dosimetry is envisioned to involve the detection of CE directly in water with placement of a high-resolution detector out of the field, avoiding perturbations encountered with traditional dosimeters. In this work, we lay out the groundwork for its implementation in the clinic and motivate CE-based dosimeter design efforts. To that end, we examine a formalism for broad-beam in-water CE-based dosimetry of external radiotherapy beams, design and test a Monte Carlo (MC) simulation framework for the calculation of CE-to-dose conversion factors used by the formalism, and demonstrate the experimental feasibility of this method.

METHODS

The formalism is conceptually analogous to ionization-based dosimetry and employs CE-to-dose conversion factors, k C θ ± δ θ , including only and all CE generated within polar angles θ ± δθ on beam axis. The EGSnrc user code SPRRZnrc is modified to calculate k C θ ± δ θ , as well as CE spectral and angular distributions. The modified code is tested with monoenergetic parallel electrons on a thin water slab. Detector configurations are examined for broad 6-22 MeV electron beams from a BEAMnrc TrueBeam model, with a focus on θ ± δ θ = 90 ∘ ± 90 ∘ (4π detection), 90 ∘ ± 5 ∘ , and 42 ∘ ± 5 ∘ ( θ = 42 ∘ is the CE angle of relativistic electrons in water). We perform a relative experimental validation at 90 ∘ with electron beams, using a simple detector design with spherical optics and geometrical optics approximation of the sensitive volume, which spans the water tank. Due to transient charged particle equilibrium, broad photon beams are generally less sensitive to beam quality, depth, and angle.

RESULTS

For 0.1-50 MeV electrons on a thin water slab, the code outputs CE photon spectral density per unit mass (calculated from dose and k C θ ± δ θ ) and angle in agreement with theory within ±0.03% and ± 0 . 01 ∘ , respectively, corresponding to the output precision. The 42 ∘ configuration was found impractical due to detection considerations. Detection at 90 ∘ ± δ θ for small δθ exhibited beam quality dependence of the same order as well as strong superficial depth dependence. A 4π configuration ameliorates these effects. A more practical approach may employ a large numerical aperture. In comparing with literature, we find that these effects are less pronounced for broad photon beams in water, as expected. Measured relative k C 90 ∘ ± δ θ at small δθ were within 1% of simulated factors (relative to their local average) for percent-depth CE (PDC) >50%. At other depths, deviations were in accordance with signal-to-noise, known detector limitations, and approximations. It was found that the CE spectrum is beam quality and depth invariant, while for electron beams the CE angular distribution is strongly dependent on beam quality and depth. However, the uncertainty of CE and PDC measurement at 90 ∘ ± δ θ detection for small δθ due to ± 0 . 1 ∘ deviations around δθ was shown to be ≤1% and <0.1% (k = 1), respectively. The robustness to expected detector setup variations was found to result in ≤1% (k = 1) local uncertainty contribution for PDC >50%.

CONCLUSIONS

Based on our MC and experimental studies, we conclude that the CE-based method is promising for high-resolution, perturbation-free, three-dimensional dosimetry in water, with specific applications contingent on comprehensive detector development and characterization.

Can Gafchromic EBT3 films effectively characterize small fields of 6 MV unflattened photon beams of Cyberknife system?

Shielded silicon diodes are commonly employed in commissioning of Cyberknife 6 MV photon beams. This study aims to measure output factors, off centered ratio (OCR), percentage depth dose (PDD) of 6 MV photons using shielded and unshielded diodes and to compare with Gafchromic EBT3 film measurements to investigate whether EBT3 could effectively characterize small 6 MV photon beams. Output factors, OCR and PDD were measured with shielded and unshielded silicon detectors in a radiation field analyzer system at reference condition. Water equivalent solid phantom were used while irradiating EBT3 films. From multiuser data, diodes underestimated output factor by 3% for collimator fields ≤ 10 mm, while EBT3 underestimated the output factor by 3.9% for 5 mm collimator. 1D Gamma analysis of OCR between diode and film, results in gamma ≤ 1 for all measured points with 1 mm distance to agreement (DTA) and 1% relative dose difference (DD). Dose at surface is overestimated with diodes compared to EBT3. PDD results were within 2% relative dose values between diode and EBT3 except for 5 mm collimator. Except for small collimator fields of up to 10 mm, results of output factor, OCR, PDD of all detectors used in this study exhibited similar results. Relative dose measurements with Gafchromic EBT3 in this work show that EBT3 films can be used effectively as an independent tool to verify commissioning beam data of small fields only after careful verification of methodology for any systematic errors with appropriate readout procedure.

Decomposition of the dose conversion factor based on fluence spectra of secondary charged particles: Application to lateral dose profiles in photon fields

PURPOSE

The dose conversion factor plays an important role in the dosimetry by enabling the absorbed dose in the sensitive volume of a detector to be converted into the absorbed dose in the surrounding medium (in most cases water). The purpose of this paper is to demonstrate that a specific fluence-based approach for the decomposition of the dose conversion factor is in particular useful for the interpretation of the influences of detector properties on measurements under nonreference conditions.

METHODS

Data for the dose conversion factor and secondary fluence spectra were obtained by the Monte Carlo method. The calculation of the secondary charged particle fluence (electrons and positrons) in the sensitive detector volume was imbedded into the code for the calculation of absorbed dose in the detector. The decomposition method into subfactors is based on the use of these fluence data applied to a stepwise transition from the dose at the point of measurement next to a pure water detector and finally to the fully simulated detector geometry. Each subfactor is obtained as a ratio, at which the stopping power only is different in the numerator and the denominator or at which the fluence only is different in the numerator and the denominator. This method was applied at photon dose profiles obtained in water at different radiation qualities and with various detectors of cylindrical type.

RESULTS

The resulting subfactors can be well identified as a stopping power ratio and as perturbation factors each reflecting particular detector properties. Two of them (f1 and f4 ) are equivalent with perturbation factors which have already been introduced by other authors previously. These are the volume perturbation factor and the extracameral perturbation factor. Subfactor f2 denoted as medium perturbation factor was found to resemble the density perturbation factor. Results obtained for the volume perturbation factor applied to dose profiles measured with cylindrical detectors confirm that the volume effect can be well described by a convolution of the true profile in water with a Gaussian kernel. It was found that the sigma parameter depends on the cylinder radius only and amounts almost exactly to half of its value. The medium perturbation factor strongly depends on the density of the detector medium. For an air-filled detector, the influence of the air again can be described by a Gauss convolution, however, with a less good agreement. For detectors with a density of the cavity medium larger than that of water, for instance, for a diamond detector, it was found that there is a tendency of compensation between the volume averaging effect and the medium effect.

CONCLUSION

The fluence-based decomposition of the dose conversion factor leads to a fluence-based formulation of perturbation factors, referred to as volume, medium, and extracameral perturbation factor. These factors offer useful explanations for the behavior of detectors in nonreference conditions. An example was given for cylindrical detectors at dose profile measurements.

Technical Note: Scanning of parallel-plate ionization chamber and diamond detector for measurements of water-dose profiles in the vicinity of a narrow x-ray microbeam

PURPOSE

Scanning of dosimeters facilitates dose distribution measurements with fine spatial resolutions. This paper presents a method of conversion of the scanning results to water-dose profiles and provides an experimental verification.

METHODS

An Advanced Markus chamber and a diamond detector were scanned at a resolution of 6 μm near the beam edges during irradiation with a 25-μm-wide white narrow x-ray beam from a synchrotron radiation source. For comparison, GafChromic films HD-810 and HD-V2 were also irradiated. The conversion procedure for the water dose values was simulated with Monte Carlo photon-electron transport code as a function of the x-ray incidence position. This method was deduced from nonstandard beam reference-dosimetry protocols used for high-energy x-rays.

RESULTS

Among the calculated nonstandard beam correction factors, P_wall , which is the ratio of the absorbed dose in the sensitive volume of the chamber with water wall to that with a polymethyl methacrylate wall, was found to be the most influential correction factor in most conditions. The total correction factor ranged from 1.7 to 2.7 for the Advanced Markus chamber and from 1.15 to 1.86 for the diamond detector as a function of the x-ray incidence position. The water dose values obtained with the Advanced Markus chamber and the HD-810 film were in agreement in the vicinity of the beam, within 35% and 18% for the upper and lower sides of the beam respectively. The beam width obtained from the diamond detector was greater, and the doses out of the beam were smaller than the doses of the others.

CONCLUSIONS

The comparison between the Advanced Markus chamber and HD-810 revealed that the dose obtained with the scanned chamber could be converted to the water dose around the beam by applying nonstandard beam reference-dosimetry protocols.

Determination of small-field correction factors for cylindrical ionization chambers using a semiempirical method

A semiempirical method based on the averaging effect of the sensitive volumes of different air-filled ionization chambers (ICs) was employed to approximate the correction factors for beam quality produced from the difference in the sizes of the reference field and small fields.We measured the output factors using several cylindrical ICs and calculated the correction factors using a mathematical method similar to deconvolution; in the method, we modeled the variable and inhomogeneous energy fluence function within the chamber cavity. The parameters of the modeled function and the correction factors were determined by solving a developed system of equations as well as on the basis of the measurement data and the geometry of the chambers. Further, Monte Carlo (MC) computations were performed using the Monaco® treatment planning system to validate the proposed method.The determined correction factors () were comparable to the values derived from the MC computations performed using Monaco®. For example, for a 6 MV photon beam and a field size of 1  ×  1 cm2, was calculated to be for a PTW 31010 chamber and for a PTW 31016 chamber. On the other hand, the values determined from the MC computations were 1.121 and 1.031, respectively; the difference between the proposed method and the MC computation is less than 2%. In addition, we determined the values for PTW 30013, PTW 31010, PTW 31016, IBA FC23-C, and IBA CC13 chambers as well.We devised a method for determining from both the measurement of the output factors and model-based mathematical computation. The proposed method can be useful in case the MC simulation would not be applicable for the clinical settings.

Detector dose response in megavoltage small photon beams. II. Pencil beam perturbation effects

PURPOSE

To quantify detector perturbation effects in megavoltage small photon fields and support the theoretical explanation on the nature of quality correction factors in these conditions.

METHODS

In this second paper, a modern approach to radiation dosimetry is defined for any detector and applied to small photon fields. Fano's theorem is adapted in the form of a cavity theory and applied in the context of nonstandard beams to express four main effects in the form of perturbation factors. The pencil-beam decomposition method is detailed and adapted to the calculation of perturbation factors and quality correction factors. The approach defines a perturbation function which, for a given field size or beam modulation, entirely determines these dosimetric factors. Monte Carlo calculations are performed in different cavity sizes for different detection materials, electron densities, and extracameral components.

RESULTS

Perturbation effects are detailed with calculated perturbation functions, showing the relative magnitude of the effects as well as the geometrical extent to which collimating or modulating the beam impacts the dosimetric factors. The existence of a perturbation zone around the detector cavity is demonstrated and the approach is discussed and linked to previous approaches in the literature to determine critical field sizes.

CONCLUSIONS

Monte Carlo simulations are valuable to describe pencil beam perturbation effects and detail the nature of dosimetric factors in megavoltage small photon fields. In practice, it is shown that dosimetric factors could be avoided if the field size remains larger than the detector perturbation zone. However, given a detector and beam quality, a full account for the detector geometry is necessary to determine critical field sizes.

Experimental determination of the lateral dose response functions of detectors to be applied in the measurement of narrow photon-beam dose profiles

This study aims at the experimental determination of the detector-specific 1D lateral dose response function K(x) and of its associated rotational symmetric counterpart K(r) for a set of high-resolution detectors presently used in narrow-beam photon dosimetry. A combination of slit-beam, radiochromic film, and deconvolution techniques served to accomplish this task for four detectors with diameters of their sensitive volumes ranging from 1 to 2.2 mm. The particular aim of the experiment was to examine the existence of significant negative portions of some of these response functions predicted by a recent Monte-Carlo-simulation (Looe et al 2015 Phys. Med. Biol. 60 6585-607). In a 6 MV photon slit beam formed by the Siemens Artiste collimation system and a 0.5 mm wide slit between 10 cm thick lead blocks serving as the tertiary collimator, the true cross-beam dose profile D(x) at 3 cm depth in a large water phantom was measured with radiochromic film EBT3, and the detector-affected cross-beam signal profiles M(x) were recorded with a silicon diode, a synthetic diamond detector, a miniaturized scintillation detector, and a small ionization chamber. For each detector, the deconvolution of the convolution integral M(x)  =  K(x)  ∗  D(x) served to obtain its specific 1D lateral dose response function K(x), and K(r) was calculated from it. Fourier transformations and back transformations were performed using function approximations by weighted sums of Gaussian functions and their analytical transformation. The 1D lateral dose response functions K(x) of the four types of detectors and their associated rotational symmetric counterparts K(r) were obtained. Significant negative curve portions of K(x) and K(r) were observed in the case of the silicon diode and the diamond detector, confirming the Monte-Carlo-based prediction (Looe et al 2015 Phys. Med. Biol. 60 6585-607). They are typical for the perturbation of the secondary electron field by a detector with enhanced electron density compared with the surrounding water. In the cases of the scintillation detector and the small ionization chamber, the negative curve portions of K(x) practically vanish. It is planned to use the measured functions K(x) and K(r) to deconvolve clinical narrow-beam signal profiles and to correct the output factor values obtained with various high-resolution detectors.

Variation of kQclin,Qmsr (fclin,fmsr) for the small-field dosimetric parameters percentage depth dose, tissue-maximum ratio, and off-axis ratio

PURPOSE

Evaluate the ability of different dosimeters to correctly measure the dosimetric parameters percentage depth dose (PDD), tissue-maximum ratio (TMR), and off-axis ratio (OAR) in water for small fields.

METHODS

Monte Carlo (MC) simulations were used to estimate the variation of kQclin,Qmsr (fclin,fmsr) for several types of microdetectors as a function of depth and distance from the central axis for PDD, TMR, and OAR measurements. The variation of kQclin,Qmsr (fclin,fmsr) enables one to evaluate the ability of a detector to reproduce the PDD, TMR, and OAR in water and consequently determine whether it is necessary to apply correction factors. The correctness of the simulations was verified by assessing the ratios between the PDDs and OARs of 5- and 25-mm circular collimators used with a linear accelerator measured with two different types of dosimeters (the PTW 60012 diode and PTW PinPoint 31014 microchamber) and the PDDs and the OARs measured with the Exradin W1 plastic scintillator detector (PSD) and comparing those ratios with the corresponding ratios predicted by the MC simulations.

RESULTS

MC simulations reproduced results with acceptable accuracy compared to the experimental results; therefore, MC simulations can be used to successfully predict the behavior of different dosimeters in small fields. The Exradin W1 PSD was the only dosimeter that reproduced the PDDs, TMRs, and OARs in water with high accuracy. With the exception of the EDGE diode, the stereotactic diodes reproduced the PDDs and the TMRs in water with a systematic error of less than 2% at depths of up to 25 cm; however, they produced OAR values that were significantly different from those in water, especially in the tail region (lower than 20% in some cases). The microchambers could be used for PDD measurements for fields greater than those produced using a 10-mm collimator. However, with the detector stem parallel to the beam axis, the microchambers could be used for TMR measurements for all field sizes. The microchambers could not be used for OAR measurements for small fields.

CONCLUSIONS

Compared with MC simulation, the Exradin W1 PSD can reproduce the PDDs, TMRs, and OARs in water with a high degree of accuracy; thus, the correction used for converting dose is very close to unity. The stereotactic diode is a viable alternative because it shows an acceptable systematic error in the measurement of PDDs and TMRs and a significant underestimation in only the tail region of the OAR measurements, where the dose is low and differences in dose may not be therapeutically meaningful.

In-vivo dosimetry for field sizes down to 6 × 6 mm2 in shaped beam radiosurgery with microMOSFET

The aim of this study is to evaluate microMOSFET as in-vivo dosimeter in 6 MV shaped-beam radiosurgery for field sizes down to 6 × 6 mm2. A homemade build-up cap was developed and its use with microMOSFET was evaluated down to 6 × 6 mm2. The study with the homemade build-up cap was performed considering its influence on field size over-cover occurring at surface, achievement of the overall process of electronic equilibrium, dose deposition along beam axis and dose attenuation. An optimized calibration method has been validated using MOSFET in shaped-beam radiosurgery for field sizes from 98 × 98 down to 18 × 18 mm2. The method was detailed in a previous study and validated in irregular field shapes series measurements performed on a head phantom. The optimized calibration method was applied to microMOSFET equipped with homemade build-up cap down to 6 × 6 mm2. Using the same irregular field shapes, dose measurements were performed on head phantom. MicroMOSFET results were compared to previous MOSFET ones. Additional irregular field shapes down to 8.8 × 8.8 mm2 were studied with microMOSFET. Isocenter dose attenuation due to the homemade build-up cap over the microMOSFET was near 2% irrespective of field size. Our results suggested that microMOSFET equipped with homemade build-up cap is suitable for in-vivo dosimetry in shaped-beam radiosurgery for field sizes down to 6 × 6 mm2 and therefore that the required build-up cap dimensions to perform entrance in-vivo dosimetry in small-fields have to ensure only partial charge particle equilibrium.

Dosimetry for small fields in stereotactic radiosurgery using gafchromic MD-V2-55 film, TLD-100 and alanine dosimeters

This work investigated the suitability of passive dosimeters for reference dosimetry in small fields with acceptable accuracy. Absorbed dose to water rate was determined in nine small radiation fields with diameters between 4 and 35 mm in a Leksell Gamma Knife (LGK) and a modified linear accelerator (linac) for stereotactic radiosurgery treatments. Measurements were made using Gafchromic film (MD-V2-55), alanine and thermoluminescent (TLD-100) dosimeters and compared with conventional dosimetry systems. Detectors were calibrated in terms of absorbed dose to water in ⁶⁰Co gamma-ray and 6 MV x-ray reference (10×10 cm²) fields using an ionization chamber calibrated at a standards laboratory. Absorbed dose to water rate computed with MD-V2-55 was higher than that obtained with the others dosimeters, possibly due to a smaller volume averaging effect. Ratio between the dose-rates determined with each dosimeter and those obtained with the film was evaluated for both treatment modalities. For the LGK, the ratio decreased as the dosimeter size increased and remained constant for collimator diameters larger than 8 mm. The same behaviour was observed for the linac and the ratio increased with field size, independent of the dosimeter used. These behaviours could be explained as an averaging volume effect due to dose gradient and lack of electronic equilibrium. Evaluation of the output factors for the LGK collimators indicated that, even when agreement was observed between Monte Carlo simulation and measurements with different dosimeters, this does not warrant that the absorbed dose to water rate in the field was properly known and thus, investigation of the reference dosimetry should be an important issue. These results indicated that alanine dosimeter provides a high degree of accuracy but cannot be used in fields smaller than 20 mm diameter. Gafchromic film can be considered as a suitable methodology for reference dosimetry. TLD dosimeters are not appropriate in fields smaller than 10 mm diameters.