The nth root percent depth dose method for calculating monitor units for irregularly shaped electron fields

This study outlines an improved method for calculating dose per monitor unit values for irregularly shaped electron fields using the nth root percent depth dose method. This method calculates the percent depth dose and output factors for an irregularly shaped electron field directly from the measured electron beam percent depth dose curves and output factors for circular fields. The percent depth dose curves and output factors for circular fields are normalized and measured at a fixed depth of maximum dose for a reference field, respectively. When compared with the sector integral lateral buildup ratio method, the percent depth dose data calculated using the nth root method accounts more accurately for the change in lateral scatter with decreasing field size. Therefore, it provides more accurate values of dose per monitor unit at different depths for all type of field shapes and beam energies. For beam energies in the range of 6-21 MeV, the differences between measured and calculated dose per monitor unit values, at different depths, were found to be within +/- 1.0% when the nth root percent depth dose method was used for calculation and 12.6% when the sector integral lateral buildup ratio method was used. The nth root percent depth dose method was tested and compared with the sector integral lateral buildup ratio method for ten clinically used irregularly shaped inserts (cutouts). For small irregularly shaped fields, a maximum difference of 2% was found between calculated dose per monitor unit values and measurements when the nth root percent depth dose method was used; this difference changed to 7% when comparisons were made between measurements and calculations based on the sector integral lateral buildup ration method. For large irregular fields this difference was found to be within 1.5% and 3.5%, respectively.     

Effect of electron beam obliquity on lateral buildup ratio: a Monte Carlo dosimetry evaluation

The impact of the oblique electron beam on the lateral buildup ratio (LBR), used in the electron pencil beam model to predict the per cent depth dose (PDD) and dose per monitor unit (MU) for an irregular electron field, was examined using Monte Carlo simulation. The EGSnrc-based Monte Carlo code was used to model electron beams produced by a Varian 21 EX linear accelerator for different beam energies, angles of obliquity and field sizes. The Monte Carlo phase space model was verified by measurements using electron diode and radiographic film. For PDDs of oblique electron beams, it is found that the depth of maximum dose (d(m)) shifts towards the surface as the beam obliquity increases. Moreover, for increasing the beam angle of obliquity, the depth doses just beyond d(m) decrease with depth. The depth doses then increase eventually in a deeper depth close to the practical range. The LBRs and pencil beam radial spread function, calculated using PDDs with different field sizes, are found varying with electron beam energies, angles of obliquity and cutout diameters. It is found that LBR increases along the normalized depth when the beam angle of obliquity increases. This results in a decrease of the radial spread function with an increase of beam obliquity. When the size of the electron field increases, the variation of LBR with beam angle of obliquity decreases. It should be noted that when calculating dose per MU for an oblique electron beam with an irregular field misunderstanding and neglecting the effect of beam obliquity would lead to a significant deviation. A database of LBRs for oblique electron beams can be created using Monte Carlo simulation conveniently and is recommended when an oblique beam is used in electron radiotherapy.     

Calculation of lateral buildup ratio using Monte Carlo simulation for electron radiotherapy

Monte Carlo simulation was used to calculate the lateral buildup ratio (LBR) used in estimating the percentage depth dose (PDD) and dose per monitor unit for an irregular shaped cutout field in electron radiotherapy. Monte Carlo code BEAMnrc/EGSnrc was used to build a simulation model for a Varian 21 EX linear accelerator producing clinical electron beams with energies of 4, 6, 9, 12, and 16 MeV. The model is optimized by adjusting the incident electron energy within the Monte Carlo simulation so that the calculated PDD curves agree with the measurement within +/-2%. The LBR is calculated from the PDD curves for different diameters of circular cutouts. Although Monte Carlo simulation requires a longer time to create a LBR database compared to measurement using scanning water tank and dosimeter, the simulation models for different electron energies, applicators, and cutouts are very similar. As the calculations can be carried out in a batch mode automatically run by a computer, human efforts in carrying out measurements in the treatment room and fabricating the circular cutouts in the mold room are greatly saved. Moreover, the simulation avoids human error in the experimental setup and can better handle the electron scattering affecting accuracy in the measurement. Using Monte Carlo simulation to calculate the LBR is proved to be useful in the commissioning of the electron beams for electron radiotherapy.     

Application of measured pencil beam parameters for electron beam model evaluation

Most current electron beam models, as are used in commercial treatment planning systems, combine measured broad beam central axis depth dose data with measured or modeled functions to approximate radial scatter and heterogeneity effects. In this paper, we extend a recently developed pencil beam model to calculate doses outside the field edge and doses in heterogeneous media. We have also explored use of this model as a tool for evaluating commercial electron planning programs. The algorithm we have developed, based on the concept of the lateral buildup ratio (LBR), enables calculation of dose at any point in an irregular electron field, and is capable of generating both on- and off-axis depth dose curves and isodose profiles. This model includes the effects of density and mass-angular scattering power in measured broad beam central axis depth dose data, which when combined with small field reference data, can be used to generate LBR ratios. From these ratios one can infer the depth dependent, effective pencil beam radial spread parameter a in water or other materials, which can be used to model any arbitrary field. We have used this approach to calculate fractional depth doses for small fields incident on aluminum and cork, which we have then compared against measurements and the calculations of several commercial planning systems.     

Monitor unit settings for intensity modulated beams delivered using a step-and-shoot approach

Two linear accelerators have been commissioned for delivering IMRT treatments using a step-and-shoot approach. To assess beam startup stability for 6 and 18 MV x-ray beams, dose delivered per monitor unit (MU), beam flatness, and beam symmetry were measured as a function of the total number of MU delivered at a clinical dose rate of 400 MU per minute. Relative to a 100 MU exposure, the dose delivered per MU by both linear accelerators was found to be within +/-2% for exposures larger than 4 MU. Beam flatness and symmetry also met accepted quality assurance standards for a minimum exposure of 4 MU. We have found that the performance of the two machines under study is well suited to the delivery of step-and-shoot IMRT. A system of dose calculation has also been commissioned for applying head scatter corrections to fields as small as 1x1 cm2. The accuracy and precision of the relative output calculations in water was validated for small fields and fields offset from the axis of collimator rotation. For both 6 and 18 MV x-ray beams, the dose per MU calculated in a water phantom agrees with measured data to within 1% on average, with a maximum deviation of 2.5%. The largest output factor discrepancies were seen when the actual radiation field size deviated from the set field size. The measured output in water can vary by as much 16% for 1x1 cm2 fields, when the measured field size deviates from the set field size by 2 mm. For a 1 mm deviation, this discrepancy was reduced to 8%. Steps should be taken to ensure collimator precision is tightly controlled when using such small fields. If this is not possible, very small fields should not contribute to a significant portion of the treatment, or uncertainties in the collimator position may effect the accuracy of the dose delivered.     

Film dosimetry of small elongated electron beams for treatment planning

The characteristics of 5, 7, 10, 12, 15, and 18 Mev electron beams for small elongated fields of dimensions L X W (where L = 1, 2, 3, 4, 5, and 10 cm; and W = 1, 2, 3, 4, 5, and 10 cm) have been studied. Film dosimetry and parallel-plate ion chamber measurements have been used to obtain various dose parameters. Selective results of a series of systematic measurements for central axis depth dose data, uniformity index, field flatness, and relative output factors of small elongated electron beams are reported. The square-root method is employed to predict the beam data of small elongated electron fields from corresponding small square electron fields using film dosimetry. The single parameter area/perimeter radio A/P is used to characterize the relative output factors of elongated electron beams. It is our conclusion that for clinical treatment planning square-root method may be applied with caution in determining the beam characteristics of small elongated electron fields from film dosimetry. The calculated and estimated relative output factors from square-root method and A/P ratio are in good agreement and show agreement to within 1% with the measured film values.     

Modeling photon output caused by backscattered radiation into the monitor chamber from collimator jaws using a Monte Carlo technique

Dose per monitor unit in photon fields generated by clinical linear accelerators can be affected by the backscattered radiation into the monitor chamber from collimator jaws. Thus, it is necessary to account for the backscattered radiation in computing monitor unit setting for a treatment field. In this work, we investigated effects of the backscatter from collimator jaws based on Monte Carlo simulations of a clinical linear accelerator. The backscattered radiation scored within the monitor chamber was identified as originating either from the upper jaws (Y jaws), or from the lower jaws (X jaws). From the results of Monte Carlo simulations, ratios of the monitor-chamber-scored dose caused by the backscatter to the dose caused by the forward radiation, R(x,y), were modeled as functions of the individual X and Y jaw positions. The amount of the backscattered radiation for any field setting was then computed as a compound contribution from both the X and Y jaws. The dose ratios of R(x,y) were then used to calculate the change in photon output caused by the backscatter, Scb(x,y). Results of these calculations were compared with available measured data based on counting the electron pulses or charge from the electron target of an accelerator. Data from this study showed that the backscattered radiation contributes approximately 3% to the monitor-chamber-scored dose. A majority of the backscattered radiation comes from the upper jaws, which are located closer to the monitor chamber. The amount of the backscatter decreases approximately in a linear fashion with the jaw opening. This results in about a 2% increase of photon output from a 10 cm x 10 cm field to a 40 cm x 40 cm field. The off-axis location of the jaw opening does not have a significant effect on the magnitude of the backscatter. The backscatter effect is significant for monitor chambers using kapton windows, particularly for treatment fields using moving jaws. Applying the backscatter correction improves the accuracy of monitor-unit calculation using a model-based dose calculation algorithm such as the convolution method.     

Monte Carlo study of si diode response in electron beams

Silicon semiconductor diodes measure almost the same depth-dose distributions in both photon and electron beams as those measured by ion chambers. A recent study in ion chamber dosimetry has suggested that the wall correction factor for a parallel-plate ion chamber in electron beams changes with depth by as much as 6%. To investigate diode detector response with respect to depth, a silicon diode model is constructed and the water/silicon dose ratio at various depths in electron beams is calculated using EGSnrc. The results indicate that, for this particular diode model, the diode response per unit water dose (or water/diode dose ratio) in both 6 and 18 MeV electron beams is flat within 2% versus depth, from near the phantom surface to the depth of R50 (with calculation uncertainty <0.3%). This suggests that there must be some other correction factors for ion chambers that counter-balance the large wall correction factor at depth in electron beams. In addition, the beam quality and field-size dependence of the diode model are also calculated. The results show that the water/diode dose ratio remains constant within 2% over the electron energy range from 6 to 18 MeV. The water/diode dose ratio does not depend on field size as long as the incident electron beam is broad and the electron energy is high. However, for a very small beam size (1 X 1 cm(2)) and low electron energy (6 MeV), the water/diode dose ratio may decrease by more than 2% compared to that of a broad beam.     

Lateral loss and dose discrepancies of multileaf collimator segments in intensity modulated radiation therapy

In the step-and-shoot technique delivery of intensity modulated radiation therapy (IMRT), each static field consists of a number of beamlets, some of which may be very small. In this study, we measured the dose characteristics for a range of field sizes: 2 x 2 to 12 x 10 cm2 for 6 and 15 MV x rays. For a given field length, a number of treatment fields are set up by sequentially increasing the field width using a multi leaf collimator. A set of fields is delivered with the accelerator operated in the IMRT mode. Using an ion chamber, the output factors at 1 cm and 3 cm laterally from a field edge are measured at different depths in a solid water phantom. Our results show that with insufficient lateral distance in at least one direction, the absorbed dose never reaches the equilibrium values, and can be significantly lower for very small field sizes. For example, the output factor of the 2 x 2 cm2 field relative to 10 x 10 cm2 at d(max0 is 0.832 and 0.790 for 6 MV and 15 MV x rays, respectively. Multiple output factor curves are obtained for different field lengths and different buildup conditions. Thus under nonequilibrium conditions, output factors are critically dependent on the field size and the conventional method of determining the equivalent square does not apply. Comparison of output factors acquired in the commissioning of the accelerator with those measured in the present study under conditions of nonequilibrium shows large discrepancies between the two sets of measurements. Thus monitor units generated by a treatment planning system using beam data commissioned with symmetric fields may be underestimated by > 5%, depending on the size and shape of the segments. To facilitate manual MU calculation as an independent check in step-and-shoot IMRT, the concept of effective equivalent square (EES) is introduced. Using EES, output factors can be calculated using existing beam data for fields with asymmetric collimator settings and under conditions of lateral disequilibrium.     

Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom

PEREGRINE is a three-dimensional Monte Carlo dose calculation system written specifically for radiotherapy. This paper describes the implementation and overall dosimetric accuracy of PEREGRINE physics algorithms, beam model, and beam commissioning procedure. Particle-interaction data, tracking geometries, scoring, variance reduction, and statistical analysis are described. The BEAM code system is used to model the treatment-independent accelerator head, resulting in the identification of primary and scattered photon sources and an electron contaminant source. The magnitude of the electron source is increased to improve agreement with measurements in the buildup region in the largest fields. Published measurements provide an estimate of backscatter on monitor chamber response. Commissioning consists of selecting the electron beam energy, determining the scale factor that defines dose per monitor unit, and describing treatment-dependent beam modifiers. We compare calculations with measurements in a water phantom for open fields, wedges, blocks, and a multileaf collimator for 6 and 18 MV Varian Clinac 2100C photon beams. All calculations are reported as dose per monitor unit. Aside from backscatter estimates, no additional, field-specific normalization is included in comparisons with measurements. Maximum discrepancies were less than either 2% of the maximum dose or 1.2 mm in isodose position for all field sizes and beam modifiers.     

The accuracy of dose calculations by anisotropic analytical algorithms for stereotactic radiotherapy in nasopharyngeal carcinoma

Nasopharyngeal tumors are commonly treated with intensity-modulated radiotherapy techniques. For photon dose calculations, problems related to loss of lateral electronic equilibrium exist when small fields are used. The anisotropic analytical algorithm (AAA) implemented in Varian Eclipse was developed to replace the pencil beam convolution (PBC) algorithm for more accurate dose prediction in an inhomogeneous medium. The purpose of this study was to investigate the accuracy of the AAA for predicting interface doses for intensity-modulated stereotactic radiotherapy boost of nasopharyngeal tumors. The central axis depth dose data and dose profiles of phantoms with rectangular air cavities for small fields were measured using a 6 MV beam. In addition, the air-tissue interface doses from six different intensity-modulated stereotactic radiotherapy plans were measured in an anthropomorphic phantom. The nasopharyngeal region of the phantom was especially modified to simulate the air cavities of a typical patient. The measured data were compared to the data calculated by both the AAA and the PBC algorithm. When using single small fields in rectangular air cavity phantoms, both AAA and PBC overestimated the central axis dose at and beyond the first few millimeters of the air-water interface. Although the AAA performs better than the PBC algorithm, its calculated interface dose could still be more than three times that of the measured dose when a 2 × 2 cm(2) field was used. Testing of the algorithms using the anthropomorphic phantom showed that the maximum overestimation by the PBC algorithm was 20.7%, while that by the AAA was 8.3%. When multiple fields were used in a patient geometry, the dose prediction errors of the AAA would be substantially reduced compared with those from a single field. However, overestimation of more than 3% could still be found at some points at the air-tissue interface.     

A calibration procedure for beam monitors in a scanned beam of heavy charged particles

An international code of practice (CoP) for dosimetry based on standards of absorbed dose to water has recently been published by the IAEA [Technical Report Series No. 398, 2000] (TRS-398). This new CoP includes procedures for proton and heavy ion beams as well as all other beam qualities. In particular it defines reference conditions to which dose measurements should refer to. For proton and ion beams these conditions include dose measurements in the center of all possible modulated Bragg peaks. The recommended reference conditions in general are used also for the calibration of beam monitors. For a dynamic beam delivery system using beam scanning in combination with energy variation, like, e.g., at the German carbon ion radiotherapy facility, this calibration procedure is not appropriate. We have independently developed a different calibration procedure. Similar to the IAEA CoP this procedure is based on the measurement of absorbed dose to water. This is translated in terms of fluence which finally results in an energy-dependent calibration of the beam monitor in units of particle number per monitor unit, which is unique for all treatment fields. In contrast to the IAEA CoP, the reference depth is chosen to be very small. The procedure enables an accurate and reliable determination of calibration factors. In a second step, the calibration is verified by measurements of absorbed dose in various modulated Bragg peaks by comparing measured against calculated doses. The agreement between measured and calculated doses is usually better than 1% for homogeneous fields and the mean deviation for more inhomogeneous treatment fields, as they are used for patient treatments, is within 3%. It is proposed that the CoP in general, and in particular the IAEA TRS-398 should include explicit recommendations for the beam monitor calibration. These recommendations should then distinguish between systems using static and dynamic beams.     

Calculation of electron beam dose distributions for arbitrarily shaped fields

A method for the calculation of absorbed dose distributions of arbitrarily shaped electron beams is presented. Isodose distributions and output factors of treatment fields can be predicted with good accuracy, without the need for any dose measurement in the actual field. A Gaussian pencil beam model is employed with two different pencil beams for each electron beam energy. The values of the parameters of the pencil beam dose distributions are determined from a set of measurements of broad beam distributions; in this way the influence of electrons scattered by the applicator walls is taken into account. The dose distribution of electrons scattered from high atomic number metal frames, which define the treatment field contour at the skin, is calculated separately and added. This calculation is based on experimentally derived data. The method has been tested for beams with 6, 10, 14 and 20 MeV electron energy. The distance between calculated and measured isodose lines with values between 10 and 90% is under 0.3 cm. The difference between calculated and measured output factors does not exceed 2%.     

Irregular field calculation on the central beam axis of photon beams using sector-integration

A method is proposed for calculation of irregular field factors on the central beam axis and homogeneous medium for x-ray beams. The irregular field factor is introduced as the ratio of the output of a field with and without blocks on the central beam axis. The algorithm is based on the sector-integration method and the circular field quantities are calculated from in-phantom measurements. These circular field quantities are the output per beam monitor unit for circular fields defined by a hypothetical secondary collimator and reduced to a circular field by blocking. A derivation of the sector-integration equation is given from first principles. As it is shown, the circular field quantities are evaluated from data measured for rectangular, block shaped fields. Such quantities contain all beam components, including photons scattered from the blocks, the block tray, and photons scattered in the phantom. Consequently, the so called primary and secondary beam components are readily incorporated in this approach. Once the circular field quantities have been determined from rectangular field data, the irregular field factors for other geometry can be calculated. Irregular field factors for square, rectangular and circular block-shaped fields were calculated for 6 MV photon beams and compared with measured values. The results agree within 0.7%, even for heavy blocked field cases, i.e., a 40 x 40 cm2 collimator field blocked to a 5 x 5 cm2 field. The method was tested for a particular source to surface distance, depth, phantom composition, and source to block distance. Calculation of irregular field factors in another set up conditions requires the measurement of the appropriate input data.     

Modified sector-integration method for predicting the output factors of electron beams including extended source to surface distance

A modified sector-integration method is presented that can predict the output factors of irregular shaped electron fields even in the case of extended source to surface distance (SSD). The model takes as input measured output factors for circular inserts of various radii. These circular fields were measured at SSDs of 100, 105 and 110 cm to determine the effective source distance as a function of radius (ESD(r)). For an arbitrary electron field at any SSD, the shape is divided into small sectors, and the contribution calculated from the radius and ESD(r). The calculated output factors were verified by direct measurements of various types of electron fields mainly based on clinical use. The energies modelled were 8, 10 and 12 MeV for applicator sizes of 10 cm x 10 cm and 14 cm x 14 cm (defined at 95 cm). The calculated values agreed with the measured data within 1% for the various rectangular cutouts including extended source to surface distance. We retrospectively modelled 97 patient inserts of irregular shape, and found agreement within 2% of measured values.     

Monte Carlo calculations and measurements of absorbed dose per monitor unit for the treatment of uveal melanoma with proton therapy

The treatment of uveal melanoma with proton radiotherapy has provided excellent clinical outcomes. However, contemporary treatment planning systems use simplistic dose algorithms that limit the accuracy of relative dose distributions. Further, absolute predictions of absorbed dose per monitor unit are not yet available in these systems. The purpose of this study was to determine if Monte Carlo methods could predict dose per monitor unit (D/MU) value at the center of a proton spread-out Bragg peak (SOBP) to within 1% on measured values for a variety of treatment fields relevant to ocular proton therapy. The MCNPX Monte Carlo transport code, in combination with realistic models for the ocular beam delivery apparatus and a water phantom, was used to calculate dose distributions and D/MU values, which were verified by the measurements. Measured proton beam data included central-axis depth dose profiles, relative cross-field profiles and absolute D/MU measurements under several combinations of beam penetration ranges and range-modulation widths. The Monte Carlo method predicted D/MU values that agreed with measurement to within 1% and dose profiles that agreed with measurement to within 3% of peak dose or within 0.5 mm distance-to-agreement. Lastly, a demonstration of the clinical utility of this technique included calculations of dose distributions and D/MU values in a realistic model of the human eye. It is possible to predict D/MU values accurately for clinical relevant range-modulated proton beams for ocular therapy using the Monte Carlo method. It is thus feasible to use the Monte Carlo method as a routine absolute dose algorithm for ocular proton therapy.     

Dosimetric evaluation of a two-dimensional, arc electron, pencil-beam algorithm in water and PMMA.

The accuracy of dose calculations from a pencil-beam algorithm developed specifically for arc electron beam therapy was evaluated at 10 and 15 MeV. Mid-arc depth-doses were measured for 0 degrees and 90 degrees arcs using 12 and 15 cm radius cylindrical water phantoms. Calculated depth-doses for the 90 degrees arced beams in the build-up region were as much as 3% less than measured values; the maximum dose was similar in magnitude but at a greater depth; and the therapeutic depth, R80, was 2-4 mm deeper. Calculated values of output (dose per monitor unit) at the depth of the maximum calculated dose were compared with measured values; for arcs ranging from 0-90 degrees, 12 and 15 cm radius water phantoms, and collimator widths of 4, 5 and 6 cm, results showed differences as great as 7%. Isodose countours for a 90 degrees arc were also measured in a 15 cm radius PMMA phantom. At the depth of maximum dose the algorithm predicted doses in the penumbral regions, both with and without collimation, which agreed within a few per cent of measured values. The largest discrepancies were 5%, which occurred in the penumbral portion of the depth-dose fall-off region. Differences between measurement and calculation are not believed to be clinically significant and are believed to be primarily due to the fact that the algorithm models neither large-angle scattering nor the effects of range straggling on the pencil-beam dose distribution.     

Field-size dependence of doses of therapeutic carbon beams

To estimate the physical dose at the center of spread-out Bragg peaks (SOBP) for various conditions of the irradiation system, a semiempirical approach was applied. The dose at the center of the SOBP depends on the field size because of large-angle scattering particles in the water phantom. For a small field of 5 x 5 cm2, the dose was reduced to 99.2%, 97.5%, and 96.5% of the dose used for the open field in the case of 290, 350, and 400 MeV/n carbon beams, respectively. Based on the three-Gaussian form of the lateral dose distributions of the carbon pencil beam, which has previously been shown to be effective for describing scattered carbon beams, we reconstructed the dose distributions of the SOBP beam. The reconstructed lateral dose distribution reproduced the measured lateral dose distributions very well. The field-size dependencies calculated using the reconstructed lateral dose distribution of the therapeutic carbon beam agreed with the measured dose dependency very well. The reconstructed beam was also used for irregularly shaped fields. The resultant dose distribution agreed with the measured dose distribution. The reconstructed beams were found to be applicable to the treatment-planning system.     

Point dose verification for intensity modulated radiosurgery using Clarkson's method

In clinical radiation physics chart checking, the dose calculation results generated by computer treatment planning software are usually verified by an independent computerized monitor unit calculation routine, or by "hand calculation" using percent depth dose (PDD), tissue phantom ratio (TPR), scatter factors, and the machine calibration factors. For intensity-modulated radiosurgery (IMRS) or intensity-modulated radiation therapy (IMRT), the "hand calculation" becomes not feasible due to the sophisticated multileaf collimator (MLC) segments created for intensity-modulated dose delivery. Therefore, an independent computerized dose calculation routine is needed for fast and reliable dose verification. In this work, a point dose calculation routine for IMRS/IMRT plan verification is developed by directly applying Clarkson's method. The method includes preparing data table by measuring TPRs for circular fields with diameters ranging 6 to 98 mm, extrapolating TPR for the zero field size (TPR0) from measured data and generating scatter phantom ratio (SPR) for each individual circular field. The segmented MLC sequences created by IMRS/IMRT inverse planning are converted into irregular fields for Clarkson's calculation. This method has been tested using 29 IMRS/IMRT cases. The results indicate that it is reliable, fast, and accurate. The average time to calculate one field is about 2 s with a 300 Mhz CPU.