A generic off-axis energy correction for linac photon beam dosimetry

Cooperative clinical trial group protocols frequently require off-axis point dose calculations. The Radiological Physics Center uses the calculative technique developed by Hanson et al. [Med. Phys. 7, 145-146 (1980); 7, 147-150 (1980)] to verify these calculations. In order to correct for off-axis energy changes, this technique requires off-axis half-value layer data, HVL, as a function of off-axis ray angle for the specific beam. This paper presents a formulism based on HVL mesurements on a limited number of therapy beams, which allows the calculation of an off-axis energy-correction factor for any clinical photon beam created by a linear accelerator using conventional flattening filters.     

Beam characteristics and clinical possibilities of a new compact treatment unit design combining narrow pencil beam scanning and segmental multileaf collimation

Not until the last decade has flexible intensity modulated three-dimensional dose delivery techniques with photon beams become a clinical reality, first in the form of heavy metal transmission blocks and other beam compensators, then in dynamic and segmented multileaf collimation, and most recently by scanning high-energy narrow electron and photon beams. The merits of various treatment unit and bremsstrahlung target designs for high-energy photon therapy are investigated theoretically for two clinically relevant target sites, a cervix and a larynx cancer both in late stages. With an optimized bremsstrahlung target it is possible to generate photon beams with a half-width of about 3 cm at a source to axis distance (SAD) of 100 cm and an initial electron energy of 50 MeV. By making a more compact treatment head and shortening the SAD, it is possible to reduce the half-width even further to about 2 cm at a SAD of 70 cm and still have sufficient clearance between the collimator head and the patient. One advantage of a reduced SAD is that the divergence of the beam for a given field size on the patient is increased, and thus the exit dose is lowered by as much as 1%/cm of the patient cross section. A second advantage of a reduced SAD is that the electron beam on the patient surface will be only about 8 mm wide and very suitable for precision spot beam scanning. It may also be possible to reduce the beamwidth further by increasing the electron energy up to about 60 MeV to get a photon beam of around 15 mm half-width and an electron beam as narrow as 5 mm. The compact machine will be more efficient and easy to work with, due to the small gantry and the reduced isocentric height. For a given target volume and optimally selected static multileaf collimator, it is no surprise that the narrowest possible scanned elementary bremsstrahlung beam generates the best possible treatment outcome. In fact, by delivering a few static field segments with individually optimized scan patterns, it is possible to combine the advantage of being able to fine tune the fluence distribution by the scanning system with the steeper dose gradients that can be delivered by a few static multileaf collimator segments. It is demonstrated that in most cases a few collimator segments are sufficient and often a single segment per beam portal may suffice when narrow scanned photon beams are employed, and they can be delivered sequentially with a negligible time delay. A further advantage is the increase of therapeutically useful photons and improved patient protection, since the pencil beam is only scanned where the leaf collimator is open. Consequently, some of the problems associated with dynamic multileaf collimation such as the tongue and groove and edge leakage effects are significantly reduced. Fast scanning beam techniques combined with good treatment verification systems allow interesting future possibilities to counteract patient and internal organ motions in real time.     

Target, purging magnet and electron collector design for scanned high-energy photon beams

A new method for producing very narrow and intense 50 MV bremsstrahlung beams with a half-width as low as 35 mm at a distance of 1 m from the target is presented. Such a beam is well suited for intensity modulation using scanned photon beams. An algorithm has been developed to minimize the width of the bremsstrahlung beam generated in a multilayer target by varying the individual layer thicknesses and atomic numbers under given constraints on the total target thickness and the mean energy of the transmitted electrons. Under such constraints the narrowest possible bremsstrahlung beam is obtained with a target composed of layers of monotonically increasing atomic number starting with the lowest possible value at the entrance side where the electrons impinge. It is also shown that the narrowest photon beam profile is associated with the highest possible forward photon yield. To be able to use the optimized target clinically it is desirable to be able to collect and stop all the electrons that are transmitted through the target. The electrons are most efficiently collected if they are kept close together, i.e. by minimizing the multiple scatter of the electrons and consequently the half-width of the generated bremsstrahlung beam. This is achieved by a thin low-atomic-number target. A dedicated electron stopper has been developed and integrated with the purging magnet. When the electron stopper is combined with a purging magnet, a primary photon collimator and a multileaf collimator, almost all of the transmitted electrons and their associated bremsstrahlung contamination can effectively be collected. The narrow photon beams from thin low-atomic-number targets have the additional advantage of producing the hardest and most penetrative photon spectrum possible, which is ideal for treating large deep-seated tumours.     

Intensity modulation with electrons: calculations, measurements and clinical applications

Intensity modulation of electron beams is one step towards truly conformal therapy. This can be realized with the MM50 racetrack microtron that utilizes a scanning beam technique. By adjusting the scan pattern it is possible to obtain arbitrary fluence distributions. Since the monitor chambers in the treatment head are segmented in both x- and y-directions it is possible to verify the fluence distribution to the patient at any time during the treatment. Intensity modulated electron beams have been measured with film and a plane parallel chamber and compared with calculations. The calculations were based on a pencil beam method. An intensity distribution at the multileaf collimator (MLC) level was calculated by superposition of measured pencil beams over scan patterns. By convolving this distribution with a Gaussian pencil beam, which has propagated from the MLC to the isocentre, a fluence distribution at isocentre level was obtained. The agreement between calculations and measurements was within 2% in dose or 1 mm in distance in the penumbra zones. A standard set of intensity modulated electron beams has been developed. These beams have been implemented in a treatment planning system and are used for manual optimization. A clinical example (prostate) of such an application is presented and compared with a standard irradiation technique.     

Two replica blotting methods for fast immunological analysis of common proteins in two-dimensional electrophoresis

Knowledge of the photon spectrum of a radiotherapy beam is often needed for three-dimensional (3-D) dose calculations using Monte Carlo methods and/or algorithms employing energy deposition kernels. Direct measurement of the x-ray energy fluence spectrum is not feasible for the high-energy photon beams used clinically. In this paper, the spectrum is extracted from basic beam data that are readily obtained for a clinical beam. We describe the photon spectrum using just two parameters. One parameter, which determines the high-energy part of the spectrum, is obtained using the measured dose in the buildup region for a small field, where electron contamination of the beam can be neglected. The other parameter is extracted from the photon beam attenuation in water. The results compare favorably to spectra generated from Monte Carlo simulations.     

Endothelin in migraine patients

AIM: Improvement of the dose homogeneity in radiation treatment of the intact breast using 3D-planning and dose volume histograms. PATIENTS AND METHOD: 3D-planning, including the calculation of dose volume histograms of the planning target volume, was performed on 15 patients, who underwent radiation therapy with tangential photon beams. A standard plan and 2 modified or optimized plans were evaluated. Different dosimetric parameters like maximum dose, mean dose, standard deviation and the fractional volume which receives doses from 95 to 105% of the reference dose were compared and correlated with breast size. RESULTS: With increasing breast size standard planning leads to increased overdosage, both in magnitude and volume. Individual optimization by modifying weights and wedges gives no improvement in dose homogeneity, whereas a photon energy of 10 MV results in a more homogeneous dose distribution. The drawback of the higher energy is the increased underdosage of the skin. CONCLUSION: Using the standard geometry of tangential fields the dose homogeneity cannot be improved significantly by 3D-planning, compared to our standard technique.     

Monte Carlo simulations of the differential beam hardening effect of a flattening filter on a therapeutic x-ray beam

A quantitative study of the differential beam hardening effect of the flattening filter on the 6-MV beam of Clinac 2100C has been conducted with Monte Carlo simulations using EGS4 code. The fluence-weighted photon energy of the unfiltered beam decreases from 1.35 MeV at central axis (CAX) to 1.22 MeV at an off-axis distance (OAD) of 20.0 cm. Compared to the unfiltered beam, the fluence-weighted photon energy of the filtered beam increases to 1.93 MeV at CAX and to 1.36 MeV at an OAD f 20.0 cm, respectively. The beam hardening effect was found to be 2.1 times higher at CAX than at an OAD of 20.0 cm. With the differential filtration of the flattening filter, the photon energy fluence reduced to 44% and 78% at CAX and an OAD of 20.0 cm respectively, resulting in the energy fluence of the filtered beam being flat from CAX to an OAD of 20.0 cm. The differential transmission ratios between the high energy and low energy photons decrease as the OAD increases. The percentage depth doses (PDDs) at field size of 10.0 cm x 10.0 cm for both the filtered and unfiltered 6-MV beams at CAX and at an OAD of 15.0 cm were calculated with a Monte Carlo technique based on the simulated spectra and fluence. The calculated PDDs were found to be consistent with the measured data for the filtered beam at CAX and an OAD of 15.0 cm. The beam quality (BQ) of the filtered beam at CAX is also higher than that of the same beam at an OAD of 15.0 cm. All the above results quantitatively demonstrate the differential beam hardening effects of a flattening filter on a therapeutic x-ray beam.     

The secretory intestinal transport of some beta-lactam antibiotics and anionic compounds: a mechanism contributing to poor oral absorption

PURPOSE: To measure the effect of silicon diode detectors used for in vivo dosimetry on beam characteristics and determine whether this effect is clinically significant. METHODS AND MATERIALS: Commercially available photon and electron diodes were placed on the central axis of photon and electron beams. The beam characteristics were measured for 6- and 10-MV photon and 6-20-MeV electron energies from a Varian Clinac 1800 medical linear accelerator. Water was used for the medium, and measurements were made for various clinically common field sizes and depths. RESULTS: Beam attenuations along the central axis were 10 and 7.5% for 6- and 10-MV photons, respectively. Electron beam dose reductions were between 13 and 25% for 20-6-MeV electrons. Photon beam flatness varied up to 7% at different depths, but the symmetry was not affected much. Electron beam flatness and symmetry were significantly changed to as much as 18 and 6%, respectively. CONCLUSION: Use of diode detectors on central axis of photon and electron beams for in vivo dosimetry causes significant attenuation and alteration of the beam characteristics. The percentage of the volume affected is significant (e.g., 23% of the volume in a 4 x 4 field gets 10% less dose for a 6-MV photon beam), especially if these diodes are used for in vivo dosimetry on the central axis every day for every treatment, as is done in some clinics. Other beam parameters such as penumbra and skin dose are also affected. It is therefore recommended that the diodes be used only as needed.     

Monte Carlo and analytical calculation of proton pencil beams for computerized treatment plan optimization

Proton pencil beams in water, in a format suitable for treatment planning algorithms and covering the radiotherapy energy range (50-250 MeV), have been calculated using a modified version of the Monte Carlo code PTRAN. A simple analytical model has also been developed for calculating proton broad-beam dose distributions which is in excellent agreement with the Monte Carlo calculations. Radial dose distributions are also calculated analytically and narrow proton pencil-beam dose distributions derived. The physical approximations in the Monte Carlo code and in the analytical model together with their limitations are discussed. Examples showing the use of the calculated set of proton pencil beams as input to an existing photon treatment planning algorithm based on biological optimization are given for fully 3D scanned proton pencil beams; these include intensity modulated beams with range shift and scanning in the transversal plane.     

Monte Carlo method to study the proton fluence for treatment planning

The proton beam at the Hahn Meitner Institute (HMI) in Berlin will be used for proton therapy of eye melanoma in the near future. As part of the pre-therapeutic studies, Monte Carlo calculations have been performed to investigate the primary fluence distribution of the proton beam including the influence of scattering foils, range shifters, modulator wheels, and collimators. Any material in the beam path will modify the therapeutic beam because of energy loss, multiple scattering, range straggling, and nuclear reactions. The primary fluence information is a pre-requisite for most pencil-beam treatment planning algorithms. The measured beam penumbra has been used as one of the parameters to characterize a proton beam for further calculations in a treatment planning algorithm. However, this phenomenological quantity represents only indirect information about the properties of the proton beam. In this work, an alternative parameterization of the beam exiting the vacuum window of the accelerator, as well as the beam right in front of the patient collimator, is introduced. A beam is fully characterized if one knows (for instance from Monte Carlo simulations) the particle distribution in energy, position, and angle, i.e., the phase space distribution. Therefore, parameters derived from this distribution can provide an alternative input in treatment planning algorithms. In addition, the method of calculation is introduced as a tool to investigate the influence of modifications in the beam delivery system on the behavior of the therapeutic proton beam.     

No association between c-myc amplification and TP53 mutation in sarcoma tumorigenesis

Accuracy of dose delivery at low monitor unit setting is studied for a dual photon energy linear accelerator. Dose delivered per MU is found to be constant for both the photon beams for MU settings above 30. For lower MUs there is definite deviation from the calibrated value and the error is found to be increasing as fewer MUs are set for dose delivery. This dose/MU ratio at low MU setting is found to be dose-rate dependent, showing an increasing trend with pulse repetition frequency (PRF). Also, the dosimetric ratio is observed to be mode dependent; its value for an 18 MV beam is almost double that observed in the case of a 6 MV beam at very low MU setting. The magnitude of this error should be determined for each energy so that appropriate corrections can be applied if very low MUs are to be used.     

Chemical control of breathing in identical twin athletes

The dosimetric characteristics of the electron beams from the Sagittaire (C.G.R. MeV) linear accelerator are presented. The variations in dose output with the distance from the source are indicated for the usual treatment distances. The measurements carried out demonstrating the deviations from the inverse square law for distances. The graphs for the variation in dose output in terms of the opening of the collimator are given for square and rectangular openings. The measurements demonstrate the preponderant influence of the short side 1 of the rectangular field of the relative variation in dose output. The variations in the graphs of the deep yield in terms of beam energy, distance from the source and field dimension were studied. For the different energies, the influence of the distance from the collimator and the dimension of the field on the dose at entry and on the depth of the maximum was shown. Measurements of the deep yields were carried out in the case of rectangular fields. In each case, the side of the equivalent square field corresponding to the same deep yield as a 1 X L rectangular field was determined; a comparison was carried out with the equivalent square field defined for colbat radiation.     

Monte Carlo dosimetry study of a 6 MV stereotactic radiosurgery unit

Small-field and stereotactic radiosurgery (SRS) dosimetry with radiation detectors, used for clinical practice, have often been questioned due to the lack of lateral electron equilibrium and uncertainty in beam energy. A dosimetry study was performed for a dedicated 6 MV SRS unit, capable of generating circular radiation fields with diameters of 1.25-5 cm at isocentre using the BEAM/EGS4 Monte Carlo code. With this code the accelerator was modelled for radiation fields with a diameter as small as 0.5 cm. The radiation fields and dosimetric characteristics (photon spectra, depth doses, lateral dose profiles and cone factors) in a water phantom were evaluated. The cone factor (St) for a specific cone c at depth d is defined as St(d, c) = D(d, c)/D(d, c(ref)), where c(ref) is the reference cone. To verify the Monte Carlo calculations, measurements were performed with detectors commonly used in SRS such as small-volume ion chambers, a diamond detector, TLDs and films. Results show that beam energies vary with cone diameter. For a 6 MV beam, the mean energies in water at the point of maximum dose for a 0.5 cm cone and a 5 cm cone are 2.05 MeV and 1.65 MeV respectively. The values of St obtained by the simulations are in good agreement with the results of the measurements for most detectors. When the lateral resolution of the detectors is taken into account, the results agree within a few per cent for most fields and detectors. The calculations showed a variation of St with depth in the water. Based on calculated electron spectra in water, the validity of the assumption that measured dose ratios are equal to measured detector readings was verified.     

A dual source photon beam model used in convolution/superposition dose calculations for clinical megavoltage x-ray beams

A realistic photon beam model based on Monte Carlo simulation of clinical linear accelerators was implemented in a convolution/superposition dose calculation algorithm. A primary and an extra-focal sources were used in this beam model to represent the direct photons from the target and the scattered photons from other head structures, respectively. The effect of the finite size of the extra-focal source was modeled by a convolution of the source fluence distribution with the collimator aperture function. Relative photon output in air (Sc) and in phantom (Scp) were computed using the convolution method with this new photon beam model. Our results showed that in a 10 MV photon beam, the Sc, Sp (phantom scatter factor), and Scp factors increased by 11%, 10%, and 22%, respectively, as the field size changed from 3 x 3 cm2 to 40 x 40 cm2. The variation of the Sc factor was contributed mostly by an increase of the extra-focal radiation with field size. The radiation backscattered into the monitor chamber inside the accelerator head affected the Sc by about 2% in the same field range. The output factors in elongated fields, asymmetric fields, and blocked fields were also investigated in this study. Our results showed that if the effect of the backscattered radiation was taken into account, output factors in these treatment fields can be predicted accurately by our convolution algorithm using the dual source photon beam model.     

Dosimetric aspects of physical and dynamic wedge of Clinac 2100C linear accelerator

AIM: To investigate variation of wedge factors on field size and depth for physical and dynamic wedges of identical wedge angles for Clinac 2100C linear accelerator and its clinical implementation. MATERIAL AND METHODS: A computer controlled water phantom dosimetric system is used to generate profile data for physical wedges, whereas a 0.6 cm3 ion chamber is used for generation of profiles for dynamic wedge and wedge factors for both types of wedges. The method has been discussed to handle the dynamic wedge dosimetry in absence of linear array of detectors or film densitometer. RESULTS: A systematic dependence on wedge factor is observed for physical wedge, with respect to depth and wedge angle but not depending on field size. Whereas dynamic wedge shows strong dependence on field size and is not systematic because the dynamic wedge is controlled by segmented treatment tables depending on field size and energy and no significant variation is observed on depth for various wedge angles. The handling of beam data in a commercially available treatment planning system is discussed and a comparison has been made for iso-doses of both types of wedges. CONCLUSION: The dynamic wedge isodose curves shows rather straight lines than physical wedge but larger hot spots at thin edge which needs careful consideration during planning.     

Field margin reduction using intensity-modulated x-ray beams formed with a multileaf collimator

PURPOSE: In axial, coplanar treatments with multiple fields, the superior and inferior ends of a planning target volume (PTV) are at risk to get underdosed due to the overlapping penumbras of all treatment fields. We have investigated a technique using intensity modulated x-ray beams that allows the use of small margins for definition of the superior and inferior field borders while still reaching a minimum PTV-dose of 95% of the isocenter dose. METHODS AND MATERIALS: The applied intensity modulated beams, generated with a multileaf collimator, include narrow (1.1-1.6 cm) boost fields to increase the dose in the superior and inferior ends of the PTV. The benefits of this technique have been assessed using 3D treatment plans for 10 prostate cancer patients. Treatment planning was performed with the Cadplan 3D planning system (Varian-Dosetek). Dose calculations for the narrow boost fields have been compared with measurements. The application of the boost fields has been tested on the MM50 Racetrack Microtron (Scanditronix Medical AB), which allows fully computer-controlled setup of all involved treatment fields. RESULTS: Compared to our standard technique, the superior-inferior field length can be reduced by 1.6 cm, generally yielding smaller volumes of rectum and bladder in the high dose region. For the narrow boost fields, calculated relative dose distributions agree within 2% or 0.2 cm with measured dose distributions. For accurate monitor unit calculations, the phantom scatter table used in the Cadplan system had to be modified using measured data for square fields smaller than 4 x 4 cm2. The extra time needed at the MM50 for the setup and delivery of the boost fields is usually about 1 min. CONCLUSION: The proposed use of intensity modulated beams yields improved conformal dose distributions for treatment of prostate cancer patients with a superior-inferior field size reduction of 1.6 cm. Treatments of other tumor sites can also benefit from the application of the boost fields.     

Quantification of mean energy and photon contamination for accurate dosimetry of high-energy electron beams

The scientific background of the standard procedure for determination of the mean electron energy at the phantom surface (E0) from the half-value depth (R50) has been studied. The influence of energy, angular spread and range straggling on the shape of the depth dose distribution and the R50 and Rp ranges is described using the simple Gaussian range straggling model. The relation between the R50 and Rp ranges is derived in terms of the variance of the range straggling distribution. By describing the mean energy imparted by the electrons both as a surface integral over the incident energy fluence and as a volume integral over the associated absorbed dose distribution, the relation between E0 and different range concepts, such as R50 and the maximum dose and the surface dose related mean energy deposition ranges, Rm and R0, is analysed. In particular the influence of multiple electron scatter and phantom generated bremsstrahlung on R50 is derived. A simple analytical expression is derived for the ratio of the incident electron energy to the half-value depth. Also, an analytical expression is derived for the maximum energy deposition in monoenergetic plane-parallel electron beams in water for energies between 2 and 50 MeV. Simple linear relations describing the relative absorbed dose and mass ionization at the depth of the practical range deposited by the bremsstrahlung photons generated in the phantom are derived as a function of the incident electron energy. With these relations and a measurement of the extrapolated photon background at Rp, the treatment head generated bremsstrahlung distribution can be determined. The identification of this photon contamination allows an accurate calculation of the absorbed dose in electron beams with a high bremsstrahlung contamination by accounting for the difference in stopping power ratios between a clean electron beam and the photon contamination. The absorbed dose determined using ionization chambers in heavily photon contaminated (10%) electron beams may be too low--by as much as 1.5%--without correction.     

A comparative study of dosimetric properties of Plastic Water and Solid Water in brachytherapy applications

In this study the dosimetric properties of Plastic Water and Solid Water phantom materials are evaluated using Monte Carlo photon transport simulations. In particular, their water-equivalence with respect to absorption and attenuation of photons in the brachytherapy energy range are examined. For the given chemical compositions of the materials, the linear attenuation coefficients were calculated for photons of 1 keV-2 MeV. Moreover, absorbed doses to water in each phantom material were calculated at distances of 0.5-12.0 cm from point sources of 20 keV to 60Co gamma rays. These results show that at low photon energies (below 100 keV), there are substantial differences (up to a factor of 5) between the absorbed dose in Plastic Water and that in liquid water. The differences decrease as photon energy increases, and they become insignificant at 60Co gamma rays, as claimed by the manufacturer. In contrast, calculations show that the difference in absorbed dose in Solid Water from that in liquid water, over the entire range of photon energies employed in this study, is less than 25%. The results of this study demonstrate the necessity of careful dosimetric evaluation of a new phantom material, before its clinical application, particularly in energy ranges outside those referred to by the manufacturer.     

A thin target approach for portal imaging in medical accelerators

A new thin-target method (patent pending) is described for portal imaging with low-energy (tens of keV) photons from a medical linear accelerator operating in a special mode. Low-energy photons are usually produced in the accelerator target, but are absorbed by the target and flattening filter, both made of medium- or high-Z materials such as Cu or W. Since the main contributor to absorption of the low-energy photons is self-absorption by the thick target through the photoelectric effect, it is proposed to lower the thickness of the portal imaging target to the minimum required to get the maximum low-energy photon fluence on the exit side of the target, and to lower the atomic number of the target so that predominantly photoelectric absorption is reduced. To determine the minimum thickness of the target, EGS4 Monte Carlo calculations were performed. As a result of these calculations, it was concluded that the maximum photon fluence for a 4 MeV electron beam is obtained with a 1.5 mm Cu target. This value is approximately five times less than the thickness of the Cu target routinely used for bremsstrahlung production in radiotherapeutic practice. Two sets of experiments were performed: the first with a 1.5 mm Cu target and the second with a 5 mm Al target (Cu mass equivalent) installed in the linear accelerator. Portal films were taken with a Rando anthropomorphic phantom. To emphasize the low-energy response of the new thin target we used a Kodak Min-R mammographic film and cassette combination, with a strong low-energy response. Because of its high sensitivity, only 1 cGy is required. The new portal images show a remarkable improvement in sharpness and contrast in anatomical detail compared with existing ones. It is also shown that further lowering of the target's atomic number (for example to C or Be) produces no significant improvement.     

Calculating dose and output factors for wedged photon radiotherapy fields using a convolution/superposition method

To account for clinical divergent and polychromatic photon beams, we have developed kernel tilting and kernel hardening correction methods for convolution dose calculation algorithms. The new correction methods were validated by Monte Carlo simulation. The accuracy and computation time of the our kernel tilting and kernel hardening correction methods were also compared to the existing approaches including terma divergence correction, dose divergence correction methods, and the effective mean kernel method with no kernel hardening correction. Treatment fields of 10 x 10-40 x 40 cm2 (field size at source to axis distance (SAD)) with source to source distances (SSDs) of 60, 80, and 100 cm, and photon energies of 6, 10, and 18 MV have been studied. Our results showed that based on the relative dose errors at a depth of 15 cm along the central axis, the terma divergence correction may be used for fields smaller than 10 x 10 cm2 with a SSD larger than 80 cm; the dose divergence correction with an additional kernel hardening correction can reduce dose error and may be more applicable than the terma divergence correction. For both these methods, the dose error increased linearly with the depth in the phantom; the 90% isodose lines at the depth of 15 cm were shifted by about 2%-5% of the field width due to significant underestimation of the penumbra dose. The kernel hardening effect was less prominent than the kernel tilting effect for clinical photon beams. The dose error by using nonhardening corrected kernel is less than 2.0% at a depth of 15 cm along the central axis, yet it increased with a smaller field size and lower photon energy. The kernel hardening correction could be more important to compute dose in the fields with beam modifiers such as wedges when beam hardening is more significant. The kernel tilting correction and kernel hardening correction increased computation time by about 3 times, and 0.5-1 times, respectively. This can be justified by more accurate dose calculations for the majority of clinical treatments.