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A novel analytical method for computing dose from kilovoltage beams used in Image-Guided radiation therapy

Published:February 25, 2022DOI:https://doi.org/10.1016/j.ejmp.2022.02.020

      Highlights

      • The XVI system was simulated by MC and results were benchmarked with measurement.
      • The S/C algorithm was utilized with material specific kernels to calculate kV dose.
      • The dose of kV beam was calculated and compared to MC calculations and measurement.

      Abstract

      Purpose

      A modified convolution/superposition algorithm is proposed to compute dose from the kilovoltage beams used in IGRT. The algorithm uses material-specific energy deposition kernels instead of water-energy deposition kernels.

      Methods

      Monte Carlo simulation was used to model the Elekta XVI unit and determine dose deposition characteristics of its kilovoltage beams. The dosimetric results were compared with ion chamber measurements. The dose from the kilovoltage beams was then computed using convolution/superposition along with material-specific energy deposition kernels and compared with Monte Carlo and measurements. The material-specific energy deposition kernels were previously generated using Monte Carlo.

      Results

      The obtained gamma indices (using 2%/2mm criteria for 95% of points) were lower than 1 in almost all instances which indicates good agreement between simulated and measured depth doses and profiles. The comparisons of the algorithm with measurements in a homogeneous solid water slab phantom, and that with Monte Carlo in a head and neck CT dataset produced acceptable results. The calculated point doses were within 4.2% of measurements in the homogeneous phantom. Gamma analysis of the calculated vs. Monte Carlo simulations in the head and neck phantom resulted in 94% of points passing with a 2%/2mm criteria.

      Conclusions

      The proposed method offers sufficient accuracy in kilovoltage beams dose calculations and has the potential to supplement the conventional megavoltage convolution/superposition algorithms for dose calculations in low energy range.

      Keywords

      1. Introduction

      Image guidance is widely used to improve the precision and accuracy of radiation therapy treatment delivery [
      • Jaffray D.A.
      • Siewerdsen J.H.
      • Wong J.W.
      • Martinez A.A.
      Flat-panel cone-beam computed tomography for image-guided radiation therapy.
      ,
      • Zelefsky M.J.
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      • Cox B.
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      • Sperling D.
      • Pei X.
      • et al.
      Improved clinical outcomes with high-dose image guided radiotherapy compared with non-IGRT for the treatment of clinically localized prostate cancer.
      ,

      D. LA, J. DA. Advances in Image-Guided Radiation Therapy. J Clin Oncol 2007;25:938-46. 10.1200/jco.2006.09.9515.

      ]. Three-dimensional Image-Guided Radiation Therapy (IGRT) using kilovoltage cone beam computed tomography (kV-CBCT) has provided for more precise target localization and margin reduction as well as normal tissue sparing [
      • Pant K.
      • Umeh C.
      • Oldham M.
      • Floyd S.
      • Giles W.
      • Adamson J.
      Comprehensive radiation and imaging isocenter verification using NIPAM kV-CBCT dosimetry.
      ,
      • Boda-Heggemann J.
      • Lohr F.
      • Wenz F.
      • Flentje M.
      • Guckenberger M.
      kV Cone-Beam CT-Based IGRTkV-Cone-beam-CT-basierte bildgeführte Strahlentherapie – ein klinischer Überblick.
      ].
      Although kV-CBCT-guided IGRT reduces target positioning errors and enables implementation of more accurate dose delivery, it increases the patient dose due to acquisition of hundreds of projection radiographs and high frequency of imaging [
      • Boda-Heggemann J.
      • Lohr F.
      • Wenz F.
      • Flentje M.
      • Guckenberger M.
      kV Cone-Beam CT-Based IGRTkV-Cone-beam-CT-basierte bildgeführte Strahlentherapie – ein klinischer Überblick.
      ,
      • Olch A.J.
      • Alaei P.
      How low can you go? A CBCT dose reduction study.
      ,
      • Ding G.X.
      • Munro P.
      • Pawlowski J.
      • Malcolm A.
      • Coffey C.W.
      Reducing radiation exposure to patients from kV-CBCT imaging.
      ]. This is of more importance in pediatric patients as this additional dose could cause higher radiogenic cancer risks [
      • Zhou L.
      • Bai S.
      • Zhang Y.
      • Ming X.
      • Zhang Y.
      • Deng J.
      Imaging Dose, Cancer Risk and Cost Analysis in Image-guided Radiotherapy of Cancers.
      ,
      • Kutanzi K.R.
      • Lumen A.
      • Koturbash I.
      • Miousse I.R.
      Pediatric exposures to ionizing radiation: carcinogenic considerations.
      ]. Therefore, it is essential to estimate and reduce the imaging dose to critical organs.
      Monte Carlo is an ideal tool for accurately estimating the IGRT imaging dose. However, it requires additional tools and expertise and is computationally intensive. Therefore, it is not a useful tool for computing 3D dose distributions on a routine basis in the clinic.
      Model-based methods such as convolution/superposition algorithms could potentially be used to estimate the dose from kilovoltage beams. However, these methods use water energy deposition kernels, which lead to inherent uncertainties of dose calculations in this energy range. Previous studies have shown that using water kernels in dose calculation of kilovoltage beams results in the underestimation of the dose by up to 300% in high atomic number structures such as bone [
      • Alaei P.
      • Gerbi B.J.
      • Geise R.A.
      Evaluation of a model-based treatment planning system for dose computations in the kilovoltage energy range.
      ]. This is due to the inability of the algorithm to account for atomic number changes which are crucial in computing the dose in this energy range due to dominance of photoelectric effect.
      Model-based methods perform a secondary computation of dose based on precomputed energy deposition kernels [
      • McDermott P.N.
      Tutorials in Radiotherapy Physics: Advanced Topics with Problems and Solutions.
      ]. They explicitly consider beam characteristics such as energy fluence, geometry of radiation beam, and presence of beam modifiers. An advantage of these methods is that they lend themselves well to 3D dose calculations in the megavoltage range. Energy deposition kernels for monoenergetic photons in water have been calculated by Mohan at el [
      • Mohan R.
      • Chui C.
      • Lidofsky L.
      Differential pencil beam dose computation model for photons.
      ], Ahnesjo at al [
      • Ahnesjö A.
      • Andreo P.
      • Brahme A.
      Calculation and application of point spread functions for treatment planning with high energy photon beams.
      ,
      • Ahnesjö A.
      Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media.
      ], and Mackie et al [
      • Mackie T.R.
      • Scrimger J.W.
      • Battista J.J.
      A convolution method of calculating dose for 15-MV x rays.
      ,
      • Mackie T.R.
      • Bielajew A.F.
      • Rogers D.W.O.
      • Battista J.J.
      Generation of photon energy deposition kernels using the EGS Monte Carlo code.
      ] for use in convolution/superposition algorithms in the megavoltage energy range. Alaei et al [
      • Alaei P.
      • Gerbi B.J.
      • Geise R.A.
      Generation and use of photon energy deposition kernels for diagnostic quality x rays.
      ], Modrick et al [

      Modrick JM, Mackie TR, Thomadsen BR. Energy deposition kernels at low photon energy including coherent scatter. Proceedings of the 22nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (Cat No00CH37143)2000. p. 1078-81. 10.1109/IEMBS.2000.897914.

      ], and Mainegra-Hing et al [
      • Mainegra-Hing E.
      • Rogers D.W.O.
      • Kawrakow I.
      Calculation of photon energy deposition kernels and electron dose point kernels in water.
      ] generated the kernels in the kilovoltage energy range and used them to estimate the dose from kilovoltage beams. Huang et al [
      • Huang J.Y.
      • Eklund D.
      • Childress N.L.
      • Howell R.M.
      • Mirkovic D.
      • Followill D.S.
      • et al.
      Investigation of various energy deposition kernel refinements for the convolution/superposition method.
      ] showed that the use of material-specific energy deposition kernels may improve the dose calculation accuracy in high-density materials as well as the vicinity of interfaces in the megavoltage range.
      Adopting the method proposed by Huang et al. [
      • Huang J.Y.
      • Eklund D.
      • Childress N.L.
      • Howell R.M.
      • Mirkovic D.
      • Followill D.S.
      • et al.
      Investigation of various energy deposition kernel refinements for the convolution/superposition method.
      ], Heidarloo et al. [
      • Heidarloo N.
      • Aghamiri S.M.R.
      • Saghamanesh S.
      • Azma Z.
      • Alaei P.
      Generation of material-specific energy deposition kernels for kilovoltage x-ray dose calculations.
      ] generated material-specific energy deposition kernels for kilovoltage beams of up to 150 keV.
      In this study, our goal was to calculate the dose from kV imaging beams using the convolution/superposition algorithm and material-specific energy deposition kernels. The resultant dose calculations were then compared to measurements and Monte Carlo calculations.

      2. Materials and methods

      2.1 X-ray tube and collimation system

      Elekta X-ray Volume Imaging (XVI) unit is an online kilovoltage CBCT imaging system integrated into Elekta linear accelerators (Elekta AB, Stockholm, Sweden). The kilovoltage tube is manufactured by Dunlee (Dunlee Inc. Aurora, IL, US) and produces photon beams of 70 to 150 kVp [
      • Spezi E.
      • Downes P.
      • Radu E.
      • Jarvis R.
      Monte Carlo simulation of an x-ray volume imaging cone beam CT unit.
      ].
      The collimators (S, M, and L) and filters (F0 and F1) are inserted into slots on the imaging tube arm. The collimator cassettes allow for small, medium, and large field of view (FOV) imaging. The two filter cassettes indicate beam filtration through a bowtie filter (F1) or no filtration (F0). The projected field width and length of the largest cassettes (S20, M20, and L20) at the isocenter is 27.67 × 27.67 cm2, with the M and L ones having an offset position. The imaging panel is mounted on a retractable arm, which could be moved laterally based on the collimator used.

      2.2 Measurements

      2.2.1 Percentage depth dose

      The percentage depth dose (PDD) was measured using two Exradin ion chambers (Standard Imaging, Middleton, WI, US): An A28 (0.125 cc) chamber for depths of up to 2 cm and an A11 Roos type parallel plate chamber (0.62 cc) for shallower depths, along with a Supermax electrometer (Fig. 1a). The measurements were carried out in a DoseView™ 3D water tank (Standard Imaging) in 2 mm increments. Measurements were performed at 75-cm SSD with the X-ray tube at the upright position. Another A28 chamber was used as the reference detector [
      • Ma C.-M.
      • Coffey C.W.
      • DeWerd L.A.
      • Liu C.
      • Nath R.
      • Seltzer S.M.
      • et al.
      AAPM protocol for 40–300 kV x-ray beam dosimetry in radiotherapy and radiobiology.
      ]. Depth dose data for a number of kVp/cassette/filter combinations were collected.
      Figure thumbnail gr1
      Fig. 1Beam data collection setup for kilovoltage beams: (a) The actual dosimetric setup of the XVI Elekta infinity Linac along with DoseView ™ 3D Water Phantom, (b) Exradin A28 ionization chamber dosimeter used to measure transverse and depth dose profiles beyond 2 cm depth, and (c) Exradin A11 Roos type parallel plate ionization chamber used for measuring shallow depth doses.

      2.2.2 Beam profile

      As shown in Fig. 1, to measure the beam profiles, an Exradin A28 ion chamber was used [
      • Spezi E.
      • Downes P.
      • Radu E.
      • Jarvis R.
      Monte Carlo simulation of an x-ray volume imaging cone beam CT unit.
      ,
      • Ding G.X.
      • Duggan D.M.
      • Coffey C.W.
      Characteristics of kilovoltage x-ray beams used for cone-beam computed tomography in radiation therapy.
      ,
      • Ding G.X.
      • Duggan D.M.
      • Coffey C.W.
      Accurate patient dosimetry of kilovoltage cone-beam CT in radiation therapy.
      ,
      • Downes P.
      • Jarvis R.
      • Radu E.
      • Kawrakow I.
      • Spezi E.
      Monte Carlo simulation and patient dosimetry for a kilovoltage cone-beam CT unit.
      ,
      • Marchant T.E.
      • Joshi K.D.
      Comprehensive Monte Carlo study of patient doses from cone-beam CT imaging in radiotherapy.
      ,
      • Spezi E.
      • Volken W.
      • Frei D.
      • Fix M.K.
      A virtual source model for kilo-voltage cone beam CT: source characteristics and model validation.
      ,
      • Kim S.
      • Song H.
      • Movsas B.
      • Chetty I.J.
      Characteristics of x-ray beams in two commercial multidetector computed tomography simulators: Monte Carlo simulations.
      ]. In this work, the direction along megavoltage beamline is denoted as in-line and that perpendicular to the beamline is denoted as cross-line. For measurements of in-line profiles, the chamber was offset in the cross-line direction by 8.7 and 5.2 cm for the L and M collimators, respectively. The S collimator required no shift as it produces symmetric fields with respect to the central axis. Based on previous studies [
      • Marchant T.E.
      • Joshi K.D.
      Comprehensive Monte Carlo study of patient doses from cone-beam CT imaging in radiotherapy.
      ], beam profiles were measured at a depth of 1 cm with a spatial interval of 2 mm within the beam penumbra, and 5 mm elsewhere.

      2.2.3 Half value layer

      Half value layer (HVL) measurements were performed using an Exradin A19 Farmer type ion chamber according to the recommendations of the AAPM TG-61 protocol [
      • Ma C.-M.
      • Coffey C.W.
      • DeWerd L.A.
      • Liu C.
      • Nath R.
      • Seltzer S.M.
      • et al.
      AAPM protocol for 40–300 kV x-ray beam dosimetry in radiotherapy and radiobiology.
      ]. The XVI tube was placed in the upright position and the dosimeter was positioned in air and aligned at the isocenter with a source to dosimeter distance of 100 cm (Fig. 2). To reduce the influence of the scattered radiation, the source – aluminum filter and the aluminum – dosimeter distances were set to 50 cm. In addition, the aluminum holder was made of wood to minimize scattered radiation.
      Figure thumbnail gr2
      Fig. 2The experimental setup for HVL measurement: (a) Schematic of the setup according to TG 61 protocol
      [
      • Ma C.-M.
      • Coffey C.W.
      • DeWerd L.A.
      • Liu C.
      • Nath R.
      • Seltzer S.M.
      • et al.
      AAPM protocol for 40–300 kV x-ray beam dosimetry in radiotherapy and radiobiology.
      ]
      , (b) The actual dosimetric setup employed here.

      2.3 Monte Carlo simulation of the unit

      The kV tube and collimation system of the XVI unit were modeled using the EGSnrc/BEAMnrc version 2019 Monte Carlo software package [
      • Rogers D.W.O.
      • Kawrakow I.
      • Seuntjens J.P.
      • Walters B.R.B.
      • Mainegra-Hing E.
      NRC user codes for EGSnrc.
      ,

      Rogers DWO, Walters B, Kawrakow I. BEAMnrc users manual. NRCC Report PIRS-509 2019:12.

      ]. The geometric shape of the inherent cone filtration of the kV tube and the materials involved in MC simulation were provided by the manufacturer. Due to the 3.5° tilt of the tube housing relative to the beamline, the simulation was divided into two parts. The first part included the tube housing and the second part the rest of the beamline including the collimator and filter cassettes.
      In the first part, XTUBE and FLATFILT component modules were used for modeling the rotating anode and inherent filtration. The electron beam impinging upon the target was simulated as a parallel rectangular source incident from the side with a monoenergetic energy. Based on the manufacturer’s specifications, the focal spot size was set to 0.08 cm in length and 0.04 cm in width. A phase space (PHSP1) file of the simulated tube housing was recorded that contained the energy, position, and directional cosines of particles crossing the back of the filtration cone and generated at 6.45 cm from the source.
      In the second part of the simulation, the PHSP1 was used as the input to simulate the rest of the beamline by rotating it by 3.5°. The remainder of the system including the clamp ring and primary lead collimator, shielding lead, collimator cassette, filter cassette, and plastic cover were modeled by PYRAMIDS and SLAB component modules. The design, material composition, and density of components were in accordance with the manufacture’s datasheets. A second PHSP (PHSP2) file was then generated for each insert at the back of the polystyrene cover, 31.5 cm from the source, and was used for the subsequent simulations of the dose distribution in water by DOSXYZnrc [
      • Walters B.
      • Kawrakow I.
      • Rogers D.W.O.
      DOSXYZnrc users manual.
      ]. The simulated geometry of the XVI unit is shown in Fig. 3.
      Figure thumbnail gr3
      Fig. 3Schematic of the XVI Elekta Infinity beamline. Due to the tilt of kV CBCT, the simulation was divided into two separate parts. Dimensions are not to scale.
      In order to increase the simulation accuracy, the Koch–Motz bremsstrahlung angular sampling [
      • Koch H.W.
      • Motz J.W.
      Bremsstrahlung cross-section formulas and related data.
      ] and NIST bremsstrahlung cross section data [

      Hubbell JH, Seltzer SM. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z= 1 to 92 and 48 additional substances of dosimetric interest. National Inst. of Standards and Technology-PL, Gaithersburg, MD (United …; 1995.

      ] were used. Also, the photoelectron angular sampling, Rayleigh scattering, atomic relaxations, spin effect, and electron impact ionization were included in the simulations [

      Kawrakow I, Rogers DWO. The EGSnrc code system. NRC Report PIRS-701, NRC, Ottawa 2000:17.

      ]. Moreover, according to Ali and Rogers’ study [
      • Ali E.S.M.
      • Rogers D.W.O.
      Benchmarking EGSnrc in the kilovoltage energy range against experimental measurements of charged particle backscatter coefficients.
      ] for improvement of the simulation accuracy, the value of the boundary tolerance parameter changed to 5 × 10-7. The simulation efficiency was also increased using a directional bremsstrahlung splitting in the first and second parts [
      • Ding G.X.
      • Duggan D.M.
      • Coffey C.W.
      Accurate patient dosimetry of kilovoltage cone-beam CT in radiation therapy.
      ,
      • Kawrakow I.
      • Rogers D.W.O.
      • Walters B.R.B.
      Large efficiency improvements in BEAMnrc using directional bremsstrahlung splitting: directional bremsstrahlung splitting.
      ].The energy cutoffs for the electron and photon transport were set to 0.512 and 0.001 MeV, respectively. The energy thresholds for secondary particle creation were set to 0.512 and 0.001 for electrons and photons, respectively.
      The PDD calculations were performed along the central axis using 0.5 × 0.5 × 0.2 cm3 voxels. The HOWFARLESS algorithm was employed for particle transport in the water phantom. This algorithm dramatically increases the dose calculation efficiency in the homogeneous phantom [
      • Walters B.
      • Kawrakow I.
      • Rogers D.W.O.
      DOSXYZnrc users manual.
      ,
      • Walters B.R.B.
      • Kawrakow I.
      A “HOWFARLESS” option to increase efficiency of homogeneous phantom calculations with DOSXYZnrc.
      ].
      To calculate the HVL using Monte Carlo method, the CAVRnrc user code was utilized [
      • Ding G.X.
      • Duggan D.M.
      • Coffey C.W.
      Characteristics of kilovoltage x-ray beams used for cone-beam computed tomography in radiation therapy.
      ,
      • Kim S.
      • Song H.
      • Movsas B.
      • Chetty I.J.
      Characteristics of x-ray beams in two commercial multidetector computed tomography simulators: Monte Carlo simulations.
      ,
      • Abuhaimed A.
      • J Martin C.
      • Sankaralingam M.
      • J Gentle D.
      • McJury M.
      An assessment of the efficiency of methods for measurement of the computed tomography dose index (CTDI) for cone beam (CBCT) dosimetry by Monte Carlo simulation.
      ]. As the first step, phase space files for energies of 100 and 120 kVp were extracted using the BEAMnrc user code. In the simulation for extracting phase space files, F0 and F1 filter cassettes were selected for 100 kVp and 120 kVp, respectively. Also, according to the dimensions of the aluminum blades (8 × 8 cm2), a 15 × 15 MV cassette (with a 15 × 15 cm2 square field in the center) was used to limit the dimensions of the field in the center (location of the dosimeter) and diaphragm (location of the aluminum blades). It is worth mentioning that the phase space files were extracted in square planes with dimensions of 40 × 40 cm2 at a distance of 100 cm from the source.
      The ionization chamber was simulated in the CAVRnrc user code based on the dimensions and materials obtained from the manufacturer. Source number 22 (full beam phase space data, incident from any angle/position) was used in modeling the radiation source. Aluminum layers with thicknesses of 0.5 mm were used.

      2.4 Dose calculations in phantom

      2.4.1 Model-based dose calculations

      Convolution/superposition algorithm convolves total energy released per unit mass (TERMA), with energy deposition kernels. TERMA T (r) is the total energy released by primary photon interactions per unit mass; it includes the energy imparted to both charged particles and scattered photons. T(r) is obtained using equation 1:
      T(r)=Eμρ(r,E)ψE(r)dE(1)


      where ρ(r) is the local density, μ/ρ(r, E) is the mass attenuation coefficient at r, and ψE(r) is the total energy fluence of all photons for polyenergetic beam in the medium.
      In a homogeneous media, due to the spacial invariance of energy deposition kernels, superposition dose integral is simplified to convolution one and the dose can be calculated by equation 2:
      D(r)=EVTE(s)k(r-s,E)d3sdE(2)


      where k(r-s, E) is energy deposition kernel at energy E and position s relative to the point of scattering of the primary photon [
      • Ahnesjö A.
      • Andreo P.
      • Brahme A.
      Calculation and application of point spread functions for treatment planning with high energy photon beams.
      ].
      For inhomogeneous media, the energy deposition kernel is not spacially invariant and can no longer account for the secondary transport. In this case, a full superposition integral needs to be carried out:
      D(r)=1ρ(r)EVTE(s)ρ(s)k(r,s,E)d3sdE(3)


      where k(r, s, E) is the energy deposition kernel normalized by the energy delivered at point r by secondary particles, associated to a primary photon of energy E interacting in s.
      The convolution/superposition algorithm implemented in this study employs material-specific energy deposition kernels instead of water-energy deposition kernels to account for dose distribution in inhomogeneity, as shown in equation 4.
      D(r)=1ρ(r)EVTE(s)ρ(s)k¯(r,s)material - specificd3sdE(4)


      The material-specific energy deposition kernels were generated using EDKnrc user code of the EGSnrc toolkit and described in a previous study [
      • Heidarloo N.
      • Aghamiri S.M.R.
      • Saghamanesh S.
      • Azma Z.
      • Alaei P.
      Generation of material-specific energy deposition kernels for kilovoltage x-ray dose calculations.
      ]. The kernels are generated only once and can be used during model-based planning depending on the beam quality and the medium the dose is to be calculated in.
      Four material-specific energy deposition kernels were used in this algorithm: cortical bone, water, lung, and air. For each material, 15 energy deposition kennels were used in the 10 to 150 keV energy range in 10-keV bins.
      The average material-specific energy deposition kernel of polyenergetic photons (100 kVp/F0/S20 beam) was approximated by a spectrum-weighted sum of monoenergetic kernels with discrete energy bins, as shown in equation 5:
      k¯(r,s)material - specificiwik(r,s,Ei)material - specific(5)


      where wi = ψE,i (r0)/ψE(r0) is the spectrum weight, ψE(r0) is the primary photon energy fluence at the reference location, and ψE,i (r0) is the energy fluence for photons with only energy Ei.
      The ramps were used to convert each voxel’s CT number to material density and assign one of four materials named above, similar to Monte Carlo calculations. The energy fluence profiles were obtained for 100 kVp/F0/S20 x-ray beam used in this study by the MC simulation techniques described by Ding et al [
      • Ding G.X.
      • Duggan D.M.
      • Coffey C.W.
      Characteristics of kilovoltage x-ray beams used for cone-beam computed tomography in radiation therapy.
      ,
      • Ding G.X.
      • Coffey C.W.
      Beam characteristics and radiation output of a kilovoltage cone-beam CT.
      ] and Spezi et al [
      • Spezi E.
      • Downes P.
      • Radu E.
      • Jarvis R.
      Monte Carlo simulation of an x-ray volume imaging cone beam CT unit.
      ]. Kernel tilting was ignored to simplify dose calculation. Ray tracing was performed using the algorithm of Siddon [
      • Siddon R.L.
      Fast calculation of the exact radiological path for a three-dimensional CT array.
      ]. The convolution calculations were performed using MATLAB v2018a (Mathworks Inc., Natick, MA, US).

      2.4.2 Monte Carlo dose calculations

      A second Monte Carlo simulation was performed to obtain dose distributions in two image datasets for benchmarking the model-based dose calculations. The datasets included the CT images of a homogeneous solid water slab phantom and a head and neck CT image set.
      The dimensions of homogeneous solid water slab phantom were 30 × 30 × 15 cm3, constructed of certified therapy-grade solid water (Sun Nuclear Gammex, Madison, WI, US). The phantom was scanned using a Philips big bore scanner (Philips Medical Systems, Cleveland, OH, US). Calculations were carried out using DOSXYZnrc to compute 3D dose distributions on both sets of DICOM images. Using these images, each voxel was converted to a specific material. The materials were assigned to each voxel based on their densities, determined from the CT number to density calibration curve. The ranges of densities for each material were 0.01–0.044 g/cm3 for air, 0.044–0.302 g/ cm3 for lung, 0.302–1.101 g/ cm3 for soft tissue/water, and 1.101–2.088 g/ cm3 for cortical bone. One of the sources of dose estimation uncertainty is tissue segmentation uncertainty. The sources of this could be mis-assignment of material based on CT ramp resulting from image noise, volume averaging, and interpatient variations of tissue densities. To overcome this, the dual-energy material assignment proposed by Bazalova et al [
      • Bazalova M.
      • Carrier J.-F.
      • Beaulieu L.
      • Verhaegen F.
      Dual-energy CT-based material extraction for tissue segmentation in Monte Carlo dose calculations.
      ] would be particularly beneficial in kV dose calculations
      The voxel size of slab phantom and head and neck images were 0.67 × 0.67 × 0.30 cm3, and 0.97 × 0.97 × 0.30 cm3, respectively. For the slab phantom, the x-ray isocenter was placed at the center of the phantom, i.e. the distance between the x-ray beam and slab surface was equal to 92.5 cm. The phase space file for beam quality of 100 kVp/F0/S20 was used as the x-ray source of simulation. For head and neck dataset, the 100 kVp/F0/S20 x-ray isocenter was placed at 100 cm.
      For both simulations, the energy cutoff /energy thresholds for secondary particle creation for the electron and photon transport was set to 0.512 and 0.001 MeV, respectively. This Monte Carlo-simulated beam was calibrated by measuring the dose to a point in a phantom of known geometry and introducing a Monte Carlo calibration factor as explained by Ding et al [
      • Ding G.X.
      • Duggan D.M.
      • Coffey C.W.
      Accurate patient dosimetry of kilovoltage cone-beam CT in radiation therapy.
      ]. The dose measurement was done using a calibrated ion chamber for kV beam qualities and followed AAPM TG-61 methodology [
      • Ma C.-M.
      • Coffey C.W.
      • DeWerd L.A.
      • Liu C.
      • Nath R.
      • Seltzer S.M.
      • et al.
      AAPM protocol for 40–300 kV x-ray beam dosimetry in radiotherapy and radiobiology.
      ].
      The dose of slab phantom was measured at 7 locations using a PTW N30003 Framer-type ionization chamber (PTW, Freiburg, Germany) by irradiating the phantom from the top down with the same beam quality (100 kVp/F0/S20).

      3. Results

      3.1 Monte Carlo and measurement comparisons

      The measured and simulated PDD curves and dose profiles of 100 kVp/F0/S20 are shown in Fig. 4. The profiles were normalized to the dose at 1 cm on the central axis. The Monte Carlo-generated and measured curves were compared using gamma analysis [
      • Low D.A.
      • Harms W.B.
      • Mutic S.
      • Purdy J.A.
      A technique for the quantitative evaluation of dose distributions.
      ]. The dose difference and distance to agreement in the calculation of gamma index were set to 2% and 2 mm, respectively. As shown in Fig. 4, the gamma index for PDD and cross profiles are lower than 1 in all depths for 100 kVp/F0/S20, indicating good agreement between measurements and MC simulations.
      Figure thumbnail gr4
      Fig. 4Measured and simulated (a) percentage depth doses, (b) dose profile in the cross-line direction at 1 cm deep, and (c) transverse dose profile in the in-line direction at 1 cm depth for 100kVp/F0/S20 beam. Monte Carlo simulated results are shown with the plus symbol and measurements are shown with solid line. For each PDD/dose profile, the corresponding values of gamma-index in various depths/ different lateral distances are also presented.
      The simulated and measured attenuation curve of the 100 and 120 kVp beams are plotted in Fig. 5. MC dose calculation uncertainties are within 1.0% for the case in which no aluminum layer is present and 1.4% for the case of the thickest aluminum layer. The mean difference between measurements and MC simulation is 1.1%. The conformity of simulations and the measured data is satisfactory and confirms the accuracy of the MC model of the XVI unit.
      Figure thumbnail gr5
      Fig. 5The measured and Monte Carlo calculated attenuation curve of 100 and 120 kVp beams. The measured attenuation curves are shown with solid symbols and Monte Carlo calculated ones are presented with plus symbol.
      The energy spectra of photons at 100 kVp for combinations of F0/S20, F1/M20, and F1/L20 were calculated by Monte Carlo simulation. The energy spectra of 100 kVp/F0/S20 beam is shown in Fig. 6. We found that the value of 105 kVp for combinations of F0/S20 provided the best fit for both depth dose and cross profiles. Each energy spectrum was computed at SSD of 100 cm and within the x-ray field of 40 × 40 cm2.
      Figure thumbnail gr6
      Fig. 6Energy spectrum for the 100 kVp/F0/S20 beam.

      3.2 Validation of the model-based algorithm in homogeneous medium

      The dose distribution in the solid water slab phantom was calculated with the model-based algorithm for a single beam of 100 kVp/F0/S20 beam as shown in Fig. 7. This Figure illustrates axial plane dose distributions along with gamma analysis showing the agreement between Monte Carlo simulation and model-based dos calculations. In addition, the measured, model-based, and Monte Carlo-calculated dose of several points are reported in Table 1. The measured, MC simulated, and model-based doses reported in table are mean absolute doses in volumes of 0.6, 1.078, and 1.078 cm3, respectively. As seen in the table, the maximum difference was 5.06%. The mean difference between the model-based vs. measured, model based- vs. Monte Carlo simulation, and measured vs. MC simulation was 1.2%, 2.85%, and 1.63%, respectively.
      Figure thumbnail gr7
      Fig. 7Dose calculation results for the modified model-based algorithm calculated 100 kVp x-ray beam incident on a 30 × 30 × 15 cm3 water phantom from above.
      Table 1Measured, model-based and Monte Carlo calculated dose of selected point for the slab phantom.
      pointsDose of selected point (cGy)Difference (%)
      Model basedMeasurementMC simulationModel Vs. Measur.Model Vs.
      MC simul.Measur. Vs. MC simul.
      A3 cm ant0.2490.2390.2374.185.060.84
      B2 cm ant0.2130.2060.2053.403.900.49
      C1 cm ant0.1820.1790.1741.684.602.87
      IsoIsocenter0.1540.1520.1491.323.362.01
      D1 cm post0.1310.1300.1260.773.973.17
      E2 cm post0.1070.1090.108−1.83−0.930.93
      F3 cm post0.0910.0920.091−1.0901.1

      3.3 Validation of the model-based algorithm in heterogeneous medium

      The dose distributions of a one-field irradiation of a head and heck image dataset, obtained with the model-based algorithm and Monte Carlo simulations are shown in Fig. 8. The Monte Carlo simulations were calculated to a statistical uncertainty of 1%. Three dimensional gamma analysis was used to compare the two methods of dose calculations. For these analyses, the dose difference (DD) and distance to agreement (DTA) in calculation of gamma index were set to 2% and 2 mm. Based on the results of gamma analysis, 94% of the points passed with a 2%/2 mm criteria.
      Figure thumbnail gr8
      Fig. 8Comparison of Monte Carlo and model-based dose calculations from a single anterior 100 kVp beam in the head and neck. The figure illustrates (a) Coronal plane, (b) Sagittal plane, and (c) Axial plane dose distributions. The result of gamma analysis is based on criteria of 2%/2 mm.

      4. Discussion

      Monte Carlo simulation of the Elekta XVI system has been previously reported in the literature [
      • Spezi E.
      • Downes P.
      • Radu E.
      • Jarvis R.
      Monte Carlo simulation of an x-ray volume imaging cone beam CT unit.
      ,
      • Downes P.
      • Jarvis R.
      • Radu E.
      • Kawrakow I.
      • Spezi E.
      Monte Carlo simulation and patient dosimetry for a kilovoltage cone-beam CT unit.
      ,
      • Marchant T.E.
      • Joshi K.D.
      Comprehensive Monte Carlo study of patient doses from cone-beam CT imaging in radiotherapy.
      ,
      • Chow J.C.L.
      • Leung M.K.K.
      • Islam M.K.
      • Norrlinger B.D.
      • Jaffray D.A.
      Evaluation of the effect of patient dose from cone beam computed tomography on prostate IMRT using Monte Carlo simulation.
      ]. Spezi et al [
      • Spezi E.
      • Downes P.
      • Radu E.
      • Jarvis R.
      Monte Carlo simulation of an x-ray volume imaging cone beam CT unit.
      ] and Downes et al [
      • Downes P.
      • Jarvis R.
      • Radu E.
      • Kawrakow I.
      • Spezi E.
      Monte Carlo simulation and patient dosimetry for a kilovoltage cone-beam CT unit.
      ] were the first to simulate the Elekta XVI CBCT tube beamline, and provided a detailed simulation of the F0 and F1 (bowtie) filters. They simulated and benchmarked the x-ray tube and few collimator cassettes for clinical use by EGSnrc (version V4-r2-2–5). In addition, Downes et al [
      • Downes P.
      • Jarvis R.
      • Radu E.
      • Kawrakow I.
      • Spezi E.
      Monte Carlo simulation and patient dosimetry for a kilovoltage cone-beam CT unit.
      ] described a method for the absolute dose calibration of the CBCT unit when used in a clinical volumetric acquisition mode. Marchant et al [
      • Marchant T.E.
      • Joshi K.D.
      Comprehensive Monte Carlo study of patient doses from cone-beam CT imaging in radiotherapy.
      ] developed and validated a Monte Carlo model of the Elekta XVI system using the GATE Monte Carlo simulation platform [
      • Jan S.
      • Santin G.
      • Strul D.
      • Staelens S.
      • Assié K.
      • Autret D.
      • et al.
      GATE: a simulation toolkit for PET and SPECT.
      ] based on the GEANT4 toolkit [
      • Agostinelli S.
      • Allison J.
      • Amako K.
      • Apostolakis J.
      • Araujo H.
      • Arce P.
      • et al.
      GEANT4—a simulation toolkit.
      ].
      In this work, we simulated the Elekta XVI unit with the latest version of the Monte Carlo tool, and evaluated its results with measurements. Given the excellent agreement between Monte Carlo results and measurements, this Monte Carlo model can be used for obtaining three-dimensional dose distributions from the XVI system. We also used the convolution/superposition algorithm along with material-specific energy deposition kernels to calculate the dose distribution from kilovoltage beams and compared its results to Monte Carlo simulations and measurements.
      The use of an analytical method such as convolution/superposition to compute kilovoltage dose is not new. For example, Alaei et al [
      • Alaei P.
      • Gerbi B.J.
      • Geise R.A.
      Evaluation of a model-based treatment planning system for dose computations in the kilovoltage energy range.
      ] used a commercial treatment planning system to compute the dose from kilovoltage beams using low energy water energy deposition kernels and pointed to inaccuracy of this method in high atomic number materials. Ding et al [
      • Ding G.X.
      • Pawlowski J.M.
      • Coffey C.W.
      A correction-based dose calculation algorithm for kilovoltage x rays.
      ], and Pawlowski et al [
      • Pawlowski J.M.
      • Ding G.X.
      An algorithm for kilovoltage x-ray dose calculations with applications in kV-CBCT scans and 2D planar projected radiographs.
      ,
      • Pawlowski J.M.
      • Ding G.X.
      A new approach to account for the medium-dependent effect in model-based dose calculations for kilovoltage x-rays.
      ] calculated the kilovoltage imaging dose using a correction-based algorithm. They improved the accuracy of kilovoltage dose calculations in the high atomic number materials by introducing a correction factor in their algorithm. Current work takes a different approach by using material specific kernels with the convolution/superposition algorithm. Using material-specific energy deposition kernels instead of water energy deposition kernels may be more straightforward than defining a new methodology in calculating the kilovoltage dose. This method utilizes different energy deposition kernels depending on each voxel’s density values, hence accounting for atomic number changes.
      This work is essentially a feasibility study of this approach and includes many simplifications in the calculations. Kernel tilting, beam hardening, and beam softening in off axis points were not considered; however, they are not deemed to make a significant difference in the dose calculation accuracy. Considering the fact that imaging dose is a fraction of therapeutic dose given the patients, a high degree of dose calculation accuracy is not necessary in these dose calculations. As stated in AAPM TG-180 report [
      • Ding G.X.
      • Alaei P.
      • Curran B.
      • Flynn R.
      • Gossman M.
      • Mackie T.R.
      • et al.
      Image guidance doses delivered during radiotherapy: Quantification, management, and reduction: Report of the AAPM Therapy Physics Committee Task Group 180.
      ]; it is acceptable for the calculated imaging dose to have uncertainties of up to ± 20%. One benefit of using this method is the time-saving over performing a full Monte Carlo simulation, as kernel generation is done once.
      The current work validated the calculation accuracy of the proposed method in two datasets and with a simple single beam arrangement. This will need to be verified in other datasets with range of inhomogeneities, and with more complex beam geometries such as cone beam CT and use of the bowtie filter. Further validation of the method will be the subject of future work.

      5. Conclusions

      This study has presented a new approach on convolution/superposition algorithm using the material-specific energy deposition kernels for kilovoltage beams of up to 150 keV for estimating the imaging dose in IGRT. This new convolution/superposition algorithm has the potential to overcome the accuracy deficiency of model-based dose calculation algorithms for kV beams when water energy deposition kernels are used. Moreover, this new algorithm can be used for dose calculations from orthovoltage and superficial x-ray systems as well.

      Declaration of Competing Interest

      The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

      Acknowledgement

      The authors would like to thank the staff of Shahid Beheshti University cluster. This work is partially supported by Iran National Science Foundation: INSF [grant number 97025338].

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