Implementation of a new EGSnrc particle source class for computed tomography: validation and uncertainty quantification

Objective. Personalized dose monitoring and risk management are of increasing significance with the growing number of computer tomography (CT) examinations. These require high-quality Monte Carlo (MC) simulations that are of the utmost importance for the new developments in personalized CT dosimetry. This work aims to extend the MC framework EGSnrc source code with a new particle source. This, in turn, allows CT-scanner-specific dose and image calculations for any CT scanner. The novel method can be used with all modern EGSnrc user codes, particularly for the simulation of the effective dose based on DICOM images and the calculation of CT images. Approach. The new particle source can be used with input data derived by the user. The input data can be generated by the user based on a previously developed method for the experimental characterization of any CT scanner (doi.org/10.1016/j.ejmp.2015.09.006). Furthermore, the new particle source was benchmarked by air kerma measurements in an ionization chamber at a clinical CT scanner. For this, the simulated angular distribution and attenuation characteristics were compared to measurements to verify the source output free in air. In a second validation step, simulations of air kerma in a homogenous cylindrical and an anthropomorphic thorax phantom were performed and validated against experimentally determined results. A detailed uncertainty evaluation of the simulated air kerma values was developed. Main results. We successfully implemented a new particle source class for the simulation of realistic CT scans. This method can be adapted to any CT scanner. For the attenuation characteristics, there was a maximal deviation of 6.86% between the measurement and the simulation. The mean deviation for all tube voltages was 2.36% (σ = 1.6%). For the phantom measurements and simulations, all the values agreed within 5.0%. The uncertainty evaluation resulted in an uncertainty of 5.5% ( k=1 ).


Introduction and purpose
The number of computer tomography (CT) examinations of patients in Europe increased by 41% between 2015 and 2018 according to the work of Frija et al (2021).The need for accurate dose monitoring and risk management for the patient has therefore grown.The dose management systems that are currently used are a good way to control the CT scanner output.Nevertheless, the reported radiation exposure indexes, such as the computer tomography dose index (CTDI) and the dose length product, provide only a rough estimate of the effective dose (Boone 2007).A CT scanner and patient-specific evaluation of the effective dose can therefore be assumed to be the next necessary step for a better risk assessment.This can be achieved by high-precision Monte Carlo (MC) simulations, which lead to the concept of personalized CT dosimetry.Personalized CT dosimetry aims to calculate the organ doses of the individual patient for the scanner used and the CT investigation performed.
A previously published work of our group by Alikhani and Büermann (2016) described an experimental method for the characterization of the spectral photon fluence of any CT scanner.This method is based on a simple set of measurements that can be performed under clinical conditions.It characterizes the CT scanner spectrum by measuring an aluminium attenuation curve and the shape of the bowtie filter by measuring the angular-dependent air kerma.This procedure does not rely on any undisclosed manufacturer information, which is mandatory for alternative approaches (Li et al 2010, Chen et al 2012, Cros et al 2017, Maier et al 2022).Based on this method, our group developed a comprehensive procedure for personalized dosimetry in CT that is presented in the work of Rosendahl et al (2019).This procedure relies on the usage of ImpactMC, a commercial software system that has been discontinued (Schmidt and Kalender 2002).To further these investigations, this work presents the implementation and validation of a new particle source class in EGSnrc, the open-source MC software (Kawrakow et al 2000), which is dedicated to being used in the context of personalized CT dosimetry.Furthermore, the new particle source class can be used for other CT-related investigations, for example, for the simulation of CT images.With the above-mentioned experimental method, the implemented source can be used to simulate any CT scanner without any knowledge of information that the manufacturer has disclosed.
There are several works presenting methods for the simulation of CT fluences using open source software, for example, (Schmidt et al 2015) using EGSnrc and (Somasundaram et al 2019) using Fluka.These approaches do not fully meet the requirements for our investigations.This is because the purpose of this project was to implement a way of simulating the fluence of any CT scanner using the data from the characterization procedure presented in the work of Alikhani and Büermann (2016).The implementation must be usable with all EGSnrc egspp user codes, like egs_chamber, cavity, egs_cbct, egs_kerma and egs_fac, to enable the use of all the calculation routines implemented in EGSnrc.For example, our source can be used to perform simulations of ionization chambers and to calculate CT images with egs_cbct so that a CT image of the simulation geometry can be obtained with the same MC algorithm and parameters.
This work therefore aims to establish a sound and extensively validated particle source class, including a well-described uncertainty budget, for calculating dose distributions based on CT scans.In the first part of the work, the implementation is presented.The second part shows the validation and uncertainty estimation.For validation, the source was benchmarked for an Optima CT 660 (GE Healthcare, USA), and simulation results were compared to air kerma measurements.In the first step, air kerma measurements were conducted free in air, to validate the implemented sampling algorithm.Secondly, air kerma measurements were performed in a cylindrical phantom followed by measurements in a thorax phantom.

Source implementation
The MC simulations during this investigation were performed with EGSnrc, which is one of the most widely used types of MC software for the calculation of ionizing radiation transport (Kawrakow et al 2000).The presented data were calculated based on the 2020 program version.
EGSnrc is based on Fortran and Mortran routines, which are extended by a C++ class library to model geometries and particle sources.This library can be used to implement user codes to perform calculations for specific scenarios.Many user codes are distributed as a part of EGSnrc and serve different purposes, like the simulation of ionization chambers (egs_chamber), the simulation of correction factors of free air chambers (egs_fac), the simulation of air kerma (egs_kerma) or the generation of CT-image data (egs_cbct).
In this work, a newly implemented C++ particle source class to model the photon fluence of a CT scanner is presented.The implemented source emits photons in a collimated fan shape of a given width to model the photon fluence output of an arbitrary CT scanner defined by given input data.The source class also calculates the attenuation and filtration characteristics of a bowtie filter modeled from aluminium.Figure 1 shows an example of the generated photon particle tracks of the implemented source.A spectrum and the information on the aluminium equivalent bowtie filter, derived from the method described in Alikhani and Büermann (2016) are given as input information.In addition, the targeted collimation in the y-direction and the distance between the zero point and the source must be specified by the user.

Source model and particle source inputs
The implemented CT particle source relies on the knowledge of the spectral photon fluence in the center of the gantry (F E ) of the CT scanner, the relative attenuation q f ( ) caused by the bowtie filter and the aluminium equivalent thickness of the bowtie filter d in dependence on the fan angle q.A detailed description of the measurements and the equipment used for the characterization of the CT source model can be found in the publications of Alikhani and Büermann (2016) and Rosendahl et al (2019).Figure 2 shows an example of bowtie distribution and spectrum measured for an Optima CT 660 (GE Healthcare, USA).The measurements performed in this work are described in section 2.2.2.

Angular distribution
In the implementation of the EGSnrc CT particle source, the direction vector  d , of a new particle generated by the source, was defined by two angles and was calculated by: where the angle q corresponds with the direction in the xz-plane, and a is defined in the yz-plane, as shown in figure 1.For the randomized sampling of the direction of particles, the angle a was implemented to be drawn from a uniform distribution limited by the collimation in the z-direction.The sampling algorithm for q was based on the relative attenuation caused by the bowtie filter q f .( ) The relative attenuation of the bowtie filter was interpreted as the probability density function (pdf) of the fan angle q.The respective cumulative density function (cdf) f ( ) is defined by the integral of the pdf.A sampling algorithm following the inversion method of Larso and Amedeo (1981) was thus implemented, which solves the following equation: where q -F 1 is the inverse of the cdf evaluated for the random value r uniformly distributed in [0,1].In the first step, the distribution was smoothed by a convolution-based algorithm and a linear interpolation was calculated.For numerical integration, the trapezoidal rule is used.To get the angle q, equation (2) is solved as a root problem using Brent's method (Brent 1973).

Spectral photon fluence
The spectral fluence of a new particle generated by the particle source was implemented to be derived from the aluminium equivalent thickness of the bowtie filter.This took place in dependence on the fan angle q and the spectral photon fluence F E in the center of the gantry, based on Beer-Lambert law: where m Al is the total attenuation coefficient of aluminium, r Al is the density of aluminium (2.702 g•cm −3 ), and d Al is the aluminum equivalent bowtie filter thickness.The values of the total attenuation coefficients with coherent scattering were obtained from the XCOM database (Berger et al 2010), and linear interpolation was used between the energy values provided in the database.

Validation
To validate the process, the implemented EGSnrc particle source class was tested for a CT scanner, and the simulated air kerma values were compared to measured values.In the first step, the source characteristics, like bowtie filter attenuation and x-ray spectra, were verified.

Measurements of air kerma
A series of air kerma measurements were performed so that the developed MC particle source model of the CT scanner could be validated.These measurements were to be compared with the results obtained from MC simulations in the same geometry.The National Metrology Institute of Germany, PTB, has an Optima CT 660 (General Electrics, S/N: 108502CT01).The x-ray tube can be operated at four voltages 80 kV, 100 kV, 120 kV and 140 kV.The anode angle of the x-ray tube was 7°.The CT scanner was also equipped with a patient table made of carbon-fibre-reinforced plastic.The table was used to position the experimental set-up and will be referred to as the patient table in this manuscript.All the measurements were performed for all the tube voltages.
The collimation was set to 40 mm, and the large body bowtie filter was used.
All the measurements were performed with an RC0.6 Farmer-type ionization chamber (RADCAL, S/N: 9414).The number of charges created in the ionization chamber was measured with a UNIDOS electrometer (PTW, S/N: 100006).Time-resolved measurements were enabled by the combination of the RCO.6 ionization chamber and the ACCU-Gold (RADCAL) read-out system.During the measurements, the air pressure was monitored with a precision-compensated pressure sensor model 278 (SETRA, S/N: 3997310).The air temperature was monitored using a PT100 sensor calibrated at the PTB facility.
The air kerma K air was calculated using the following equation: where M Q is the number of charges measured by the electrometer.The calibration coefficient N K Q , air was measured for the ionization chamber at the x-ray facilities of PTB.This chamber is calibrated against the primary standard for different radiation qualities Q.The radiation qualities used were RQT8, RQT9 and RQT10 according to ('IEC 61267:2005-Medical Diagnostic x-ray Equipment-Radiation Conditions for Use in the Determination of Characteristics' 2005).The air density correction r k was calculated based on temperature and atmospheric pressure measurements during the experiment.

Source model
The source model of the CT scanner was measured as described in the publications of Alikhani and Büermann (2016) and Rosendahl et al (2019).
This was realized by the measurements described below.The x-ray spectra used in this work were determined by measuring the aluminium attenuation characteristics of the photon fluences f .E A Radcal RC0.6 chamber was placed in the gantry with a distance of » r 25 cm p from the center.A holder with aluminium plates with increasing thicknesses was positioned on the patient table (see figure 3).The chamber was connected to an ACCU-Gold digitizer, and a time-resolved signal was detected while the x-ray tube was rotating, and the patient table was moved.An attenuation curve was extracted from the signal.With an in-house optimization algorithm, a spectrum calculated with the SpekPy software (Poludniowski et al 2021) was modified by adding additional aluminium filtration until the spectrum met the measured attenuation characteristics.
CT scanners are equipped with shape filters (bowtie filters) to obtain a uniformly radiated image detector while scanning a patient.To characterize the filtration properties, the COBRA formalism (characterization of bowtie relative attenuation) was used (Boone 2010).The attenuation was measured as shown in figure 3 with an RC0.6 chamber positioned outside the gantry center at a distance of » r 25cm.
p A time-resolved attenuation curve (see figure 2(a)) was detected by rotating the x-ray tube.With the previously calculated spectrum, an angular-dependent aluminium equivalent bowtie filter was calculated that meets the measured attenuation curve q F ( ) (Rosendahl et al 2019).

Measurement of the air kerma distribution in phantoms
Validation measurements were performed for two phantoms: a CTDI (PTW, Germany) and a thorax phantom (CIRS, USA).The CTDI phantom is made of a 15 cm long PMMA cylinder with a diameter of 32 cm.It has five holes for the placement of an ionization chamber.There are four holes in the peripheral area and one central hole.The second phantom used was an anthropomorphic thorax phantom (CIRS) consisting of three different materials modeling the three tissue types: soft tissue, lung, and bone.This phantom also has five holes equivalent to the CTDI phantom.Measurements were performed successively in all possible positions within both phantoms, while the remaining holes in the phantom were closed with rods made of the phantom material.The axial scan mode with one rotation was used during the measurements with a 2 s rotation time, and a tube current of 100 mA was used.The measurement set-ups are shown in figure 4. Both phantom centers were positioned in the isocentre of the CT. from the center of the gantry.Aluminium sheets of increasing thickness can be aligned with the chamber.The bowtie filter shape was measured free in air with the patient table outside the gantry.

Monte carlo simulation of air kerma
The MC simulation of the air kerma 3D distribution in the CTDI and thorax phantoms was performed based on the C++ user code cavity.Data analyses were done with Python3 Version 3.8.13.The MC transport parameters that were used were the default values.No variance reduction methods were applied.Additional Information on the MC simulation is provided in table 1.
To model axial scans in the simulations, the source was rotated and translated by the user to mimic the scan path of the CT scanner particle source.For every source position, one simulation was performed.The scan type, axial step width and angular step can be specified in a control file.For the simulations in this work, we used an angular step size of  1 .The air kerma was determined in two different ways.For the bowtie attenuation simulation, the photon fluence with respect to energy (F E ) was scored with the user code cavity.From this, the air kerma was calculated based on mass energy-transfer coefficients m r tr / ( ) simulated with the user code g: For the aluminium attenuation curve and the phantom simulations, the air kerma was calculated as the quotient of the scored energy and the mass of the scoring volume ( = K E m air dep / ).For the used energy range, the absorbed dose is sufficiently close to air kerma.

Determination of the monte carlo normalization correction factor
As the results obtained through MC simulations are weighted by the number of particles N simulated, the determination of a normalization factor k N Q , is required to enable a quantitative comparison with the air kerma measured.Usually, the CT output is characterized by the current-time product Q.The conversion factor between the current-time product and the number of particles simulated can therefore be derived from: where K exp,ref is the air kerma obtained experimentally at the center of the gantry, and N K MC,ref / is obtained from MC simulations at the same position.To determine K Q, exp,ref / an RC0.6 Farmer-type ionization chamber was placed in the center of the gantry, and the K exp,ref was measured for a defined Q.
To obtain the simulated air kerma per current-time product K Q, MC / the air kerma per particle K N MC / needs to be multiplied with the conversion factor k ,

Attenuation in the CT scanner's table
To obtain a realistic energy deposition in the phantom material, the attenuation of the primary photon beam through a CT scanner table must be correctly modeled.The attenuation, and therefore the attenuation through the table, highly depends on the table material and density.The table is made of carbon-fibre-reinforced plastic, and since the exact material composition of the CT table is unknown, an equivalent material is defined for the simulations.The table's material composition was assumed to consist of 40% epoxy resin and 60% carbon fibres (Grund et al 2019).In table 2, the volume fractions V , i the mass fractions m , i the densities r , i and the chemical composition of epoxy and carbon fibres are listed (Kaiser 2007).The mass fraction for component i is calculated by r = m V .
i i i • Based on the mass fraction calculated for the patient table material, an elemental composition of 68% carbon, 27% hydrogen and 5% oxygen was determined.
The attenuation through the patient table was experimentally characterized by the ratio of the air kerma at the top K p12 exp ( )and bottom K p6 exp ( ) of a standard CTDI PMMA body phantom (see figure 4) measured for a full rotation of the x-ray tube: Simulations were performed with an identical set-up for a range of different densities between 1.5 g•cm −3 and 3.5 g•cm −3 with the patient table being modeled from the material defined above.
A linear fit between the simulated ratio k MC and the  where a and b are the fitting parameters.The table's density that should be implemented can therefore be calculated with the following equation: To further validate the table density, measurements of the primary photon attenuation were performed in the center of the gantry with a Farmer-type ionization chamber.A time-resolved measurement curve was obtained for a full rotation of the x-ray tube around the chamber.The same curve was reproduced through MC simulations.

Simulations to obtain the air kerma
All simulation geometries were defined as voxel phantoms in the Egsphant EGSnrc format and were created from pre-processed and edited NifTI files based on real CT scans.The used geometry classes were EGS_NDGeometry and EGS_XYZGeometry.The material assignment of the voxels was performed by a Hounsfield unit (HU) ramp.The materials used and the HU-value ranges for the two phantoms used are presented in Table 3 with the related density correction files.The HU values were not used in the sense of their definition but only for the material assignment.assign specific materials to the table and the scoring volumes, the HU-values in the specific regions of the CT-Scan were manually changed using a Python program.
For the validation, the two phantoms used during measurements were simulated (see figure 4).The scored quantity is the deposited energy per particle in the corresponding media and volume.

Uncertainties
The uncertainty evaluation follows the JCGM 100:2008 (Bipm et al 2008).The air kerma estimation for the MC simulation is described by the following model equation: Equation (10) describes the estimation of a simulated air kerma value K MC for a given current-time product Q.
The factor k N Q , allows a conversion between the normalization of the simulation per particle and the normalization of the CT measurement parameter Q (see section 2.3.1).To describe the other influence quantities, several correction factors are used.The factors considered are the spectrum k , SPEC the material definition k , M the shape of the bowtie filter k BT and the density of the CT scanner's table k .PT The corresponding uncertainties s i are listed in section 3.4.The uncertainty of the measured air kerma values was estimated for measurements free in air and in phantoms.For measurements with the RC0.6 Farmer-type chamber free in air, a combined uncertainty (s c,exp ) of 0.72% ( = k 1) was evaluated.The detailed uncertainty budget is presented in section 3.4.The combined measurement uncertainty s c,exp of the air kerma measurement free in air was the dominating part of the uncertainty of the normalization factor k .

N Q ,
To estimate the uncertainty of the simulation, a sensitivity analysis of the different influencing factors was carried out.For the material definition factor k M the material density of PMMA was varied between r = -g 1.17 1.19 cm .
3 In order to determine the uncertainty of the patient table the uncertainties resulting from the linear regression described in equation (8) were used as an input for uncertainty propagation for the density value calculated with equation (9).Then the density was varied in this uncertainty range of  3 The effect on the simulated air kerma results was used to determine the uncertainty based on a rectangular distribution.
As the same experimental method was used as in Rosendahl et al (2019), and the uncertainty of the shape of the bowtie was already evaluated in a previously published investigation, no sensitivity analysis was performed and the same uncertainty was used.The statistical uncertainty of the simulated value K sim is taken directly from the simulation output.
To evaluate the impact of the uncertainty in the spectra, the simulations at the CTDI phantom were performed with two additional spectra shown in figure 5, one for a higher and one for a lower mean energy.The spectrum with the lower energy was calculated with the SpekPy Python module (Poludniowski et al 2021).The spectrum was generated for the corresponding voltage, anode angle and filter materials taken from the manufacturer's information.For the higher energetic spectrum, an additional aluminium filter was added until the same absolute shift in mean energy was achieved.

Source model
In figure 6 the comparison between the measured and the simulated bowtie filter profiles over the fan angle of the x-ray beam is shown.The air kerma values were normalized to the maximum value.Simulated and measured values agree with the limits of the shown uncertainties.
To evaluate if the correct spectra were generated with the MC simulation, an aluminium attenuation curve was simulated with the same geometry as described in section 2.2.2 for the measurement.The comparison between the measurement and the simulation of the aluminium attenuation curve is shown in figure 7. The upper figures show the simulated and measured air kerma values in dependence on the aluminium filter thickness d .
Al In the graphs below, the relative deviation d rel between the measurement and the simulation is shown.For nearly all the measurements, the uncertainty intervals shown by the error bars intersect the zero line.
In addition to the aluminium attenuation curve, table 4 shows the HVL (half value layer) and mean energy computed from the measured and simulated spectrum free in air.

CT scanner table
The simulation results for the table attenuation characterized by equation (9) (dashed lines) for different table densities in comparison to the measured values are shown in figure 8.The table density with the best agreement with the measurements is ⋅ -2.15 28 g cm .

3
( ) This density was used for all the following simulations.In figure 9, the deviations between the measurement and the simulation of the angle-resolved measurement curve are shown.Deviations in the central area of the table were 4.7% on average.The largest deviation observed was 53% at the edges of the CT scanner's table.

Experiments with phantoms
The comparison between measured and simulated air kerma values inside the CTDI phantom at the five different positions and for the lowest and highest energy are presented in table 5.For the 100 kV spectrum, the mean The softer spectrum (a) is obtained using SpekPy with the given manufacturer information.The harder spectrum is calculated by adding additional aluminium filtration until the same difference in mean energy is achieved as for the softer spectrum.
deviation between the measurement and the simulation is less than 2%, which lies therefore in the limits of the uncertainties.The deviation of the 140 kV spectrum amounts to a maximum of 5.0% for the air kerma value in the center of the phantom.
The evaluation of the air kerma values inside the thorax phantom is shown in table 6.In comparison to the CTDI phantom, the deviation between the measurements and the simulation is by a maximum of 4.8% but for 80 kV.

Uncertainties
The air kerma estimation for the MC simulation is described by the following mathematical model, as presented in section 2.4 The corresponding uncertainties s i are listed in table 7.
All the considered influence quantities result in a combined uncertainty of 5.5% (k = 1) for the simulated air kerma values.
For measurements with the RC0.6 farmer-type chamber free in air, a combined uncertainty (s c,exp ) of 0.72% (k = 1) was evaluated (see table 8).For the measurements with the CTDI phantom, the uncertainty of the air kerma measurements was estimated as 0.98% ( = k 1).The main difference to the measurement free in air was the uncertainty linked to the reproducibility of the measurements.For the measurement free in air, the reproducibility was 0.34%.For the phantom measurements, the reproducibility was estimated based on a set of five measurements to the value of 0.75%.

Discussion
With a final goal of personalized CT dosimetry, we created a new particle source class in the MC Framework EGSnrc.
The validation was done in several steps.In the first step, free-in-air measurements and simulations were performed to validate the source output.The simulated and measured aluminium attenuation curves show agreement within the uncertainties.The largest deviation was 6.86% for the 80 kV spectrum.On average, the deviations are 2.36%.The measured and simulated results for the bowtie filter shape also agree for most values within the uncertainties.In the second validation step, air kerma values in two phantoms were obtained from simulations and measurements.The simulation of the patient table shows good agreement with the measurements.The deviations of the profile curves in the central area of the table were 4.7% on average.The largest deviation observed was 53% at the edges of the patient table.This might have been caused by the limited spatial resolution of the measurement, leading to an averaging effect of the ionization chamber signal, and thus, the decrease of the signal would be smeared out.For the air kerma values in the phantoms, the measured and simulated values agree within 5.0%.Larger deviations are found for the central phantom positions and have been shown to be energy dependent.With the increasing energy of the radiation, the simulated air kerma values in the center of the two phantoms are underestimated in comparison to the measurements.This could be caused by the mean energy of the x-ray spectrum being too low.The spectrum being too soft might have been caused by the filtration not being realistic enough due to the bowtie filter material used in the simulation.In the simulation, the weakening because of the bowtie filter is realized only by different thicknesses of aluminium.Typical CT spectra-as defined in the IEC 61267:2005 standard ('IEC 61267:2005-Medical Diagnostic x-ray Equipment-Radiation Conditions for Use in the Determination of Characteristics' 2005)-are realized by an additional copper filtration.Therefore, the hardening effect following filtration by aluminium is not large enough.The evaluated uncertainty of 5.5% = k 1 ( ) for the simulated air kerma values is a conservative approximation.This is because all the values agree-within the range of uncertainties-with the experimentally determined values for a confidence interval of 68%.

Conclusions
This work shows the successful implementation of a new EGSnrc particle source class for the simulation of CT dose distributions.The presented procedure allows the user to perform simulations with EGSnrc and any CT scanner or patient geometry by using the described measurement procedure.The simulation was validated against high-accuracy measurements at Optima CT 660 (GE Healthcare, USA).The simulation results are shown to be within the limits of the uncertainty of 11.0% for a confidence interval of 95% = k 2 ( ) with the experimental results.Therefore, the presented method is suitable for generating high-quality dose distributions describing realistic CT scans.The detailed uncertainty evaluation allows the quality-assured further usage of the simulated data.

Figure 1 .
Figure 1.Example of photon track output of the implemented aluminium equivalent CT source and spatial orientation.

Figure 2 .
Figure 2. Example of a measured angular-dependent bowtie filter attenuation curve F(θ) (a).Example of a normalized energy x-ray spectrum for a tube voltage of 80 kV(b). q

Figure 3 .
Figure 3. Experimental setup.With this setup, an aluminium attenuation curve and form filter characteristic can be measured.An RC0.6 chamber was positioned at a distance » r 25 cm p

Figure 4 .
Figure 4. Measurement set-ups of the phantom measurements at the GE OptimaCT 660 with marked measurement positions (top).Simulation geometries of the two phantoms (bottom).CTDI phantom (left) and thorax phantom (right).

Figure 5 .
Figure 5. Example of spectra used (80 kV) for sensitivity analysis of the simulated air kerma values for uncertainty estimation.The measured spectrum (solid line) in both graphs is the spectrum determined from the measured aluminium attenuation curve ( = E 52.78 keV .

Figure 6 .
Figure 6.Validation between measured and simulated bowtie filter profiles for four tube voltages 80 kV, 100 kV, 120 kV, 140 kV (top) and relative deviation between measurement and simulation (bottom).

Figure 7 .
Figure 7.Comparison between measured and simulated aluminium attenuation curves for the four tube voltages.The figures show the air kerma values K air in mGy in dependence on the aluminium filter thickness d Al (top) and the relative deviation between measurement and simulation (below).

Figure 8 .
Figure8.Graphical representation of the table density estimation.The plot shows the table-density-dependent attenuation calculated from the ratio of the dose value at the top (pos.12) and the bottom (pos.6) of a CTDI phantom κ.Additionally, the linear fits are presented.The horizontal dotted lines show the measured values of κ (same value for 140 kV and 120 kV).

Figure 9 .
Figure 9. Simulated and measured relative air kerma profile of the CT scanner's table in dependence on the angle f for a tube voltage of 140 kV (top).The relative deviation between measurement and simulation (bottom).

Table 2 .
The material composition of the CT scanner table.The table shows the two material components' volume density, mass fraction and chemical composition.

Table 3 .
Materials used in the MC simulation, HU ranges used and respective density correction files.Elemental compositions were provided by the phantom manufacturer.

Table 4 .
Comparison of aluminium HVL and mean energy between measured and simulated energy spectra.

Table 5 .
Comparison between measured and simulated air kerma values in a CTDI phantom for the GE Optima CT 660.

Table 6 .
Comparison between measured and simulated air kerma values in a thorax phantom for the GE Optima CT 660.Position K air,exp. in mGy K air,sim. in mGy K air,exp./K air,sim.

Table 7 .
Uncertainty budget for simulation of air kerma with the newly implemented aluminium equivalent CT source with the MC framework EGSnrc.The table shows several uncertainty components and the resulting total uncertainty.

Table 8 .
Uncertainty budget for air kerma measurements free in air and in phantoms.The table shows several uncertainty components and the resulting total uncertainty.ComponentSymbol Impact on air kerma free in air m A,B (%) Impact on air kerma in phantom m A,B(%)