Validation of a Monte Carlo model used for simulating tube current modulation in computed tomography over a wide range of phantom conditions/challenges

Abstract

Purpose:

Monte Carlo (MC) simulation methods have been widely used in patient dosimetry in computed tomography (CT), including estimating patient organ doses. However, most simulation methods have undergone a limited set of validations, often using homogeneous phantoms with simple geometries. As clinical scanning has become more complex and the use of tube current modulation (TCM) has become pervasive in the clinic, MC simulations should include these techniques in their methodologies and therefore should also be validated using a variety of phantoms with different shapes and material compositions to result in a variety of differently modulated tube current profiles. The purpose of this work is to perform the measurements and simulations to validate a Monte Carlo model under a variety of test conditions where fixed tube current (FTC) and TCM were used.

Methods:

A previously developed MC model for estimating dose from CT scans that models TCM, built using the platform of mcnpx, was used for CT dose quantification. In order to validate the suitability of this model to accurately simulate patient dose from FTC and TCM CT scan, measurements and simulations were compared over a wide range of conditions. Phantoms used for testing range from simple geometries with homogeneous composition (16 and 32 cm computed tomography dose index phantoms) to more complex phantoms including a rectangular homogeneous water equivalent phantom, an elliptical shaped phantom with three sections (where each section was a homogeneous, but different material), and a heterogeneous, complex geometry anthropomorphic phantom. Each phantom requires varying levels of x-, y- and z-modulation. Each phantom was scanned on a multidetector row CT (Sensation 64) scanner under the conditions of both FTC and TCM. Dose measurements were made at various surface and depth positions within each phantom. Simulations using each phantom were performed for FTC, detailed x–y–z TCM, and z-axis-only TCM to obtain dose estimates. This allowed direct comparisons between measured and simulated dose values under each condition of phantom, location, and scan to be made.

Results:

For FTC scans, the percent root mean square (RMS) difference between measurements and simulations was within 5% across all phantoms. For TCM scans, the percent RMS of the difference between measured and simulated values when using detailed TCM and z-axis-only TCM simulations was 4.5% and 13.2%, respectively. For the anthropomorphic phantom, the difference between TCM measurements and detailed TCM and z-axis-only TCM simulations was 1.2% and 8.9%, respectively. For FTC measurements and simulations, the percent RMS of the difference was 5.0%.

Conclusions:

This work demonstrated that the Monte Carlo model developed provided good agreement between measured and simulated values under both simple and complex geometries including an anthropomorphic phantom. This work also showed the increased dose differences for z-axis-only TCM simulations, where considerable modulation in the x–y plane was present due to the shape of the rectangular water phantom. Results from this investigation highlight details that need to be included in Monte Carlo simulations of TCM CT scans in order to yield accurate, clinically viable assessments of patient dosimetry.

1. INTRODUCTION

Monte Carlo (MC) methods have been applied in a variety of different scientific fields and, as described by Rogers,¹ it has been used for over 50 years in the field of Medical Physics in the context of radiation transport for the purpose of radiation dosimetry. There are four commonly used general purpose Monte Carlo radiation transport packages (EGSnrc, geant4, penelope, and mcnp) which are used in the field of Medical Physics. A recent AAPM Task Group, TG 195, was established to compare these four codes and benchmark them against each other using a series of simulation tasks relevant to diagnostic radiology, including some computed tomography (CT) scenarios.

One of the earliest papers on Monte Carlo model for simulating absorbed dose in CT investigated the dose variation within the x–y plane of an elliptical geometry.² In 1991, Jones and Shrimpton³ published the first set of normalized organ doses simulated using Monte Carlo methods and normalized using CTDI_vol,air. This study became the basis for the CT dosimetry package ImPACT.⁴ These general methods have also been used to investigate the effects of photon energy spectrum, bowtie filter, and size and composition of the scanned object on the dose distribution within the object using Monte Carlo simulations.⁵ In one of the earliest validation exercises, Caon et al. used Monte Carlo methods to simulate axial CT scans and used physical computed tomography dose index (CTDI) phantom measurements to validate their model, achieving results that agreed to within 7% of physical measurements; they then applied this model to estimate dose to a computational phantom, named Adelaide.^6–8 WinDose is a Monte Carlo-based program that was developed to estimate organ dose and effective dose values for arbitrary scan parameters in both axial and spiral CT.⁹ ImpactMC is the improved version available today for calculating dose distribution within irradiated body.^10–12 Jarry et al.¹³ used mcnp4b to model spiral CT, which was validated using measurements in phantoms with varying complexity. That work was extended^14,15 to estimate organ dose from multidetector CT (MDCT) scanners with more validation in cylindrical and anthropomorphic phantoms, and investigating the effect of patient size on effective dose using the GSF family of voxel phantoms.¹⁶

As application of Monte Carlo methods in CT advanced, so did the patient models used in simulations. Following the geometric MIRD phantom,¹⁷ several voxelized and computational patient models¹⁶ were used in MC simulations. These were extended to assess dose to the fetus in pregnant patients.¹⁸ In addition to organ dose to adolescent,¹⁹ organ dose to pediatric patient models using Monte Carlo methods was also addressed in a couple of publications,^20,21 one of which used simulated organ doses to estimate cancer risk in pediatric chest CT.²¹ The extension of Monte Carlo methods to the simulation of tube current modulated scans was the latest improvement. One approach used actual tube current modulation (TCM) data (extracted from the raw projection data of patient scans) to estimate organ dose to voxelized patient models generated using actual patient CT images.^22,23

There have been significant developments in Monte Carlo simulation techniques which have led to improvements in the ability to simulate radiation dose to patients from CT scans using advanced technologies such as TCM. To obtain accurate estimates, Monte Carlo-based simulations require an extensive knowledge of the simulated CT scanner and the patient, such as the CT x-ray source spectrum (energy and flux), filtration, bowtie filtration, collimation, and imaging parameters for a specific examination such as, kilovolt, tube current (and TCM as a function of table location and source angle), scan length, pitch, tube start angle, and rotation time.

Because the complexity of these Monte Carlo simulation models has increased, so have the requirements for validation of these models. For most groups reporting patient dose estimates from MC simulations, these validation steps have involved homogeneous phantoms with simple geometries such as the CTDI phantoms where the simulated and measured CTDI measurements are compared. Some recent publications have incorporated more complex anthropomorphic phantoms to provide a more challenging test condition.^11,24–26 Li et al.²⁵ validated a Monte Carlo-based model of a GE VCT scanner using both cylindrical and anthropomorphic phantoms and reported a difference from −5% to 2% from actual measurements, while the differences ranged from −17% to 13% in anthropomorphic phantoms for helical scans. However, these validations did not incorporate the variation of tube current such as that observed in patient scans (e.g., those reported in Angel et al.²² or Khatonabadi et al.²³) and have primarily focused on validation of fixed tube current (FTC) settings. One exception was the work published by Deak et al.¹¹ in which they validated a Monte Carlo model of a MDCT in a variety of different objects, including CTDI phantoms and, specifically, a liver phantom used to validate TCM modeling within the Monte Carlo tool. They reported their calculated doses to be within 10% of dose measurements across all phantoms and conditions. Specifically, their TCM simulations were reported to be within 10% of TCM dose measurements. The liver phantom used was an elliptical phantom with inserts that were homogeneous along the z-axis. This provides a good test for x–y axis modulation but did not evaluate z-axis modulation variations (which were shown to be substantially different from x–y–z modulation). In addition, the simulated protocol was a single axial scan, which also provides a good mechanism to evaluate the x–y modulation, but not the z-axis modulation.¹¹

Therefore, the goal of this study is to validate a MC code using TCM under a variety of test conditions that will challenge all aspects of the TCM modeling in helical mode. The test conditions will range from phantoms with simple geometry and homogeneous composition to anthropomorphic phantoms with complex geometry and composition.

2. MATERIAL AND METHODS

2.A. MC simulation code

MC simulations were performed using mcnpx (Monte Carlo N-particle extended v2.6.0).^25,26 For all simulations, the detailed photon transport mode with a low-energy cutoff of 1 keV was used. The detailed physics treatment includes coherent scattering with form factors and Compton scattering with incoherent form factors. Photoelectric effect is modeled as analog absorption plus possible K- and L-shell fluorescence. The incoherent, coherent, and photoelectric cross-section data are based on ENDF/B-IV.²⁷ Simulations physics options are set so that the photon transport mode does not explicitly create photoelectrons but rather assumes all secondary electrons deposit their energy at the photon interaction site. This is reasonable given the incident photon energy distribution for a 120 kV(peak) beam. This assumption satisfies charged particle equilibrium and allows absorbed dose to be approximated as collision kerma.²⁸

2.A.1. MDCT and source models

A multidetector CT scanner (Sensation 64, Siemens Healthcare, Forchheim, Germany) was used for all measurements and simulations. Modifications were made to the standard mcnpx source code in order to be able to randomly sample from all possible starting positions corresponding to a helical scan performed for a given nominal beam collimation (i.e., cone angle), pitch, and scan length. Further modifications of the mcnpx source code allowed for scanner-specific fan angles and measured beam widths (as opposed to nominal beam collimations) to be accounted for when sampling photon trajectories. An equivalent source model previously described by Turner et al.²⁹ was used to generate a scanner-specific spectrum and bowtie filter description. The energy of each simulated photon is obtained by sampling this scanner-specific energy spectrum. Attenuation due to the bowtie filter is modeled by adjusting the statistical weighting factor of each photon. The bowtie filter description is used to determine the path length each simulated photon traverses through the bowtie filter as a function of the photon’s trajectory. Using the path length and the linear attenuation coefficients of aluminum, the resulting exponential attenuation factor is calculated. Multiplying this exponential attenuation factor by an initial particle weight of 1 yields the new weighting factor for that photon in mcnpx. The scanner source model was previously validated by simulating CTDI₁₀₀ at the center and periphery of both 32 and 16 cm CTDI phantoms and comparing simulated values to physical measurements. An average root mean square (RMS) error of approximately 5% between the measured and simulated values was reported.²⁹

2.A.2. Monte Carlo tube current modulation model

For each phantom scan that was physically performed, a detailed description of the TCM data was extracted from the raw projection data. These data were used to model the TCM function in mcnpx using the method described by Angel et al.²² The TCM data consist of three variables: tube current I, table location z, and tube angle Θ. The tube current value I is a function of table position z and tube angle Θ, I(Θ, z). For a given scan, all tube current values, I(Θ, z), were normalized to the maximum tube current value.²² The normalized tube current data are used in the Monte Carlo simulations as source weights for simulated photons sampled from the table location and tube angle data.

2.B. Physical phantoms used for measurements

Five different geometries, ranging from simple to complex, were used for validating the modifications to the source code of mcnpx to simulate Siemens Sensation 64 CT scanner. These geometries included the 32 and 16 cm cylindrical CTDI phantoms, which are used in almost all Monte Carlo-based validation studies, as well as an elliptical phantom, water equivalent rectangular phantoms, and an anthropomorphic chest phantom; these phantoms are summarized in Table I and shown in Fig. 1.

TABLE I.

Summary description of the five different phantoms and their characteristics.

Phantom	Geometry	Composition
16 cm CTDI dosimetry phantom	Simple cylinder	Homogeneous PMMA
32 cm CTDI dosimetry phantom	Simple cylinder	Homogeneous PMMA
Three section elliptical phantom	Simple ellipse	Three homogeneous sections: fat, soft tissue, lung
Rectangular solid water	Rectangle	Homogeneous solid water
Anthropomorphic	Complex	Heterogeneous: lung, soft tissue, bone

FIG. 1.

(a) Three-sectional elliptical phantom, consisting of fat, lung, and muscle equivalent martials from left to right. (b) Rectangular solid water phantom. (c) Anthropomorphic chest/lung phantom with removal lungs.

The first two phantoms provide the simplest geometry as they are homogeneous in composition and homogeneous in shape. They are cylindrical phantoms of two different sizes (32 and 16 cm in diameter), known as CTDI phantoms, and are used regularly in CT dosimetry. These are homogeneous cylindrical phantoms made of polymethyl methacrylate (PMMA) with insert holes at five different positions: center, 12:00, 3:00, 6:00, and 9:00 o’clock positions.

The next phantom provides a slightly more complex environment as the shape is not homogeneous and the composition changes only across sections. This elliptical phantom was custom made (CIRS, Inc., Norfolk, VA) with large axis of 15 cm and small axis of 10 cm and consists of three (each 10 cm wide) different homogeneous sections: muscle, lung, and fat. While each section is of homogeneous composition in the x–y plane, when combined, they provide a phantom that is heterogeneous along the z-axis. All three sections have insert holes at five different positions: center, 12:00, 3:00, 6:00, and 9:00 o’clock positions [Fig. 1(a)].

The next phantom is homogeneous in composition but provides some shape complexity in the x–y plane. The rectangular water equivalent phantoms are regularly used in radiation oncology for IMRT QA procedures. These are 30 × 30 cm with a thickness of 5 cm. The elemental composition (% by weight) of these therapy grade solid water phantoms is 8.09% hydrogen, 67.18% carbon, 2.41% nitrogen, 19.87% oxygen, 0.14% chlorine, and 2.31% calcium. Their physical density is 1.0434 g/cm³. These were used because of their unique shape to provide extreme variation of the tube current in the x–y component of the detailed x–y–z TCM function. These phantoms are either solid blocks of equivalent water or have an insert hole in the middle for dose measurement purposes [Fig. 1(b)]. Three of these phantoms, with one having an ion chamber insertion hole, were used in this study.

The anthropomorphic chest/lung phantom (Radiology Support Devices, Inc., Long Beach, CA) was used as the most complex scanned phantom in this validation study. This phantom is a thorax phantom, extending from the neck to below the diaphragm, and is constructed using the skeleton of a male subject who is 175 cm tall and weighs 73.5 kg. The materials used in this phantom are equivalent to soft tissue and bone. Animal lungs similar to the size of average adult male lungs were molded to fit the pleural cavities of the phantom in their inflated state [Fig. 1(c)].

2.C. Physical dose measurements

An ionization chamber was used for the absolute dosimetry measurements of this section. A small ionization chamber with an active volume of 0.6 cm³ was utilized (Radcal, Monrovia, CA) along with a calibrated electrometer (MDH 1015, Radcal, Monrovia, CA) for all dose measurements. The pulse mode of the electrometer was utilized for making all measurements. The 0.6 cm³ chamber’s small volume can serve as an approximate point dosimeter and was small enough to fit in all of the phantoms described above.

For geometries described above, a set of either four or six measurements was performed depending on the object shape and availability of holes for inserting the ion chamber. All measurements were performed on a Siemens Sensation 64 CT scanner. All scans were performed using helical mode, while the scan length covered the entire phantom. To assess measurement variation which were expected to be small based on Ref. 30, each measurement was repeated three times to ensure reproducibility of measured values.

Raw projection data for a total of 22 acquisitions, FTC and TCM, were collected and used to extract information such as detailed tube current data, tube start angle, and scan length, for the simulations. Additionally, images for each acquisition were reconstructed at 500 mm FOV and 1.2 mm slice thickness and collected for creating voxelized models of each acquisition. For the z-axis only analysis described below, the tube current for each table location was extracted from the DICOM header data of the image dataset.

All acquisitions were performed with 120 kV(peak), 0.5 rotation time, pitch of 1, 24 × 1.2 collimation, and 200 quality reference milliampere seconds, when using CareDose 4D, and 200 effective milliampere seconds during fixed tube current acquisitions.

When the ion chamber position was changed for performing measurements at a different position, the position of the phantom itself remained unchanged and kept in the center of the gantry at all times. The following physical measurements were performed.

• 1.Homogeneous 32 cm diameter CTDI phantom. For the 32 diameter CTDI phantom, the entire length of the phantom was scanned using the operating conditions described above. Measurements were made at center and 12:00 o’clock positions for scans performed for each mode: FTC and TCM using CareDose 4D.
• 2.Homogeneous 16 cm diameter CTDI phantom. For the 16 diameter CTDI phantom, the entire length of the phantom was also scanned using the operating conditions described above. Measurements were also made at center and 12:00 o’clock positions for scans performed for each mode: FTC and TCM using CareDose 4D.
• 3.Elliptical phantoms. For the elliptical phantom, the entire length of the phantom (all three sections) was scanned using the operating conditions described above. Measurements were made at three positions: center, 12:00, and 3:00 o’clock, using both FTC and TCM (CareDose 4D) modes.
• 4.Rectangular water phantom. The section containing the insertion hole for the ion chamber was placed between two other sold rectangular water phantoms, and the entire length of the phantom was scanned. Two measurements were made, one inside the rectangular water phantom and one on the surface of the phantom, using both modes, FTC and TCM (CareDose 4D).
• 5.Anthropomorphic phantom. For the anthropomorphic phantom, the lungs of the phantoms can be removed and separated from the rest of the phantom; this capability was used to perform dose measurements inside the anthropomorphic phantom by taping the chamber inside the phantom parallel to the scan direction (z-direction). Figure 2 illustrates the procedure of making in-depth measurements inside the anthropomorphic phantom. Therefore, the anthropomorphic phantom was scanned along its entire length, and measurements were made in depth and on the surface of the phantom in both modes, FTC and TCM (CareDose 4D).

FIG. 2.

Setup of in-depth dose measurements using the anthropomorphic phantom.

2.D. Building phantom models in mcnpx—Geometric and voxelized models

To assess the effects of two approaches to creating phantom models in mcnpx, each of the phantom geometries described above was constructed using two approaches: (a) predefined cell and surface cards available in mcnpx and (b) voxelized models using Hounsfield-to-tissue lookup table. The exception was the anthropomorphic phantom for which only a voxelized model using a HU-to-tissue lookup table was feasible.

The geometries of CTDI phantoms, elliptical phantoms, and rectangular water equivalent phantoms were built in mcnpx using surface cards such as planes described by PX, PY, and PZ, surfaces defined by macrobodies such as right circular cylinder (RCC) and rectangular parallelepiped (RPP). Additionally, the chamber and its active region were modeled as explicitly as possible. The active region of the modeled chamber was used as the tally region in all simulations. The CT scanner table was approximated as a 1 cm thick rectangular carbon slab since the exact material composition of the table is unknown.¹⁵ Figure 3 illustrates these geometries in two views, axial and sagittal, plotted using mcnpx geometry plotter.

FIG. 3.

(a) Sagittal view of the 0.6 cm³ ionization chamber with the narrower tip representing the active region. (b) Axial and sagittal view of the 32 cm CTDI phantom geometry built in mcnpx with visible ion chamber in the center. (c) Axial sagittal view of the 16 cm CTDI phantom geometry built in mcnpx and with visible ion chamber in the center. (d) Axial and sagittal view of the three rectangular water slabs with the middle slab containing the chamber for in-depth dose measurement. (e) Axial and sagittal view of the three-sectional elliptical phantom with ionization chamber in the center hole.

For the more complex geometry of the anthropomorphic phantom, only the voxelized model generated from the axial CT images was utilized in the simulations. The active region of the ionization chamber was identified and segmented on all corresponding images. The segmented region was set to air, while a HU-to-tissue lookup table (Table II) was used to assign different materials within the image to the pixels making up the image.³¹ The CT table was segmented out independently and set to carbon. Figure 4 shows three views of the voxelized model visualized using the mcnpx geometry plotter.

TABLE II.

HU-to-tissue lookup table used to create voxelized models from axial CT images.

	Lung		Fat		Muscle		Bone
Level	CT # (HU)	ρ(g/cm3)	CT # (HU)	ρ(g/cm3)	CT # (HU)	ρ(g/cm3)	CT # (HU)	ρ(g/cm3)
1	(−930) → (−800)	0.048	(−200) → (−135)	0.85	(+5) → (+53)	1.06	(+280) → (+460)	1.48
2	(−800) → (−650)	0.1254	(−135) → (−70)	0.925	(+53) → (+100)	1.14	(+460) → (+640)	1.68
3	(−650) → (−500)	0.2987	(−70) → (−5)	0.98	(+100) → (+280)	1.26	(+640) → (+820)	1.89
4	(−500) → (−350)	0.4721					(+820)	2.1
5	(−350) → (−200)	0.6455

FIG. 4.

From left: axial, coronal, and sagittal view of the voxelized model of the anthropomorphic phantom.

2.E. Monte Carlo simulations and dose calculations

For each model and each construction available (voxelized and mcnpx-built geometries for all but the anthropomorphic phantom), two sets of simulations corresponding to fixed tube current and modulated tube current were performed using a Monte Carlo-based model of Siemens Sensation 64 MDCT. Collected raw projection data were used to extract information such as tube start angle and scan length for the fixed tube current simulations. As shown by Zhang et al.,³² tube start angle can affect surface dose; therefore, for the purpose of validation of the Monte Carlo model, exact tube start angle was implemented for each individual simulation, rather than using a single random tube angle for all simulations. For all TCM acquisitions, tube current data were also extracted from collected raw projection data using a matlab script. Using scanning parameters and extracted information from projection data, mcnpx input files were generated for each physical measurement performed.

In addition to simulations utilizing raw projection data for extraction of TCM data, TCM simulations were performed using z-axis-only tube current information from the DICOM header of the image data. This approximated TCM function is readily accessible; however, it eliminates the x–y modulation of the TCM function, which, depending on the geometry, does not significantly contribute to dose reduction in TCM mode.³³ As it will be presented in this study, x–y modulation can be significant if the geometry results in large differences between the minimum and maximum tube current and therefore not appropriately represented by an average value. This case is illustrated with the rectangular phantom.

For each simulation, absorbed dose to the ion chamber was calculated. Doses were calculated using collision kerma, which is equal to absorbed dose under the assumption of charge particle equilibrium. For each simulated photon, mcnpx tally type ^∗F4 was used to track energy fluence in regions of interest and multiplied by mass energy-absorption coefficients (μ_en/ρ) to convert to collision kerma.²⁷ The resulting dose per simulated photon for each tally region was converted to dose per tube current (milliampere) by multiplying the Monte Carlo output by a normalization factor,¹³ which is scanner, collimation, and kilovolt(peak) dependent and is used to take into account the fluence changes from varying the beam collimation. For TCM simulations, absolute doses were obtained by multiplying dose per milliampere second by the maximum tube current value obtained from each measurement’s raw projection data multiplied by scan’s rotation time.²² While for FTC simulations, absolute doses were calculated by multiplying dose per milliampere second by total milliampere seconds. For each condition, the number of simulated photons was chosen to ensure a relative error less than 1%. For the above experiments, these numbers ranged from 10⁶ to 10⁸.

To compare simulated to measured dose values, one set of measured dose values was used for each condition (phantom, position, etc.) and compared to the resulting simulation dose values for that exact condition using the information (start angle, detailed TCM function or z-axis-only function, as appropriate) extracted from that single measurement condition. The differences were expressed as percentage differences, using the measured value as the reference.

Simulated doses in all conditions were compared to physical dose measurements by calculating percent differences. Table III summarizes the phantoms, different geometries, and simulations performed.

TABLE III.

Summary of all simulations performed across different phantoms.

			TCM simulations
Phantom	Geometry	Fixed simulations	Detailed TCM	z-axis-only TCM
CTDI-16	Build/voxelized	✓	✓	✓
CTDI-32	Build/voxelized	✓	✓	✓
Elliptical	Build/voxelized	✓	✓	✓
Rectangular water blocks	Build/voxelized	✓	✓	✓
Anthropomorphic	Voxelized	✓	✓	✓

3. RESULTS

Table IV summarizes all measurements and simulated doses for phantom geometries built using predefined cell and surface cards available in mcnpx, while Table V summarizes the results for voxelized geometries using image data and HU-to-tissue lookup table, along with percent differences calculated between measured and simulated values. The RMS of the absolute percent error is 5.2% and 4.9% for fixed and TCM simulations, respectively, using mcnpx-built geometries. While using voxelized models, RMS values increased to 7.5% and 6.2% for FTC and TCM, respectively. The z-axis-only simulations resulted in the highest RMS of 14.4% and 13.6% using mcnpx-built and voxelized geometries, respectively. These large differences were mostly caused by rectangular solid water slabs which resulted in highest percent difference of 372% (38.3%) and 15.9% (6.9%), for in-depth and surface positions, respectively. Except for the rectangular water phantom, the overall agreement between measurements and simulated values is within less than 10%.

TABLE IV.

Comparison of measured and simulated doses performed using differently shaped phantoms at a variety of positions. Simulations were performed using mcnpx-built geometries of all four phantoms.

	Fixed tube current			Tube current modulation
Phantoms/positions	Measured (mGy)	Simulationa (mGy)	% difference	Measured (mGy)	Detailed TCM simulationa (mGy)	% difference	z-axis-only simulationa (mGy)	% difference
16 cm CTDI center	27.6	29.6	7.4	7.2	7.4	2.6	7.1	−2.2
16 cm CTDI 12:00	27.7	28.8	4.0	7.2	7.8	7.6	7.2	−0.1
32 cm CTDI center	10.1	10.3	2.2	12.2	12.1	−0.4	11.5	−5.6
32 cm CTDI 12:00	15.5	16.3	5.5	18.1	17.7	−2.5	17.4	−4.0
Elliptical center	36.3	35.3	−2.8	11.9	12.9	8.6	13.1	9.7
Elliptical 12:00	27.9	28.3	1.1	7.9	8.0	1.8	8.4	6.1
Elliptical 3:00	20.9	19.5	−6.8	6.6	6.2	−5.8	6.1	−6.6
Water equivalent depth	19.2	20.9	8.9	10.3	10.8	5.4	14.1	37.2
Water equivalent surface	23.7	22.9	−3.1	13.4	13.1	−2.1	15.5	15.9
% Min	−6.8			−5.8			−6.6
% Max	8.9			8.6			37.2
% Average (STD)	1.8(±5.2)			1.7(±4.9)			5.6(±14.1)
% RMS	5.3			4.9			14.4

^aFor each simulation, number of simulated photons was chosen to ensure a relative error less than 1%.

TABLE V.

Comparison of measured and simulated doses performed using differently shaped phantoms at a variety of positions. Simulations were performed using voxelized geometries.

	Fixed tube current			Tube current modulation
Phantoms/positions	Measured (mGy)	Simulationa(mGy)	% difference	Measured (mGy)	Detailed TCM simulationa (mGy)	% difference	z-axis-only simulationa (mGy)	% difference
16 cm CTDI center	27.6	27.5	−0.4	7.2	7.2	0.0	7.17	−0.6
16 cm CTDI 12:00	27.7	27.9	0.9	7.2	7.5	4.6	7.41	2.9
32 cm CTDI center	10.1	9.5	−6.2	12.2	11.1	−9.0	11.04	−9.2
32 cm CTDI 12:00	15.5	14.9	−3.8	18.1	18.0	−0.8	18.74	3.4
Elliptical center	36.3	39.2	8.2	11.9	11.1	−6.5	11.98	0.7
Elliptical 12:00	27.9	30.2	8.2	7.9	7.4	−6.5	8.42	6.9
Elliptical 3:00	20.9	22.6	8.0	6.6	6.1	−6.9	6.67	1.7
Water equivalent depth	19.2	21.1	10.1	10.3	10.8	5.1	14.18	38.3
Water equivalent surface	23.7	25.1	6.0	13.4	14.6	9.4	14.28	6.9
% Min	−6.2			−9.0			−9.2
% Max	13.7			9.4			38.3
% Average	4.1(±6.7)			−1.2(±6.5)			5.7(±13.2)
% RMS	7.5			6.2			13.6
Anthropomorphic depth	29.4	29.7	0.8	13.5	13.6	0.7	13.58	0.4
Anthropomorphic surface	18.1	19.1	5.6	9.4	9.6	1.7	10.16	7.6
% Min	−6.2			−9.0			−9.2
% Max	13.7			9.4			38.3
% Average	4.7(±6.5)			−1.4(±6.2)			6.3(±13.1)
% RMS	7.8			6.1			13.8

^aFor each simulation, number of simulated photons was chosen to ensure a relative error less than 1%.

4. DISCUSSION

Monte Carlo methods have been shown to be excellent tools when estimating patient dose from medical imaging exams. However, the complexity of CT scanning in current clinical practice (helical scanning, tube current modulation, patient heterogeneities, etc.) has placed significant demands on Monte Carlo simulation tools when attempting to provide accurate estimates of patient dose. This requires ongoing evaluation of the validation of such methods, when reporting simulated organ dose results. In this paper, a multistep validation process was conducted to confirm the accuracy of Monte Carlo simulation results. These simulations included validation of the process of creating voxelized model using tissue lookup table, validation of fixed and modulated tube current in simple and complex geometries, and validation of the z-axis-only simulations in case of unavailable detailed TCM data.

Overall, the calculated percent difference across all models and scanning modes was within 10%, except for z-axis-only simulation results from rectangular water phantoms, which resulted in up to 38% difference compared to physical dose measurement. This phantom is homogeneous in z-direction but its geometry varies considerably in x–y direction. This resulted in a noticeable large difference between the peak and valleys in the tube current (maximum and minimum tube current values), generated due to the extreme asymmetric shape of the phantom. Figure 5 illustrates the detailed TCM data versus z-axis-only modulation of the TCM, extracted from the DICOM header of the image data for this phantom. The minimum and maximum tube current values (min of 150 mA and max of 480 mA) due to the x–y modulation of the tube current are significantly different from each other; hence, the averaged values (approximately 250 mA) of these minimum and maximum tube current values across table location (represented by z-axis-only modulation) have a large standard deviation. Therefore, the approximation of the x–y–z modulation by z-axis-only modulation is a very rough approximation for this specific phantom. Figure 6 demonstrates the detailed TCM versus z-axis-only TCM for all of the other phantoms, none of which behave as the rectangular phantom does due to their more elliptical/circular shapes.

FIG. 5.

Detailed TCM function illustrates an extreme modulation in the x–y direction caused by the asymmetric shape of the water phantom. The thickness of the homogeneous water phantom in AP direction was much smaller than the lateral dimension, resulting in extreme minimum and maximum tube current values in the x–y planes. z-axis-only modulation with minor modulation along the z-axis, is a rough average of the minimum (150 mA) and maximum (480 mA) tube current values, hence not a good estimate of the detailed TCM function.

FIG. 6.

Detailed TCM function extracted from the raw projection data and z-axis-only TCM extracted from the DICOM header of the image data shown for the 16 cm cylindrical CTDI phantom (a), 32 cm CTDI phantom (b), three-sectional elliptical phantom (c), and anthropomorphic phantom (d). Neither one of the TCM functions demonstrates extreme x–y modulation as seen with the rectangular phantom shown in Fig. 5.

Overall, simulated results from mcnpx-built geometries and their corresponding voxelized models are very similar. Discrepancies in this case can be due to differences between assigned material composition using the HU-to-tissue lookup table and the material composition of the phantoms used in mcnpx-built geometries.

One possible explanation for the small discrepancies seen in Tables IV and V can be due to the imperfect model of the CT x-ray spectrum. The spectrum and bowtie filter modeling is based on the work of Turner et al.²⁹ which is based on some physical measurements to characterize bowtie filter and to establish spectrum’s HVL and QVL. As it was reported by Turner et al., CTDI measurements and simulations using the equivalent energy spectrum and filtration resulted in an average RMS of approximately 5% across all scanners, bowtie filter combinations, and all kilovolt(peaks). Although, this is a small difference, it can contribute to differences seen between physical dose measurements and simulations reported in Tables IV and V.

Other possible source of error, which is considered to be insignificant, is the modeling of the ion chamber itself. As mentioned previously, the active volume of the chamber was set to air as a whole to represent the tally region, and any explicit modeling, such as the electrodes, was excluded for simplicity.

While there are uncertainties in the simulations attributed to x-ray spectrum and filtration, and inability to know exact material composition and density of some of the phantoms used in this study, there are also uncertainties in physical dose measurements. As reported by RadCal, the provided calibration factors for the 0.6 cm³ ionization chamber used in this study are based on a specific beam quality which could be different from actual scanner’s output and, hence, result in uncertainties of ±4% in dose measurements.

5. CONCLUSION

The focus of this study was to validate a Monte Carlo model of a MDCT scanner used for organ dose simulation, specifically the validation of the retrospective modeling of the tube current modulation. Overall, simulated and measured doses proved to be within 10% agreement. This was established not only in simple, homogeneous models but also in more complex, heterogeneous phantoms for both fixed and variable tube current scanning modes. In general, while discrepancies can be due to the Monte Carlo model itself, such as modeling of the spectrum, filtration, and source movement, discrepancies could also be caused by inadequate information on scan parameters, such as detailed x–y–z (3D) tube current in TCM, which was shown to have a significant impact on dose in special cases. In this case, as seen by the rectangular water phantom, knowledge of the detailed x–y–z modulation of the tube current is required to obtain reasonable agreement between simulated and measured dose values.

While the lookup table proved to be an adequate approach for creating voxelized models from axial CT images, there are essential requirements that images have to meet to be usable for creation of voxelized models. These requirements include images reconstructed at largest FOV to ensure complete visibility of the object (patient) and proper representation of the object’s/patient’s position within the scan geometry (i.e., no reconstructed offset in x or y to center patient’s images) to ensure the transfer of actual patient position within the gantry to the virtual scanner. In addition to these requirements, there are scanning parameters that are equally important to be known for the simulations; these include tube start angle, scan length, and possibly the x–y plane shift in cases where images were reconstructed with an offset (to center the patient’s images with the reconstructed field of view).

Although presented results in this study can only be used to confirm validation of a scanner-specific Monte Carlo model, the basics used to generate spectrum and filtration equivalent information and model scanner’s geometry is applicable across all scanners.