Validation of a deterministic linear Boltzmann transport equation solver for rapid CT dose computation using physical dose measurements in pediatric phantoms

Abstract

Purpose:

The risk of inducing cancer to patients undergoing CT examinations has motivated efforts for CT dose estimation, monitoring and reduction, especially among pediatric population. The method investigated in this study is Acuros CTD (Varian Medical Systems, Palo Alto, CA), a deterministic linear Boltzmann transport equation (LBTE) solver aimed at generating rapid and reliable dose maps of CT exams. By applying organ contours, organ doses can also be obtained, thus patient-specific organ dose estimates can be provided. This study experimentally validated Acuros against measurements performed on a clinical CT system using a range of physical pediatric anthropomorphic phantoms and acquisition protocols.

Methods:

The study consisted of: (1) the acquisition of dose measurements on a clinical CT scanner through thermoluminescent dosimetry (TLD) chips, and (2) the modeling in the Acuros platform of the measurement set up, which includes the modeling of the CT scanner and of the anthropomorphic phantoms. For the measurements, 1-year-old, 5-year-old, and 10-year-old anthropomorphic phantoms of the CIRS ATOM family were used. TLDs were placed in selected organ locations such as stomach, liver, lungs, and heart. The pediatric phantoms were scanned helically with the GE Discovery 750 HD clinical scanner for several examination protocols. For the simulations in Acuros, scanner-specific input, such as bowtie filters, overrange collimation and tube current modulation schemes, were modeled. These scanner complexities were implemented by defining discretized x-ray beams whose spectral distribution, defined in Acuros by only six energy bins, varied across fan angle, cone angle, and slice position. The images generated during the CT acquisitions were used to create the geometrical models, by applying thresholding algorithms and assigning materials to the HU values. The TLD chips were contoured in the phantom models as sensitive cylindrical volumes at the locations selected for dosimeters placement, to provide dose estimates, in terms of dose per unit photon. To compare measured doses with dose estimates, a calibration factor was derived from the CTDI_vol displayed by the scanner, to account for the number of photons emitted by the x-ray tube during the procedure.

Results:

The differences of the measured and estimated doses, in terms of absolute % errors, were within 13% for 153 TLD locations, with an error of 17% at the stomach for one study with the 10-year-old phantom. Root-mean-squared-errors (RMSE) across all TLD locations for all configurations were in the range of 3% - 8%, with Acuros providing dose estimates in a time range of a few seconds up to two minutes.

Conclusions:

An overall good agreement between measurements and simulations was achieved, with average RMSE of 6% across all cases. The results demonstrate that Acuros can model a specific clinical scanner despite the required discretization in spatial and energy domains. The proposed deterministic tool has the potential to be part of a near real-time individualized dosimetry monitoring system for CT applications, providing patient-specific organ dose estimates.

1. Introduction

The increase of CT examinations, and consequently patient exposure to radiation, raises health concerns from the radiation protection perspective. The stochastic risk of inducing cancer from CT examinations, especially among the pediatric population, motivated efforts for CT dose reduction and CT dose monitoring^1–4. To achieve dose reduction, optimized image protocols minimize the exposure without compromising the diagnostic quality of the CT image, thanks to advanced CT scanner features such as automatic exposure control, dynamic collimation, and bowtie filters⁵. In addition, radiation concerns, including overdosing accidents⁶, have prompted the implementation of radiation dose monitoring systems. The dose metric currently included in CT reports, which are required by IEC⁷, is the CT dose index (CTDI). However, the CTDI represents the average absorbed dose to the standard 16-cm or 32-cm-diameter cylindrical phantoms, and not the dose distribution in the patient’s organs^8–11. As CTDI is measured using a standardized phantom, it is a useful metric of comparison between different protocols and scanners to assess the x-ray tube output, but it is not representative of the dose absorbed by the patient. The International Commission on Radiation Protection states that assessment of individual risk due to radiation exposure should only be based on organ dose¹². A focus on organ dose enables accounting for the varying radiosensitivity and exposure of different organs. This may enable more meaningful monitoring of dose and estimation of risk, as well as the potential of optimizing CT protocols based on the most sensitive or most irradiated organs. Furthermore, children needing repeated CT scans will benefit the most from CT protocol optimization based on organ dose.

Despite several studies that showed the suitability of Monte Carlo simulations to provide reliable patient-specific dose maps, its application in the clinical workflow was traditionally limited by the high computation time. Efforts have been done at this regard and Monte Carlo implementation on GPU (Graphics Processing Unit) cards have reduced computation time^13–16.

The alternative dose map generation method investigated in this study is Acuros CTD (Varian Medical Systems, Palo Alto, CA), a deterministic linear Boltzmann transport equation solver aimed at generating rapid and reliable dose maps for CT applications¹⁷. Acuros CTD was previously compared for realistic scanner configurations against the gold standard Monte Carlo method Geant4¹⁸, for different scanner acquisition parameters and anthropomorphic phantom models¹⁹. Good agreement was shown between the dose distributions generated by the two algorithms, with differences of the absorbed dose values of approximately 3.5%. Although the scanner model used in our previous comparison study enabled a good approximation of a real scanner, some features were generic and not scanner specific, such as the bowtie filter model and the spectral distribution of the x-ray source. Additionally, the studied scan length used for the computational comparison of Acuros CTD against Monte Carlo did not represent a clinical scan length, therefore it was not representative of a clinical protocol.

In this study, Acuros CTD was validated against measurements performed on a clinical CT scanner, across a range of scanning protocols and body regions on physical pediatric anthropomorphic phantoms. The experimental validation is necessary to verify that Acuros CTD can rapidly and accurately estimate patient-specific dose distributions, resulting from a specific clinical CT scanner and protocols.

To evaluate the ability of Acuros CTD to model a clinical CT scanner, experiments were performed with varying tube voltage, bowtie filters, and tube current modulation techniques. The focus of this study on pediatrics is motivated by the higher biological risk consequent to radiation exposure in children, as they are more radiosensitive than adults^20,21. Also, in children there is less intervening material between the entrance surface of the radiation beam and the internal tissues, meaning that the most sensitive organs may be exposed to a greater extent in children than in adults. The unique radiation concerns of pediatric patients highlight the relevance of reliable and patient-specific dose monitoring systems. The ultimate objective is to develop a more comprehensive tool that uses Acuros CTD for dose map generation and deep learning organ segmentation for organ dose determination, resulting in a near real-time individualized dosimetry tool for CT applications in the clinical practice²². The purpose of this paper is to provide experimental validation of the dose map generation component of this tool.

2. Methods

This study consisted of:

1. the acquisition of dose measurements on a physical CT scanner through thermoluminescent dosimetry chips (TLDs), located inside pediatric anthropomorphic phantoms, for several examination protocols.

2. the modeling in the Acuros CTD platform of the measurement set up, which includes scanner-specific and protocol-specific features, anthropomorphic phantom models, and the TLDs represented as sensitive scoring volumes.

2.1. Experimental set-up

CT acquisitions were performed on a GE Discovery 750 HD scanner (GE Healthcare, Chicago, IL). Lithium fluoride (LiF) thermoluminescent dosimeters (TLDs) with nominal size of 3.2x3.2x0.9 mm³ and mass density of 2.64 g/cm³ were used. Specifically, TLDs-100 were employed as they guarantee a well-defined energy response over the diagnostic energy range. The CIRS ATOM 1-year-old, 5-year-old, and 10-year-old phantoms (ATOM, Models 704D, 705D, 706D, respectively; Norfolk, VA) were used and are composed of 25-mm-thick tissue-equivalent slabs with organ-specific locations for TLDs placement. The CIRS phantoms model five different tissues: soft tissue, lung, age-dependent bone, spinal disc, and spinal cord. Each of the three phantoms employed has a different bone composition that varies with age. TLDs were placed in several organ locations, such as stomach, liver, lungs, heart, and ribs, to name a few. Three TLDs per location were used to improve the statistics of the measurements. The 5-year-old and 1-year-old ATOM phantoms are shown in Figure 1.

Figure 1.

ATOM phantoms (a) Model 705D, 5-year-old, and (b) Model 704D, 1-year-old. The red laser lights denote the locations of the isocenters. The head model is from the 1-year-old phantom, and it was used on the three phantoms to generate scatter at the level of the neck.

The experiments were organized into three studies to provide a broad validation across a range of scanner options and of phantom sizes. The first study validated the accuracy of the Acuros CTD platform for one anthropomorphic phantom (705D, 5-year-old) and for three different x-ray beams at constant tube current. The second study validated Acuros CTD for the three phantoms at constant tube current. Finally, the third study validated Acuros CTD accuracy in the presence of tube current modulation (TCM). The three studies are described in more detail below:

• Study 1: The 5-year-old phantom was scanned helically at constant tube current and tube voltages of 80, 100, and 120 kVp for the chest-abdomen-pelvis (CAP) protocol.

• Study 2: The 1-year-old, 5-year-old, and 10-year-old phantoms were scanned helically at constant tube current for the CAP protocol and for protocols with a smaller scan range (abdomen / chest).

• Study 3: The 1-year-old, 5-year-old, and 10-year-old phantoms were scanned helically with angular and longitudinal tube current modulation (SmartmA, GE Healthcare, Chicago, IL) for the CAP protocol and for abdomen / chest scans.

Table 1 summarizes the scan parameters and other relevant settings used for the fourteen protocols. Each protocol is identified as Study#.Scan#.

Table 1.

Scan settings during the CT acquisitions.

Protocol ID	Phantom	Body region	kV	mA	Gantry rotation period (s)	Bowtie filter Type	Coll (mm)	Pitch	TCM (SmartmA/No)	TLD locations	NI	CTDIvol (mGy)	CTDI Phantom used for dose reporting
1.1	705D-5yo	CAP	80	625	0.6	Medium	40	0.984	No	Config. 1	---	24.94	16-cm-diameter
1.2	705D-5yo	CAP	100	400	0.6	Medium	40	0.984	No	Config. 1	---	28.93	16-cm-diameter
1.3	705D-5yo	CAP	120	175	0.6	Medium	40	0.984	No	Config. 1	---	19.36	16-cm-diameter
2.1	704D-1yo	CAP	80	500	0.6	Medium	40	0.984	No	Config. 2	---	19.95	16-cm-diameter
2.2	706D-10yo	CAP	100	500	0.6	Medium	40	0.984	No	Config. 2	---	36.61	16-cm-diameter
2.3	705D-5yo	Chest	100	500	0.6	Medium	40	0.984	No	Config.2a	---	34.71	16-cm-diameter
2.4	706D-10yo	Abdo	100	500	0.6	Medium	40	0.984	No	Config.2b	---	36.16	16-cm-diameter
3.1	704D-1yo	CAP	80	500	0.6	Small	40	0.984	SmartmA	Config. 3	12	3.61	32-cm-diameter
3.2	705D-5yo	CAP	100	500	0.6	Small	40	0.984	SmartmA	Config. 3	14	4.59	32-cm-diameter
3.3	706D-10yo	CAP	100	500	0.6	Medium	40	0.984	SmartmA	Config. 3	14	20.98	16-cm-diameter
3.4	705D-5yo	Chest	100	500	0.6	Small	40	0.984	SmartmA	Config. 3a	14	3.76	32-cm-diameter
3.5	706D-10yo	Abdo	100	500	0.6	Medium	40	0.984	SmartmA	Config. 3b	14	19.52	16-cm-diameter
3.6	705D-5yo	Chest	100	500	0.4	Small	40	1.375	SmartmA	Config. 3a	14	3.38	32-cm-diameter

Config. 1 - TLDs placed in: stomach (4), liver (5), lungs (6), heart (2), and spinal disc (1).

Config. 2 - TLDs placed in: lungs (2), heart (2), ribs (2), kidneys (2), stomach (1), liver (1), bladder (1).

Config. 2a (chest scan) - TLDs placed in: thyroid (2), lungs (2), heart (1), breasts (2).

Config. 2b (abdomen scan) - TLDs placed in: ribs (2), kidneys (2), stomach (1), liver (1).

Config. 3 - TLDs placed in: thyroid (2) – except for the 1yo phantom –, breast (2), lungs (2), heart (1), ribs (2), kidneys (2), stomach (1), liver (1), bladder (1).

Config. 3a (chest scan) - TLDs placed in: thyroid (2), breast (2), lungs (2), heart (1), rib (1).

Config. 3b (abdomen scan) - TLDs placed in: rib (1), kidneys (2), stomach (1), intestine (1).

The number in parenthesis indicates the number of locations where the TLDs were placed for each studied organ or tissue. mA indicates either the constant tube current value when there is no TCM, or the maximum tube current value when TCM is applied. Coll in mm indicates the nominal collimation. SmartmA indicates longitudinal + angular modulation of the tube current. NI indicates the noise index, defined only when TCM is applied. CTDI_vol is the volumetric CTDI displayed by the CT scanner.

2.1.1. TLD calibration and readout

Calibration and readout of the TLDs were performed by the TLD Laboratory at the University of Wisconsin - Medical Radiation Research Center (UWMRRC). Because the lower detection limit of the TLDs is 1 cGy, the CT acquisitions were repeated three times for each protocol in the case of constant tube current, in order to achieve more reliable TLD readings. When TCM was applied, CT acquisitions were repeated 4 to 5 times for the 1-year-old and 5-year-old phantoms to compensate for the reduced exposure due to TCM. The expanded uncertainty associated to the TLD readouts is approximately 10% for a coverage factor K=2 (95% confidence level). The 10% uncertainty takes into account potential energy differences and energy corrections, repeatability, calibration setup and air kerma-rate measurement. Room temperature and pressure during calibration have little to no effect on TLDs, therefore these variations were not accounted for, while the energy correction is the largest contributor to the overall uncertainty. The beam used for the energy calibration matched the x-ray beam quality M100 from the National Institute of Standard and Technology (NIST), characterized by peak kV of 100 kV, added filtration of 4.77 mmAl, first HVL (Half Value Layer) of 4.98 mmAl, and effective energy of 42.1 keV. When the TLDs were irradiated by the clinical scanner using x-ray qualities with peak kV different from 100 kV (such as 80 kV and 120 kV), energy corrections were applied accounting for an approximate 4% overresponse for irradiations with 80 kVp and 3.5% underresponse for 120 kVp, relative to the 100 kVp calibration.

The TLD readout were also weighted individually by a correction factor, which represents the response of an individual TLD relative to the mean response of the entire group of TLDs. Each correction factor associated to a specific TLD (TLD_i) was obtained as the ratio of the readout of the TLD_i and the average of the readouts of the whole batch, after being exposed to a controlled calibration with Cobalt-60. The TLD raw output is given in terms of electric charge (nC), thus a calibration curve was applied from the TLD lab in order to convert charge (nC) to dose (cGy). Also, a few dosimeters were not exposed to the CT irradiation, so that background signal could be subtracted from the TLD readout.

2.2. Modeling on the Acuros CTD platform

The dose map generation method experimentally validated in this study is Acuros CTD. Acuros CTD applies the same deterministic approach used by software Acuros XB^23,24 and Acuros CTS^25,26, both also developed by Varian Medical Systems. Acuros XB is a commercially available tool for radiation therapy planning, and Acuros CTS estimates scatter in projection images of a CT scan. Acuros CTD was developed to generate rapid dose maps for CT applications, and it will be referred to as Acuros throughout this paper. The Acuros approach is based on deterministically solving linear Boltzmann transport equations (LBTE), which describe the interactions of photons with an object across spatial, energy, and directional domains. Therefore, in order to solve the LBTE, the problem must be discretized in space, energy, and angle. Details on how Acuros numerically solves the LBTE can be found in previous works^17,25,26. Acuros is designed with a generalized framework for specifying the intensity and distribution of the x-ray fluence field incident on the patient as the source rotates and the patient advances, which enables modeling scanner complexities such as bowtie filter, overrange collimation, and angular + longitudinal TCM. Acuros was previously tested against Monte Carlo, using Geant4 as the benchmark code^17,19.

The Acuros workflow requires three inputs: (a) the definition of the source, (b) the CT acquisition parameters, and (c) the voxelized geometry.

In Acuros, each scan is modeled by a collection of discrete sources. The sources are defined by their discrete locations, spectra, fluence, and spatial extents in both the fan and cone directions. Modifying the source definition enables modeling specific bowtie filters, overrange collimation schemes, and tube current modulation approaches. In this work, we used this generalized framework to model acquisitions from a specific clinical scanner (GE Discovery 750 HD, GE Healthcare). Information for modeling the spectral distribution of the beams generated by the scanner (tube output spectrum, bowtie filter and TCM effects) were provided by the manufacturer. The bowtie filters were analytically implemented by defining discretized x-ray beams, whose spectra and fluence vary across the fan angle. Further details on how Acuros modeled bowtie filters are provided in previous work¹⁹. The overrange collimation was modeled so that portions of the x-ray beam were blocked at the beginning and end of the helical scan, limiting the exposure beyond the field of view, according to the scheme described by Yang et al. for the GE Discovery 750 HD²⁷. This effect is implemented in Acuros by discretizing the spectral fluence of the x-ray beams across the cone angle and is affected by the discretization in view angle. The present study simulated 18 views per rotation, as our previous Acuros benchmarking studies demonstrated that 18 projection views per rotation provided sufficient accuracy even when modeling scanner effects such as tube current modulation and overrange collimation^17,19. The longitudinal + angular TCM (SmartmA, GE Healthcare, Chicago IL) implemented on the GE Discovery 750 HD scanner was modeled by a previously validated custom MATLAB program developed in collaboration with the manufacturer²⁸. The TCM simulator program takes as input the noise index (shown in Table 1) and the scout acquired prior to each CT examination and outputs the tube current modulation profile as a function of the slice and projection angle, for each studied protocol and phantom. The generated profiles were used to scale the spectral distribution exiting the source for each projection angle. Figure 2 shows the tube current modulation profiles (longitudinal and longitudinal + sinusoidal angular) plotted over the 5yo-phantom scout for protocol 3.

Figure 2.

Tube current modulation profiles (z-angular-dependent and z-dependent modulation) plotted over the AP scout of the 5yo CIRS ATOM phantom.

The modeled acquisition parameters included some specific features of the clinical scanner, such as source-to-isocenter and isocenter-to-detector distances, which were extracted from the DICOM header of the CT images.

The voxelized geometry was created from the CT images acquired during the scans. Material IDs were assigned to each voxel of the phantom models based on the HU values of the CT images through thresholding algorithms. Specifically, four phantom materials were defined: soft tissue, lung, spinal discs, and age-dependent bone. The elemental composition and mass density of each material were taken from the CIRS manual (Norfolk, VA). Breast tissue is not defined for the CIRS ATOM pediatric population, therefore breasts were modeled as soft tissue. To simulate the table that is present during the clinical acquisitions, a simplified table model made of carbon fibers and foam was added to the phantom geometry. Voxels outside of the phantom and table were modeled as air. The TLD chips were contoured in the resulting CT images and modeled as LiF cylinders of approximately 3 mm height and 5 mm diameter. Figure 3 shows one scanned axial CT image of the CIRS ATOM 5yo phantom, with TLDs inserted at two lung and two breast locations (within the yellow circles), and the corresponding model with cylindrical sensitive volumes at the locations selected for dosimeter placement. Different colors correspond to different materials in the model.

Figure 3.

(a) A slice CT image of the CIRS ATOM 5yo phantom, showing TLDs at lung and breast locations, highlighted within the yellow circles, and (b) corresponding section modeled in Acuros CTD with cylindrical sensitive volumes at the selected organ locations, and the defined materials are identified as: 0=air; 1=lungs; 2=soft tissue; 3=bone; 4=LiF; 5=cushion foam; 6=carbon fibers.

The doses estimated by Acuros at each dosimeter location were tallied and compared to the corresponding experimental values. Acuros was executed on a commonly available Nvidia GeForce GTX 1080 GPU card. Because Acuros simulations are limited by the memory of the GPU, the voxelized volumes needed to be downsampled. We chose a downsampling factor of 8x8x3 with respect to the original resolution of the CT images, resulting in nearly isotropic voxels, with size dimension of approximately 4 mm. The x-ray tube start angle at which the acquisition begins is random, depending on where the x-ray tube happens to be at the starting table position.

After verifying that the TLDs sensitivity threshold of 1 cGy was reached for protocol 2.3 (5yo-chest, without TCM), irradiations were repeated three times for this case, and after each irradiation the TLDs were replaced. This allowed us to have specific measurements for specific tube start angles, where the latter were provided by information from the manufacturer and used in the Acuros modeling. The dose plots resulting from the tube start angle study are presented in the Results section 3.2.2.

To ensure a sufficient signal for reliable TLD readings in all other protocols, the scans were repeated at least three times with the same set of TLDs for all repeated acquisitions. The TLD readings were therefore divided by the number of repeated irradiations. Likewise, Acuros modeled each irradiation with its specific tube start angle. The Acuros dose estimates from the different tube start angles were then averaged to model the multiple acquisitions performed with the TLDs. The dose plots resulting from the studies with multiple irradiations are presented in the Results section 3.2.3 and in the Supplementary Material.

TLD readings were given in units of cGy, whereas Acuros estimates were given in units of cGy/photon.

2.3. Experimental validation of the simulations

In order to compare experimental doses (D_meas) with simulated doses (D_sim), a calibration factor (CF) is needed to account for the number of photons emitted by the scanner during the procedure, as the simulation output D_sim is given in terms of dose per unit photon (cGy/photon). The CF was obtained as the ratio of the CTDI_vol provided by the CT scanner during a CT examination (CTDI_vol,scanner) and the CTDI volume estimated by simulating the CTDI phantom in Acuros (CTDI_vol,sim) :

$$CF=CTD{I}_{\mathit{vol},\mathit{scanner}}/CTD{I}_{\mathit{vol},\mathit{sim}}$$ (1)

To corroborate the reliability of the CTDI_vol,scanner provided by the CT scanner, measurements were also performed with RaySafe X2 CT ionization chambers (Billadl, Sweden) at the center and at the periphery of the 16-cm-diameter CTDI phantom.

The volumetric CTDI (CTDI_vol) is defined as the ratio of the weighted CTDI (CTDI_w) to the helical pitch²⁹. The calculation of the CTDI_w assumes that the radiation decreases from the outside to the center of the cylindrical phantom for an axial scan configuration²⁹, and is calculated as:

$$CTD{I}_w=\left[(1/3)\ast D_{\mathit{\text{center}}}+(2/3)\ast D_{\mathit{\text{periphery}}}\right]\ast \mathit{\text{ChamberLength}}/\mathit{\text{BeamCollimation}},$$ (2)

where D_center and D_periphery are the air kerma readings from the CT ionization chambers located at the center and periphery of the CTDI phantom, respectively. The active length of the ionization chamber (ChamberLength) was 10 cm, and the beam collimation at the isocenter (BeamCollimation) for all studied cases was 4 cm. Therefore, in order to estimate the CTDI_vol,sim to obtain CF, D_center and D_periphery were estimated by modeling the CTDI measurement in Acuros.

The CTDI_vol,scanner provided by the scanner manufacturer is based on either the 16-cm or 32-cm-diameter phantom, as shown in Table 1, depending on parameters selected prior to the CT acquisition. Consequently, both the 16-cm and 32-cm-diameter CTDI phantoms were modeled in Acuros as polymethylmethacrylate cylinders, with air ionization chambers at the center and periphery for the estimation of D_center and D_periphery, respectively. The CTDI_vol,scanner is reported for an axial configuration with equivalent acquisition parameters of the clinical helical scan. Therefore, the CTDI phantoms were simulated for an axial scan and the resulting CTDI_w (and CTDI_vol,sim) were computed according to equation (2). The CF, derived from equation (1), is then associated with a specific protocol (tube current-time product, tube voltage, collimation, bowtie filter).

However, in order to generalize the CF to any protocol with same acquisition parameters of tube potential, total beam collimation, and bowtie filter, the CF should be independent from the tube current–time product (mAs). Because the relation between mAs and dose is linear, the estimate (D_est) of the simulated dose is computed as:

$$D_{\mathit{\text{est}}}=D_{\mathit{\text{sim}}}\ast \frac{CF}{mA{s}_{calibration}}\ast mA{s}_{protocol}\ast \mathit{No}.\mathit{Rotations}$$ (3)

Where D_sim is the Acuros output in units of cGy per unit photon, $\frac{CF}{mA{s}_{calibration}}$ is the CF normalized by the mAs of the calibration scan, mAs_protocol is the tube current-time product value for the current protocol, and No.Rotations is the number of rotations of the helical scan. The number of rotations can be obtained from the scan length, the pitch, and the beam collimation.

To validate the CF, free-in-air measurements were performed with the RaySafe X2 CT ionization chamber located at the isocenter of the CT gantry (Figure 4), for an axial configuration with setting parameters of the protocols 1.1, 1.3, and 3.6, specified in Table 1. The CT images from the scanner were used to identify the location of the isocenter of the chamber with respect to the isocenter of the gantry, to account for misplacement (see upper left corner in Figure 4). The corresponding scenario was simulated in Acuros. The chamber was modeled as a 10-cm-long pencil with outer walls of air-equivalent material and density of 1.76 g/cm³ (red circle in Figure 4, upper left corner), and inner active chamber of air with density 0.00123 g/cm³, where the dose was tallied in units of cGy/photon (yellow area in Figure 4, upper left corner). Acuros dose estimates were then converted to units of cGy, by applying the CF for the corresponding experimental scenario (tube voltage, bowtie, and beam collimation combination), and were compared to the measured dose.

Figure 4.

Ionization chamber dose measurements for an axial scan, with example of the model of the chamber section in Acuros in the upper left corner of the image.

In summary, the CF is first determined for each tube voltage, bowtie filter, and total beam collimation combination, according to equations (1) and (2), using CTDI_vol,scanner from calibration irradiations (at mAs_calibration). Although in clinical practice the beam profile is wider than the nominal collimation to ensure complete coverage of all the detector rows and due to penumbra effects, this was not considered in the Acuros modeling. Then, for a specific phantom or patient, the dose is estimated by applying equation (3). For the anthropomorphic phantoms, the dose values D_est, estimated by Acuros after applying the calibration factor CF, were then compared to the measured values D_meas at the corresponding organ locations. The measured values were obtained as the average over the three TLD readings per each location, and further divided by the number of repeated scans that were performed to ensure good SNR.

The metric used to verify the agreement between D_est, obtained from Acuros, and D_meas, obtained from the TLD readings, for each TLD location was the % dose error, calculated as:

$$Error(\text{\%})=\frac{D_{\mathit{\text{est}}}-D_{\mathit{\text{meas}}}}{D_{\mathit{\text{meas}}}}\ast 100$$

The metric used to quantify the general agreement between Acuros and the measurements across all TLD locations for each specific protocol is the % root-mean-squared organ dose error (RMSE). The RMSE of the Acuros dose estimates (D_est) relative to the measured doses (D_meas) is defined as:

$$RMSE(\text{\%})=\sqrt{\frac{1}{N}\sum _i{\left(\frac{D_{es{t}_i}-D_{mea{s}_i}}{D_{{\text{meas }}_i}}\ast 100\right)}^2},$$

where the sum is performed over all N TLD locations where the TLD chips were placed for each protocol.

3. Results

3.1. Validation of calibration factor

The CTDI_vol obtained from measurements performed with ionization chambers and the CTDI_vol,scanner provided by the CT scanner showed good agreement, with maximum difference of 3.4%, showing the reliability of the CTDI_vol,scanner. The free-in-air measurements, performed to validate the CF with the ionization chamber at the center of the gantry for axial scans, agreed with the corresponding simulated scenarios, with differences shown in Table 2.

Table 2.

Differences (%) between free-in-air measurements and corresponding simulated scenarios performed to validate the CF for axial scans.

Protocol ID	Simulations vs. Measurements (%)
1.1 (80 kV, Medium Bowtie, 0.6s, 625 mA)	+0.3%
1.3 (120 kV, Medium Bowtie, 0.6s, 175 mA)	−3.8%
3.6 (100 kV, Small Bowtie, 0.4s, 200 mA)	−0.8%

3.2. TLD precision

For all irradiations, the sensitivity threshold of the TLDs of 1cGy was reached, ensuring reliability of the measurements. Also, because three TLDs were used for each organ location, the standard deviation of the three dosimeters was calculated. The average standard deviation across all groups of 3 TLDs was 1.7%, with range of 0.2% - 8.5%. It is worth mentioning the three TLDs in the same group were not necessarily exposed to the same radiation, because of anatomy heterogeneities, and this may explain those groups characterized by higher standard deviation.

3.3. Comparison of measurements against simulations

3.3.1. Overall results

The differences between the measured and estimated doses across all configurations with anthropomorphic phantoms were, in terms of absolute % error, within 10% for most TLD locations. In few cases the absolute % error increased to ~13%, especially for TLDs located at the ribs, and in one case to 17% for TLDs located at the stomach for the 10-year-old phantom with TCM. This translates to maximum absolute dose error of 3.2 mGy (out of corresponding measured dose value of 25.0 mGy) for cases where the TCM is not applied, and to maximum absolute error of 2.6 mGy (out of corresponding measured dose value of 15.3 mGy) for the cases where TCM is applied. The higher error in the ribs may be due to the fact that TLDs at rib locations were at the interface between bone, lung and soft tissue, where dose calculations are more challenging, especially for deterministic solvers. Figure 5 plots the distribution of dose errors across all organs and all test configurations.

Figure 5.

Percent dose errors between Acuros and measurements. Each circle represents the error for each of the 154 TLD locations, plotted against the corresponding organ. The errors shown are for all protocols in Table 1, where the cases without tube current modulation (noTCM) are represented by black circles, and with tube current modulation (TCM) by green circles. The stars (*) represent the mean dose error across protocols for all TLD locations per each organ without TCM (red) and with TCM (blue).

Table 3 shows the RMSE across TLD locations for all configurations, which varied between 3% to 8%.

Table 3.

RMSE across all TLD locations for each simulated scenario.

RMSE	No TCM	With TCM
80 kV – 5yo - CAP	4%
100 kV – 5yo - CAP	5%	6%
120 kV – 5yo - CAP	4%
100 kV – 10yo - CAP	7%	8%
80 kV – 1yo - CAP	4%	3%
100 kV – 10yo - Abdomen	6%	8%
100 kV – 5yo - Chest	5%	6%
100 kV – 5yo - Chest (case 3.6)		7%

3.3.2. On the comparison for a specific tube start angle

For case 2.3 in Table 1, measurements were performed with one irradiation for each of three specific tube start angles, where the start angle is random for each scan. Figure 6 shows a bar plot where simulated (blue bars) and measured (orange bar) dose values are compared. The error bars represent the 10% uncertainty of the TLD measurements for a coverage factor of K=2 (95% confidence level). The results represent overall good agreement between Acuros and the measurements, with the Acuros estimates within the uncertainty of the TLD measurements for all cases. The RMSE across all measurements for each start angle was of 4% to 5%. The maximum error between measurements and simulations was 8% for case (b) for the TLDs in correspondence of the right thyroid. The thyroid locations are at the edge of the helical scan, therefore more sensitive to the modeling of the overrange collimation.

Figure 6.

Bar plot of simulated doses for specific tube start angle (blue bars), measured dose (orange bar), for each location studied in case 2.3 - 5yo chest without TCM; The error bars represent the 10% uncertainty of the TLD measurements. The dashed line indicates the CTDI_vol = 34.71 mGy reported on the 16-cm-diameter standard phantom.

3.3.3. On the comparison for CAP protocols with TCM

Figure 7 plots the measured and simulated doses in units of cGy at all TLD locations for the CAP protocols with applied TCM, which are cases 3.1, 3.2, and 3.3 (1yo, 5yo, 10yo respectively). For cases 3.1 and 3.2 (Fig. 7.a and 7.b), irradiations were repeated four times to ensure that the sensitivity threshold of the TLDs of 1 cGy was reached, and three times for case 3.3 (Fig. 7.c). The first four (Fig. 7.a and 7.b) and three (Fig. 7.c) bars show the Acuros estimates for the tube start angles, and the overlapped light gray bar represents the average of the Acuros estimates. This latter value is compared to the measured dose (last bar). The dashed line indicates the CTDI_vol displayed by the scanner for the CTDI standard phantom used for dose reporting. The error bars represent the 10% uncertainty of the TLD measurements for a coverage factor of K=2 (95% confidence level). For most organs, the Acuros average is well within the uncertainty of the TLD measurements. Similar plots for all other studied cases are available in the Supplementary Material (Figures S1, S2, S3). Furthermore, Figure 8 shows the axial view of the dose distribution in correspondence of a specific slice, where stomach and liver TLD locations are highlighted, for the three phantoms.

Figure 7.

Bar plot of simulated doses for each start angle, measured dose (last bar in green), and average simulated dose across the different tube start angles represented as an overlapped bar, for each location studied in: (a) Case 3.1 - 1yo CAP with TCM; CTDI_vol = 3.61 mGy reported on the 32-cm-diameter standard phantom; (b) Case 3.2 - 5yo CAP with TCM, of which TLDs at organ location ‘breast L’ were lost; CTDI_vol = 4.59 mGy reported on the 32-cm-diameter standard phantom; (c) Case 3.3 - 10yo CAP with TCM; CTDI_vol = 20.98 mGy reported on the 16-cm-diameter standard phantom. The dashed line indicates the CTDI_vol for each case.

Figure 8.

Simulated dose map for cases 3.1, 3.2, 3.3 (with TCM), where modeled TLDs at liver (purple arrow) and stomach (green arrow) are indicated.

4. Discussion

In our previous study, Acuros was compared against Monte Carlo code Geant4 showing overall agreement of 3.5% (RMSE), proving to be a reliable, fast, and patient specific radiation dose assessment tool for modeled CT examinations¹⁹. In the present study, to verify the reliability of the method for dose estimation on clinical CT scanners, Acuros was validated against measurements conducted with TLDs on pediatric anthropomorphic phantoms. We calculated and validated calibration factors (CFs) for few specific scenarios to convert the Acuros estimates to absolute dose and we extrapolated generalized CFs for protocols with same scan-specific parameters, such as kVp, collimation, bowtie filter, and accounting for the CTDI phantom used for dose reporting. The comparison of the Acuros dose estimates against measurements was performed with TLD chips at several locations within selected organs in the pediatric anthropomorphic phantoms. The resulting agreement between the Acuros dose estimates and the TLD measurements (0% to 17% error at each TLD location and 3% to 8% RMSE) are of similar order to previous studies validating Monte Carlo codes. Sharma et al. performed a complete validation of the GPU-based Monte Carlo code MC-GPU³⁰. The comparison of their MC-GPU estimates against TLD measurements yielded an agreement within 10% for all TLD locations and for the four validation cases, with the exception of the spinal bone insert for which the difference was ~12.5%. They evaluated a pediatric 5yo phantom and an adult male phantom, both scanned helically at 80 kV and 120 kV and at constant tube current. All four validation cases were using a CAP protocol. Akhavanallaf et al. helically scanned an adult male phantom at 100 kV with tube current modulation³¹. In their study, instead of evaluating dose at specific locations, as in our case or in Sharma et al. work, they distributed dosimeters in all TLD locations within the studied organs, in order to enable volume-averaged organ dose estimation. These values were then compared to Monte Carlo organ dose estimates, obtained by simulating the phantom model with contoured organs. This study presented differences between Monte Carlo organ dose estimates and organ doses retrieved by TLD measurements within the range of −8.3% to 22%, with a mean absolute difference of 14%.

Because Acuros is a deterministic solver, unlike the stochastic Monte Carlo method, there is no stochastic error associated with the dose outputs. However, the estimates depend on the calibration factors CFs, which are sensitive to variations of the volumetric CTDI displayed by the scanner console. The maximum difference between the CTDI_vol obtained from the measurements performed with ionization chambers in the CTDI phantoms and the CTDI_vol provided by the CT scanner was 3.4%. These differences could increase the discrepancy between experimental TLD measurements and the simulated dose values. Also, at low photon energies, such as the CT energy range, each TLD throughout the phantom is exposed to different effective energy, due to attenuation and scattered radiation from the phantom itself. Although broad energy correction factors have been applied to the TLD readouts, in order to account for an expected ~4% overresponse for 80 kVp and ~3.5% underresponse for 120 kVp, relative to the 100 kVp spectrum used for the calibration of the TLDs, these corrections are still approximate, and the uncertainty of the measured doses can be up to 10% for a coverage factor of K=2 (95% confidence level). The expanded uncertainty can be reduced by a few percent if the effective energy at each TLD location was known. Further simulations to calculate the effective energy correction factors at each TLD location could potentially improve the agreement between measurements and simulations.

The results demonstrated errors of <=13% across 153 dosimeter locations and 17% error for one dosimeter location, which are reasonable errors considering the uncertainty of the TLD measurements and the approximations introduced by the modeling of the geometry, such as the definition of the sensitive materials as cylindrical volumes and the model of the table couch. The discrepancies can be also due to uncertainties with the scanner modeling, that could be resolved if the exact mA values for each rotation angle and table position was known. Also, slight displacement of the tube start angle and longitudinal position might lead to an out of phase modeling of the helical trajectory. However, the scanner is modeled to the best of our knowledge, and despite that agreement could potentially be improved with more information from the vendor, we considered that dose errors to within 13% for 153 TLD locations is encouraging.

We evaluated the variation of the dose depending on the tube start angle for experiments where one scan was performed per TLD reading (protocol 2.3, results in Figure 6). Table 4 shows the standard deviation of the dose across the three tube start angles, both for the Acuros estimates and for the measured doses at the locations for protocol 2.3. Specifically, the breast TLD locations (considering left and right breast together) demonstrated the highest dose variability across different start angles, as they represent the most peripheral tissue among the selected organs for this case.

Table 4.

Dose standard deviation across three different tube start angles (354 deg, 91 deg, 228 deg) for case 2.3, both from Acuros estimates and TLDs readings.

	Thyroid	Lungs	Heart	Breasts
Acuros	10%	13%	1%	24%
TLDs	6%	6%	2%	13%

Thyroid=thyroid L+R; Lungs=lung L+R; Heart=heart; Breasts=breast L+R, from Figure 6.

The effect of the initial position of the gantry was evaluated by Zhang et al. through Monte Carlo simulations. They found a dose reduction at specific organs (breast, testes, thyroid, and eye lenses) on the order of 20% or more for pediatric models, only by selecting the tube start angle.

For cases 3.1, 3.2, 3.3, where TCM is applied, Figure 7 shows that the variation of dose across organs increases with patient age and size. The difference of the dose measurements between the most and least irradiated organs can be used as a metric to quantify the spread of dose values for a specific case study. This difference for the 1-year-old phantom was 0.15 cGy, and it increased to 0.38 cGy for the 5-year-old and to 0.84 cGy for the 10-year-old phantoms, showing the relevance of patient-specific modeling. From Figures 6 and 7 we can also see that a larger dependence of the dose on the tube start angle is generally shown for the 10yo phantom, compared to the 1yo and 5yo phantoms. This is most likely due to the fact that the 10yo has the largest extent in the axial plane. Hence, the dose estimates in peripheral regions (such as ribs and breast) are more sensitive to the starting position of the x-ray tube and table during a helical scan. The peripheral location of the stomach TLDs for the 10yo (see Figure 8) suggests that the 17% error may be due to the sensitivity of this location to accurate modeling of the helical scan. If we had considered the dose averaged across the volume of the whole organ or tissue, i.e. across the whole stomach, the influence of the tube start angle would probably be reduced. For further observations on the tube start angle, we recommend the reader to see the Supplementary Material. Figures S3.a and S3.b plot the simulated doses for each start angle together with the measured dose, for cases 3.4 and 3.6. In both cases, a helical chest scan is performed on the 5yo phantom, with pitch of 0.984 and of 1.375 for case 3.4 and 3.6, respectively. Although the start angles are random for each scan and thus they are different among the two cases, it is evident that the dose variation by angle was much greater at a higher pitch. Also, Figures S2.c, S2.a, S2.b, S2.c in the Supplementary Material, plot the simulated and measured doses for cases 2.4, 3.4, 3.5, and 3.6, where organ locations on the periphery and outside of the scan coverage were added. Dose errors were within 12% for organ locations not fully inside the scanned volume, which are the most sensitive to the effect of the overrange collimation.

Although our work is limited to one specific scanner, the GE Discovery 750 HD, the photon source definition within Acuros is generalized such that other components, for example bowtie filters, tube spectra or tube current modulation approaches, can be easily modeled by adjusting the discrete source definitions. The overall good agreement between Acuros dose estimates and measurements performed at 154 TLD locations on three anthropomorphic phantoms (from the pediatric population of the ATOM CIRS family) and for different acquisition parameters, with average RMSE of 6% among all cases, is achieved despite the discretization across energy, space, and angle, necessary for the implementation in Acuros. The discretization of the spectral distribution across fan and cone angle is required for the modeling of the bowtie filter and overrange collimation, respectively. This latter effect, together with the modulation of tube current, is also affected by the discretization in view angle. Nevertheless, the modeling of only 18 views per rotation is sufficient to achieve accuracy for the dose estimates in this clinical validation study, despite the fact that the physical scanner acquires thousands of projections in a single gantry rotation.

Another relevant aspect of this work is Acuros run time. Acuros, running on a GeForce GTX 1080 GPU, provided dose estimates in a time range of few seconds up to two minutes. The simulation time depends mainly on the number of voxels used to define the phantom models and on the number of total views. The shortest simulation was reached for protocol 3.6, where the chest of the 5yo phantom was scanned with a pitch of 1.375 and the run time was 9 seconds. The longest simulation belonged to cases where the 10yo phantom was scanned for a CAP protocol, where approximately 280 projections were required to ensure the exposure of the selected scan length, resulting in a simulation time of ~2 minutes.

A long-term goal of this project is to combine Acuros with automated image segmentation using deep learning approaches, in order to generate patient-specific anatomical models based on the CT images acquired during the examination^22,32. The proposed tool will then provide near real-time individualized dosimetry for CT applications and therefore patient-specific organ doses, which would overcome the time constraint and the inaccuracy of the methods currently employed for dose monitoring in clinical practice.

5. Conclusions

This study demonstrated that the experimental validation of Acuros was successful for a specific clinical scanner, with average RMSE across all cases of 6%, maximum dose errors of 13% for 153 TLD locations and 17% for one location, and simulation time up to two minutes. These levels of dose error are low enough to capture the variation of dose across organ locations and across pediatric patient-sizes, which provides more relevant information for protocol optimization than CTDI. The results support the potential of Acuros to be a reliable tool for clinical CT dosimetry, aimed at near real-time and patient-specific dose monitoring.

Supplementary Material

Figure 2 (Supplement)

Figures S2. Plot of the simulated dose (1^st bar), and measured dose (2^nd bar), for each location in Study 2 (at 300 mAs) from Table 1 : (S2.a) Case 2.1 - 1yo CAP without TCM; CTDI_vol = 19.95 mGy reported on the 16-cm-diameter standard phantom; (S2.b) Case 2.2 - 10yo CAP without TCM; CTDI_vol = 36.61 mGy reported on the 16-cm-diameter standard phantom; (S2.c) Case 2.4 - 10yo Abdo without TCM; CTDI_vol = 36.16 mGy reported on the 16-cm-diameter standard phantom. For this latter case, the bladder (indicated as bladder ##) was outside the longitudinal coverage. Although the readout for this location was below the TLD sensitivity threshold of 1 cGy (actual TLD reading at bladder ≈ 0.6 cGy, as the irradiation was repeated three times), we show anyway the comparison between Acuros and the measurement, and the uncertainty bar of 10% was not represented on purpose.

The dashed line indicates the CTDI_vol for each case.

Figure 3 (Supplement)

Figure S3. (S3.a) Plot of simulated doses for each start angle (first 5 bars), measured dose (6^th bar), average simulated dose across the 5 start angles represented as an overlapped bar, for each location for Case 3.4 - 5yo chest with TCM and pitch of 0.984; CTDI_vol = 3.76 mGy reported on the 32-cm-diameter standard phantom; (S3.b) Plot of simulated doses for each start angle (first 5 bars), measured dose (6^th bar), average simulated dose across the 5 start angles represented as an overlapped bar, for each location for Case 3.6 - 5yo chest with TCM and pitch of 1.375; CTDI_vol = 3.38 mGy reported on the 32-cm-diameter standard phantom; (S3.c) Plot of the simulated dose (1^st bar), and measured dose (2^nd bar), for each location for Case 3.5 - 10yo abdomen with TCM; CTDI_vol = 19.52 mGy reported on the 16-cm-diameter standard phantom.

The pound symbol “#” in the x-axis indicates that the TLD location is at the periphery of the scan coverage, while the double pound “##” indicates that the TLD location is outside of the scan coverage.

The dashed line indicates the CTDI_vol for each case.

Figure 1 (Supplement)

Figure S1. Plot of the simulated dose (1^st bar), measured dose (2^nd bar), for each location in Study 1 from Table 1 : (S1.a) Case 1.1 - 5yo CAP without TCM, 80 kV; CTDI_vol = 24.94 mGy at 375 mAs, reported on the 16-cm-diameter standard phantom; (S1.b) Case 1.2 - 5yo CAP without TCM, 100 kV; CTDI_vol = 28.93 mGy at 240 mAs, reported on the 16-cm-diameter standard phantom; (S1.c) Case 1.3 - 5yo CAP without TCM, 120 kV; CTDI_vol = 19.36 mGy at 105 mAs, reported on the 16-cm-diameter standard phantom. The dashed line indicates the CTDI_vol for each case.

Data availability statement

Measurement data that support this study are available from the corresponding author upon request.