Techniques producing highly conformal dose distribution such as intensity-modulated radiation therapy (IMRT) can facilitate normal tissue sparing and escalating the dose to the target. However, in thoracic radiotherapy, geometric uncertainty increases, and dose conformality decreases in spite of applying this technique because the organs and tumor are moved and deformed by respiratory motion. Accordingly, underdosing to target and overdosing to normal tissue could occur. Four-dimensional (4D) computed tomography (CT) offers information regarding respiration-induced tumor and organ motion in the form of three-dimensional (3D) CT data sets according to the respiratory cycle.^1,2) Generally in clinics, internal target volume (ITV)-based treatment planning, which uses an additional margin to consider the geometric uncertainties caused by respiratory motion,³⁾ is performed using 4D CT data. Although the ITV-based treatment planning is performed, a planned dose distribution, which was calculated from the treatment planning systems, may differ from the corresponding delivered dose distribution, which was the actual radiation dose to patient.

One of the reasons for the discrepancy between the planned and delivered dose is that the planned dose, i.e., a 3D dose, may not reflect the dosimetric impact of respiration-induced organ motion and deformation despite ITV-based treatment planning.⁴⁾ Currently, a 4D dose calculation, which could reflect the dosimetric impact of respiratory motion and estimate a more realistic delivered dose than a 3D dose, can be performed using the 4DCT data and a deformable image registration (DIR), and various studies related to the 4D dose calculation have been conducted.^5–13)

Guckenberger et al.¹⁰⁾ compared the 3D and 4D dose in terms of a biological effective dose (BED) in seven patients. There was no significant difference between the 3D and 4D dose for gross tumor volume (GTV) and ITV at the isocenter. However, the 3D dose significantly underestimated the 4D dose at a planning target volume (PTV) margin. Starkchall et al.⁷⁾ investigated 15 patients with Stage III non-small-cell lung cancer. In six patients, the difference between the 3D and 4D dose in the clinical target volume (CTV) coverage was more than 3%, and in five patients, a significant difference of at least 5% in the PTV coverage was identified, which warranted replanning.

Several prior studies of liver and lung tumors identified that tumor size and motion could be linked to the difference.^8,12) In particular, in lung cancer patients, Valdes et al.⁸⁾ expected that small tumor with large motion will show significant difference. Estimating the condition of factors such as tumor size and motion underlying this significant difference is important because the 4D dose does not always provide significant advantage than the 3D dose to all patients, despite reflecting the dosimetric impact of the respiratory motion.¹³⁾

To estimate this condition of the factors causing the significant difference, a quantitative evaluation of the difference according to these factors is required. However, a large number of patient cases are required to perform such evaluation because variables such as tumor location, size, and motion vary among the cases. Furthermore, a retrospective study of patients involves several uncertainties such as irregular breathing patterns.^22,23) Consequently, a systematic phantom study is required to quantitatively analyze the effects of these factors. In this context, we developed a deformable lung phantom that can independently control factors such as tumor motion and size to quantitatively analyze the dosimetric impact of the respiratory motion according to the factors.

1. Phantom design and construction

A phantom design was based on the deformable lung phantom of Chang et al., which was developed for evaluating deformable registration.¹⁴⁾ The phantom consisted of target, motion, and respiratory signal components to simulate the lung, diaphragm motion, and thorax motion (Fig. 1a).

The target component was manufactured to simulate the lung and consisted of two acrylic cylinders of different sizes, a sponge, and a silicone tumor. The acrylic cylinders were 18 cm in height, with diameters of 12 cm and 18 cm. The cylinder of 12 cm diameter was inserted and fixed inside the cylinder of 18 cm diameter. A wet sponge was used to emulate the deformation and electron density of the lung. This method was referred from prior studies.^15,21) The wet sponge including the tumor was inserted into the cylinder set as shown in Fig. 1b. To mimic flexible tumors of different sizes, tumor molds of different tumor sizes were created using a 3D printer (K-wilson printer, 3D-items, Seoul, Korea). Room temperature vulcanizing-type liquid silicone rubber (Liquid silicone RTV-S3, Korea) of 24 durometer hardness within the real tumor and a soft tissue hardness range of 18~69 durometer¹⁶⁾ were mixed with a silicone hardener, and the mixture was poured into the tumor molds. The liquid silicone mixture was allowed to harden for seven days. Fig. 2 shows the produced silicone tumors and created custom tumor molds of different sizes that can produce 10 cm³ and 90 cm³ tumors. Detailed construction and motion of the target component are shown in Fig. 3.

The motion component that mimicked the diaphragm motion was designed to adjust the amplitude of the phantom diaphragm motion in the range 1~7 cm and period up to ≥2 s with a regular breathing. A circular acrylic plate that simulated the diaphragm directly compressed the sponge. To verify the phantom diaphragm motion, a spherical metal marker of 2.5 mm diameter was attached on the circular acrylic plate (Fig. 1c). A length adjustment driving rod that delivered the power of a programmable motor to the diaphragm connected to an adjustable rotation axis crank. Fig. 4 shows a detailed diagram of the adjustable rotation axis crank. The joint hole of the adjustable rotation axis crank served as the connection point with the length adjustment driving rod, and the radius of rotation was equal to the distance between the center of the crank and the joint hole (Fig. 4). The coupling radius of the linear rod on the rotation axis crank controls the amplitude of the phantom diaphragm motion according to Eq. (1).

where r is the radius of rotation, θ_i is the initial angle before moving the phantom and θ_f is the final angle after moving the phantom.

In addition, the programmable motor can control the period with regular breathing via programmable motor functions. Therefore, the amplitude of the phantom diaphragm motion was controlled by adjusting the radius of rotation using the adjustable rotation axis crank and length adjustment driving rod. In addition, to simulate tumor motion by ≥3 cm, the phantom diaphragm motion could be controlled in the range 1~7 cm.

The respiratory signal component was manufactured to simulate the thorax motion and acquire a respiratory signal using an ANZAI belt (Anzai Medical Company, Tokyo, Japan) or a real-time position management (RPM) system (Varian Medical Systems, Palo Alto, CA) for the 4DCT data, and synchronize the phantom diaphragm motion.

2. Verification of the phantom diaphragm motion

The accuracy of the phantom diaphragm motion was evaluated by comparing the phantom equation of motion (set by Eq. (1)) with the measured phantom motion. The angles of 180° and 0° in Fig. 4 produce phantom motions of end-inhalation and end-exhalation, respectively. Therefore, an angle of 180° was set as the initial angle in Eq. (1), and the final angle in Eq. (1) was set at almost 0°. The final angle and phantom diaphragm motion according to the radius of rotation were measured using a digital protractor (2&1 Digital AngleRule, BLUEBRID, China) and electronic digital calipers (Carbon Fiber Composite Digital Caliper, Joro Electronics, Zhejiang, China). The resolutions of the digital protractor and electronic digital calipers were 0.1° and 0.1 mm, respectively, and their accuracies were ±0.3° and ±0.2 mm, respectively.

3. 4DCT data acquisition

To evaluate the phantom performance in terms of controlling the tumor size and motion, the 4DCT data were acquired using a CT scanner (SOMATOM Definition AS, Siemens Healthcare, Erlangen, Germany) with the ANZAI belt (Fig. 5) according to the change in the phantom diaphragm motion amplitude and tumor size. The 4DCT data consisted of 10 phases of 3DCT image data sets using a phase-based sorting method. The slice thickness of the 4DCT image was 0.15 cm.

4. Assessment of tumor motion and position

On the basis of the center-of-mass (COM) of the tumor and the spherical metal marker (Fig. 1c), 3D vectors that describe the tumor motion and phantom diaphragm motion were acquired by comparing the end-exhalation phase image with the end-inhalation phase image from the acquired 4DCT image data according to the amplitude of the phantom diaphragm motion.

To estimate and control the tumor motion, the correlation curve between the phantom diaphragm and tumor motion was calculated using a cubic polynomial function that is curve fitting method.

Kashani et al.¹⁷⁾ developed a deformable lung phantom for image-based patient modeling, and showed that the distance between the tumor and phantom diaphragm affected the tumor motion. In our phantom, to fix the impact of this distance affecting the tumor motion, tumor set-up positions based on this distance were set as identical as possible, although the tumor size was altered. Therefore, the tumor set-up positions, defined as the distance between the tumor surface and the phantom diaphragm in the end-inhalation phase, were compared according to the tumor size.

1. 4DCT image of the phantom

Fig. 6a shows an example of the coronal views from the 4DCT image of the 10 cm³ tumor case with the application of the diaphragm motion of amplitude 2 cm. Indirect tumor motion caused by the contraction and expansion of the sponge was identified. In Fig. 6b~d, the difference maps between the end-inhalation and end-exhalation phase images from the 4DCT data varied according to the phantom diaphragm motion amplitude. The variations of the difference map increased with increasing amplitude.

2. Verification of phantom diaphragm motion

The difference between the equation and measured motion was less than 1 mm, ranging from 0.1~0.9 mm, in all cases (Table 1). A maximum difference of 0.9 mm occurred for a radius of rotation of 10 mm, and the mean absolute error (MAE) between the equation and measured motion was 0.34 mm.

3. Tumor motion and position

The trajectories of the tumor COM were mainly in the superior-inferior (SI) direction for the 10 cm³ and 90 cm³ tumor cases (Table 2). In the case of a 10 cm³ tumor and the diaphragm motion case ≥2.71 cm, as the diaphragm motion increased, the magnitudes of the tumor motions in the left-right (LR) and anterior-posterior (AP) directions increased. In the case of a 90 cm³ tumor case, the tumor motion magnitudes in the LR and AP directions increased with increasing diaphragm motion, except for the LR direction and diaphragm motion case ≥5.67 cm. For both tumor sizes, the tumor motion magnitudes in the LR and AP directions were less than 1 mm in most cases, and the tumor motion in the SI direction increased with increasing phantom diaphragm motion in all cases. Fig. 7 shows a correlation curve between the phantom diaphragm and tumor motion, which were calculated based on a spherical metal marker and the tumor COM from the 4DCT data. The correlation curve shows that as the diaphragm motion increased, the tumor motion in the SI direction increased. In addition, Fig. 7 shows that the small tumor case exhibits greater movement than the large tumor case. The MAE values derived from fitting the correlation curve were 0.33 and 0.21 mm for the 10 cm³ and 90 cm³ tumors, respectively.

Coronal views of end-exhalation phase images of the 4DCT according to the tumor size are shown in Fig. 8. On the basis of the distance between the diaphragm and tumor surface, the tumor set-up positions for one data set in the SI direction were 2.70±0.15 cm and 2.55±0.15 cm for the 90 cm³ and 10 cm³ tumor cases, respectively. The difference in the set-up position for these cases ranged from 0~0.45 cm.

The developed deformable lung phantom simulated indirect tumor motion and deformation via compression and decompression of a sponge using the phantom diaphragm motion instead of directly moving a tumor using a motor. Thus, the direction of the tumor motion was affected by the phantom diaphragm motion. Several studies showed that lower lobe tumor motions occurred mostly in the SI direction and had larger amplitude movement than upper lobe tumors.^18,19) In addition, large tumor motion may be more closely associated with the difference between the 3D and 4D dose calculations than small motion. Therefore, the phantom simulated a tumor located in the lower lobe.

The MAE of 0.34 mm for the verification of the phantom diaphragm motion from Table 1 suggests no significant difference between the phantom equation motion and real phantom diaphragm motion, and the developed phantom simulates the diaphragm motion in the SI direction with an accuracy better than 1 mm. The tumor motion in the AP and LR directions increased slightly with the phantom diaphragm motion increment for almost all cases, which is similar to the results of the deformable phantom developed by Serban et al.¹⁵⁾

The correlation curve between the phantom diaphragm and tumor motion in the SI direction (Fig. 7) had a similar tendency to that of Mageras et al.²⁰⁾, who evaluated the diaphragm position according to the GTV position in lung cancer patients. Moreover, the tumor motion in the SI direction can be extracted from the phantom diaphragm motion using the correlation curve. In other words, the tumor motion can be artificially controlled using the correlation curve. However, the uncertainties caused by curve fitting and 4DCT slice thickness were reflected in the correlation curve. The MAE of the curve fitting were 0.33 and 0.21 mm for the 10 cm³ and 90 cm³ tumor cases, respectively, and the slice thickness is subject to an inaccuracy of up to 3 mm in calculating the tumor and phantom diaphragm motion in the SI direction. These uncertainties could affect the tumor motion estimation and control. The error introduced by the slice thickness inevitably occurs by using CT. However, improving the CT resolution could reduce this error, and the error caused by the curve fitting is sufficiently small compared to that from the slice thickness.

The difference in the tumor positions according to the tumor size was up to 4.5 mm considering the slice thickness uncertainty that cannot calculate the values less than 1.5 mm (Fig. 8). Errors derived from the slice thickness and tumor set-up were reflected in this difference in tumor positions. The error caused by the slice thickness can be reduced by decreasing the slice thickness. Although the tumor positions were similarly set, the small tumor had greater motion than the large tumor (Fig. 7) because of the physical characteristics of the sponge surrounding the tumor. However, identical tumor motions can be applied regardless of the tumor size using the correlation curve within the range of motion of the large tumor.

This study was dedicated to developing a deformable phantom that can quantitatively verify the effects of the tumor size and motion affecting the difference between the 3D and 4D dose calculations. To achieve this aim, inaccurate dose calculation and DIR errors from the 4DCT artifact, which affect the difference between 3D and 4D dose calculations, should be minimized. Accordingly, the phantom was designed to simulate a regular breathing signal to avoid the 4DCT artifacts caused by irregular breathing signals. This deformable lung phantom did not have a realistic lung shape because the phantom development was focused on controlling the tumor motion and size. However, the electron density of the lung and tumor hardness were simulated by referring to previous studies.^15,16) Dosimeters such as film and thermoluminescent dosimeters were not considered because this phantom is intended for a comparative analysis between the 3D and 4D dose calculations. However, it is technically possible to embed these dosimeters in the silicone tumors or sponge.

In this study, an example of a 4D dose distribution based on 3D conformal radiation therapy planning was additionally calculated using the developed phantom. The prescription dose for this treatment planning was 60 Gy in 2 Gy fractions. A 4D dose calculation process is shown in Fig. 9, and this process is similar to that from previous studies.^6,12)Fig. 10 shows the 3D dose distribution, 4D dose distribution, and the distribution of difference between the 3D and 4D dose, and this difference mainly occurred in the SI direction. The tendency of this difference was similar to that reported by a previous study using patient cases.¹²⁾ In further study, the effects of the factors that influence the difference between the 3D and 4D dose calculations, such as tumor size and motion, will be quantitatively analyzed using this phantom. Ultimately, the phantom could contribute to the discrimination of patients who would benefit from the 4D dose by estimating the condition of significant difference between the 3D dose and 4D dose according to the tumor size and motion.

The developed deformable lung phantom was designed to control the tumor size and motion. The tumor motion can be controlled using the acquired correlation curve between the phantom diaphragm and tumor motion. Furthermore, the tumor size can be controlled by producing tumors of various sizes using liquid silicone rubber and custom tumor molds created using a 3D printer. This phantom could be used to quantitatively analyze the dosimetric impact of the respiratory motion according to the factors that influence the difference between the 3D and 4D dose, such as the tumor size and motion.

We would like to thank Jae-Hong Jung and people of the department of radiation oncology in Gangnam Severance Hospital for their aid in acquiring the 4DCT data. We acknowledge Geum Seong Cheon for aiding treatment planning. This work was supported by the Radiation Technology R&D program (No. 2015M2A2A7038291) and the Mid-career Researcher Program (2014R1A2A1A10050270) through the National Research Foundation of Korea funded by the Ministry of Science, ICT and Future Planning.

The authors have nothing to disclose.

All relevant data are within the paper and its supporting information files.