BANG-3-type (Bis, Acrylamide, Nitrogen and Gelatin) polymer gels (BANG3PRO; MGS Research, Inc., Guilford, CT), and PAGAT (Polyacrylamide Gel and THPC) gels [14] were prepared. The BANG-3 type polymer gels were prepared using a BANG kit. The unmodified gel melted at 55˚C; thus, several additives were used [15] . PAGAT gels were prepared using 89% w/w water, 3% acrylamide, 3% N,N’-methylenebisacrylamide (Bis), 5% gelatin (300 bloom) and 5 mM tetrakis (hydroxymethyl) phosphonium chloride (THPC). Gelatin was added to water, followed by heating at 50˚C on a hot plate/magnetic stirrer. After the solution became clear, it was cooled to 45˚C and Bis was added. After the Bis dissolved completely, THPC was added.

Prepared gels were poured into polyethylene-terephthalate (PET) vials and containers. Vials were 45 × 30 × 30 mm³ and were used for dose-R₂, R₁ calibration. Containers were 177 × 74 × 74 mm³ and were used to measure clinical irradiations by 3D dose distribution. Gels in the PET vials and containers were stored wrapped in aluminum foil in a refrigerator at 4˚C until irradiation, as the gels melt at high temperature.

Figure 1 shows a gel phantom using PAGAT gel for clinical irradiation. The phantom was 200 × 140 × 125 mm³, made of Styrofoam, and housed the gel container. The phantom was filled with water and then scanned in A-helical scan mode using an X-ray CT device (Aquilion LB; Toshiba Medical Systems, Tochigi, Japan) during the treatment plan. CT exposure conditions were as follows: tube voltage, 120 kV; tube current, 400 mA; exposure time, 0.5 s; slice thickness, 3.0 mm; and imaging field of view, 550 × 500 mm². The number of slices per CT image was 70.

Treatment plans were prepared using the RTPS system (Pinnacle³; Philips

Healthcare, Andover, MA) and used a four-field box irradiation technique (Figure 2). The four-field box technique (crossfire) irradiation plan prescribed a total dose of 4 Gy and the same beam weight in each direction. The four beam irradiation calculations assumed the treatment of esophageal cancer and determined the dosimetric results of the polymer gel.

The prepared BANG-3-type gels and PAGAT gels were irradiated with a 6 MV X-ray beam on a linear accelerator (ELEKTA Synergy; ELEKTA, Stockholm, Sweden) at Tsukuba Medical Center Hospital.

Plan dose map (left, blue) was exported from RTPS and dose map from R₂ image (right, red) was calculated from in-house program. This figure was shown that crossfire 4 beams irradiation calculations supposed that treatment of a esophageal cancer and dosimetric result of polymer gel using 6 MV photon beam. The profiles between plan dose and dose map from R₂ were compared.

First, the polymer gels in PET vials were irradiated with no collimator at the isocenter of a 300 × 300 × 300 mm³ water tank to calibrate the dose versus R₂ and R₁ from 0 to 20 Gy in the beam axis. After irradiation, gels were stored in a

refrigerator at 4˚C until MRI scanning.

Second, gel phantoms were irradiated with 6 MV X-ray beams at the isocenter in order to simulate clinical irradiation. The average dose rate was 300 MU/min (Figure 1).

MRI measurements for dose evaluation of the gels were performed on a 1.5-T Siemens AVANTO 1 day after irradiation. Irradiated gels were positioned in a quadrature (QD) coil for scanning.

For R₂ measurements, gels were imaged using a multi-echo fast spin echo pulse sequence. Ten echoes of the sequence were used (echo time: TE = 15 to 150 ms; echo time interval, 15 ms). For each scan, a repetition time (TR) of 1000 ms was used, with a 1 mm² resolution (field of view (FOV) = 192 mm, matrix number = 192 × 192) using 5-mm-thick planes. The obtained data were used to calculate T₂ images using the MapIt program (Siemens) [16] .

For R₁ measurements, gels were imaged using a 3D volumetric interpolated breath-hold examination (3D-VIBE) sequence (TE = 1.62 ms, TR = 15 ms). For each scan, a resolution of 0.5 mm² was used (FOV = 192 mm, matrix number = 384 × 384) using 5-mm-thick planes, the same as for R₂. R₁ and R₂ images was created to invert these pixel values using the original program.

The Styrofoam container described earlier was set in the QD coil and filled with water at 5.0˚C. Irradiated gel samples in vials and in containers were individually set in the center of the Styrofoam container and the water temperature in the container was raised from 5.0˚C to 41.0˚C at 5.0˚C /min.

The obtained data were used to calculate R₂ images using the MapIt program. Two-dimensional (2D) R₁ and R₂ images were constructed from the T₁ and T₂ images using an in-house program. Data points for the dose R_2, R₁ characteristic curve were obtained by averaging the R₂ values from the region of interest (ROI) in the polymer gel.

The acquired R₂ images were converted into dose images using calibration data from the dose-R₂ curve. Dose images from the R₂ images of the irradiated gels in the center profile were compared with the calculated plan data from the RTPS with four-box irradiation fields from the simulated clinical situation (Figure 2).

Figure 3 shows the R₂ values of the BANG polymer gels as a function of photon dose between 0 and 20 Gy. Each R₂ calibration curve was fit to a straight line for doses below 20 Gy. The fitted straight line for photon dosimetry at 20˚C had a gradient of 1.17 Gy⁻¹∙s⁻¹ and an intercept of 3.87 s⁻¹, and the coefficient of correlation was 0.998.

Figure 4 shows the R₂ values of the BANG polymer gels as a function of dose between 5.0˚C and 40˚C. The fitted straight line of the data collected at 0 Gy provided a gradient of −0.19˚C⁻¹∙s⁻¹ and an intercept of 8.10 s⁻¹, and fitting of the data collected at 20 Gy provided a gradient of −0.96˚C⁻¹∙s⁻¹ and an intercept of 47.45 s⁻¹. The coefficient of correlation of the 0 Gy data was 0.894 and that of the 20 Gy data was 0.991.

Figure 5 shows the R₁ values of the BANG polymer gels as a function of photon doses between 0 and 20 Gy. Each R₁ calibration curve was fit to a straight line for

doses below 20 Gy. Data points were obtained by averaging the R₁ values in the polymer gel. The fitted straight line for data collected at 20˚C had a gradient of 0.034 Gy⁻¹∙s⁻¹ and an intercept of 0.72 s⁻¹. The coefficient of correlation was 0.962.

Figure 6 shows the R₁ values of the BANG polymer gels as a function of dose between 5.0˚C and 40˚C. The fitted straight line of the data collected at 0 Gy had a gradient of −0.020˚C⁻¹∙s⁻¹ and an intercept of 1.12 s⁻¹, whereas the data collected at 20 Gy had a gradient of −0.029˚C⁻¹∙s⁻¹ and an intercept of 1.94 s⁻¹. The coefficient of correlation of the 0 Gy data was 0.925 and that of the 20 Gy data was 0.985.

The dose uncertainties (%) of R₁ and R₂ between 5˚C and 39˚C are shown in Table 1. An increase in temperature results in large dose uncertainties of R₁ and R₂. The temperature-related errors in dose are 8.3% for R₁ and 7.5% for R₂. The dose-related error of the dose response results of the gel is below 8% at temperatures below 20˚C.

Dose uncertainties (%).

Figure 7 shows the dose profile for PAGAT polymer gel on a planned RTPS of the oblique center line of the four-field box technique and planned data for comparison. The full width at half maximum (FWHM) of the GEL (20˚C), GEL (5˚C), and Plan (RTPS) curves were 57.48 mm, 55.22 mm and 58.48 mm, respectively. The dose-related error of the results obtained using the gel at irradiation doses over 2 Gy at 20˚C is 4.87% on average and the error at 5˚C is 5.18% on average.

The results confirmed dose R₁ and dose R₂ linearity between 0 to 20 Gy. The dose-R₂ gradient was steeper at low temperature, as reported previously [10] [11] . Dose-R₁ curves with respect to temperature have not previously been reported and were found to parallel the dose-R₂ gradient.

Dose gradient with temperature is less pronounced in the dose R₁ curves than in the dose R₂ curves and therefore the temperature dependence has less effect on dose R₁ linearity than on dose R₂ linearity. In contrast, the gradient of the R₁ dose linearity was 40 times smaller than that of the R₂ dose linearity. Furthermore, the overall standard deviation (SD) and coefficient of variation (calculated by dividing the R₂ or R₁ value by SD) of the R₁ images are larger than that of the R₂ images. The dose images obtained from the R₁ images included more noise when compared with the dose images obtained from the R₂ images. Therefore, the dose images obtained from the R₁ images were less precise compared with the dose images obtained from the R₂ images.

R₂ and R₁ are dependent on both the correlation time (τ_c) and the Larmor frequency (ω) from the Bloembergen-Purcell-Pound (BPP) relaxation theory [17] [18] [19] . τ_c of the gels shows an inverse correlation with their temperature: raising the temperature correspondingly decreases the τ_c of the gels. T₁ and T₂ are dependent on an inverse relationship with viscosity [17] . Here, I assumed that an increase in temperature decreased the viscosity of the gels. Therefore, the gel R₁ and R₂ values decreased as temperature increased, resulting in a larger τ_c, and the gradients (Figure 4 and Figure 5) changed gradually with temperature. The change in the gradients of the dose R₂ curves was assumed to depend on both the viscosity of the gels arising from the degree of polymerization and the temperature.

The dose profile is presented in Figure 7 and shows differences in the temperature dependence and a comparison of the dose profile obtained by gel dosimetry and the RTPS plan. The dose images obtained from the R₂ polymer gel data are precise regarding the process of conversion from the R₂ images to the dose image using the same temperature dose R₂ curve. Because the prepared gels melt at high temperature, it was difficult to maintain the inside of the gels at a constant temperature as required during scanning MRI. Although BANG gels have a high R₂ gradient, with changing temperature, they are less stable than PAGAT gels for the experiment to irradiated gels using RTPS. Methacrylic acid-based gel dosimeters such as BANG gel have the disadvantage of temperature dependency, in contrast to acrylic acid-based gel dosimeters such as PAGAT. BANG gels melt above 25˚C, while PAGAT gels melt at about 30˚C. At high and low temperatures, dose images were less precise and disagreed with the RTPS plan dose data. In this study, the dose-related error at irradiation doses over 2 Gy at 20˚C was less than the error at 5˚C.

The difference in the FWHM of the dose profiles between the gels at 20˚C and the RTPS plan dose data was 0.51 mm, whereas at 5˚C, the difference was 1.8 mm, despite the dose error of the dose response at low temperature being smaller than at high temperature, as shown in Table 1. The inhomogeneity related to the temperature of the irradiated gels in the containers may have caused the high dose error at low temperature. In addition, it is difficult to maintain a constant low temperature inside the gel phantom during MRI scanning and thus the temperature inhomogeneity inside the large phantom rose during exposure to the scanning RF pulse [20] . The temperature inhomogeneity resulting from RF exposure in a high field MRI scanner is large. Accordingly, dose evaluation using high field MRI scanning gives rise to data with large uncertainties. Dosimetric evaluation at MRI room temperature is required due to the stability of the scans during scanning MRI. Thus, it is necessary to maintain a constant at temperature inside the gels for precise measurements.

Future work will be aimed at clinical applications and will assess the temperature-related dose error using γ analysis, dose differences, and distance-to-agreement measurements.