Building a graphite calorimetry system for the dosimetry of therapeutic X-ray beams
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Building a graphite calorimetry system for the dosimetry of therapeutic X-ray beams. The noise level of the temperature measurement system was approximately 0.08 mK (peak to peak). The temperature of the core part rose by approximately 8.6 mK at 800 MU (monitor unit) for 6-MV Xray beams, and it increased as X-ray energy increased. The temperature rise showed less spread when it was normalized to the accumulated charge, as measured by an external monitoring chamber.
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Building a graphite calorimetry system for the dosimetry of therapeutic X-ray beams. The noise level of the temperature measurement system was approximately 0.08 mK (peak to peak). The temperature of the core part rose by approximately 8.6 mK at 800 MU (monitor unit) for 6-MV Xray beams, and it increased as X-ray energy increased. The temperature rise showed less spread when it was normalized to the accumulated charge, as measured by an external monitoring chamber..
N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6 811
temperature than is the case for water at the same absorbed
dose. Another is that graphite has no thermal [8,9].
The sensitive volume or sensitive medium of a graphite
calorimeter is called a core. Thermal isolation of the core from
the environment is very important because the temperature
at the core increases by only a few milliKelvins when a
graphite calorimeter is irradiated by therapeutic X-rays. Thus,
the core is usually covered with many layers of jackets in
vacuum. In the core, there are one or more thermometers and
heaters. The thermometer(s) is needed to measure the tem-
perature rise of the core at irradiation. The heater(s) is needed
for the calibration of the temperature rise to the energy
absorbed in the core. The calibration is performed by
comparing the temperature rise at irradiation to the temper-
ature rise caused by known amounts of electric heat or energy.
Thermistors, or resistive thermometers, are used for tem- Fig. 1 e Schematic layout of the graphite calorimeter core
perature measurements at the core as well as for heating. (C1505-4).
Thermistors have poor linearity and poor stability; however,
they have sensitivity to temperature and are not affected by
irradiation up to megaGrays . In addition, thermistors are
available in very small sizes, which is helpful for minimizing
impurities in the core.
resistances of 20 kU at room temperature; they contained
To ensure the repeatable measurement of the core tem-
nickel alloy lead wires (0.101 mm thick). Hollow Kapton tubes
perature, the calorimeter must run under a quasi-adiabatic
were used to support the core. Epoxy resin was used to glue all
condition [11,12]. Under this condition, thermal transfer
of the components of the core together. During the integration
from the core to the inner jacket is kept nearly constant, and
of the core, the core was weighed at each step to detect im-
the temperature rise at the core is always proportional to the
purities (nongraphite ingredients). The jackets were prepared
energy absorbed during its runs. A French group recently
in the same manner as the core, but they were not weighed.
achieved this condition by introducing thermal feedback
The inner surfaces of the jackets were lined with thin alumi-
[13,14] to the inner jacket. In this study, a similar type of
nized Mylar foils to reduce radiative heat transfer. The outer
thermal feedback was developed and applied to achieve this
jacket used a Manganin wire (LakeShore, OH, U.S.A.) (diam.:
0.202 mm) as a heater, instead of using thermistors.
In this study, a graphite calorimetry system was built to
After all parts were built, the thermistors were calibrated
measure the high energy X-ray absorbed dose. Experiments
for temperature in a high precision water bath (7008, Fluke).
were performed to investigate system properties, and the re-
The parts were separately placed in thin and watertight
sults are discussed. In Section 4, the uncertainties of some
polyethylene bags (100 mm thick) and placed in the water bath.
values are given, but details are not provided as to how they
The temperature of the bath was measured using an SPRT
were evaluated, because that is outside the scope of this
(Standard Platinum Resistor Thermometer, 5187SA, Tinsley).
The resistance of the thermistors and the SPRT was read using
a high precision half-bridge (1595A, Fluke). Calibration was
2. Materials and methods performed within a range of 20e30 C at each degree Celsius.
2.1. Apparatus 2.1.2. Electronics and external monitoring chambers
Wheatstone bridges were built to measure the temperature of
2.1.1. Building graphite calorimeter the core and of the inner jacket. High precision standard re-
The graphite calorimeter (C1505-4) adopted a pan-shaped sistors and decade resistors were used to build the bridges. A
vacuum housing and double-layered jackets as in the design high precision voltage calibration source (3350A, Transmille)
of the GR9 of the French group . The core was covered with was used to supply the excitation voltage to the bridges.
two layers of jackets and graphite mediums, and then placed Nanovoltmeters (34420A; Agilent, CA, U.S.A.) were used to
in a vacuum housing and a graphite phantom. All of the read the voltage difference across gaps in the bridges.
graphite parts were composed of a batch product of high- An electric heating and power measurement circuit was
density pyrolytic graphite (M507; Morgan Korea, Daegu, built, as shown in Fig. 2. In the figure, Vx represents the voltage
South Korea), whose density was separately determined to be drop across the heating thermistor of the core. Rs and Vs
(1.8154 ± 0.0014) g/cm3. represent the resistance of a standard resistor and the voltage
The core was 16 mm in diameter and was 3 mm thick, with drop across the resistor, respectively. Then, the electric power
three sensing thermistors, one heating thermistor and three dissipated at the heating thermistor, Px, is given as Px ¼ VxVs/
supports, as shown in Fig. 1. NTC-type thermistors with micro Rs. Electric power was fed by a multichannel dc power supply
glass beads (diam.: 0.3 mm) were used (AB6B4-BR11KA103; GE (2230-30-1, Keithley) to the heating thermistor. A precision
Measurement & Control, U.S.A.). The thermistors had resistor (SRL-10k; IET Labs., MA, U.S.A.) was used as the Rs; its
812 N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6
core and the inner jacket from the bridges, and used thermal
feedback to control the temperature difference. The second
module interfaced with the electric heating and power mea-
surement circuit so that the circuit could control the electric
power fed to the core and measure it. The third module
interfaced with the external monitoring chamber system to
read the accumulated electric charge of the ionizing current.
Through the platform, all data points were acquired every
0.6 s. The temperature of the outer jacket was controlled
separately using a standalone-type automatic temperature
controller (350, Lakeshore).
A temperature analysis tool was coded using Mathematica
9.0.1. When it opened a file of the measured temperature data,
Fig. 2 e Diagram of a circuit for electric heating of the core
it automatically found heating events (irradiation or electric
and for measurement of electric power.
heating) and analyzed the magnitude of the temperature rise.
This tool used the interpolation function, provided by Math-
ematica 9.0.1, to enhance the capability of finding heating
events. Heating events were easily recognized from the time
resistance was 9,999.2 ± 0.3 U. The voltage drop across the Rs derivative plot of interpolated points of the temperature data.
and the heating thermistor was measured by two nano- The magnitude of the temperature rise was determined by
voltmeters (34420A, Agilent), whose calibration coefficients linearly fitting the points, as shown in Fig. 3. The analysis was
were 1.00005 ± 0.00002 and 1.00001 ± 0.00002. automatically performed, but required a manual input for
An external monitoring chamber system consisted of a set initialization; this input was a roughly estimated value of the
of two thimble-type ion chambers (0.53 cm3) and a high pre- time width, that is, the period of events heating the calorim-
cision electrometer. The chambers (Exradin A2, Standard eter by electric power or irradiation.
Imaging) were held at 660 mm from the target, between the
multileaf collimators and the calorimeter, and were separated
by 125 mm in the cross-line direction. For the sake of buildup, 2.2. Experiments
the chambers were covered with high density pyrolytic
graphite cylinders (inner diam.: 12.8 mm; outer dia.: 25 mm), 2.2.1. Experimental set
and connected in parallel to the electrometer (6517B, Keith- The calorimeter was mounted on a precision stage. The stage
ley). Bias voltage at e300 V was applied to the ion chambers. was moved so that the center of the core was placed 1,000 mm
The room temperature and pressure were also measured to from the target of the accelerator; this accelerator was an
correct their effects on the ionization current measurement. Elekta Synergy Platform (Elekta, Stockholm, Sweden). The
calorimeter was covered with graphite slabs, which made the
2.1.3. Calorimeter operation and temperature analysis mass thickness of graphite from the entrance of X-ray beams
An operation platform was built using the LabVIEW program to the center of the core equal to approximately 10 g/cm2.
(National Instruments, TX, U.S.A.). The platform consisted of The mass thickness was separately determined to be
three modules. The first module read the temperature of the (9.951 ± 0.008) g/cm2.
Fig. 3 e Temperature rise analysis at the core.
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The temperature of the outer jacket was maintained at 26 C.
Table 1 e Measured mass of the core components (C1505-4).
The Wheatstone bridges were activated at 0.8 V, and the heater
Value (g) ustd (g) urel (%) Mass fraction thermistor of the inner jacket was also activated at 1.0 V to
Graphite disk 1.098188 0.000006 0.0005 0.9952 warm it up. When the temperatures of the core and the jackets
Supports (Kapton) 0.000763 0.000002 0.20 0.0007 were equilibrated, the temperature difference between the core
Thermistor beads 0.001748 0.000060 3.4 0.0016 and the inner jacket was set (at approximately 21 mK), and the
Thermistor lead wires 0.001826 0.000086 4.7 0.0017
thermal feedback was turned on. Then, the calorimeter was
Glue (Epoxy) 0.000943 0.000002 0.17 0.0009
prepared for operation in the quasi-adiabatic mode.
Total 1.10347 0.00011 0.0095 1
2.2.2. Electric heating and irradiation
The calorimeter’s response to the electric energy dissipation
Table 2 e Estimation of heat capacity of the core (C1505-4) to the core was investigated. Electric energy was fed to the
based on the measured mass of components. core for 140e172 s within a range of 6e8 mJ.
Specific heat Heat capacity The calorimeter was irradiated at 800 monitor units (MU)
Value ustd Value ustd using 6-MV, 10-MV, and 18-MV X-rays at 300 MU/min, 410 MU/
(J/kg/K) (J/kg/K) (J/K) (J/K) min, and 350 MU/min, respectively. It took approximately
140e172 s to complete an irradiation of 800 MU for each X-ray
Graphite  disk 706.9 0.6 0.7763 0.0007
Supports (Kapton)  1,090 e 0.0008 e beam. Prior to or between every irradiation, electric heat was
Thermistor beads  600 200 0.0010 0.0004 also provided to the core to compare the core’s response to
Thermistor lead wires  900 200 0.0016 0.0004 irradiation and to electric heating
Glue (Epoxy)  1.800 300 0.0017 0.0003
Total e 0.7815 0.0009
3. Results and discussion
Table 3 e Results of thermistor temperature calibration.
The measured mass values of the core components are shown
Parameters in Table 1. The total mass values of the core and its impurities
A (10e6) B (10e6) C (10e9) were 1.10347 ± 0.00011 g and 0.00528 ± 0.00011 g, respectively.
Core (C1505-4) 440 ± 11 247.9 ± 1.5 108.5 ± 4.0 Thus, the portion of the core that consisted of impurities was
Inner jacket 332.8 ± 7.8 253.9 ± 1.0 90.3 ± 2.7 0.48%, which was as good as the number reported by the
Outer jacket 516.9 ± 1.0 253.38 ± 0.14 98.89 ± 0.42 French group (GR-09, 0.59%; GR-10, 0.90%; GR-11, 0.35%) [14,15]
Here, Te1 ¼ A þ B ln(R) þ C (ln(R))3, or by the Japanese group (1.5%) . Based on the measured
where T is temperature given in K and R is resistance given in U. mass of the core components, the heat capacity of the core
was expected to be as shown in Table 2. According to the
Fig. 4 e Measured temperature change of the core (T_core) and the inner jacket (T_jac).
814 N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6
measured mass and the known values of specific heat, the uncertainty of the temperature measurement (>0.9%), the
core heat capacity was estimated to be 0.7815 ± 0.0009 J/K. ambiguity of the cited specific heat values or thermal loss
Thermistors were calibrated to temperature by applying from the core to the inner jacket.
the SteineHart model equation , as shown in Table 3. The The intercept (0.056 mK) of the fit was not ignorable
uncertainty of the fitting parameters for the core was slightly compared with its uncertainty (0.023 mK), but it was suffi-
large. According to the error propagation equation, the un- ciently small compared with the noise level (0.08 mK). Thus, it
certainty of the temperature rise by 10 mK at 26 C was ex- was determined that the intercept could be ignored for the
pected to be 0.9%. Furthermore, it is known that Wheatstone calibration of the temperature rise to the energy absorbed in
bridges with DC excitation voltage are not very stable , the core. So, the effective heat capacity of the core was ob-
which means that the uncertainty of the absolute value of the tained at every run as the ratio of electric energy dissipation to
temperature rise will be larger than 0.9%. the temperature rise. The coefficient of variance of the effec-
The temperature of the core and the inner jacket rose, as tive heat capacity was approximately 0.2%, which was mainly
shown in Fig. 4, under irradiation and electric heating. The attributable to the uncertainty of the determination of the
noise level at the Wheatstone bridge was about 0.3 mVpp (peak electric energy dissipated in the core.
to peak), which corresponded to approximately 0.08 mK in Under irradiation, the temperature rise of the core showed
temperature. The core temperature rose by approximately good correlation with the accumulated charge of the external
8.6 mK at 800 MU for 6-MV X-ray beams; core temperature
increased as X-ray energy increased. It was possible to very
accurately measure the electric power dissipated in the core
(ustd ¼ 0.015%) because of the small uncertainties of the
resistance and of the voltmeters. However, owing to the poor
time resolution of the data sampling (0.6 s), it was expected
that the amount of electric energy dissipated might have a
larger spread. Assuming a uniform distribution, uncertainty of
time might be 0.35 (¼0.6/√3) s, which would cause the
determined electric energy to spread by 0.2%.
The calorimeter’s response to the electric energy dissipa-
tion at the core is shown in Fig. 5. It was very linear, within
6e8 mJ (R2 ¼ 0.9997), with a slope of 1.242 ± 0.003 K/J. The in-
verse of the slope (0.805 J/K) corresponded to the effective heat
capacity of the core, but it was larger by 3% than the heat
capacity, which was expected according to the data shown in
Table 2. This discrepancy might be attributable to the
Fig. 6 e Correlation between temperature rise of the core
Fig. 5 e Plot of core temperature rise according to electric and accumulated charged of the external monitor chamber
energy dissipation. at 6-, 10-, 18-MV X-ray beams.
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monitoring chamber. If the internal monitoring chamber of rise of the core should be normalized to the accumulated
the accelerator had been sufficiently accurate to monitor the charge of the external monitoring chamber. Also, the co-
X-ray beams, the temperature rise of the core should have efficients of variance of the temperature rise were around
shown no correlation with the accumulated charge of the 0.2% or 0.3%, but dropped by approximately 0.1% when they
external monitoring chamber, because all irradiation was were normalized to the accumulated charge of the external
performed at 800 MU. However, the measured temperature monitoring chamber. The measured temperature rise
rise showed obvious correlations for the 6-MV and 10-MV X- normalized to the external monitoring chamber (hereafter
ray beams, as shown in Fig. 6. Even at 18 MV, the data points, called “the normalized temperature rise”) was as shown in
except those measured on June 30, 2016 still showed good Fig. 7.
correlation. The reason for the anomaly that surfaced on June The amount of radiation energy absorbed by the core was
30 is not understood yet, but will be further investigated. In determined by taking the product of the normalized tempera-
any case, the overall correlation coefficients at 6 MV, 10 MV, ture rise and the effective heat capacity. The results are as
and 18 MV (excepting the abnormal data points) were 0.64, shown in Fig. 8. The mean energy absorbed by the core had
0.94, and 0.47, respectively. Thus, it was convincingly values of 0.798 J/mC, 0.389 J/mC, and 0.352 J/mC at 6 MV, 10 MV, and
demonstrated that, to achieve better data, the temperature 18 MV, respectively. These values were so consistent among
runs that their coefficient of variance was less than 0.15%.
Fig. 7 e Measured temperature rise of the core by
irradiation. The temperature rise was normalized to Fig. 8 e Determined energy absorbed by the core under
accumulated charge of the external monitoring chamber. irradiation at 800 MU. Error bars represent standard error.
816 N u c l e a r E n g i n e e r i n g a n d T e c h n o l o g y 4 9 ( 2 0 1 7 ) 8 1 0 e8 1 6
4. Conclusion references
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