A High-Resolution Ultrasonic Thermometer for Measuring Absorbed Dose in Water Calorimeters

We are testing a high-resolution ultrasonic thermometer with a noise floor at the μK level to improve the accuracy of radiation dosimetry methods that rely upon water calorimetry as a primary standard. Conventional water calorimeters, based upon the original design of Domen, detect temperature changes in irradiated water with thermistors that are sealed inside a thin sheath of glass. Recovering absorbed dose to water from these measurements requires the application of correction factors to compensate for the effects of self-heating of the thermistors, of excess heat induced in nonwater materials by the radiation, and of heat transfer due to dose gradients within the phantom. The ultrasonic approach dispenses with nonwater materials inside the water phantom, thereby eliminating or reducing sources of excess heat and the corresponding dose gradients. The prototype instrument, which involves a single ultrasonic transducer and an analog pulsed phase-locked loop, has been tested in Co, and initial measurements have yielded values of absorbed dose to water that are within 10 % of the nominal value, with a temperature sensitivity of 10 μK. A digital prototype of this instrument can improve temperature sensitivity by an order-of-magnitude and make practical two dimensional dose profiles in water by using tomographic reconstruction of multiple-channel ultrasonic projections. Introduction The presently accepted primary standard for absorbed dose to water for medical radiation dosimetry is by accurate measurement of temperature rise in a Domen-type water calorimeter [1]. The Domen design, with two thermistor probes inside a sealed glass vessel mounted within a large water phantom, exhibits heat conduction and, in some cases, convection effects due to the nonwater materials. Mitigating the impact of these effects on accurate dose determinations generally entails extensive computation of correction factors and experimental modifications – e.g., refrigerating the phantom to 4 C to eliminate convection – that can be bulky and expensive. Because of the small temperature rise induced by therapy level radiations (0.24 mK/Gy at room temperature), few other temperature sensing techniques apart from thermistors can provide the microkelvin sensitivity needed for the dose measurement. We have been investigating an alternative temperature sensing approach based on a noninvasive high-resolution ultrasonic technique through a National Institute of Standards and Technology (NIST) Small Business Innovation Research (SBIR) project [2]. A pulsed phase-locked loop (PPLL) technology is the driving mechanism for detecting small changes in ultrasound speed in water caused by the change in temperature as small as a few μK. The first two versions of the prototype instruments have been tested in a Co radiation field at NIST for temperature response, signal to noise, and problems associated with convection in a large water phantom with temperature gradients. Methods and materials The principle of operation of the ultrasonic thermometer is based on an empirical quadratic relationship between the speed of sound and the temperature in water at constant atmospheric pressure, v = v0 + a(T-T0) + b(T-T0), where v0 is the speed of sound in water at temperature T0. A transducer sends out a low power (estimated upper limit of power absorbed by water ≈ 4.5 μW out of the estimated 70 μW input to the transducer), compared to 25 μW produced by thermistor) ultrasound wavepacket with a mean frequency f0 = 5 MHz that traverses the water at an average speed that depends on water temperature. The width of the cross section of the sound wave is about 1 cm. The transmitted wavepacket then reflects off the opposite wall in the phantom and is measured by the same transducer at the point of origin. Thus, changes in water temperature manifest as changes in the time of flight, which are registered by comparison to a reference waveform in the instrument. The analog version of this instrument effects the comparison by adjusting the frequency of the reference waveform to achieve phase matching with the delayed wavepacket, thereby converting temperature-induced changes in the speed of sound into changes of frequency (for small changes, the two are proportional). The digital version, to be incorporated in the next prototype, is able to measure these changes in time of flight directly without adjusting the frequency. The effect of thermal expansion of the phantom wall is determined to be negligible for this study. As noted, the deviation, Δf, from the original frequency f0 is linearly proportional to the change of the sound speed Δv, which depends quadratically on temperature. This relationship is written as ΔT = α(f,T)Δf, where α can be experimentally calibrated and is typically about 95.5 μK/Hz for f0 = 5 MHz at 20 ̊C, where the speed of sound is 1482 m/s. Given that the frequency measurement can be resolved to 0.01 Hz or better, such as in a temperature-stabilized experiment, the temperature resolution therefore should be on the order of μK. A root-mean-square (RMS) noise of 3.2 μK has been measured in a (30x30x30) cm water tank by averaging over 400 s at a sampling rate of 4 per second. By comparison, the traditional set-up, involving two 10 kΩ thermistors (size usually less than 1 mm) in a Wheatstone bridge with a lock-in detection scheme, has an root-meansquared noise in the output voltage of 50 nV with our measurement parameters, or about 3 μK. Therefore, the ultrasound technique should be comparable to the thermistor technique in terms of the measurement resolution in temperature. Results and Discussion Initial tests of a smaller prototype made with a (7.6x7.6x7.6) cm water tank, using an incandescent light source periodically pulsed at 30 s and 40 s intervals for two hours, show that the system responded adequately. The recorded data were analyzed using a frequency-domain technique developed for water calorimetry [3], and show a temperature rise at a rate equivalent to a radiation dose rate of 5 Gy/min (2 % 1σ). The system was then tested in a Co radiation field yielding a measured value of 1.8 Gy/min (3 % 1σ) over 30 cycles of periodic excitation of 60 s on/off radiation exposures [4]. This, however, is about 9 % higher than the nominal dose rate of 1.65 Gy/min estimated for the geometry used. The statistical uncertainty corresponds to 13 μK for a temperature rise of 430 μK. The discrepancy might be attributed to the small tank size and the uncertainties in the calibration procedures. A larger water tank, (30x30x30) cm, conforming to the standard calibration protocol for medical dosimetry [5], has subsequently been constructed, and an improved calibration method has been implemented. The typical operational parameters are listed in Table 1. The new calibration method calculates α by directly measuring the speed of sound at a given time rather than relying on external temperature sensors. The transducer was mounted 7 cm below water surface. Table 1. Operational parameters for the NIST ultrasound temperature measurement system. f0 Ultrasound detection frequency 5x10 Hz T0 Ultrasound period 0.2 μs L Nominal length of ultrasound path 60 cm Δt Time delay for a round trip in the water tank 0.4 ms Reference pulse rate 6000 Hz Reference pulse width (number of cycles at T0 period) 12 Measurements performed with the larger tank showed evidence of convection, manifested as oscillations after a single shot of radiation even at very low dose rate (Fig. 1). The “natural” period of this oscillation is about 300 s, and it remains visible for almost an hour. The theoretical estimate of this phenomenon is under investigation, but is believed to give a value with the correct order of magnitude for this system. Fig.1 Observed convection in the large water phantom by ultrasound temperature measurements. The shutter opens for 60 s, the temperature rises initially, then enters into oscillations after the shutter closes. Fig. 2. Measured dose rate using ultrasound as a function of radiation shutter period. The estimated nominal dose rate of 4.5 mGy/s is plotted for comparison In spite of the observed convection-related interference, a series of measurements was carried out using modulated irradiations to evaluate the feasibility of dose determination under controlled conditions. The shutter periods were varied from 60 s to 960 s (50 % duty cycle) at 30 cycles each. Frequency-domain analysis was applied to each data set to obtain estimates of a temperature rise and dose rate. The results are plotted in Fig. 2 where a nominal dose rate (estimated based on geometry including the distance and beam width) of 4.5 mGy/s is also shown. The dependence on irradiation time is similar to our previous observation of thermistor measurements that has a maximum and then significantly drops at longer irradiation times [6]. There we have been able to interpret the behavior as a consequence of heat conduction inside the glass vessel that is enhanced at longer irradiation times by the effect of stirring the water outside the vessel. Although stirring is not employed here (because of acoustical noise), natural convection induced by radiation within the phantom is having a similar influence on temperature measurements. Fig. 3. (a) Simultaneous recording of time domain temperature data with the ultrasonic detector and a thermistor, placed at 10 cm and 5 cm below the water surface, respectively. (b) Enlargement of a given time interval showing radiation on/off of 180 s cycles and the response from the thermistor (larger amplitude) and the ultrasound. (c) Frequency spectrum of the sound data showing peaks corresponding to the radiation modulation frequency and the odd harmonics. The vertical scale is the amplitude of the Fourier Transform. (d) The same as (c) but for the thermistor data. The first even harmonic is visible as a sign of convection (see text for more discussions). To gain a better understanding of the effect of conduction and convection, simultaneous measurements with the ultrasound and a thermistor were performed and analyzed with the frequency-domain technique. The ultrasound transducer was mounted on the NIST water calorimeter phantom at 10 cm below water surface. In the first set of measurements, a submersible thermistor (not in a sealed glass core) was mounted 5 cm below water surface, near the center of the 10 cm x 10 cm radiation field. Simultaneous recording of sound and thermistor data for a series of radiation on/off sequences is carried out for about 65 hours. The overall drifts in temperature measured by both methods track each other (the thermistor data is offset by a constant to match the initial temperature by ultrasound), shown in Fig.3 (a). During this time, a continuous 240 cycles of 180 s on/180s off cycles of radiation were delivered. Figure 3 (b) shows 2 hours worth of the data (with the linear rising trend removed) representing the temperature change as measured by ultrasound and by the thermistor. As expected, the temperature change measured by the ultrasound is smaller than that by the thermistor because the sound signal is averaged over the entire 30 cm of path, of which only 1/3 is heated, whereas the thermistor measures one point at the center. In addition, the depth-dose curve of Co radiation in water indicates that the dose rate at 10 cm below the water surface is 25 % lower than that at 5 cm due to attenuation by the water volume above. Frequency-domain analysis that measures the tone amplitude of the peak at the fundamental frequency of 2.783 mHz (inverse of 360 s period) averaged over the entire time domain waveform indicates a temperature rise of 0.38 mK (2.6 % 1σ) and 1.58 mK (0.7% 1σ) per radiation cycle from the sound and thermistor data, respectively. The ratio of the amplitudes is comparable to the expected value. A very interesting observation in the frequency domain is the emergence of the small peaks corresponding to even harmonics of the fundamental frequency. Even harmonics are normally absent for a square wave excitation such as the radiation produced by the period modulation of the shutter. This has first been observed in a separate experiment where modulated electrical heating is used to induce convection that produces a signature of even harmonics in the frequency domain [7] and has been confirmed by finite-element modeling, and is understood as a coupling term in the heat equation involving the velocity field and the temperature gradient [8]. The next set of measurements was performed with the thermistor in the same depth as the ultrasound path, 10 cm below water surface, but out of the path itself laterally. To obtain dependence of measured dose rate on shutter opening time, we varied the modulated shutter opening times from 60 s to 3600 s, again with the sound and thermistor data being recorded simultaneously. The dose rates obtained from frequency-domain analysis as a function of shutter opening time are plotted in Fig. 4. Similar to the past results obtained from using the standard practice of sealing thermistors inside a small vessel [6], the feature of a sudden drop off after a maximum is observed here, but now is sharper, possibly due to the more convection cooling that directly affects the thermistor in open water than in a closed vessel. Frequency-domain analyses indicate an observable onset of convection starting at 240 s. Qualitatively, the thermistor and sound data track each other, and at longer shutter opening times they reach the same asymptote, suggesting some state of equilibrium is approached. Finally, we show in Fig. 5 a set of measurements with two thermistors sealed inside of a vessel 5 cm below the surface as in the standard Domen geometry, with the sound path remaining at 10 cm. The thermistor results are now similar to the earlier studies [3,6,9], with a relatively less prominent maximum, and convection much suppressed. Fig. 4. Measured dose rate as a function of shutter opening times from ultrasound and the thermistor, both located 10 cm below water surface. The nominal dose rate is approximately 0.015 Gy/s at the measurement position. Fig.5. Measured dose rate with two thermistors sealed inside a vessel in the standard Domen geometry at 5 cm below water surface and 1 m from the source, with the ultrasound path remaining 10 cm below surface. The nominal dose rate is plotted for reference. Tomographic reconstruction of 2D temperature profiles in water The μK sensitivity and rapid response to small temperature rises in water lead to the possibility of mapping of spatial distribution with the ultrasonic technique. The output of a single-channel ultrasonic thermometer is proportional to the average temperature change along a straight line representing the wave trajectory in the absence of refraction or scattering. In this way our measurement system behaves similarly to the medical x-ray Computed Tomography (CT) systems that record integral attenuation of x rays along the straight lines they travel in a human tissue. We have assembled and tested a laboratory thermal imaging system with 128-element circular ultrasonic array; each element consists of a Polyvinylidene Fluoride (PVDF) transducer custom bonded to an acoustic lens [10]. In one test, a 385 W incandescent light source mounted over the center of the water tank was turned on for 30 s. The tomographic experiment involved 64 projections, 45 rays per projection, resulting in 2880 ultrasonic waveforms (90 MB of data) that were acquired and stored every 4 seconds. From each of these 4 s data set we reconstructed a 2D temperature profile of a (230x 230) mm region using digital phase detection software. Figure 6 shows a reconstruction of the temperature profile after 30 s of heating. The area in the center represents the hottest (within 0.003 K) spot in the tank. This result demonstrates the ability for quantitative measurements of temperature change in the sub-mK range with a spatial resolution of several millimeters. Summary We have experimentally evaluated an ultrasound thermometer for radiation dose determination in conjunction with water calorimetry. The change of the ultrasound speed is a function of the average of the temperature of the entire water path the sound waves traverse, whereas the thermistor measures one point in space. The preliminary measurements show that the frequency-domain technique developed for thermistor-based detections can be readily applied to the ultrasound technique to obtain a dose value at long radiation times. However, convection in an open water tank under radiation heating poses the same problem, which is the original reason for using a convection barrier for the thermistor based calorimeters. The frequency-domain technique allows us to observe the onset of convection by monitoring the emergence of even harmonics. For the ultrasound thermometer to be useful as a dosimetry tool, the convection issue must be addressed. The preliminary study here serves as a basis for understanding and perhaps controlling convection under modulated conditions. In addition, the preliminary results using arrays of transducers for tomographic reconstruction demonstrate feasibilities for rapid two to three dimensional dose mapping in water.