Clinical trials of hypothermic brain treatment for newborn babies are currently hindered by the difficulty in measuring deep brain temperatures. As one of the possible methods for noninvasive and continuous temperature monitoring that is completely passive and inherently safe is passive microwave radiometry (MWR). We have developed a five-band microwave radiometer system with a single dual-polarized, rectangular waveguide antenna operating within the 1–4 GHz range and a method for retrieving the temperature profile from five radiometric brightness temperatures. This paper addresses (1) the temperature calibration for five microwave receivers, (2) the measurement experiment using a phantom model that mimics the temperature profile in a newborn baby, and (3) the feasibility for noninvasive monitoring of deep brain temperatures. Temperature resolutions were 0.103, 0.129, 0.138, 0.105 and 0.111 K for 1.2, 1.65, 2.3, 3.0 and 3.6 GHz receivers, respectively. The precision of temperature estimation (2σ confidence interval) was about 0.7°C at a 5-cm depth from the phantom surface. Accuracy, which is the difference between the estimated temperature using this system and the measured temperature by a thermocouple at a depth of 5 cm, was about 2°C. The current result is not satisfactory for clinical application because the clinical requirement for accuracy must be better than 1°C for both precision and accuracy at a depth of 5 cm. Since a couple of possible causes for this inaccuracy have been identified, we believe that the system can take a step closer to the clinical application of MWR for hypothermic rescue treatment.
 Moderate cooling of the brain after hypoxia-ischemia has been shown to reduce neonatal mortality and improves neurological function after asphyxia [Azzopardi et al., 1999; Eicher et al., 2005; Perlman and Shah, 2009; Perrone et al., 2010]. However, individual studies do not necessarily provide unequivocal evidence of the benefit from hypothermic therapy [Jacobs et al., 2003; Edwards et al., 2010]. A major cause of this situation thus far is that no one can monitor the deep brain temperature during hypothermic rescue therapy. There is little data available on the temperature distribution and/or absolute temperature in the deep region of a neonate's brain. Successful clinical application of brain cooling, as a matter of course, requires that deep brain temperatures be adequately monitored during treatment. As an invasive measurement of infant brain temperature cannot be justified for ethical reasons, there is a requirement for noninvasive monitoring of brain temperature in infants, with accuracy better than one degree centigrade [Hand et al., 2001]. In addition, the measurement should be available over prolonged periods for mild hypothermia, being maintained for periods of several hours to a couple of days.
 Magnetic resonance thermometry (MR thermometry) has been used for noninvasive temperature sensing [Childs et al., 2007; Corbett et al., 1995; Karaszewski et al., 2006; Rieke and Pauly, 2008; Weis et al., 2009]. MR thermometry can also provide information about biological structure. Although reliable temperature measurements in fat and in the presence of motion as well as absolute temperature quantification remain to be anticipated technologies, MR thermometry is promising for various medical applications in the near future. However, at present, this method requires access to complex equipment and/or complicated calculations and is not suitable for routine measurement over a prolonged period of time at bedside. Alternative bloodless methods for core temperature monitoring are oral, ear-based, temporal artery, and rectal temperature measurement, but all have their strong and weak points. Ear-based measurement is least accurate and precise [Lawson et al., 2007], brain temperature at any moment can not be predicted from rectal temperature [Childs et al., 2005] while intubation and diaphoresis affect oral and temporal artery temperatures, respectively [Lawson et al., 2007].
 A possible alternative approach for noninvasive temperature monitoring that is completely passive and inherently safe is microwave radiometry (MWR). MWR has been used as temperature sensing technique in various medical applications [Arunachalam et al., 2008; Lee et al., 2004; Leroy et al., 1998; Toutouzas et al., 2011]. However, retrieving absolute deep brain temperatures from a limited number of brightness temperatures is a tough challenge. The present authors have shown that a feasible solution is the use of multiple frequency MWR [Maruyama et al., 2000; Hand et al., 2001] and reported a temperature retrieving algorithm which uses a priori knowledge of the temperature profile in an infant's head [Sugiura et al., 2010], but a systematic measurement experiment has not been conducted all this time.
 In this paper, we describe a phantom experiment with a five-band microwave radiometer system, a water-bath and agar to evaluate the current feasibility as noninvasive thermometry for use with infants. A brief overview of the hardware developed using commercially available microwave components and the temperature retrieval process is also presented. We use degrees centigrade (°C) for physical temperatures and Kelvin (K) for radiometric temperatures.
2. Five-Band Microwave Radiometer System
2.1. System Configuration
 A simplified block diagram of the system is shown in Figure 1. The multi-frequency microwave radiometer system consists of a single dual-polarized, rectangular waveguide antenna filled with highly permitive (ɛr = 60), low loss material (tanδ < 0.001), a cable to transmit extremely weak thermal radiation to the radiometer, five Dicke radiometers (center frequencies: 1.2, 1.65, 2.3, 3.0, 3.6 GHz, 0.4 GHz bandwidth each) operating in the radiation balance mode [Lüdeke et al., 1978], and two lock-in amplifiers. Antenna aperture size was 2.1 × 2.7 cm2. Each receiver has a reference noise source (RNS) with a Peltier device and a platinum thermometer. Details of the system configuration and operation are described elsewhere [Maruyama et al., 2000].
2.2. Radiation Balance Mode
 Radiation balance mode provides insensitivity to the gain variations of each receiver and compensates for power reflections at the tissue/antenna interface, enabling the brightness temperatures to be determined independently of the reflection coefficients. Figure 2 shows the power flow in the radiation balance mode. Incident thermal radiation on the antenna is fed to the Dicke switch and modulated at a rate of 1 kHz square wave. When the switch is closed, the thermal power from biological object (Pobj,i) and that from RNS (PRNS,i) are fed to the receiver, and given by
where Ri is the reflection coefficient at the tissue/antenna interface at frequency fi. When the switch is open, the thermal noise power from RNS is fed to the receiver, and given by
where the reflection coefficient at the switch is assumed to be 1. The input polarity of the lock-in amplifier was changed at 1 kHz, plus or minus according to on or off of the switch, and thus the total output of the amplifier (Vo) is given by
Computer adjusts the RNS temperature so that Vo reduces to zero, and then Pobj,i = PRNS,i. Since the thermal noise power for frequencies in microwave band is proportional to a source temperature [Ulaby, 1981], the brightness temperature of an object (TB,obj,i) can be obtained as the physical temperature of RNS (TRNS,i) without a clear knowledge of Ri.
2.3. Temperature Retrieving Process
 The thermal radiation power emitted by tissue is proportional to the absolute temperature and radiometric weighting function [Maruyama et al., 2000]. Since the 3-D temperature field in the head under external cooling can be approximated by isomorphic, iso-temperature shells and WFs have significant values only in a limited region near the antenna aperture [Abe et al., 1995], the temperature profile and WFs can be expressed as a function of z, where z is the distance from the surface along the axis of the antenna field of view with its origin zero at the bolus-head surface. The measured brightness temperature TB,meas,i (= TB,RNS,i) is thus expressed as
where T(z) is the absolute temperature in dz located at z, Wi(z) is the radiometric weighting function (WF) along the z-axis, Ri is the reflection coefficient at the antenna/bolus interface, i denotes the frequency fi. Wi(z) can be obtained from SAR calculation based on the antenna reciprocal theory [Mizushina et al., 1993].
 Our task is to find T(z) from a set of radiometric measurement data TB,meas,i and the weighting functions Wi(z)/(1 − Ri). This is a typical inverse problem to which the existence of a unique and stable solution is not guaranteed. To alleviate this difficult situation, a functional form for temperature distribution in an infant's head [Leeuwen et al., 2000] was introduced as a priori knowledge as a shape function (SF). One dimensional temperature profile can be expressed as
where T0 is the surface temperature, DT the magnitude of temperature elevation above T0, and SF(z) the shape function of profile with ∣SF(z)∣max = 1 [Sugiura et al., 2010]. The unknown parameter DT in (5) can be determined by fitting the model to radiometric measurements. This is achieved by finding DT that minimizes the error function,
where n is the number of radiometric channels (n = 5 in our system). We obtain an estimated profile by substituting DT into (5). Since MWR measures thermal noise, the radiometric measurement data fluctuate randomly, and so do the estimated profiles. A method for evaluating the performance of MWR is thus very important [Racette and Lang, 2005]. We estimated the propagation of random fluctuations from the data to the profile by a Monte Carlo technique, and the average temperature with standard deviations (2-σ interval) at each depth from the surface was finally presented as the estimated profile by MWR [Sugiura et al., 2010]. The 2-σ interval is defined as a precision or confidence interval of the measurement.
2.4. System Calibration
 Prior to the measurement, MWR was calibrated by measuring the brightness temperature of a water-bath which was stirred to maintain a uniform temperature, TW. The water temperature was elevated gradually (0.07°C/min) so that there was enough time to reach a zero balance between the water and RNS brightness temperatures. The integration time of lock-in amplifiers was 5–10 seconds. Figure 3a shows a result for a 1.2 GHz receiver. A regression or calibration line was drawn through a series of balanced points on a graph and a standard deviation of the points was defined as a temperature resolution of the receiver. Figure 3b shows the calibration results of five receivers which resulted in five different straight lines. Temperature resolutions thus obtained were 0.103, 0.129, 0.138, 0.105 and 0.111 K for 1.2, 1.65, 2.3, 3.0 and 3.6 GHz receivers, respectively. These resolutions were used in Monte Carlo process in section 2.3 to estimate the propagation of random fluctuations form measured data to the profile.
3. Phantom Experiment
 Using the five-band microwave radiometer system and the data analysis procedure described in section 2, we made a temperature measurement experiment on a phantom. An arrangement for the phantom experiment is illustrated in Figure 4. The phantom consists of water, agar and acrylic layers. The preset temperatures of the controllers for water-bath and the circulated water on agar were 40°C and 10°C, respectively. The thicknesses of agar and acrylic layers were determined to approximate the temperature distribution of a priori knowledge as closely as possible [Leeuwen et al., 2000]. The antenna was positioned at 5 mm from the agar surface and the cooling water was circulated in between. For comparison, thermocouples were positioned at depths of 0, 5, 10, 15, 20, 25, 30, and 50 mm. They were separately-placed in a transverse direction at 5 cm from the center of the antenna aperture so that the perturbation from thermocouples could be minimally suppressed.
 The WF was obtained for the phantom model in the antenna active mode using the finite-difference time-domain method (FDTD method, Mafia, CST). A quarter model of the phantom shown in Figure 5 was used for electromagnetic simulation. Analytical space was 150 × 150 × 240 mm. The set of one-dimensional WFs (1-D WFs) at the five center frequencies is shown in Figure 6. These 1-D WFs were used to generate the model brightness temperature, TB,model,i, in (6).
 Once the measurement operation is initiated, all steps, including frequency band selection, the feed-back control of RNS temperature, the decision of zero output at lock-in amplifiers, data acquisition, data analysis, and display of the results are automatically executed. One cycle of measurement operation was completed in 1–1.5 min. Although shorter cycle is desirable for a practical measurement, 1 min cycle still seems to work as the temperature of brain is rather stable and newborn infants are usually sedentary during hypothermic treatment. Typical measured brightness temperatures and the temperature resolutions of the five receivers are listed in Table 1. The temperature profile retrieved by using the data in Table 1 and the algorithm described in section 2 is shown in Figure 7 where the depth from the agar surface, given in mm, is plotted along the abscissa and the temperature given in °C is plotted along the ordinate. The smooth solid lines represent the estimated temperature profile (center line) and 2-σ confidence interval (two lines above and below the center line). Solid circles are temperature readings obtained by the thermocouples at a 0, 2, 10, 15, 20, 25, 30, and 50 mm depth from the agar surface. The confidence interval (2-σ interval) of the measurement at a depth of 50 mm was 0.7°C. The error was about 2°C at the same depth. Although there are points that can supposedly be improved such as the thermal insulations of the water-bath tank and the temperature stability of the whole system [Camps, 2010], and the susceptibility to electromagnetic interference (EMI), the margin of error was still large. A major cause for the error could be due to the microbubbles in the circulating cooling water which was in direct contact with the surface of the antenna aperture in the phantom experiment. Although the whole surface was not actually covered with bubbles, we simulated the effect of air bubbles on the temperature measurement under the assumption that air bubbles took the form of a uniform layer on the aperture surface because it is very difficult and time consuming to calculate the effect of bubbles which are homogeneously-distributed in the cooling water. FDTD calculation indicated that a uniform bubble layer of 100 μm thickness on the aperture surface may cause 3–4% decrease in measured brightness temperatures and eventually 2.3°C decrease in estimated temperature at 5 cm depth from the surface. A future study will include the removal of air bubbles from the cooling water in a phantom or the fabrication of a waterless phantom.
Table 1. Measured Brightness Temperatures and Temperature Resolutions
 This paper described a result of the temperature measurement experiment on a phantom with a five-band microwave radiometer system. The experiment demonstrated the capability of the current system for noninvasive temperature measurement of deep brain temperatures in infants. The 2σ-confidence interval which is equivalent to the precision of the measurement was 0.7°C and the error was about 2°C at a 5-cm depth from the surface (supposed center of the brain). Since a couple of possible causes for this inaccuracy were identified, we believe that the system will move a step closer to the clinical application of the MWR for hypothermic rescue treatment.
 The authors thank T. Ishii and N. Umehara for development of the control software of the system. This work was supported in part by a Grant-in Aid for Scientific Research (C), 20560394, the Japan Society for the Promotion of Science.