IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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Abstract—Objective: The purpose of this work was to develop 
an electronically tunable resonator operating at 750 MHz for 
continuous-wave electron paramagnetic resonance (CW-EPR) 
imaging of a mouse tumor-bearing leg. Methods: The resonator 
had a multi-coil parallel-gap structure with a sample space of 16 
mm in diameter and 20 mm in length. Microstrip line couplers 
were used in conjunction with varactor diodes to enable 
resonance frequency adjustment and to reduce the non-linear 
effects of the varactor diodes. The resonator was modeled by the 
finite-element method and a microwave circuit simulation was 
performed to clarify its radiofrequency characteristics. Results: A 
tunable resonator was evaluated in terms of its resonance 
frequency, tunable frequency band, and conversion efficiency of 
the RF magnetic field. The developed resonator provided a 
tunable frequency band of 4 MHz at a central frequency of 747 
MHz and a conversion efficiency of 34 µT/W1/2. To demonstrate 
the application of this tunable resonator to EPR imaging, 
three-dimensional EPR images of a sample solution and a mouse 
tumor-bearing leg were obtained. Conclusion: The developed 
tunable resonator satisfied our initial requirements for in vivo 
EPR imaging and may be able to be further improved using the 
present finite-element and circuit models if any problems arise 
during future practical applications. Significance: This work may 
help to promote EPR imaging of tumor-bearing mice in 
cancer-related studies. 
 
Index Terms—Coils, couplers, electromagnetic waves, electron 
paramagnetic resonance, magnetic resonance imaging, 
radiofrequency. 
 
Manuscript received May 21, 2017; revised July yy, 2017. First published 
xxx yy, 2017. This work was supported by JSPS KAKENHI grant number 
26249057 and 16K12862. Asterisk indicates corresponding author. 
T. Amida was with the Division of Bioengineering and Bioinformatics, 
Graduate School of Information Science and Technology, Hokkaido 
University, Sapporo, Japan (e-mail: amida.tatsuya@gmail.com). 
R. Nakaoka, D. A. Komarov, S. Matsumoto, and *H. Hirata are with the 
Division of Bioengineering and Bioinformatics, Graduate School of 
Information Science and Technology, Hokkaido University, North 14, West 9, 
Kita-ku, Sapporo, 060-0814, Japan (r.nakaoka@ist.hokudai.ac.jp; 
dkomarov@ist.hokudai.ac.jp; smatsumoto@ist.hokudai.ac.jp; 
hhirata@ist.hokudai.ac.jp). 
K. Yamamoto and O. Inanami are with Laboratory of Radiation Biology, 
Graduate School of Veterinary Medicine, Hokkaido University, North 18, 
West 9, Kita-ku, Sapporo, 060-0818, Japan (e-mail: 
k_yamamoto@vetmed.hokudai.ac.jp; inanami@vetmed.hokudai.ac.jp). 
I. INTRODUCTION 
ISUALIZATION of the microenvironment of tumor 
tissues is important for understanding their 
pathophysiological status and their response to treatments [1]. 
Tumor tissues often have a low oxygen content, which makes 
them resistant to radiation therapy [2,3]. The oxygen partial 
pressure can be measured by electron paramagnetic resonance 
(EPR) using oxygen-sensitive free radical molecules called 
spin probes [4–7]. For better penetration of electromagnetic 
waves into biological tissues, relatively low magnetic fields (8 
to 42 mT) and the corresponding frequencies of 
electromagnetic waves in the range of 250 MHz to 1.2 GHz 
are used for EPR spectroscopy and imaging in small animals 
[8]. Optimization of a radiofrequency (RF) resonator is always 
desirable for a specific application of EPR. In animal studies 
of radiation therapy and oncology, tumor cells are often 
implanted in hind legs of mice [9,10]. Therefore, an RF 
resonator should be able to accommodate a tumor-bearing leg. 
The stability of EPR signal acquisition is also important for 
the study of tumors because motion of a subject animal may 
cause a significant reflection of RF electromagnetic waves at 
the RF resonator and degrade the signal-to-noise ratio (SNR) 
of EPR spectra. For continuous-wave (CW) EPR spectroscopy 
and imaging, an RF resonator with a high quality factor is 
desirable for improving the EPR signal sensitivity [11]. The 
RF characteristics of a resonator with a high quality factor are 
sensitive to the motion of the subject animal. Thus, 
voltage-controlled frequency adjustment of either the RF 
resonator or the RF signal source in an EPR reflection-type 
bridge should be useful for compensating for perturbations 
caused by the motion of an animal in the EPR resonator. 
Several approaches to controlling the resonance frequency 
have been reported in the context of in vivo EPR spectroscopy 
and imaging. Frequency adjustment has been achieved by 
changing the capacitance in the RF resonator through the 
movement of a dielectric substrate with an induction motor 
[12] or a piezoelectric actuator [13], and through the use of 
varactor diodes [14–16]. The use of induction motors or 
piezoelectric actuators requires high stability of the movement 
of mechanical elements in the resonator. On the other hand, 
A 750-MHz electronically tunable resonator 
using microstrip line couplers for electron 
paramagnetic resonance imaging of a mouse 
tumor-bearing leg 
Tatsuya Amida, Ririko Nakaoka, Denis A. Komarov, Kumiko Yamamoto, Osamu Inanami, 
Shingo Matsumoto, Hiroshi Hirata* 
V 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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while a varactor diode-based tuning approach does not require 
the movement of mechanical elements, with this approach, the 
frequency of the resonator can only be tuned within a limited 
range. To take the limited range of varactor diodes into 
account, an appropriate model of a tunable resonator is 
necessary when the resonator is designed for EPR imaging. In 
addition, the non-linear effects of varactor diodes on the 
tunable resonator should be reduced [17]. A tunable resonator 
that uses microstrip line couplers for CW-EPR imaging has 
not yet been discussed. Therefore, a model of a tunable 
resonator for a mouse tumor-bearing leg should be established. 
 The purpose of this work was to develop an electronically 
tunable resonator operating at 750 MHz for CW-EPR imaging 
of a mouse tumor-bearing leg. To solve the technical problem 
of non-linear effects of varactor diodes, we used microstrip 
line couplers to remove frequency-tuning varactor diodes from 
the RF transmission line of the resonator, which should reduce 
the non-linear effects of the resonator. The resonator structure 
and numerical modeling using a microwave field simulator 
and microwave circuit simulator are described. A multi-coil 
parallel-gap resonator (MCPGR) was used in our design in 
conjunction with microstrip line couplers and varactor diodes 
to enable frequency adjustment. The MCPGR is a modified 
form of a lumped element resonator, such as a loop-gap 
resonator or a split-ring resonator [18–20]. MCPGRs have 
been successfully used for CW-EPR imaging at 650 and 750 
MHz [21,22]. To support our model of a tunable resonator, the 
characteristics of the physically constructed resonator were 
compared to the results of a computer simulation. Finally, 
application of the developed resonator to EPR imaging of a 
sample solution and tumor-bearing mice is demonstrated. 
II. DESIGN AND EVALUATION METHODS 
A. Design requirements 
Several requirements must be considered in the design of a 
tunable resonator for CW-EPR imaging of tumor-bearing mice. 
(i) The resonance frequency of the resonator has to be in the 
range of 740 to 760 MHz. This is because the static magnetic 
field in our EPR spectrometer is generated by permanent 
magnets of 27 mT. Thus, an RF frequency of approximately 
750 MHz is required for EPR detection of paramagnetic 
species with a g-factor of 2 (most organic radicals). The 
central value of the magnetic field can be adjusted somewhat 
by the use of field scanning coils. (ii) The resonance frequency 
of the tunable resonator should be able to be controlled by the 
application of a reverse-bias voltage to varactor diodes. Our 
CW-EPR spectrometer has an automatic tuning control (ATC) 
system that allows us to adjust the resonance frequency of the 
RF resonator to the frequency of the incident RF waves 
[23,24]. To enable negative feedback control of the resonance 
frequency, it should be possible to change the resonance 
frequency of the resonator over a range of several MHz. This 
would enable ATC to compensate for perturbations of the 
resonance frequency caused by the motion of a subject animal. 
A shift in the resonance frequency due to tumor growth can be 
compensated by tuning the carrier frequency of the RF 
synthesizer that corresponds to a shift in the magnetic field. 
The tunable band of 4 MHz allows ATC to compensate for the 
shift in resonance frequency due to the motion of an animal 
during EPR data acquisition. (iii) To improve the sensitivity of 
EPR detection, a higher conversion efficiency of the RF 
magnetic field is desirable [25]. (iv) The MCPGR should be 
able to accommodate a mouse tumor-bearing hind leg. In our 
previous study, tumor volumes reached approximately 1.5 cm3 
10 or 11 days after the implantation of squamous cell 
carcinoma (SCC) [26]. Taking this into account, we chose an 
inner diameter of 16 mm and a length of 20 mm for the 
MCPGR. (v) Finally, the sample space of the resonator has to 
be upright for easy animal handling in our experiments. 
B. Structure of the resonator 
Figure 1(a) illustrates the structure of a tunable resonator 
that uses microstrip line couplers. The MCPGR consists of 
three conductive loops connected to a copper-clad dielectric 
substrate, capacitors connected in series between the dielectric 
substrate and the coaxial lines, a parallel transmission line 
formed by two coaxial lines, microstrip line couplers, varactor 
diodes for adjusting the resonance frequency and 
impedance-matching of the resonator, and a half-wave line 
balun made of a coaxial line. Tin-plated copper wires (18 
British Standard Wire Gauge, thickness of the wire was 1.2 
mm) were connected to the copper-clad 
polytetrafluoroethylene (PTFE) dielectric substrate (0.38 mm 
in thickness, CuFlon® 15-7-7, Polyflon Company, Norwalk, 
CT) as shown in Fig. 1(b). An equivalent circuit of the 
MCPGR composed of three loops and a dielectric substrate is 
shown in Fig. 1(c). While there are many combinations of the 
number of coils and capacitance Cp, three coils were suitable 
to make the resonance frequency approximately 750 MHz 
with the 0.38-mm CuFlon® substrate. When more coils are 
used, a greater capacitance can be achieved through the use of 
a very thin dielectric substrate. For ease of handling, a 
0.38-mm CuFlon® substrate was chosen for the MCPGR. 
The capacitors Cs were made with a 0.25-mm thick PTFE 
substrate (CuFlon® 10-7-7). Fifty-ohm non-magnetic 
semi-rigid coaxial lines (5.0 mm in diameter, 207 mm in 
length, SC-500/50, COAX Company, Yokohama, Japan) were 
used for the parallel transmission line. The length of the 
transmission line was determined by a λ/4-impedance 
transform for the MCPGR and extension of the line (λ/2, no 
impedance transform) that would keep the tuning and 
matching circuits away from the field modulation coils 
(described in section II-D). 
The microstrip line coupler structure was composed of a 
1.27-mm-thick microwave substrate with dielectric constant εr 
10.2 and dissipation factor tanδ 0.0022 (RO3010TM, Rogers 
Corp., Rogers, CT). The use of microstrip line couplers was 
intended to reduce the RF power applied to the varactor diodes 
for frequency tuning. Varactor diodes (BB181, NXP 
Semiconductors, Eindhoven, Netherlands) were connected to 
the ends of the coupler lines to enable adjustment of the 
resonance frequency. Another pair of varactor diodes (1SV217, 
Toshiba, Tokyo, Japan) was used to adjust the impedance of 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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the resonator. Reverse-bias voltages for tuning and matching 
adjustment were applied to varactor diodes through RF choke 
coils. The half-wave line balun was made of a 50-ohm 
non-magnetic semi-rigid coaxial line (2.2 mm in diameter, 138 
mm in length, SC-219/50-SC, COAX Corporation, Yokohama, 
Japan). 
 Figure 2 shows a cross-section of the tunable resonator. 
The MCPGR was held with a cylindrical sleeve made of 
cross-linked polystyrene (REXOLITE® 1422, C-Lec Plastics 
Inc., Philadelphia, PA). The inner and outer diameters of the 
sleeve were 16 and 18 mm, respectively. The MCPGR was 
placed in the RF shield made of REXOLITE® and covered 
with strips of copper foil (50 µm in thickness, 10 mm in 
width). The inner and outer diameters of the shield were 38 
and 40 mm, respectively. This RF shield suppresses unwanted 
radiation from the MCPGR and allows the penetration of 
magnetic field modulation at 90 kHz to the sample. The 
position of the RF shield is not symmetric with respect to the 
MCPGR to make it easier to access the sample space and to 
provide an open area for the body of a subject mouse. 
C. Modeling of the resonator 
The characteristics of the tunable resonator were computed 
using an HFSS 3-D full-wave microwave field simulator 
(version 13.0.0) and the Designer environment (version 6.1.0) 
by ANSYS Inc. (Canonsburg, PA). The tunable resonator was 
modeled on the basis of a previous report regarding a 1.1-GHz 
surface-coil resonator for EPR tooth dosimetry [27]. Figure 
3(a) shows a three-dimensional (3D) finite-element model of 
the MCPGR. For simplicity, Fig. 3(a) does not show the RF 
shield made of strips of copper foil, although the shield was 
included in the finite-element model. The space of 120 mm × 
120 mm × 120 mm was modeled with a radiation boundary 
condition. The MCPGR was placed in the center of the space. 
Microstrip line couplers on the microwave substrate were 
modeled with HFSS as presented in Fig. 3(b). The geometry 
and sizes of the couplers are given in Fig. 3(c). The width of 
microstrip lines (1.2 mm) was chosen to achieve an impedance 
of 50 Ω. Coaxial lines were modeled with Q3D Extractor 
(version 10.0.0, ANSYS). Figure 3(d) presents the whole 
model of the tunable resonator built in the Designer 
environment. The solution converged in our simulation. To 
calculate the conversion efficiency in our simulation, the 
generated RF magnetic field at the center of the MCPGR was 
divided by the square root of the input RF power Pin to the 
resonator. In our calculations, the input RF power Pin was 1 W. 
Thus, the RF magnetic field (in Tesla) is directly related to the 
conversion efficiency in units of T/W1/2. 
To compare the simulated and measured RF characteristics, 
the scattering-matrix parameter S11 of the tunable resonator 
was measured with a vector network analyzer (E5062A, 
Keysight Technologies, Santa Rosa, CA). 
 
Fig. 1. Schematic diagram of the electronically tunable resonator. (a) Configuration of a tunable resonator with microstrip line couplers, (b) structure of the 
multi-coil parallel-gap resonator (MCPGR), and (c) equivalent circuit of the MCPGR with three conductive loops. 
 
 
 
 
Fig. 2. Cross-section of the multi-coil parallel-gap resonator (MCPGR) 
and the RF shield. 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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D. Construction of the resonator and magnetic field 
modulation coils 
After we simulated the RF characteristics of the resonator, 
the tunable resonator was physically constructed to evaluate 
its RF characteristics and EPR imaging. The microstrip line 
couplers, varactor diodes, reverse-bias circuits, and the 
half-wave line balun were contained in a copper shield box (5 
mm in thickness) to reduce interference with magnetic field 
modulation at 90 kHz. A Helmholtz coil pair with an inter-coil 
distance of 50 mm and a mean diameter of 100 mm was used 
for magnetic field modulation. The coils were made on 
1.6-mm-thick glass-reinforced epoxy laminate sheets (model 
no. 34, Sunhayato Corp., Tokyo, Japan, equivalent of FR-4). 
The MCPGR and the RF shield were attached to a 1-mm-thick 
Bakelite plate, which in turn was attached to the modulation 
coils. 
E. EPR imaging of a sample solution 
To examine the developed tunable resonator for 3D EPR 
imaging, a sample of radical solution was visualized with a 
CW-EPR-based single-point imaging (SPI) protocol [28–30]. 
For the imaging experiments, the developed tunable resonator 
was installed into the magnet of a laboratory-built 750-MHz 
CW-EPR spectrometer/imager. The details of the CW-EPR 
spectrometer/imager have been reported previously [31,32]. 
Nitroxyl radical, 
trans-3,4-dicarboxy-2,2,5,5-tetra(2H3)methylpyrrolidin-(3,4-2
H2)-(1-15N)-1-oxyl (2H,15N-DCP), was used as the imaging 
probe [33]. The 2H,15N-DCP radical was synthesized and 
kindly provided by Dr. Igor A. Kirilyuk, Novosibirsk Institute 
of Organic Chemistry, Novosibirsk, Russia. The radical was 
dissolved in phosphate-buffered saline (PBS) and the pH was 
adjusted to 7.4. An Eppendorf microcentrifuge tube containing 
1.3 mL 3 mM 2H,15N-DCP radical solution was placed into the 
MCPGR. Note that the length of the tube (40 mm) was greater 
than the height of the MCPGR (20 mm). Thus, the bottom of 
the tube was outside of the sensitive region of the resonator. 
For EPR image-acquisition, the central magnetic field was 
adjusted to the absorption peak at a lower magnetic field 
(2H,15N-DCP shows two absorption peaks). The measurement 
parameters of EPR imaging were as follows: scan time 100 ms, 
magnetic field scanning 1.5 mT, magnetic field modulation 60 
µT, modulation frequency 90 kHz, time-constant of a lock-in 
amplifier 100 µs, number of data acquisition points 512 per 
 
 
Fig. 3. Modeling of the tunable resonator. (a) Three-dimensional (3D) models of the MCPGR, (b) 3D model of microstrip line couplers on a printed circuit 
board, and (c) the geometry of the microstrip line couplers (not depicted proportional to the actual sizes of the couplers). Models constructed with the 
finite-element method (FEM) for electromagnetic field simulation were built with an ANSYS HFSS electromagnetic wave simulator. (d) RF circuit 
modeling of the tunable resonator in the ANSYS Designer environment. 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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scan, and incident RF power 14 mW. Incrementally ramped 
field gradients in equal steps were used for EPR 
image-acquisition. The projections were acquired at 15 × 15 
×15 field gradients for the X-, Y-, and Z-directions (total of 
3375 projections). The maximum field gradient for each 
direction was 30 mT/m. Two sets of projection data were 
accumulated to improve the SNR of the resulting EPR images. 
The total image-acquisition time was 15 min. 
F. In vivo EPR imaging 
 Three tumor-bearing mice were prepared to demonstrate in 
vivo EPR imaging with the developed resonator. The details of 
animal preparation have been reported previously [34]. In 
brief, six-week-old C3H/HeJ male mice were purchased from 
Japan SLC (Hamamatsu, Japan). Murine squamous cell 
carcinoma (SCC VII) cells [35] were subcutaneously injected 
into the right hind leg. The cells were cultured as previously 
reported [34]. In vivo EPR imaging of tumor-bearing mice was 
performed 6 days after the implantation of SCC VII cells. At 
that time, the mice body weights were 20 to 21 g and the 
tumor volumes were approximately 0.6 cm3. The 
tumor-bearing hind leg of an anesthetized mouse was placed 
into the MCPGR. The imaging probe 2H,15N-DCP was 
intravenously injected as a bolus (1.5 mmol/kg body weight) 
into a subject mouse through a tail vein. EPR data-acquisition 
was started 5 minutes after the injection and a total of 3375 
projections were acquired over the next 7.5 minutes. In our 
previous study, we showed that this acquisition scheme 
ensures a high intensity for the EPR signal and a steady 
concentration of 2H,15N-DCP radical in the tumor tissue [34]. 
The incident RF power for imaging of a tumor-bearing mouse 
leg was 23 mW. The other EPR settings were similar to those 
in imaging of the sample solution. All experiments were 
performed in accordance with the ‘Law for The Care and 
Welfare of Animals in Japan' and were approved by the 
Animal Experiment Committee of Hokkaido University 
(approval no. 15-0120). 
III. RESULTS AND DISCUSSION 
A. Simulation of resonance characteristics and RF magnetic 
field 
The tunable resonator model presented in Fig. 3 was used for 
calculations of the RF magnetic field distribution and the 
scattering-matrix parameter S11. Figure 4(a) shows the 
simulated distribution of the RF magnetic field inside the 
MCPGR. Figure 4(b) shows scattering-matrix parameter S11 
for the tunable resonator under the conditions of coupling 
capacitance Cs 3.5 pF, capacitance mimicking matching 
varactor diodes 6.0 pF, and capacitance mimicking tuning 
varactor diodes 11.0 pF. A resonance peak was observed at 
755 MHz with no other spurious peaks in the vicinity. A solid 
line in Fig. 4(c) shows the tunable frequency band as a 
function of coupling capacitance Cs. As can be seen from Fig. 
4(c), the tunable frequency band increased with an increase in 
the coupling capacitance and reached a plateau at Cs > 6 pF. 
The tuning varactor diode connected to the coupler behaves 
like a capacitor connected in series to the capacitor Cs. 
Therefore, a small value of Cs reduces the influence of the 
varactor diode on the resonance frequency, and this results in a 
decrease in the tunable frequency band. The conversion 
efficiency for the resonator was calculated from the RF 
 
 
Fig. 4. Simulated results of RF characteristics of the tunable resonator. (a) 
The RF magnetic field at the center of the MCPGR when an RF power of 
1 W was applied to the feeding port of the tunable resonator, (b) 
reflection characteristics (scattering-matrix parameter S11) of the tunable 
resonator (Cs 3.5 pF), (c) tunable frequency band as a function of 
coupling capacitor Cs, and (d) the conversion efficiency of the RF 
magnetic field as a function of coupling capacitor Cs. In Fig. 4(c) and (d), 
solid lines show the simulated results for the tunable frequency bands and 
the conversion efficiencies. Closed plots show the experimental results 
for the tunable frequency bands and the conversion efficiencies. 
 
 
Fig. 5. Photographs of a 750-MHz tunable resonator. (a) The MCPGR 
and RF shield, and (b) the tunable resonator and a Helmholtz coil pair. 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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magnetic flux density at the center of the MCPGR. The solid 
line in Fig. 4(d) shows the simulated conversion efficiency of 
the RF magnetic field as a function of coupling capacitance Cs. 
The conversion efficiency increased when the coupling 
capacitance Cs decreased. The influence of coupling 
capacitance Cs on the conversion efficiency is due to a change 
in the transmission coefficient from the parallel transmission 
line to the MCPGR. A few bumps were seen in the solid line 
of the conversion efficiency due to alterations in the resonance 
frequency caused by changes in the coupling capacitance Cs. 
While the capacitance Cp of the MCPGR can be adjusted to 
keep the resonance frequency constant by changing the 
dimensions of the dielectric substrate, we made an allowance 
for the resonance frequency in the range of 740 to 760 MHz. 
As can be seen in Figs. 4(c) and 4(d), the conversion 
efficiency of the RF magnetic field can be increased with a 
sacrifice of the tunable frequency band. If the perturbation of 
the resonance frequency due to animal motion is not 
problematic, a smaller value of coupling capacitance Cs can be 
used to achieve a higher conversion efficiency of the RF 
magnetic field and to improve the EPR signal sensitivity. 
B. RF characteristics of the tunable resonator 
 To verify our modeling of the tunable resonator, we 
physically constructed the tunable resonator, as shown in Fig. 
5, based on the above-mentioned design and simulated results. 
The dimensions of the copper-clad dielectric substrate in the 
MCPGR (see Fig. 1(b)) were 10 mm × 20 mm × 0.38 mm, and 
the electrodes were made by partially removing a copper foil 
on the substrate. The capacitance Cp (Fig. 1(c)) was 3.9 pF. 
The coupling capacitance Cs was chosen to be 3.0 pF. 
Measured insertion loss and coupling of a fabricated 
microstrip line coupler at 750 MHz were 0.36 dB and 12.2 dB, 
respectively. Thus, only 6 % of the RF power flowing in the 
main line of the coupler is applied to the varactor diode for 
frequency tuning. We think that this small fraction of the RF 
power in the coupler reduced the non-linear effects of the 
varactor diodes. When the varactor diodes and transmission 
lines were connected in series, the received signal with twice 
the frequency of FM modulation for ATC phase-sensitive 
detection was distorted (data not shown). However, the 
received signal showed a less-distorted sinusoidal signal with 
the tunable resonator using microstrip line couplers. 
 The resonance frequency and the tunable frequency band of 
the physically constructed resonator were compared to the 
simulated results. Figure 6(a) shows the scattering-matrix 
parameter S11 of a physically constructed tunable resonator 
with various matching-control voltages VM. The reflection 
characteristics exhibited a resonance peak around 750 MHz, as 
we designed. Critical coupling of the resonator at 748.6 MHz 
was observed at a matching-control voltage of 9.3 V. For the 
constructed resonator, the unloaded quality factor was 190, 
and the conversion efficiency of the RF magnetic field was 34 
µT/W1/2. The metal perturbing sphere method was used to 
obtain the conversion efficiency [36,37]. Figure 6(b) shows 
the measured resonance frequency as a function of the 
tuning-control voltage VT. From 1 V to 15 V, the resonance 
frequency shifted from 745 MHz to 749 MHz (4 MHz). This 
tunable band satisfies the specifications given above. The 
tunable frequency band and the conversion efficiency of the 
RF magnetic field were measured with four different coupling 
capacitors Cs. Closed plots in Fig. 4(c) and Fig 4(d) show the 
measured values of the tunable frequency band and the 
conversion efficiency, respectively. As can be seen in Figs. 
4(c) and 4(d), the measured parameters are in good agreement 
with the simulated results, which validates the numerical 
modeling of the tunable resonator. For the constructed 
resonator, the unloaded quality factor was approximately 380 
when coupling capacitance Cs was 1.0 pF. A quality factor of 
190 was measured when Cs was 3.0 pF, as mentioned above. 
Thus, the quality factor and the conversion efficiency can be 
increased by decreasing Cs. However, smaller Cs did not 
provide the desired tunable frequency band. 
A previously reported 750-MHz tunable resonator (24 mm 
in inner diameter, 30 mm in length) for a mouse head had a 
conversion efficiency of 42 µT/W1/2 [32]. Although smaller 
loops were used in the present resonator, the conversion 
efficiency of the resonator was slightly less than that of the 
previous resonator. There are three explanations for why the 
present resonator had a lower conversion efficiency: (i) use of 
a quasi-open RF shield, (ii) a longer transmission line between 
the MCPGR and the matching circuitry, and (iii) a trade-off 
relationship between the conversion efficiency and the tunable 
frequency band. For RF shielding, one end of the MCPGR is 
open to the ambient space in contrast to the 100-mm long RF 
shield of the previous resonator (see Figs. 2 and 5). Therefore, 
the radiation of electromagnetic waves to the ambient space 
increases the loss of the resonator. The longer transmission 
line stores more RF energy than that in the previous resonator. 
This decreases the RF energy in the MCPGR. Also, the 
conversion efficiency was sacrificed to achieve the target 
tunable frequency band in the present resonator (see Fig. 4). 
C. EPR imaging of a sample solution 
EPR imaging of a sample solution was performed with the 
developed tunable resonator. Figures 7(a) and 7(b) show the 
chemical structure of the 2H,15N-DCP imaging probe and its 
first-derivative EPR absorption spectrum measured with the 
developed tunable resonator. Figures 7(c) and 7(d) show a 
 
Fig. 6. Resonance characteristics of the tunable resonator. (a) 
Scattering-matrix parameter S11 as a function of matching control voltage 
VM, and (b) the resonance frequency as a function of tuning control 
voltage VT. 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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photograph and the surface-rendered EPR image for 
2H,15N-DCP solution in the tube, respectively. A threshold of 
30% of the maximum signal intensity in the 3D data was 
applied to a process of surface rendering. Figure 7(e) shows 
the slice-selective EPR signal intensity maps generated from 
the 3D image data. The bottom part of the tube was not 
visualized because it was outside the sensitive region of the 
MCPGR. No significant distortion of the reconstructed image 
was observed. 
 While the solution of the imaging probe was uniform in the 
tube, some intensity variations were observed in EPR intensity 
maps in Fig. 7(e). The EPR signal intensity profile depends on 
several factors such as inhomogeneity of the RF magnetic 
field, the spatial resolution of an EPR image, and eddy 
currents in a conductive sample solution. The areas at the top 
and bottom edges of the MCPGR have a lower intensity of the 
RF magnetic field. Also, the limited spatial resolution of the 
image makes the edge of the sample solution a blurred profile. 
In addition, since PBS is a conductive medium, eddy currents 
are generated and suppress the RF magnetic field in the 
solution. These factors influence the EPR signal intensity and 
help to vary the intensity over the image. 
D. In vivo EPR imaging of a mouse tumor-bearing leg 
Tumor-bearing mice were scanned to demonstrate in vivo 
EPR imaging with the tunable resonator. When a 
tumor-bearing leg (tumor volume 0.6 cm3) was placed in the 
MCPGR, the loaded quality factor was 120 and the shift in the 
resonance frequency was less than 0.1 MHz. 
Figure 8(a) illustrates the arrangement of a tumor-bearing 
hind leg in the resonator. Figure 8(b) shows the 
surface-rendered image of EPR signals in the tumor-bearing 
leg. Figures 8(c) and 8(d) show slice-selective maps of the 
EPR intensity and relaxation time T2*, respectively. A 30% 
threshold of the maximum signal intensity was applied to 
surface rendering and T2* mapping. 
The results shown in Fig. 8 confirm that the developed 
tunable resonator could be used for in vivo EPR imaging of a 
mouse tumor-bearing leg. The 2H,15N-DCP imaging probe 
exhibits very low toxicity [34] and none of the subject mice in 
our experiments died. Nevertheless, the lowest possible dose 
of imaging agent is always preferable for animal studies. 
Optimization of the experimental conditions and improvement 
of the conversion efficiency of the RF magnetic field may be 
able to further improve the EPR signal sensitivity and allow a 
decrease in the dose of the imaging probe. 
A region of low signal intensity in the tumor-bearing leg is 
 
 
Fig. 7. Three-dimensional EPR imaging of a sample solution. (a) 
Chemical structure of 2H,15N-DCP, (b) first-derivative EPR absorption 
spectrum of 2H,15N-DCP, (c) photograph of the sample tube containing 3 
mM 2H,15N-DCP radical solution (1.3 mL), (d) surface-rendered image of 
the sample solution, and (e) slice-selective EPR intensity maps. The 
field-of-view (FOV) of the 3D image is 39 mm × 39 mm × 39 mm in Fig. 
6(d), and the image matrix size is 64 × 64 × 64. 
 
 
Fig. 8. Three-dimensional EPR imaging of a mouse tumor-bearing leg. (a) 
Illustration of the mouse tumor-bearing leg in the MCPGR, (b) 
surface-rendered image of EPR signals in the tumor-bearing leg, (c) 
slice-selective EPR intensity maps, and (d) transverse relaxation time T2* 
maps corresponding to the intensity maps in Fig. 8(c). The FOV of the 3D 
image in Fig. 8 is 33 mm × 33 mm × 33 mm, and the image matrix size is 
48 × 48 × 48. 
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, TBME-00666-2017.R1 
 
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shown in Fig. 8(c), and results in a void of T2* data in Fig. 8(d). 
This observation can be explained by taking into account the 
fact that fast-growing tumors typically have underdeveloped 
vasculature and delivery of the imaging probe to the tumor 
tissue by blood flow is hindered. Relaxation time T2* is 
sensitive to the oxygen partial pressure as well as to the 
concentration of the imaging probe. The T2* maps can be 
converted to oxygen partial pressure maps if we account for 
the influence of the concentration on T2*. While we did not 
convert T2* maps to oxygen partial pressure in this paper, this 
will be a subject for future studies. Mouse tumor-bearing legs 
have been measured in a vertical orientation in previous 
studies of in vivo EPR imaging [10,29,30]. Physiological 
problems regarding a vertical orientation of the legs have not 
been reported. 
From a technical point of view, ATC could work with the 
tunable resonator during EPR image-acquisition. Critical 
coupling of the resonator was obtained without any difficulties. 
This suggests that the second or higher harmonics of reflected 
RF waves caused by the non-linearity of varactor diodes have 
a negligible impact on RF signal reflection in the developed 
tunable resonator. 
IV. CONCLUSION 
A 750-MHz tunable resonator was designed and tested for 
CW-EPR imaging of tumor-bearing mice. The developed 
tunable resonator satisfied our initial requirements for in vivo 
EPR imaging and may be able to be further improved using 
the present finite-element and circuit models if any problems 
arise during future practical applications. The introduction of 
microstrip line couplers to the tunable resonator avoided any 
difficulties in achieving critical coupling of the resonator. The 
present resonator may promote EPR imaging of tumor-bearing 
mice in cancer-related studies. 
ACKNOWLEDGMENT 
The nitroxyl radical probe used in this study was kindly 
provided by Dr. Igor A. Kirilyuk, Novosibirsk Institute of 
Organic Chemistry, Novosibirsk, Russia. 
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