Resonant Circuit

An RF resonator is an electrical circuit that stores electrical and magnetic energy. The simplest resonant circuit is a series LC circuit and a parallel LC circuit. Figure 10.1 illustrates the RLC series resonant circuit, which is driven by a sinusoidal voltage source V (t). In this circuit, a resistor R satisfies Ohm’s law, a capacitor C stores electric charges, and an inductor L stores magnetic fields.

Fig. 10.1

An RLC series resonant circuit with a sinusoidal voltage source V (t)

Let us consider a sinusoidal signal of frequency f. The impedance $Z_{a-a^{\prime }}$ of the RLC circuit at port a−a′ is given by

When the imaginary part in Eq. (10.1) vanishes, the impedance becomes minimal and consists of only the real part R. At this point, current i(t) is expressed as

In Eq. (10.2), current i(t) is frequency-dependent, and is maximal at angular frequency

From Eq. (10.4), the resonant frequency f_r is given by

At the resonant frequency, current i flowing in the circuit is maximized, and magnetic flux in the inductor also becomes maximized. Therefore, RF magnetic fields are efficiently generated at the resonant frequency f_r.

Sensitivity of EPR Detection

The sensitivity of EPR signal detection is well documented [2]. In a reflection-type EPR bridge, as illustrated in Fig. 10.2, the RF resonator is connected to the transmission line to apply the electromagnetic waves to a sample. Figure 10.3 illustrates a resonator connected to the transmission line.

Fig. 10.2

General schematic of a simplified reflection-type bridge for CW-EPR

Fig. 10.3

Transmission line and a resonator

The signal intensity V_S of an EPR absorption spectrum in CW-EPR is given by

Filling Factor and Quality Factor

The filling factor is generally defined as the ratio between the stored magnetic energy in the resonator and the stored magnetic energy in the sample that can contribute to EPR phenomena. Figure 10.4 illustrates the resonator and the sample, as well as the magnetic fields.

Fig. 10.4

Geometry of magnetic fields , a resonator, and a sample regarding the filling factor

The RF magnetic field B_1⊥ perpendicular to the static magnetic field B₀ is taken into account in EPR phenomenon. The density of magnetic energy w_m in the space can be calculated as

The quality factor is a dimensionless value that quantifies a resonator’s ability to store and dissipate energy, and can be evaluated as

However, direct measurements of the stored energy in the resonator and the energy dissipated per cycle are not practical. Another equation for the quality factor is often used:

For CW-EPR , a high quality factor and a high filling factor are both required to ensure sufficient EPR signal intensity according to Eq. (10.6). A high filling factor with a biological sample, which has a loss in terms of electromagnetic waves, results in an increase in energy dissipation in the resonator, which results in a low quality factor. In contrast, when a small part of a biological sample is placed in the resonator, the losses due to the resonator decrease, which results in a low filling factor and a high quality factor. In biological EPR spectroscopy and imaging, the balance between the quality factor and the filling factor should be optimized so that the biological sample can be measured adequately. Therefore, the resonator should be designed for a specific application to obtain the maximal EPR signal intensity with the optimal conditions for the quality factor and the filling factor. For pulsed EPR, the quality factor is significantly lowered to reduce the ring-down time after the RF pulses and to have a broader bandwidth. This aspect of pulsed EPR is explained in another chapter.

Frequency Selection of Preclinical and Clinical EPR

The RF frequency η for EPR spectroscopy and imaging is determined by the static magnetic field B₀ applied to a subject, according to the fundamental equation for the EPR phenomenon, hv = gβ_BB₀, where h is Plank constant (6.626 × 10⁻³⁴ Js), g is the g-factor of the species to be measured (2.002 for the free electron), and β_B is Bohr magneton (9.274 × 10⁻²⁴ JT⁻¹) [3]. In laboratories, an X-band EPR spectrometer is commonly used as an analytical tool for various samples. However, the penetration of microwaves into biological tissues is critical in biomedical applications for small animals and even human subjects. As a measure of the penetration of electromagnetic waves in a subject, the skin depth is considered. The skin depth defines the distance at which the amplitude of electromagnetic waves becomes 1/e = 0.3679, where e is Napier’s constant. At angular frequency w, the skin depth d can be calculated as

In vivo EPR measurements with mice were initially conducted in the X-band (ν = 8.5 GHz, B₀ = 0.3 T) [5], but soon thereafter the frequency of electromagnetic waves was reduced to a lower frequency to allow increased penetration of electromagnetic waves in biological tissues [6]. The EPR studies below the X-band are well documented by Eaton and Eaton [7]. From the 1990s to the present, most in vivo small animal studies have been performed at frequencies from 250 to 1200 MHz (VHF/UHF to L-band). EPR imaging on human skin has been conducted in the S-band (2 GHz) [8, 9], since it does not require a significant penetration of electromagnetic waves in tissues and provides better sensitivity.

Frequency selection is important for biomedical applications of EPR spectroscopy and imaging, since it may limit the detection volume and the overall sensitivity of the EPR measurements. Several factors that affect EPR measurements should be taken into account. The criteria for frequency selection are as follows:

(a)

The penetration depth of electromagnetic waves

A higher frequency may limit the penetration depth (see Eq. (10.11)).

(b)

The sensitivity of EPR signals

A higher magnetic field and a corresponding frequency give stronger EPR signals. If there is no problem regarding the penetration depth, a frequency as high as possible is beneficial.

(c)

Size of the species to be measured

How large is the subject? A mouse, rabbit, pig, or even a human?

(d)

What will be measured, and where will it be measured?

The region of interest, such as superficial tissues or a deep region, determines the required penetration depth.

(e)

Specific absorption rate (SAR) and safety regulations

To avoid unwanted effects in a subject, energy absorption in biological tissues should be below certain levels, which are promulgated in safety regulations by national governments or international organizations.

Types of Resonators

The resonators used for biological EPR applications can be divided into two major categories: volume resonators and surface resonators (similar to clinical magnetic resonance imaging (MRI)).

Samples are typically placed inside a volume resonator, which can accommodate a whole body or part of a subject animal. These types of resonators, such as a loop-gap resonator, benefit from a higher filling factor [10]. Since the sample is placed in the volume of the resonator where the magnetic flux generated by the resonator is the highest, the spins in the sample are stimulated more efficiently. The wavelength of electromagnetic waves may limit the dimensions of the resonator. When a large sample space is needed and the sample is not small in comparison to the wavelength, the resonator structure should be considered to obtain homogeneous RF magnetic fields in the sample space.

Surface resonators are typically placed on the surface of a sample. A surface resonator can measure EPR signals from localized regions of a subject animal, such as the skin or tissues close to the external surface of the animal [11]. As mentioned above, the region of interest is a key factor when choosing the type of resonator. In addition to these major categories, implantable resonators have been developed for small animal experiments, which address the problem of the penetration depth. Surgical procedures may be required for the use of an implantable resonator in animals. Specific examples of EPR resonators are introduced in section “Brief History of Technical Developments for In Vivo EPR Resonators ”.

Other Technical Aspects for RF Resonators in EPR

Previous sections addressed several technical aspects (filling factor, quality factor, and penetration depth). This section briefly explains other important aspects of the resonators used in EPR spectroscopy and imaging.

Homogeneity of RF Magnetic Fields

As mentioned previously, the EPR signal intensity depends on the square of RF magnetic field B₁. To achieve a uniform sensitivity of EPR detection within the resonator, a homogeneous B₁ field needs to be established. Three factors alter the RF magnetic field:

(a)

The distance from the currents. In the radial direction, the RF magnetic field is weakest at the center of the resonator. However, as the distance from the current source to the observation point decreases, the RF magnetic field increases.

(b)

In many cases, the physical length of the resonator is not negligibly small in comparison to the wavelength of electromagnetic waves. In this case, the RF current flowing in the conductors is no longer uniform.

(c)

Also, the electrical properties of biological tissues in animals are not the same. These properties affect the RF electromagnetic fields.

Figure 10.5 shows the calculated RF magnetic field for a single-turn loop driven at 300 MHz (55 mm in diameter) [19]. Figure 10.5a, b show the loop segments and the distribution of the RF current flowing in the loop. Since the length of the loop circumference is not negligibly small in comparison to the wavelength at 300 MHz, the RF current in the loop is no longer uniform. Figure 10.5c shows the calculated RF magnetic energy that contributes to EPR. As mentioned above, the RF magnetic energy (square of the RF magnetic field B₁, see Eq. (10.7)) at the center of the loop is less than that in the proximity of the loop. To investigate the RF magnetic fields in the resonator, the finite-element method (FEM) or the finite-difference time-domain (FDTD) method can be used, and commercially available simulators for electromagnetic waves have been used to investigate the resonator and its RF electromagnetic fields. These simulations can then guide the manufacture, geometric dimensions and tolerance of resonators and their components to ensure that a given resonator design delivers maximal performance .

Fig. 10.5

Calculated RF magnetic field for a single-turn loop driven at 300 MHz (55 mm in diameter) [19]. (a) Modeling and segments of the loop for the calculation of the current and the magnetic field, (b) RF current distribution on the loop, and (c) the distribution (more...)

First In Vivo EPR Experiment Using a Helix Coil

In a report by Feldman et al. in 1975, a helix coil was implanted in the liver of a rat, and EPR spectra from exogenously injected free radical spin probes were observed [5]. Helices were made of gold-coated brass wire and enclosed in thin-wall Teflon tubing. The diameter of helices was in the range 1.6–2.4 mm. The helix coil was connected to a Varian X-band spectrometer via a waveguide-to-coax adapter. EPR spectra were recorded at a magnetic field of 0.3 T, which corresponds to a microwave frequency of 8.5 GHz.

Surface Coils

A helix coil and a flat coil were used as resonators at 1.86 GHz for animals in vivo [11]. A single-turn flat loop coil was used for in vivo EPR imaging of a living murine tumor (Cloudman S-91 melanoma in the tail of a mouse) [6]. An electronically tunable surface coil operating at 3 GHz was used for in vivo skin measurements in a human forearm [21]. A surface coil (4 mm in diameter) at 2.4 GHz was used for EPR spectroscopy and imaging of the surface domain of a large subject [22]. In that report, Herrling et al. explained two imaging approaches using a surface coil. One approach uses mechanical scanning of the surface coil and the other uses a magnetic field gradient as a conventional spatial imaging. Skin measurements are a good application for EPR spectroscopy and imaging using surface coils. Another skin study was performed by Takeshita et al. with a surface coil at 1.1 GHz [23, 24]. Another surface coil resonator, called an external loop resonator, was used for small animal experiments [15]. The single-turn loop was placed on the surface of tissue within which the oxygen-sensitive crystal LiPc was implanted.

Loop-Gap Resonators

In 1982, Froncisz and Hyde reported a loop-gap resonator (LGR) for EPR in the range of 1–10 GHz. They demonstrated EPR spectroscopy with LGRs at 3 and 9 GHz [10]. Figure 10.6 shows the structure of the LGR in the literature [10]. It is considered to be a lumped circuit when the dimensions of the LGR are smaller than 1/4 wavelength. Also, Nardy and Whitehead reported a split-ring resonator in the context of NMR in a frequency range from 200 to 2000 MHz [25]. These resonators are lumped circuits and are considered to be an LC resonant circuit. The LGR has the advantage of a high filling factor, which results in a greater EPR signal intensity. In the context of in vivo small animal EPR, a part of or the whole body of a subject animal can be placed in the loop. As previously mentioned, the resonant frequency should be appropriately selected to give enough penetration depth for electromagnetic waves in biological tissues.

Fig. 10.6

Structure of the loop-gap resonator (two-gap one-loop) reported in 1982 [10]. (Reprinted from Journal of Magnetic Resonance, Vol. 47, Froncisz W, Hyde JS, The loop-gap resonator: A new lumped circuit ESR sample structure, pp. 515–521, Copyright (more...)

A modified structure of the LGR, called a bridged loop-gap resonator (BLGR), was reported in 1988 [26]. Curved conductive plates (or thin foils) called bridges are placed near the gap(s). In Pfenninger’s BLGR, the bridge was located outside of the loops, and they intended to use BLGR for pulsed EPR at an X-band frequency. In the context of in vivo EPR, Ono et al. reported another structure for BLGR at an L-band frequency [27], in which electric shields are located inside the gaps to prevent the heating of biological tissues due to the electric field. LGR and BLGR have been used in small animal EPR spectroscopy and imaging [28, 29].

The design of an LGR is important for specific applications. Diodato et al. reported optimization of the axial RF field distribution in an LGR [30]. They showed that the coupling loop influenced the axial RF magnetic field and proposed the combination of two LGRs, with the coupling loop between the two LGRs. Ono et al. reported that electric shields influenced the RF magnetic field distribution in a BLGR [31]. The RF magnetic and electric fields inside the BLGR were measured. Their experiments clarified that appropriate angles of the electric shields can improve the homogeneity of the RF magnetic field .

Reentrant Resonators

Another type of resonator is a reentrant resonator . In 1983, Giordano et al. reported a reentrant cavity with a gap and a path for magnetic flux, which operated at 2 GHz [32]. They intended to use their reentrant resonator in studies on anisotropic line broadening. Later, Sotgiu and coworkers reported the designs of reentrant resonators that operated in the range of 2–10 GHz [33, 34]. Since reentrant resonators can operate at a low frequency, they have been used in small animal experiments. Figure 10.7 shows a cross-section of the reentrant resonator reported by Sotgiu in 1985 [35]. Chzhan et al. also developed reentrant resonators that operated at 1.2 GHz [36]. Chzhan et al. improved their reentrant resonator by making it capable of frequency tuning using piezoelectric actuators [14]. After that, Zweier and colleagues continued to develop reentrant resonators for EPR imaging in small animals at 750 MHz and 1.2 GHz [37, 38].

Fig. 10.7

Cross-section of a reentrant resonator reported in 1985 [35]. (Reprinted from Journal of Magnetic Resonance, Vol. 65, Sotgiu A, Resonator design for in vivo ESR spectroscopy, pp. 206–214, Copyright (1985), with permission from Elsevier)

Surface Coils for Teeth or Fingernails

In human subjects, resonators can be used for the retrospective measurement of radiation dose, called EPR dosimetry. Stable free radicals in enamel in teeth and keratin in fingernails can be measured by EPR [39]. In measurements of the teeth, the surface coil is placed on an incisor or a molar.

Regarding EPR tooth dosimetry , Hochi et al. reported an X-band EPR spectrometer that used a cavity resonator with a small aperture [40]. In their approach, a human subject bit the cavity resonator and the electromagnetic waves from the aperture of the cavity resonator excited free radicals in the enamel of a tooth [41]. While a cavity resonator in the X-band can provide highly sensitive EPR signals because of greater Zeeman energy splitting, it requires a significantly larger magnet to establish the necessary fields, as compared to a magnet for low-field EPR, such as for L-band measurements. A lower magnetic field generated by an air-core magnet is suitable in a portable EPR spectrometer for triage dosimetry [42]. A 1.1-GHz surface loop resonator was used for EPR-based human tooth dosimetry. This application is explained in another subsection of this chapter.

For EPR dosimetry with fingernails, EPR measurements require the shallow penetration of electromagnetic waves in the fingernail. This is because fingernails are approximately 1 mm thick, and deeper penetration leads to a loss of electromagnetic waves in tissue in the fingertips. To satisfy this requirement, surface coil resonators in the X-band (9.5 GHz) were developed for in vivo EPR fingernail dosimetry. Sidabras et al. developed a microwave surface resonator array (SRA) in the X-band that is suitable for EPR-based fingernail dosimetry [43]. Grinberg et al. also reported a dielectric-backed aperture resonator in the X-band for in vivo nail dosimetry [44].

Volume Resonators

Parallel Coil Resonator

In low-field pulsed EPR , the ring-down time of the resonator is critical [56]. After an RF pulse is transmitted to the resonator and a subject, the RF energy in the resonator remains stored for a period and disturbs signal detection at the receiver of a pulsed EPR instrument. This signal disturbance after the RF pulse is called dead time and is related to the ring-down time of the resonator. To overcome the problem regarding ringing after an RF pulse, the quality factor of the resonator is significantly reduced. A parallel coil resonator at 300 MHz has been reported by Devasahayam et al. [57]. The parallel coil resonator has been used in mouse whole-body imaging [58] and pO₂ mapping for tumor-bearing legs [59] at 300 MHz. A low quality factor (20–25) was achieved by over-coupling of the resonator [58]. The parallel coil resonator operating at 300 MHz could be used for EPR and 7 T proton MRI, which is important for EPR/NMR co-registration imaging of an animal subject.

Figure 10.8 shows a schematic of the parallel coil resonator [57]. The coils are connected to the coupling and tuning capacitors. Trimmer capacitors are adjusted to obtain the desired resonance frequency and a degree of coupling for the resonator. Since pulsed EPR does not require magnetic field modulation, a modulation coil is no longer needed. Thus, the structure of the parallel coil resonator is simple in comparison to a resonator with a modulation coil.

Fig. 10.8

Circuitry and schematic of a parallel coil resonator used for 300-MHz pulsed EPR [57]. (Reprinted from Journal of Magnetic Resonance, Vol. 142, Devasahayam N, Subramanian S, Murugesan R, Cook JA, Afeworki M, Tschudin RG, Mitchell JB, Krishna MC, Parallel (more...)

Alderman-Grant Resonator

The Alderman-Grant resonator (AGR) has been used in EPR and NMR. An important characteristic of the AGR is that the RF magnetic field is perpendicular to the axis of the AGR. The AGR was first reported by Alderman and Grant in 1979 [60]. In EPR-related studies, AGR has been used to excite electron spins in proton-electron double resonance imaging (PEDRI), which is also called Overhauser-enhanced magnetic resonance imaging (OMRI). Petryakov et al. developed an AGR at 590 MHz for exciting electron spins and demonstrated experiments with a high input power (up to 60 W for 3 min and 10 W for 10 min) [61]. Figure 10.9 illustrates the structure of the original AGR. This resonator can be used with other types of resonator such as a solenoid-type resonator because the RF magnetic fields are orthogonal to each other. This is necessary for double-resonance techniques (PEDRI/OMRI) [62].

Fig. 10.9

Schematic of the Alderman-Grant resonator reported in 1979 [60]. (Reprinted from Journal of Magnetic Resonance, Vol. 36, Alderman DW, Grant DM, An efficient decoupler coil design which reduces heating in conductive samples in superconducting spectrometers, (more...)

Surface Resonator

Surface coil resonators have been used for measurements of the superficial regions of subject animals. A surface coil can be located at the region of interest for a measurement, even if a volume coil such as an LGR cannot accommodate a large subject. The simplest surface coil is just a combination of a single-turn loop and a capacitor to form a resonant circuit. However, additional circuitry is usually added to the coil to make it both possible and practical to adjust the resonant frequency and enable impedance matching. This section introduces several concepts regarding surface coil resonators.

Surface Coil/Loop Resonators

An electronically tunable resonator is useful for low-field EPR because perturbation due to motion of the subject should be accommodated. Figure 10.10 shows a circuit diagram of an electronically tunable surface coil resonator at 1.1 GHz [63]. This resonator uses varactor diodes for impedance matching and frequency adjustment. Also, a half-wavelength balun was used to ensure that the resonant circuit was properly balanced. A pair of varactor diodes that are connected in the opposite direction can increase the ability of the resonator to tolerate an incident RF power. This reduces the generation of the harmonics of incident RF signals. This type of surface coil resonator can be used for in vivo EPR spectroscopy .

Fig. 10.10

Schematic of a tunable surface coil resonator reported in 2003 [63]. (Reprinted from Journal of Magnetic Resonance, Vol. 164, Hirata H, Kuyama T, Ono M, Shimoyama Y, Detection of electron paramagnetic resonance absorption using frequency modulation, pp. (more...)

A surface coil resonator is also called an external loop resonator (ELR). Figure 10.11 shows a circuit diagram of an ELR at 1.1 GHz [16, 64]. Varactor diodes are used to adjust the resonant frequency, and a photo-resistor and a light-emitting diode (LED) are used to control the quality factor. A shift in the quality factor can control impedance-matching between the 50-Ω transmission line and the resonator. Thus, the voltage applied to the LED controls the impedance of the ELR. An inductive coupling scheme is also used in the ELR. The length of a twisted wire connected to the inductive coupling loop is adjusted to minimize the shift of the resonant frequency due to the adjustment of impedance-matching [65].

Fig. 10.11

Circuit diagram of the external loop resonator (ELR) reported in 2005 [16]. (Reprinted from Walczak T, Lesniewski P, Salikhov I, Sucheta A, Szybinski K, Swartz HM. 2005. L-band electron paramagnetic resonance spectrometer for use in vivo and in studies (more...)

An ELR has been used for in vivo L-band EPR spectroscopy. However, the details of the ELR were published in 2005. More recently, the ELR was modeled and analyzed by the FEM [66]. Sugawara et al. reported a FEM analysis and optimization of a 1.1-GHz surface coil resonator for EPR tooth dosimetry [67].

Surface Coil Array

To overcome the limited sensitive region of the surface coil resonator, an array of surface coil resonators can be used. This approach is also used in clinical MRI. Due to the higher RF frequency in EPR than in NMR/MRI, the size of the surface coil is usually limited. If the circumference of the loop is not negligibly short in comparison to the wavelength, i.e., <1/4 wavelength, of the RF electromagnetic waves, the fields generated by the loop are no longer in the correct phase relative to each other. This leads to an inhomogeneous RF magnetic field in the loop. This section briefly introduces a surface coil array for in vivo EPR imaging.

There are two approaches to image acquisition using a surface coil array : (1) sequential acquisition and (2) simultaneous (parallel) acquisition. Sequential acquisition refers to when one of the surface coil resonators within the array is selected for EPR signal recording. This is a simple approach to EPR imaging. However, the interaction between the neighboring coils should be suppressed to avoid interference while an image is being acquired. This is because inductive coupling between coils that are located in close proximity affects the resonance characteristics of the surface coil resonator to which the RF electromagnetic waves are fed. Enomoto et al. used PIN-diode switches to suppress the interaction between the neighboring resonators in a CW-EPR detection protocol [68, 69]. Figure 10.12 shows a four-channel surface coil array operating at 750 MHz. This array was tested with a living mouse [69]. The array was placed on the back of a subject mouse. After the mouse was injected with spin probes, EPR image-acquisition was performed with each surface coil in sequence. The reconstructed images were then combined. In pulsed EPR, the quality factor of the resonator is significantly decreased. This can reduce the influence of the interaction between the neighboring coils. Enomoto et al. demonstrated a surface coil array in pulsed EPR imaging at 300 MHz. As in CW-EPR, the resonant frequencies of unexcited resonators in the array were shifted to reduce the mutual inductive coupling of the coils [70]. In addition, passive decoupling of the coils was also tested for a four-channel surface coil array [71]. The feasibility of the simultaneous acquisition of multiple coils has also been reported [72]. Development of a surface coil array for EPR imaging is an important direction for preclinical and clinical applications .

Fig. 10.12

Photograph of a four-channel surface coil array operating at 750 MHz for EPR imaging in mice [69]. (Reprinted from Journal of Magnetic Resonance, Vol. 234, Enomoto A, Emoto M, Fujii H, Hirata H, Four-channel surface coil array for sequential CW-EPR image (more...)

Surface Detection Using LGR

Another approach to detecting EPR signals from a superficial region in biological subjects uses the fringe magnetic field of a volume coil resonator such as the LGR instead of a surface coil. A surface probe using a double split-ring resonator operating at 1 GHz was reported by Nilges et al. [73]. In a more clinically related application, EPR imaging for human skin was performed with a surface probe using a BLGR in the S-band (2.2 GHz) [8, 9]. With a higher frequency in the S-band, nitroxide probes in human skin were successfully detected and the distribution of nitroxide radicals was visualized. While the frequency of 2 GHz limits the penetration depth of electromagnetic waves in biological tissues, measurements in human skin do not require deep penetration by electromagnetic waves .

Implantable Resonator

As mentioned above, surface coils have a limited sensitive volume, although there are some advantages of a comparatively high sensitivity and no limitation to the subject size. When a region of interest is deep in tissue that is a part of a large object, neither a surface coil nor a volume coil, e.g., the LGR, can be applied. In particular, the internal organs of human subjects are difficult to measure with either a surface coil or an LGR with a commonly used low-field EPR spectrometer/imager. One possible solution is an implantable resonator.

Li et al. demonstrated an implantable resonator for an EPR oximetry study in rat brain [74]. The implantable resonator has oxygen-sensitive materials in a small loop or multiple small loops that are located at the end of a twisted pair of transmission lines [75]. Figure 10.13 shows a photograph of an implantable resonator for rabbit brain [76]. The length of the twisted wires can be adjusted to reach the region of interest. The other end of the twisted wires has a larger loop that can be coupled with the loop located on the surface of the object.

Fig. 10.13

Schematic of implantable resonators for rabbit brain [76]. (Reprinted from Stroke, Vol. 46, Khan N, Hou H, Eskey CJ, Moodie K, Gohain S, Du G, Hodge S, Culp WC, Kuppusamy P, Swartz HM, Deep-tissue oxygen monitoring in the brain of rabbits for stroke research, (more...)

RF signals can be delivered to the oxygen-sensitive probe in a small loop (or multiple loops) of the implantable device. After the implantable device is placed in the subject, EPR spectroscopy can be repeatedly conducted noninvasively. The small loop can increase the sensitivity of EPR detection because a strong RF magnetic field is generated in a small loop. This phenomenon is a primary reason why an implantable resonator can work effectively in deep tissues. With an implantable resonator with multiple loops, the partial pressure of oxygen at multiple sites can be measured, and, for example, it is possible to compare oxygenation at several regions of interest in rat brain. These measurements could be useful for studies in an animal model of ischemic stroke [75, 76] or in a tumor xenograft model [77, 78].

From an engineering point of view, the materials used to make an implantable resonator should be biocompatible if the resonator is to be placed in biological tissues for a long time. An implantable resonator made of copper can be coated with a biocompatible material. For oxygen measurements, the coating materials should be oxygen-permeable.

Surface Resonators for Human Skin/Surface

EPR spectroscopy and imaging on human skin have been reported by He et al. [8]. They reported the distribution and metabolism of nitroxide radicals in human skin using a loop-gap surface resonator operating at 2.2 GHz [9]. A penetration depth of electromagnetic waves of approximately 2 mm is enough for skin EPR measurements. Reports of in vivo EPR measurements in human skin are still limited. For in vivo studies in human skin, the microwave frequency can be higher than conventional in vivo frequencies (L-band or lower RF frequencies), since the limited penetration depth is not a problem, but rather a desirable feature, for studies in skin. Successful applications of EPR spectroscopy and imaging in human skin help foster the further development of surface resonators. Wolfson et al. developed an LGR-based surface-detection resonator operating at 2.3 GHz [79]. This resonator was intended for transcutaneous oxygen-monitoring using the oxygen-sensitive crystal LiNc-BuO. The dimensions of this resonator are 13 mm in outer diameter, 3.6 mm in inner diameter, and 19 mm in height. The gap in the loop is 0.1 mm. This LGR was installed in an array of small magnets that generate a static magnetic field .

L-Band Surface Loop Resonators for Tooth Dosimetry

When teeth receive ionizing radiation in medical treatments, or because of other reasons such as an accident in a nuclear power plant, very stable CO₂⁻ radical is generated in the enamel [39]. EPR spectroscopy can detect these radiation-induced free radicals in human teeth after they have been exposed to ionizing radiation. Surface coil resonators have been developed for EPR-based in vivo tooth dosimetry.

An ELR at 1.15 GHz was developed and used for human EPR tooth dosimetry [80]. To improve the detection capabilities to more accurately estimate the radiation dose, surface coil resonators were further developed [66, 67, 81]. The loop was placed on an incisor to detect free radicals in the enamel. Recently, a unique EPR resonator was developed for tooth dosimetry. It consisted of a combination of an inductively coupled ELR printed on a flexible substrate which was driven by a non-resonant quarter-wavelength-loop antenna [82]. The printed ELR can be affixed to an incisor for an in vivo measurement. The advantages of this wireless flexible surface coil resonator are as follows:

(a)

A printed ELR can be mass-produced to have a low unit cost, and therefore be disposable. This is important for biomedical applications and high throughput if a large number of people are to be measured in a short period of time, e.g., a triage operation in the event of a nuclear incident.

(b)

A printed ELR can be easily affixed to a tooth via suitable medical double-sided tape outside of the magnet, reducing the need for cumbersome placement inside the restricted space of the magnet.

(c)

The field generated by the antenna coupler encompasses both of the front incisor teeth, and therefore precise placement of the coupler inside the magnet during the measurement is not necessary—the coupler can simply be placed universally for all measurement subjects, reducing the burden on the operator and increasing the potential for automated actions of the EPR dosimeter.

Resonators for tooth dosimetry were tested in human subjects [83]. Since tooth dosimetry is a topical EPR measurement, the small surface loop operating at 1.1–1.2 GHz is not limited by the penetration depth of electromagnetic waves, and loss of the tooth itself is not so significant in comparison to the loss of other soft biological tissues [84].

X-Band Resonators for Fingernail Dosimetry

Several types of resonators have also been developed for another EPR-based dosimetry application: in vivo fingernail dosimetry. Fingernail dosimetry is commonly performed in the X-band, as radiation-induced signals in the fingernails are significantly weaker than those in tooth enamel. This increased frequency provides a high sensitivity of EPR detection due to a greater energy gap of Zeeman splitting. Since the region of EPR spectroscopy detection in the X-band is superficial and is suitable only for nails.

The radiation-induced EPR signal in human fingernails has been reported [85]. Radiation-induced signals in chipped fingernails were initially measured with a conventional X-band cavity resonator to qualify and generally characterize the dosimetry technique as a suitable candidate for physically based dosimetry [86]. This approach of using a microwave cavity is not suitable for in vivo human fingernails, as the conventional cavity resonator is designed for glass capillary tubes. Therefore, X-band resonators have been developed for in vivo studies of fingernails.

A microwave surface resonator array (SRA) has been developed for in vivo EPR nail dosimetry as a practical in vivo replacement for a conventional microwave cavity [43]. Figure 10.14 shows a photograph of an SRA for EPR fingernail dosimetry. This metallic arrayed structure was designed to limit the depth of penetration of the stimulating magnetic field so as to focus the field generated by the SRA into the fingernail itself rather than the underlying tissue. The intent of this is to help ensure that no energy applied to the resonator is then deposited into tissues where there is not expected to be any signal, i.e., the tissue under the nail. For a given nail dosimetry measurement, the resonator is simply placed on the fingernail within (or outside) the magnet, and then the finger and resonator assembly are then mated to an ergonomic receptacle within the EPR dosimeter .

Fig. 10.14

Photograph of an SRA for EPR fingernail dosimetry [43]. (Reprinted from Sidabras JW, Varanasi SK, Mett RR, Swarts SG, Swartz HM, Hyde JS. 2014. A microwave resonator for limiting depth sensitivity for electron paramagnetic resonance spectroscopy of surfaces. (more...)

Several resonators that use dielectric resonant structures have also been developed for the purpose of surface measurements at an X-band frequency, e.g., in vivo nail dosimetry. These dielectric resonator assemblies seek to more closely match the dielectric of the resonant structure to the dielectric of the tissue being measured to maximize the amount of RF energy transferred into the tissue of interest, i.e., the fingernail. Proper high-dielectric substrates also provide the opportunity for a higher quality factor for a resonator, given a suitable selection of dielectric resonator for the application. For the dielectric resonator in Ref. [44], RF power is driven to the dielectric resonator via the use of a modified resonant microwave cavity, and Ref. [87] describes a resonator topology where RF power is driven to the dielectric resonator via the use of a non-resonant antenna.

Implantable Resonators

Another direction for resonator development in human subjects is to measure EPR signals from tissues that are not on the surface of the body or superficial to the surface, i.e., at depths >10 mm below the skin. This is primarily of concern when attempting to measure oxygen levels in a given organ in vivo in a noninvasive fashion. While resonator implantation is invasive, repeated measurements can be performed by placing an ELR over the coupling loop of the implanted resonator [88] and collecting EPR data as in a usual surface EPR oximetry measurement.

A possible solution is the use of an implantable resonator to detect EPR signals deep in tissue. A clinically acceptable implantable EPR resonator is currently under development [89], and an implantable resonator for a rat brain [75, 76, 78] is a similar model of such an implantable resonator for human subjects. A rabbit brain was also measured with an implantable resonator [77]. Implantable coils have been investigated in proton magnetic resonance imaging (MRI) [90, 91]. The implantable resonator being developed in Ref. [89] seeks to accommodate and address aspects of clinical acceptance, including insertion/removal procedures, biocompatibility, MRI compatibility, and other aspects associated with obtaining an investigation device exemption from the U.S. Food and Drug Administration (FDA) with the goal of bringing implantable resonators closer to reality in the clinic. The development of implantable resonators for use in EPR spectroscopy and imaging in human subjects is a potential direction for future studies .

A Resonator for Superficial Tissues

As mentioned above, this is the most practical target for present EPR resonators. For example, skin, teeth, and fingernails are easy to access. When the RF frequency for EPR decreases to an RF frequency similar to that in clinical MRI, the problem of the penetration depth of electromagnetic waves may be partly solved; however, the absolute EPR amplitude sensitivity will suffer. A small resonator used for endoscope-like EPR measurement may also be considered for measurements of superficial regions.

An Implantable Resonator

Surgery is required to place implantable resonators deep in tissue. This is a drawback in clinical EPR. However, once placed, implantable resonators enable repeated, noninvasive measurements in EPR spectroscopy and imaging. The risks and benefits of implantable resonators should be considered, as with any other clinical treatment. However, technologies regarding implantable resonators should be explored further to achieve clinical EPR, as each implantable resonator should meet the specific needs of the clinical application of EPR spectroscopy and imaging .

A Volume Coil Resonator for Further Low-Frequency Clinical EPR

To overcome the limited penetration depth of electromagnetic waves in tissues, a further low RF frequency might be used. MRIs with magnetic fields of 1.5 T and 3 T operate at 64 MHz and 128 MHz, respectively. By analogy with MRI, such a lower RF frequency provides better penetration of electromagnetic waves in tissue as well as a smaller energy gap in Zeeman splitting, thereby resulting in a decrease in the sensitivity of EPR detection. In contrast to a smaller energy gap, a volume coil operating at a frequency similar to that in clinical MRI can accommodate a larger subject. This might compensate for the weaker EPR signals at a lower magnetic field and a corresponding RF frequency. Both the resonator and other parts of EPR instruments should be further improved to achieve a reasonable sensitivity of EPR detection at a low RF frequency to approach that of clinical MRI. Whole-body human EPR imaging, like proton MRI, is a dream in the application of EPR spectroscopy and imaging.

The future development of resonators for clinical EPR is not limited to these directions. Innovative technologies in RF/microwave electronics and advanced manufacturing techniques such as 3D printing may provide breakthroughs for EPR resonators in the future.