Rapid Scan EPR: Automated Digital Resonator Control for Low-latency Data Acquisition

Abstract

Automation has become an essential component of modern scientific instruments which often capture large amounts of complex dynamic data. Algorithms are developed to read multiple sensors in parallel with data acquisition and to adjust instrumental parameters on the fly. Decisions are made on a time scale unattainable to the human operator. In addition to speed, automation reduces human error, improves the reproducibility of experiments, and improves the reliability of acquired data. An automatic digital control (ADiC) was developed to reliably sustain critical coupling of a resonator over a wide range of time-varying loading conditions. The ADiC uses the computational power of a microcontroller that directly communicates with all system components independent of a personal computer (PC). The PC initiates resonator tuning and coupling by sending a command to MC via serial port. After receiving the command, ADiC establishes critical coupling conditions within approximately 5 milliseconds. A printed circuit board resonator was designed to permit digital control. The performance of the resonator together with the ADiC was evaluated by varying the resonator loading from empty to heavily loaded. For the loading, samples containing aqueous sodium chloride that strongly absorb electromagnetic waves were used. A previously reported rapid scan (RS) electron paramagnetic resonance (EPR) imaging instrument was upgraded by the incorporation of ADiC. RS spectra and an in vivo image of oxygen in a mouse tumor model have been acquired using the upgraded system. ADiC robustly sustained critical coupling of the resonator to the transmission line during these measurements. The design implemented in this study can be used in slow-scan and pulsed EPR with modifications.

Graphical Abstract

1. Introduction

Rapid scan (RS) electron paramagnetic resonance (EPR) has been gaining interest among researchers and developers in the field of magnetic resonance, both in academia and industry [1–19]. RS EPR promises two important deliverables: snapshot spectroscopy and enhanced sensitivity. In principle, a spectrum can be measured in nanoseconds. In practice, averaging is often needed to increase signal-to-noise ratios (SNR) of the measured signals. EPR sensitivity enhancement, when compared to the standard slow-scan methods, is achieved through desaturation of the electron spins system. Rapid passage through resonance reduces the interaction time between the spins and the excitation field, B₁, resulting in an increased power threshold for saturation. Maximum enhancement is achieved when the rate of passage is accelerated by increasing the scan frequency (or reducing the scan period) rather than widening the scan amplitude. The latter is selected to cover the spectral width of interest. Increasing scan rates permit the use of higher excitation powers without distorting EPR spectra. In this regime, the spin system is well-approximated as a linear system, and SNR enhancement becomes proportional to the amplitude of the B₁ field [1, 20–22].

The use of higher powers to boost SNR may come with elevated challenges for signal detection. For example, in continuous-wave (CW) RS EPR, an incident excitation wave produces reflection that may overwhelm the EPR signal. The power of the reflected wave is proportional to that of the incident wave. Excessive levels of reflection in the RS experiment may cause EPR signal distortion and increased levels of noise and background [23–25].

An automatic digital control (ADiC) method has been developed to protect EPR detection from elevated reflection. ADiC reliably establishes the critically coupling condition (CCC) for a wide range of coupling and tuning conditions (from empty to fully loaded resonator) within a time interval of tens of milliseconds. Within several milliseconds after establishing CCC, ADiC automatically initiates RS data acquisition. User input is not typically required; EPR measurements can be started from the moment the sample is placed in the resonator.

The robust performance of ADiC is achieved with the use of a global resonance frequency search. In every retuning event, a 20 MHz frequency sweep is generated, and the frequency of the lowest reflection is calculated. As a result, CCC is reliably established provided that the frequency drift does not exceed the sweeping range. In the case of failed tuning, which is very unlikely, ADiC changes the tuning range. In comparison with the standard automatic frequency control (AFC), the ADiC frequency search is non-continuous. After tuning/coupling is completed, ADiC switches to CW operation. As a result, the risk of EPR spectra distortion caused by simultaneous tuning and data acquisition is eliminated. This is especially important for EPR imaging, where probes with very narrow lines are used. For example, EPR oximetry is based on the conversion of linewidth into oxygen concentration or partial pressure [26–29]. Any line broadening due to the shift of the frequency would skew measured oxygen values.

The method of automatic digital tuning and coupling described here was successfully tested on a wide range of samples, including for a series of in vivo imaging experiments. The key control measurements are reported in this manuscript together with a detailed description of the ADiC methods, including enabling resonator design, software, firmware, and hardware. The main components of the presented technology are the microcontroller, the digitally tuned capacitor (see Fig. 1), the digital frequency source, and the arbitrary waveform generator (see Figs. 2, 3).

Fig. 1.

Function diagram of a digitally tunable capacitor. The net capacitance between points A and B depends on the state (on/off) of the five switches permitting 2⁵ = 32 net discrete capacitance values.

Fig. 2.

Fully functional printed circuit board resonator (PCBR). Photos of the top and bottom of the PCBR (left part of the figure) show essential resonator parts soldered on the PCB. The schematic diagram of the resonator is presented on the right part of the figure. Digital inputs to the PCB include clock, data, power, ground, and chip enable lines following Serial Peripheral Interface (SPI).

Fig. 3.

Block diagram of major components used for ADiC. The PC communicates with MC via serial protocol by sending short commands. MC communicates in real-time (there are no interruptions) with all units involved in ADiC. The microcontroller sends commands to AWG, DFS, the switch, and DTCs, and reads reflection levels from RP. A pair of DTC values are sent to RES via SPI. A frequency sweep waveform (pre-loaded into AWG) is output upon receiving a trigger from MC. Immediately before this event, MC flips the digitally-controlled switch to pass the frequency sweep signal to the resonator. The signal reflected from the resonator is measured by RP and digitized by MC, which also computes the frequency corresponding to the lowest reflection. Depending on the result, this process is repeated for neighboring DTC values. The DTC values for CCC are set at the end of this procedure. The resonance frequency is established by sending a digital command via SPI to DFS. The digital switch is flipped back to enable CW data acquisition. To reduce overhead time and ensure the collection of relevant RS EPR signals, MC blocks digitizer (DIG) from receiving incoming triggers during the tuning process. The entire tuning/coupling procedure is executed in real-time without involving the PC.

2. EPR resonator with digital components enables fast automation

CW EPR remains one of the most commonly used methods to excite and detect responses from the electron spin system. In comparison with the pulse modality, CW methods are dead-time-free [30]. However, EPR signals are measured in the presence of continuous excitation, and therefore continuous reflection. The reflected power is at its minimum (CCC) when the net resonator impedance is close to 50 Ohms. Reactive elements, such as variable inductors and/or trimmer capacitors [31–33] are introduced into the resonator circuitry to permit impedance adjustability to establish CCC. Depending on the reactive elements used, their inductance and capacitance values can be changed either mechanically [34–41] or electrically [5, 42–48]. The latter can be described as a semi-digital method because an impedance controlling voltage is used that is often generated by a digital circuit.

The mechanical approach is reliable but rather slow. A trimmer capacitor, coupling screw, or coupling inductance loop are used to change the resonator impedance. Despite its limitations, the mechanical approach remains a practical necessity for pulse EPR. Only manually adjustable elements are available that can withstand high-power (kilowatts) radiofrequency pulses.

In the semi-digital approach, the use of a digital-analog converter (DAC) permits remote control of reactive elements, such as voltage-tunable capacitors (VTC) recently developed by STMicroelectronics (Switzerland). The VTCs demonstrated improved performance when used in EPR resonators [6]. The downside of using voltage-controlled capacitors is that any voltage variations directly translate into EPR noise. Low-pass filtering [42, 44, 49] can be used to partially suppress the noise at the expense of a prolonged (dead) time with which the capacitance can be changed. An additional complication related to the use of analog controls is that magnetic field modulation (or field scan in RS) induces a small yet detectable voltage that contributes to the background signal [5, 16, 50].

A fully digital approach to resonator coupling is proposed that is both fast and noise insensitive. The enabling technology for this method is UltraCMOS Digitally Tunable Capacitors (DTC). A DTC is a millimeter-sized chip containing several fixed capacitors with associated fast digital switches (see Fig. 1). This chip communicates with external devices through Serial Peripheral Interface (SPI). A total of five wires are required for communication. Two wires provide power and ground connections. Three digital lines are used for the clock, data, and chip-enable signals. The data sent to the chip defines positions (‘on’ or ‘off’) for all switches. The total number of on/off combinations is 2^N, where N is the number of fixed capacitors. For the example in Figure 1, N = 5 and the net capacitance between points A and B has 32 discrete values. The advantage of DTC-based tuning/coupling is that digital signals are insensitive to noise. There are only two states, low and high, defined by the corresponding voltage levels (see Table 1). The switching speed of capacitances depends on data transfer rates (~ megabits per second).

Table 1.

PCB Resonator Specifications

Parameter	Range	Unit
Resonance frequency range (TC-defined)	700 – 1000	MHz
Max RF power (continuous)	34	dBm
DTC resolution	5	bits
Effective DTC1 & 2 resolution	6.6	bits
DTC range	0.9 – 4.6	pF
SPI clock	1 – 25	MHz
Capacitance switching time	1 – 20 (depends on SPI clock frequency)	μs
Quality factor (unloaded, CCC)	83
Digital input high	1.2–3.1	V
Digital input low	0–0.6	V
Power supply	2.3–4.8	V

A printed circuit board resonator (PCBR) has been developed (see Fig. 2) with incorporated DTCs that constitutes a functional EPR resonator. The schematics for this PCB resonator were designed using Eagle software (Autodesk, CA, USA). The boards were manufactured by PCBWay (Shenzhen, China). The resonator was originally designed for in vivo EPR imaging at 800 MHz. However, a wider range of frequencies (see Table 1) can be used. Frequency can be adjusted using a trimmer capacitor (2.5 pF - 10 pF), denoted in the figure as TC. The purpose of the fixed coupling capacitors (FCC in Fig. 2) is to optimize the coupling range so that the lowest DTC value permits the tuning of an empty resonator, while the highest DTC value establishes CCC when the resonator is fully loaded (see Table 2). For the single-loop resonator shown in Fig. 2, the capacitances for FCC₁ and FCC₂ were 2.4 pF and 0.3 pF, respectively. A chip balun (TCN2-122+, Mini-Circuits US) was used in the circuit that permits design miniaturization. Decoupling inductors (300nH, LQW18AN_8Z, Murata Electronics, Japan) decouple RF from the digital control circuit. DTCs PE64906 developed by Peregrine Semiconductors (San Diego, USA) were used that give a capacitance range from 0.9 to 4.6 pF. Digital control pins (DCP in Fig. 2) connect power, ground, clock, data, and chip-enabled wires, according to SPI protocol. Any device that outputs digital signals can be used to control DTCs such as Arduino, Teensy, Raspberry Pi, and a wide range of other available digital cards.

Table 2.

Measurements at critical coupling condition and filling factor of 70%.

Sample	DTC1/DTC2	Resonance frequency	Quality factor	Bandwidth
Empty	1/2	824.5 MHz	83	≈ 10 MHz
Deionized water	2/2	810.5 MHz	70	≈ 12 MHz
NaCl solution, 50 g/L	31/31	798 MHz	20	≈ 40 MHz

Specifications related to the EPR resonator shown in Fig. 2 are summarized in Table 1. The DTC chip used in the PCB resonator has a 5-bit resolution, permitting capacitance change from 0.9 pF to 4.6 pF with an increment ≈ of 0.15 pF. It was found experimentally that a small one-increment asymmetry between DTC₁ and DTC₂ can be used to effectively increase the total coupling resolution to 94 combinations (≈ 6.6 bits). For example (see Table 2), CCC of the empty resonator is achieved when DTC₁ index = 1 and DTC₂ index = 2 (the index runs from 0 to 31, a total of 32 positions). This small asymmetry does not negatively affect resonator performance.

The transition time between two steady-state reflection conditions was measured using a digital oscilloscope during DTC switching from index 10 to index 1. The reflection level was measured using Minicircuit’s ZX47-40+ power detector. For the clock rate of 1 MHz, the transient time is approximately 20 μs. The DTC specifications permit 25-times faster data transfer speed.

Resonator performance related to coupling range was tested experimentally by varying the resonator loading conditions. To mimic a lossy sample, a sodium chloride solution in water was used with different concentrations of salt. A glass bottle ( ID = 9 mm, OD = 11mm, height of 25 mm) was used to hold the solution. Three boundary cases are presented in Table 2. For an unloaded resonator, CCC is achieved at a low DTC index. Deionized water shifts the resonance frequency due to its high dielectric constant but does not strongly affect the coupling. A NaCl solution is conductive, and as such, strongly absorbs RF, changing both the resonator frequency and the quality factor. At the salt concentration of 50 g/L in the sample, DTCs indices reach their maximum value (highest capacitance). Any further increase in sodium chloride concentration made it impossible to critically couple the resonator. It is worth noticing that the 50 g/L concentration exceeds physiologically relevant salt concentration (e.g., in the blood) by a factor of five. As a result, this PCBR can be used for in vivo imaging.

Several resonator models analogous to the one shown in Fig. 2 have been tested using a previously reported rapid scan (RS) EPR imaging system [5]. For example, additional loops coaxial to L shown in Fig. 2 were soldered together to increase the resonator volume. A three-loop resonator was found to be optimal for volume imaging of extended samples, while a single-loop resonator gives better results for surface measurements. These resonators have been used to measure a wide variety of samples as well as for in vivo oxygen imaging of breast tumors in mouse models.

3. The automatic digital control unit

3.1. Block diagram and working principles

A previously described modular RS EPR imaging system [5] was upgraded to permit automated tuning and coupling. In the previous system, all the external hardware units were controlled by a personal computer (PC). PC continuously runs a multitude of processes most of which are not related to EPR. Several tasks requiring external control of the imaging system are not time sensitive. External magnetic field control in RS EPR is an example. In comparison, the task of resonator tuning and coupling must be performed within the shortest possible time. The PC, which coordinates signal flow between multiple external devices and internal computer components, may not be the optimal choice for this task. When it comes to automation, a standard industrial approach is to use microcontrollers (MC) that are the ‘brains’ of many electronic devices surrounding us in everyday life. In comparison with the PC, MC performs only the tasks explicitly programmed by the software developer. Many types of microcontrollers are commercially available, including the well-known Arduino. For ADiC, a Teensy 4.1 board was selected that has a clock rate of 600 MHz (it can be overclocked to up to 1 GHz). This MC supports three SPI ports and provides data handling capabilities (both analog and digital) sufficient to perform fast automated resonator tuning and coupling. Two separate ports SPI are used to control DTC and DFS as shown in Fig. 3.

The block diagram in Fig. 3 shows the essential components of the automatic digital control unit (ADiC) that perform the task of resonator tuning and coupling. Descriptions of these components are presented in Table 3.

Table 3.

Descriptions of the components in the block diagram shown in Figure 3

	Name	Vendor	Key specifications and use details
MC	Teensy 4.1	PJRC, USA	Clock: 600 MHz
DIG	U1084	Keysight, USA	Averaging at sampling rate: 62.5 MS/s
AWG	33600A	Keysight, USA	The output frequency is multiplied by eight
Switch	ZSW2-63DR+	Minicircuits, NY USA	Switching time: 1.6 μs
DFS	SC5511a	SignalCore, TX USA	Phase noise 1GHz@10kHz: −137 dBc/Hz
RP	ZX47-40+	Minicircuits, NY USA	Pulse response time: 800ns
DI	LQW18AN_8Z	Murata Elect., Japan	300 nH
DTC	PE64906	Peregrine Semi., USA	0.9 – 4.6 pF, 5 bits

As shown in Fig. 3, ADiC interfaces with the PC and the resonator. The automated tuning procedure is initiated by a MATLAB program that communicates with MC via a serial port. Upon receiving a command from the PC, the MC executes an algorithm (see Fig. 4) that establishes CCC in the shortest possible time. Following the tuning initiation command, the PC sets the digitizer (DIG in Fig. 3) into data acquisition mode. A U1084 PCIe card is used to capture and average periodic RS EPR signals. DIG does not measure RS data during the tuning/coupling process because MC blocks trigger signals to the digitizer. When CCC is established, MC releases triggers and DIG averages a pre-defined number of RS EPR signals. Data are transferred to the MATLAB software for further post-processing [3, 16, 51].

Fig. 4.

Firmware algorithm executed by Teensy MC. The PC initiates the tuning procedure by sending a serial command. After receiving this command, MC performs several steps aimed to find a pair of DTC values and the frequency that minimizes reflection from the resonator. Immediately after initiating tuning, the PC sends a command to the digitizer (DIG in Fig. 3) to measure RS EPR data. However, MC blocks the acquisition until the critical coupling conditions are established. As a result, there is no delay between the end of the tuning cycle and data acquisition. The reflection threshold is selected to satisfy the critical coupling (≈ −40 dB reflection compared to the incident power).

3.2. Software and firmware

The main user-interacting program that communicates with MC and acquires data from DIG is written using MATLAB graphical user interface (GUI) application App Designer (appdesigner). In addition, this GUI software controls the magnetic field scan, main magnet, and gradient units, as previously described [5]. Two major experimental modes can be distinguished: (S) spectroscopy and (I) imaging. ADiC is performed immediately before the initiation of either mode. However, if the goal in the S-mode is to acquire a series of RS spectra over a relatively long period, retuning is performed with user-defined time intervals. In the I-mode, the acquisition of 2500 – 3500 projections (depending on the imaging protocol) is divided into blocks with approximately 100 projections in each. Each data block is acquired within several seconds, depending on the number of averages. Retuning is automatically executed at the beginning of each block of measurements.

MATLAB-generated frequency sweep waveforms are uploaded into the 33600A AWG module (see Table 3). This instrument operates in the frequency range from DC (direct current) to 120 MHz. To permit resonator tuning at a central frequency (CF) of approximately 800 MHz, an eight-fold frequency multiplication was implemented. After multiplication, the sweeps cover a range of CF ± 10 MHz. The software permits the selection of the CF using serial communication.

As discussed above, microcontrollers have the advantage of real-time operation after a code is loaded into its firmware (see Supplemental Materials). The Arduino integrated development environment (IDE) is used towards this goal in conjunction with a Teensyduino loader. Both Arduino and Teensy supporting software can be downloaded from their corresponding websites. A C++ library was created to coordinate commands to the DFS (see Supplemental Materials). The block diagram describing the firmware algorithm executed by Teensy MC is shown in Fig. 4. The goal of this algorithm is to establish CCC within the shortest time interval. This goal is achieved by sequential switching of DTC values and measuring two parameters: (i) the lowest level of reflection and (ii) the frequency corresponding to this level. The search continues until the reflection is below a pre-selected threshold or all DTC combinations are tried. As discussed above, there are a total of 94 coupling indices, corresponding to 94 DTC values. In its search, the algorithm starts with the index i, selected during the previous tuning execution. If the threshold is not reached at i, the closest lower index (i − 1) is tried, followed (i +1), (i − 2), (i +2), etc. The process proceeds until either the reflection level is below the threshold, or all 94 indices are analyzed.

MC digitizes the reflection signal from the RP synchronously with the AWG-produced frequency sweep. The measured time-domain signal is translated into the frequency domain using a linear calibration function. Short-term Fourier analysis (change of frequency as a function of time) was used for the calibration. The function’s slope equals the known rate of change (20 MHz over 1 ms). The function’s offset is a measured delay between the trigger and the acquisition of the first digitized data point. The major contributor to the delay is the ZX47-40+ probe which has a rise time of 400 ns. This time is much smaller compared to the one-millisecond duration of the frequency scan. The bandwidth of the probe is larger enough not to cause significant distortion of the measured reflection signal. Additional fine-tuning of the resonance frequency is achieved by sampling two neighboring frequencies and measuring the corresponding reflection levels (see Fig. 4). The frequency corresponding to each measured block of data is transferred to the PC to be used for spectral alignment in post-processing.

3.3. Timing and trade-offs

The firmware algorithm described in the previous section is aimed to reduce the experimental overhead tuning/coupling time, OT, in comparison with the data acquisition time, AT. The signal-to-noise ratio (SNR) reduction expressed in percentage units can be estimated as:

$$SNRreduction=\left(1-\sqrt{\frac{AT}{AT+OT}}\right)*100\%$$ (1)

PC to MC serial communication constitutes the longest fixed period of approximately 10 milliseconds. Generating and acquiring reflection signals for a given DTC index takes ≌ 1. Fine frequency tuning (see Fig. 4) requires an additional ≈ 2 ms. After the initial tuning and coupling when the sample is placed in the resonator, ADiC tracks and corrects incremental deviations from CCC. As a result, changes in the resonator DTC index change do not normally exceed one, |Δi|≤1, and OT < 20 ms. SNR reduction can be evaluated for a given ADiC repetition period using Eq. (1).

4. Experimental evaluations

4.1. ADiC response to abrupt change in resonator loading conditions

A test was conducted to evaluate ADiC performance under the conditions of abrupt resonator impedance change. Towards this goal, a vial containing NaCl solution was placed in and removed from the resonator. A capillary containing degassed lithium phthalocyanine (LiPc) [52] crystals was used to measure changes in EPR spectra under loaded and unloaded conditions with and without the use of ADiC. The movement of this sample did not affect the position of the LiPc crystals. Figure 5 describes the results of the conducted experiment. First, the empty resonator was tuned to CCC and the EPR spectrum (blue trace in Fig. 5) was acquired. After the ADiC was turned off, the salt-containing sample was inserted. As expected, neither the frequency nor DTC values changed. The corresponding spectrum is shown as a green trace in Fig. 5. Turning on ADiC resulted in the purple trace, as the ADiC changed DTCs values from (1,1) to (31, 31) and readjusted the resonator frequency. The ADiC was turned off and the sample was removed. The EPR spectrum under the unloaded resonator conditions was measured (red trace).

Fig. 5.

ADiC test over widely varied resonator loading conditions. EPR spectra were measured with and without ADiC when a tube filled with NaCl solution was used to abruptly change the resonator impedance.

The most dramatic change in EPR intensity was observed in the transition from an empty tuned to a loaded untuned resonator (blue to green). This is the result of a resonator frequency shift (≈18 MHz) exceeding the resonator bandwidth (≈ 10 MHz). Also, the resonator was under-coupled, which is an unfavorable condition [53]. The difference between loaded/tuned and loaded/untuned is not as substantial due to a more favorable over-coupling condition [53] and the fact that the frequency still remains within the resonator bandwidth of ≈ 40 MHz (see Table 2).

4.2. Long-term stability of ADiC using a sample with time-varying electric properties

The experiment described in this section was designed to test the ability of ADiC to reliably maintain CCC over a long period of time during a gradual change of resonator loading from fully loaded to empty (see Fig. 6). A tube containing 200 μL of saturated salt (NaCl) solution was placed in the resonator. The solution underwent electrolysis using a pair of platinum wires. A voltage of 5V was applied to these electrodes. The purpose of using electrolysis, also accompanied by heating and evaporation, was to gradually remove the volume of water from the sample, thereby changing both resonance frequency and DTC values required to achieve CCC. As in the previous test, LiPc crystals loaded into a capillary tube provided the EPR signal. The ADiC sustained critical coupling over the entire measurement period (25 hours). As expected, an overall increase in EPR frequency, in synchronization with the decrease of DTC indices, can be observed during the loaded to empty resonator transition. At the beginning of the experiment, there was an increase in DTC index values and a decrease in frequency which was attributed to an increase in the sample salinity. Continuing electrolysis caused further reduction in the sample volume which resulted in less loading. Throughout the experiment, the resonator quality factor increased fourfold, which was also reflected in EPR intensity.

Fig. 6.

Long-term experiment showing critical resonator coupling as resonator coupling conditions change. a) Resonance frequency (blue) and DTC values (red and black) change over time as the resonator coupling conditions change. b) EPR spectral intensity remains optimal over time. A total of 3000 EPR spectra were successfully measured with a time interval of 30 seconds without a single failure.

4.3. In vivo imaging demonstration

Functional imaging of oxygen distribution in a breast tumor mouse model was performed using a homebuilt RS EPR Imaging system (see Fig. 7). During data acquisition, ADiC was engaged. As a result, the resonator remained critically coupled throughout the experiment. A set of 3276 projections was measured. RS signals were acquired at a constant scan frequency of 8130 kHz. The four-dimensional spectral-spatial image (355 × 80 × 80 × 80 points) was reconstructed from projections using the algorithm developed by Komarov et al [54]. 3D oxygen maps were obtained by fitting EPR spectra within each voxel.

Fig. 7.

In vivo EPR image quantifying oxygen partial pressure (pO₂) in a murine mammary tumor. (a) 2D cross-section of 3D oxygen map. (b) Histogram of pO₂ values obtained from 3D image.

Oxygen-sensitive probe Oxo71, synthesized in-house using recently published protocols [55], was used in the experiments. A 14-week-old female FVB/N MMTV-PyMT+ breast tumor-bearing mouse was anesthetized using airway isoflurane (1.5% at 1L/min). 50μL of 2mM Ox071 was injected into the tumor (number four mammary gland). The tumor size of 6 × 8 mm was measured with a caliper. The tumor depth was estimated as 6 mm. The mouse was then positioned into the resonator so that the tumor was placed inside the resonator loop (ID = 11 mm). The in vivo experiment was performed in strict accordance with protocols (Eubank, PI: #1602000254) approved by the Institutional Animal Care and Use Committee at West Virginia University. A 2D pO₂ cross-section across the image and distribution of pO₂ within the tumor and surrounding area are shown in Fig. 7.

Projections were acquired in blocks of 126. At the beginning of each block, zero-gradient spectra were measured. These spectra were used to correct the magnetic field drift occurring due to the permanent magnet heating by the gradients.

5. Discussion

Automation has been and remains a major trend and the goal for many industrial applications, from washing machines to self-driving cars. The microcontroller is a key enabling technology; it is compact, fast, and highly reliable. Personal computers may be more computationally powerful compared to MC. However, you would not trust a critical industrial process or an autopilot to a computer that may decide to install an update, reboot, or perform a noncritical task when least expected. An interruption caused by the computer may result in lost experimental time and/or sample.

The ADiC approach to EPR resonator handling is aligned with the industrial trend of digital automation. This trend is in the use of microcontrollers in concert with other digitally controlled devices that intercommunicate using several established protocols. Serial Peripheral Interface (SPI) is one such protocol. ADiC, which uses SPI to control both resonator tuning and coupling, is compatible with any digitally controlled EPR device. It can be easily integrated into new spectrometer/imager designs and/or be used as an upgrade for existing instruments.

The PCB resonator design described (see Fig. 2) in this article can be modified to create a wide variety of resonators tailored to a specific application of interest. For example, the loop can be replaced by a coil with a complex shape, such as the Alderman-Grant [31, 56, 57] or birdcage designs [58–60]. In addition to coupling, digital resonator tuning can be implemented by the addition of a DTC in parallel with TC (see Fig. 2) for the use of a wider frequency tuning range. The coupling range can be increased by changing the values of fixed capacitors FCC₁ and FCC₂. However, this change will increase the related increment of the net resonator impedance, increasing the chance the desired critical coupling conditions are not established. Finer adjustments can be made by the addition of a second DTC pair parallel to FCC₁. However, this may increase the overall tuning/coupling time. The latency can be decreased by reducing the frequency sweep time and /or increasing the digital communication speed. However, there would be an upper limit for both parameters beyond which the ADiC performance may be negatively impacted. Also, that change would require the use of a faster MC or, alternatively, the clock rate can be increased. For example, Teensy 4.1 can be over-clocked from 600 MHz to 1 GHz. The latter would require the installation of MC cooling elements. In addition, overclocking may result in clock frequency instability which would negatively impact the time to frequency domain reflection signal conversion used to compute the first guess of the resonance frequency (see Fig. 4). Increasingly more powerful microcontrollers are continually becoming available for the users. As a result, ADiC performance will only improve over time. Field Programmable Gate Array (FPGA) technology can be used as an alternative to the MC. FPGAs have several advantages, including high-frequency operation. However, they are more expensive and require high-level expertise.

Due to the use of a localized surface coil placed on the mammary gland of a mouse in the experiment described in the in vivo section 4.3, animal breathing did not affect tuning and coupling conditions to the extent of changing CCC. In the past, slow animal spontaneous repositioning would cause resonator decoupling and data corruption, making it challenging to perform long-term imaging. If a volume resonator was used the effect would be stronger, as the whole animal body would move inside the resonator. In this case, ADiC would help to maintain CCC.

Since the true distribution of oxygen is not known in vivo, a quantitative evaluation of ADiC in an imaging experiment is not feasible unless an independent method is used. However, it is obvious from the presented experimental results (Fig. 5) that decoupling and detuning of the resonator lead to SNR reduction which would directly translate into reduced accuracy of oxygen values in the images.

The ADiC method suits RS EPR the most because of its fast data acquisition capability. However, this method can be applied to the first-derivative continuous-wave (CW) EPR with modifications. For example, automatic tuning/coupling can be performed before every magnetic field sweep. However, such sweeps are often relatively slow compared to RS data acquisition times. As a result, ADiC would not help if a substantial deviation from critical coupling occurs during the sweep. A recently proposed fast scan EPR imaging method [34, 61] would benefit from this technology. ADiC can also be used in pulsed EPR; however, DTCs and the balun (see Fig. 2) must be protected from excessive peak power. This can be done by the introduction of a limiter, either passive or active. CCC is not required for pulse experiments. The resonator is often over-coupled. The use of ADiC will be beneficial if the frequency changes become comparable to the resonator bandwidth (see Fig. 5).

Highlights:

• An automatic digital control (ADiC) of EPR resonator is presented

• Microcontroller (MC) directly communicates with critical ADiC components

• Critical coupling is established within tens of milliseconds

• ADiC performance is evaluated using rapid scan EPR imaging system

• ADiC permits long-term measurements of dynamic samples