A Versatile High Speed 250 MHz Pulse Imager for Biomedical Applications

Abstract

A versatile 250 MHz pulse electron paramagnetic resonance (EPR) instrument for imaging of small animals is presented. Flexible design of the imager hardware and software makes it possible to use virtually any pulse EPR imaging modality. A fast pulse generation and data acquisition system based on general purpose PCI boards performs measurements with minimal additional delays. Careful design of receiver protection circuitry allowed us to achieve very high sensitivity of the instrument. In this article we demonstrate the ability of the instrument to obtain three dimensional images using the electron spin echo (ESE) and single point imaging (SPI) methods. In a phantom that contains a 1 mM solution of narrow line (16 μT, peak-to-peak) paramagnetic spin probe we achieved an acquisition time of 32 seconds per image with a fast 3D ESE imaging protocol. Using an 18 minute 3D phase relaxation (T_2e) ESE imaging protocol in a homogeneous sample a spatial resolution of 1.4 mm and a standard deviation of T_2e of 8.5% were achieved. When applied to in vivo imaging this precision of T_2e determination would be equivalent to 2 torr resolution of oxygen partial pressure in animal tissues.

INTRODUCTION

Knowledge of the distribution of oxygen concentrations in tissues is of great interest in medicine, especially in tumor radiation therapy and chemotherapy (1–3) and heart disease (4). Therefore, several methods that can provide information about partial oxygen pressure, pO₂, have been investigated including reductive retention of positron emission radiotracer (5, 6), Overhauser magnetic resonance imaging (7, 8) and ¹⁹F MRI (9). Electron Paramagnetic Resonance Imaging (EPRI) provides a fast and non-invasive method for the measurement of pO₂ in tissues using a spin probe exogenously administered to the animal (10–16). In this article we apply three dimensional pulse EPRI methodologies for in vivo imaging at 250 MHz, low enough for application to human-size animals.

Although the basic principles of in vivo EPRI are very similar to the principles of Nuclear Magnetic Resonance Imaging (MRI), the methodology of EPRI is considerably different from the conventional MRI due to the five to six order of magnitude reduction in phase (T_2e) and spin-lattice (T_1e) relaxation times of the spin probes. This makes impossible the application of pulsed magnetic field gradients for imaging macroscopic objects, including living species. Microscopic objects can be imaged using pulse gradients, see e.g. (17) for a recent example.

Application of static magnetic field gradients (`gradients') allows the use of multiple EPRI modalities. Current EPRI applications are dominated by continuous wave (CW) imaging, which appears to be the most flexible modality considering the simplicity of the equipment and the broad variety of spin probes it can use. Conventional CW imaging is based on the filtered back projection reconstruction algorithm (FBP). Magnetic field swept spectra in the presence of gradients are acquired. The gradient directions and/or amplitudes are changed and the process repeated until the number of projections sufficient for image reconstruction is acquired. For a determination of pO₂, a spectral-spatial spectroscopic image can be obtained (18). The oxygen concentration is measured from the linear relation between pO₂ and the spin-packet line width. The spin-packet line width is obtained by fitting the fourth (spectroscopic) dimension of the 4D spectral-spatial image (19). The disadvantage of CW imaging is its relatively slow acquisition speed because the EPR spectrum requires the magnetic field to be swept. Because magnetic field coils typically have a large inductance, the imaging time is dependent on the maximum achievable magnetic field sweep rate. At present in our 250 MHz CW EPRI instrument (11) the time for one scan of magnetic field is from 0.3 to one second. In our laboratory, a spectral-spatial CW image of a living animal limb takes about 45 minutes to acquire. This time is on the order of the clearance time of spin probes from tumors in the living organism and, therefore, can limit the use of CW imaging for time-critical biological applications.

Recently there has been increasing interest in developing alternative fast EPRI techniques, such as spinning gradient EPRI (20), rapid scan (21), saturation CW imaging (22) as well as pulse imaging. In the pulse methodology the EPR spectrum can be acquired in a time comparable to the T_1e of the spin probe. Most spin probes used for pulse imaging have T_1e of the order a few microseconds. Even taking into account that for reasonable SNR the acquisition and averaging of 1000 or more measurements is required, a faster acquisition time than CW EPRI seems possible – milliseconds rather than seconds. The straightforward approach of using pulsed free induction decay (FID) imaging (23) was found to be not very successful at low frequencies since the T_2e * of most spin probes is comparable with the `dead time' of EPR imagers. Truncation of FID time traces leads to serious artifacts in the obtained projections. In order to overcome imager `dead time' problems, a single point imaging methodology (SPI) has been applied to EPR imaging (24). In the simplest form a single point on the FID at a known time, t_p, is recorded as a function of stepped gradient amplitudes sampled on a cubic grid. This signal forms a 3D “pseudo-echo”, the FT of which generates a spatial image. The spatial information is encoded into the phase of FID. The relaxation times are extracted from multiple images obtained at different t_p. Since no information prior to t_p is required, SPI has no artifacts caused by the `dead time'. Despite being the most artifact-free low frequency pulse EPR imaging methodology SPI has some disadvantages, the primary one of which is the acquisition time. A high resolution 3D SPI image (e.g. 100×100×100) requires almost a half million measurements, each in the presence of a different gradient (see the Materials and Methods section). Analogous to the MRI spin echo experiment (25, 26), a number of laboratories have developed electron spin echo imaging (ESE) at high frequencies (27–30). Mailer et al. demonstrated accurate oxygen images using three dimensional time-domain ESE imaging at 250 MHz (31). The application of this modality to living animals was presented briefly elsewhere (32). Time-domain ESE requires a considerably smaller number of measurements than SPI and accurately and directly measures T_2e. As a drawback, since this method is based on the FBP algorithm, it requires application of somewhat higher gradients for the comparable with SPI spatial resolution. The details of the ESE imaging modality will be described in the Materials and Methods section.

From the above it is clear that there is no single imaging method that can satisfy all experimental needs of in vivo imaging. Therefore, a versatile instrument that can easily switch between different imaging techniques is essential. An important requirement for such an instrument is a minimum imaging time. Therefore, it has to have high signal-to-noise ratio (SNR) and exhibit an efficient control of devices and data acquisition. Although a number of low frequency instruments for in vivo imaging exist, see e.g. (21, 31), none of them satisfies all of our requirements.

In this article we present the salient technical features of our redesigned 250 MHz pulse EPR instrument for the imaging of small animals. This flexible imager executes virtually any pulse EPR imaging experiment with a high SNR and excellent performance of the pulse forming and data acquisition systems. We demonstrate the performance of this instrument in ESE and SPI imaging experiments. For the ESE method we present promising acquisition strategies, enabled by high-speed data acquisition.

MATERIALS AND METHODS

Spin probe and the phantom

The spin probe used for the EPR imaging was a 1mM solution of OX063H radical (methyl-tris[8-carboxy-2,2,6,6-tetrakis[(2-hydroxyethyl]benzo[1,2-d:4,5-d']bis[1,3]dithiol-4-yl]- trisodium salt, molecular weight = 1,427 from GE Healthcare. This probe is a pharmaceutical grade MR contrast agent. The spin probe was contained in a flat-bottomed borosilicate glass cylinder of 9.5 mm inner diameter and 45 mm length. The sample was deoxygenated using a multiple-cycle freeze-pump-thaw technique and flame-sealed. The sample was placed into the resonator horizontally, along the resonator's axis of symmetry and centered in the axial plane of the resonator. Because the sample was half-full this produced a meniscus at the liquid - air contact surface. The volume and concentration of the sample are similar to those in mice during EPR oxygen imaging experiments (14).

Pulse EPR Imager

Figure 1 shows a schematic drawing of our time-domain EPRI system operating at 250 MHz (magnetic field ~9 mT). The imager has a four coil air-core magnet with 4^th order field compensation and Anderson-type X-, Y- and Z- gradient coils (33, 34). A BMN 3x±40/60 C5 (Bruker BioSpin Corporation, Billerica, MA 01821-3991, USA) linear current supply was used to drive the main coil and the X- and Y- gradients. The Z- gradient coil was driven by a BOP 20-20M (KEPCO, Inc., Flushing, NY 11355, USA) linear current supply. Quine et al. originally built the RF bridge of the imager according to the design of a 250 MHz homodyne pulse EPR spectrometer for relaxation measurements (35). Here we present a greatly modified version of this bridge tailored to enhance performance for the purposes of in vivo imaging. Modifications include the use of a different resonator operated in reflection mode; a new transmit/receive (T/R) switch capable of interfacing with the reflection type resonators; an optimized design of the pulse arm and DC coupled video amplifiers. Additionally we constructed a new data acquisition and gradient control system.

Figure 1.

A block diagram of the pulse EPR imager. The bold line represents the pulse channels of the pulse generator. 1 – HP8662A source (Agilent Technologies, Inc., Santa Clara, CA 95051, USA); 2 – ZMSC-2-1 power splitter (Mini-Circuits, Brooklyn, NY 11235, USA); 3 – MO-B2-412 phase shifter (Pulsar Microwave Corporation, Clifton, NJ 07012, USA); 4 – Mini-Circuits ZFL-500 amplifier; 5 – Mini-Circuits ZASWA-2-50DR switch; 6 – Mini-Circuits SHP-100 filter; 7 – 50CAL10 0–10dB adjustable attenuator (Alan Industries, Columbus, IN 47201, USA) and P/N 50DR-046 rotary step-attenuator (JFW Industries Inc., Indianapolis, IN 46237, USA); 8 – 2 kW power amplifier (Tomco Technologies, Norwood, SA 5067, Australia); 9 – Mini-Circuits CAT-10 attenuator; 10 – cross-coupled diodes 1N4151; 11 – 3A2BC circulator (Renaissance Electronics Corporation, Harvard, MA 01451, USA); 12 – HMC546MS8G switch (Hittite Microwave Corporation, Chelmsford, MA 01824, USA); 13 – Mini-Circuits ZYSWA-2-50DR switch; 14a – P240-270VDG low noise amplifier (Advance Receiver Research, Burlington CT 06013, USA); 14b – 250GT low-noise amplifier (Anglelinear, Lomita, CA 90717–0035, USA); 14c – AU-1A-0150 amplifier (MITEQ, Hauppauge, NY 11788, USA); 15 – Mini-Circuits ZYSWA-2-50DR; 16 – Mini-Circuits SHP-100 filter; 17 – Mini-Circuits ZFSC-2-1 splitter; 18 – MITEQ AUP-1479 amplifier; 19 – Pulsar MO-B2-412 quadrature phase shifter and Sage 6709 mechanical variable phase shifters (Sage Laboratories Inc, NH 03051, USA); 20 – Alan Industries 50CAL10 0–10dB adjustable attenuator; 21 – QHM-6-165 90° hybrid splitter (Merrimac, West Caldwell, NJ 07006, USA); 22,23 – AD831-EB multipliers (Analog Devices Inc., Norwood, MA 02062, USA); 24,25 – home-made video amplifiers; 26,27 – Mini-Circuits BBLP-39 low pass filter.

The reference frequency was generated by a HP8662A RF generator {1}. Here numbers in braces that follow the device name refer to the part numbers in Figure 1. The output power of 1.3 mW divides equally between the pulse and the reference arms of the RF bridge. The low-power part of the pulse arm of the imager includes a digitally controlled Pulsar phase shifter {3}, a Mini-Circuits RF amplifier {4}, a Mini-Circuits switch {5}, and a high pass filter {6}. These components allowed us to generate RF pulses with rise and fall times better than 8 ns and phase controlled in 90±5 degree steps. The manual rotary step-attenuator that controlled the pulse power {7} was placed before the power amplifier. The two-stage high power linear RF amplifier {8} (240–260 MHz, maximum power in the linear regime - 2 kW, 2% maximum duty cycle) manufactured by Tomco Technologies, Norwood SA, Australia (36) was used to amplify pulses to ~1 kW peak power. The 10 dB fixed attenuator {9} on the output of the amplifier reduced the power to 100 W (maximum power was restricted by the power rating of components following the amplifier output). These amplified RF pulses had rise and fall times of ~12 ns. The gate of the amplifier's high power stage was controlled externally. The leading edge of the gate pulse preceded the RF excitation pulse by 325 ns. To reduce the switching noise of the preamplifier the preamplifier was not gated, i.e. it was always on. The amplifier has noise blanking that reduces the amplifier noise to within 20 dB above Johnson noise in less than 100 ns after the trailing edge of the RF pulse.

Unlike our earlier instrument in which we employed a bimodal cross-loop resonator (31,37) in this work we used a reflection mode single-loop single-gap resonator (LGR) consisting of a cylindrical inductive sample holding element (16 mm diameter, 15 mm long) with a single bridged capacitive element (11). The resonant structure was fabricated from ABS (acetonitrile-butadiene-styrene) plastic that has a good dimensional stability and can be easily plated. Conducting surfaces were fabricated by accurate plating of 12.5 μm silver (approximately 3 skin depths at 250 MHz) and a 2 μm flash of gold for protection. The plating was provided by the facility in the laboratory of Prof. Eugenijus Norkus at the Department of Catalysis, Institute of Chemistry, University of Vilnius, Vilnius Lithuania as a kind gift. For the fine adjustment of resonator frequency we added a non-magnetic 1–30 pf variable capacitor Johanson 5601 (Johanson Manufacturing Corporation, Boonton, NJ 07005, USA) connected in parallel with the resonator's capacitive gap. The open structure of the LGR allowed easy access to the inner volume, which is useful for good animal placement. The quality factor, Q, of the empty resonator was 280 but for pulse experiments the loaded quality factor was reduced to 17 using a shunting resistor of 750 Ohms across the resonator's gap. The cavity was critically coupled to avoid a high level of reflections that can impair the detection system. A very important advantage of the LGR is its very high power conversion factor B₁/√W so that an RF power of only 50 W was required for the 35 ns π/2- and 70 ns π- pulses needed for echo generation. A broadband high-isolation-low-insertion loss transmit/receive (T/R) switch whose overall isolation exceeded 110 dB was designed for use with this resonator. A Renaissance 3A2BC circulator {11} was used to direct power to and from the resonator. This circulator has a sufficient bandwidth (220–400 MHz) to pass RF pulses as short as 20 ns with minimal distortion and reflections (an RF pulse of 20 ns has an approximate bandwidth of 50 MHz). Our previous attempts to use circulators with narrower bandwidths (e.g. less than 30 MHz) failed due to the high level of reflections found. The Renaissance RF circulator, along with a high power Hittite switch (capable of handling up to 20 W power applied continuously) {12} and a high isolation Mini-Circuits switch {13} have together only 2.6 dB of insertion loss. The circulator itself is a source of a spurious signal, comparable with the signal of our typical samples. The two pulse EPR sequence generated a narrow distinctive “echo” from the circulator. With the increase of delay between pulses this spurious echo intensity decreased with a characteristic decay time of about 400 ns. This signal was very stable and thus was easily corrected by the baseline subtraction. It did, however, limit the dynamic range of the imager. The true dead time of the imager was about 280 ns, however due to the circulator “echo” the protection switch was opened only after 350 ns after the last pulse. The bandwidth of the low noise (0.5 dB NF) amplifier (LNA) from Advance Receiver Research {14a} was 30 MHz. The components of the T/R switch, the LNA and the second stage RF amplifier were housed in a separate case and placed close to the resonator. The EPR signal (further amplified by two broadband single-stage amplifiers {14b} and {14c}) was demodulated using Analog Devices multipliers {22, 23} and fed into custom built DC coupled 20 MHz bandwidth video amplifiers {24, 25} with selectable gains from 34 dB to 54 dB. The signals were then filtered by low pass filters {26, 27} and digitized by fast analog-to-digital converters.

Imager control and data acquisition

The imaging experiment was controlled by two standard PC stations operated under Windows XP (Microsoft Corporation, Redmond, WA 98052, USA). The pulse console computer (Figure 1, PC 1) contained a PulseBlasterESR pulse programmer (SpinCore Technologies, Inc., Gainesville, FL 32606, USA; 21 channels, 2.5 ns resolution, 2.5 ns minimum pulse and 12.5 ns minimum delay duration), an Acqiris AP235 ADC board equipped with 24 MBytes of memory (Agilent Technologies, Inc., Monroe, NY 10950-1430, USA; 2 channels, 8 bit ADC resolution, 2 ns minimum dwell time in a 2 channel configuration; phase-locked to the HP8662A source) and a PCI-GPIB board (National Instruments, Austin, TX 78759, USA) for interfacing with the HP8662A RF source {1}. The pulse programmer controlled the phase of the phase shifter {3}, triggered the RF pulse switch {5}, the gate of the power amplifier {8}, the protection switches {12, 13 and 15} and triggered the ADC board. The repetition rate of the experiment was controlled by the PulseBlasterESR unit.

The front-end program of the pulse console, SpecMan4EPR (www.specman4epr.com), is multipurpose pulse EPR software, which can generate arbitrary pulse sequences using a variety of third party devices (38). The magnetic field and gradients were controlled from another computer, PC 2, under control of a home-written program that uses the Labview™ environment (32). CW imaging in our laboratory is performed using the same software. The analog signals to drive the magnetic field and the linear current gradient amplifiers were generated using a PCI-6733 16-bit DAC board (National Instruments, Austin, TX 78759, USA). PC 1 and PC 2 stations were synchronized using handshake protocol organized between the printer port LPT-1 of PC 1 and the digital I/O port of PCI-6289 board housed in PC 2. The sequence of gradients and magnetic fields was defined using look up tables loaded from a file generated prior to the experiment in MATLAB (The Mathworks, Inc., Natick, MA 01760, USA).

Electron spin echo imaging and data processing

ESE imaging protocol uses the protocol for 3D FBP reconstruction (12, 31) and requires the acquisition of a number of projections with different orientations and fixed gradient amplitude, $\mid \overrightarrow{G}\mid$. The optimum gradient layout requires gradient directional vectors to be uniformly distributed on the surface of the unit hemisphere. The equal solid angle scheme (39) is very close to this layout. The overall number of projections required for the imaging is

$$N=\sum _{k=1}^{N_{\mathit{polar}}}\mathit{round}\left(N_{az}\sin \left(\frac{\pi }{2}+\frac{\pi }{N_{\mathit{polar}}}\left(\mathrm{k}-\frac{1}{2}\right)\right)\right),$$ [1]

where N_az and N_polar are the maximum numbers of azimuthal and polar projections respectively. round() is a function that rounds its argument towards nearest integer number. In the text an image with N_az and N_polar projection is referred to as N_azxN_polar. The number of projections derived from Equation [1] reduces the total number of projections by approximately 2/3. Thus, an equal solid angle 14×14 image requires 126 projections, while a 32χ32 image requires 654 projections. For the reduction of FBP reconstruction artifacts the original set of projections was four-fold linearly interpolated to obtain a larger set of projections (39). These projections are filtered with a 3D Ram-Lak filter with a cutoff at 0.5 times the Nyquist frequency. The ESE images presented in this article were reconstructed using FBP code developed in our laboratory (39, 40).

The electron spin echo was detected using the two-pulse sequence (π/2)_i−τ−(π)_j−τ− echo : here i and j indices denote the possible ±x, ±y phases of the RF pulses and τ is the time delay between pulses. The π/2– and π – pulses had the same amplitude and durations of 35 ns and 70 ns respectively. The applied RF power was optimized by maximizing the echo signal. A CYCLOPS 8-step phase cycling scheme (x, y; −x, y; x,−y; −x,−y; y, x;−y, x; y,−x; −y,−x) was employed (unless mentioned separately). The sequence repetition time was 15 μs, and the shortest allowed by the duty cycle of the Tomco power amplifier. To obtain the image of phase relaxation five separate measurements with different τ delay values were performed. These delays have to cover the range of times suitable for correct determination of the relaxation time. For samples with a broad distribution of relaxation times (e.g. in a living organism), the precision of relaxation time determination was greater when these delays were spaced logarithmically. Consequently, ESE T_2e images were taken with τ spaced logarithmically between 0.63 μs and 2.4 μs.

All imaging protocols used in this work are summarized in Table 1. The ESE-I protocol demonstrates the basic timing of the technique. The “high speed” and “quality” protocols ESE-II and ESE-III include the gradient settling times and have off-resonance data collection for baseline subtraction. The “a” protocols are simply the multiple echo versions of ESE-II and ESE–III.

Table 1.

Imaging protocols.

Protocol	Description
ESE-I	Two pulse echo sequence(π/2)–τ–(π)–τ–echo; 35 ns π/2- and 70 ns π- pulses; τ = 0.63 μs; 1000 averages, including 8-step phase cycling, repetition time 15 us; time domain trace 1400 points, 4 ns dwell time; no baseline correction
ESE-Ia	The same like ESE-I except for five sequences with different τ logarithmically spaced between 0.63 μs and 2.4 μs are obtained
ESE-II	Two pulse echo sequence(π/2)–τ–(π)–τ– echo; 35 ns π/2- and 70 ns π- pulses; τ = 0.63 μs; 8000 averages, including 8-step phase cycling, repetition time 15 us; time domain trace 1400 points, 4 ns dwell time; baseline correction every fourth trace (33 traces); FBP, equal solid angle 14×14 (126 projections), $\mid \overrightarrow{G}\mid =10\mathrm{mT}∕\mathrm{m}$
ESE-IIa	The same as ESE-II except for five sequences with different τ logarithmically spaced between 0.63 μs and 2.4 μs are obtained
ESE-III	Two pulse echo sequence(π/2)–τ–(π)–τ–echo; 35 ns π/2- and 70 ns π- pulses; τ = 0.63 μs; 16000 averages, including 8-step phase cycling, repetition time 15 us; time domain trace 1400 points, 4 ns dwell time; baseline correction every fourth trace (165 traces); FBP, equal solid angle 32×32 (654 projections), $\mid \overrightarrow{G}\mid =15\mathrm{mT}∕\mathrm{m}$
ESE-IIIa	The same as ESE-III except for five sequences with different τ logarithmically spaced between 0.63 μs and 2.4 μs are obtained
SPI-I	FID detection using single π/2- pulse of 30 ns 1000 averages, including 4-step phase cycling correction, repetition time 7 us; time domain trace 400 points, 4 ns dwell time; no baseline correction
SPI-II	FID detection using single π/2- pulse of 30 ns; 16000 averages, including 4-step phase cycling correction, repetition time 7 us; time domain trace 400 points, 4 ns dwell time; baseline correction for every ninth trace (113 traces); SPI, 11×21×11 gradients grid restricted using $\mid \overrightarrow{G}\mid \le G_{\max }$ inequality (1007 projections), $\mid {\overrightarrow{G}}_{\max }\mid =15\mathrm{mT}∕\mathrm{m}$, tp = 0.9 μs

To avoid truncation artifacts due to the dead time of the imager we used only the falling portions of the echoes rather than the full echo. The peaks of the echoes were fitted with Lorentzians for all projections separately. It was found experimentally that Lorentzian function provides the best approximation of the echo peak shape. The maximum of the statistical distribution of Lorentzian centers was taken as the ESE zero time for all traces. Phase correction using the two signals in quadrature was applied independently to every echo to maximize the real part of signal at zero time. The data were Fourier transformed (FT) to obtain spatial projections ready for inverse Radon transformation. Only the real part of Fourier transformed data was used for further reconstruction. These frequency projections were truncated using the relation: $FOV=\gamma \cdot \mid \overrightarrow{G}\mid \cdot \Delta L$. Here FOV is the field of view in MHz, γ = 28.02 MHz/mT is the electron gyro-magnetic ratio and ΔL is the desired spatial field of view. All data processing was performed using script command files written in the MATLAB (The Mathworks, Inc., Natick, MA 01760, USA) programming language.

Each set of projections recorded with different τ was reconstructed separately. A T_2e map was obtained by fitting the dependence of each image voxel amplitude on 2τ using the exponential decay function:

$$A\left(t\right)=A\left(0\right)\cdot \exp (-2\tau ∕T_{2e}).$$ [2]

Here A(0) is the amplitude of the signal at τ = 0 and T_2e is the phase relaxation time. Only voxels with signal amplitude above 20% of the maximum (from the image recorded with shortest τ) were used. The results were three-dimensional spatial (i.e. amplitude at zero-time) and 3D T_2e images. For the analysis of the precision of the relaxation time determination the outer layer of voxels in the T_2e image was excluded from the statistics. For the pO₂ determination the conversion coefficients for the OX063H radical from Ref. (14) were used.

Single Point Imaging

The basic SPI technique is described elsewhere (24). The required FIDs were generated by 30 ns pulses with a repetition time of 7 μs. This pulse duration corresponds to a 71° Ernst angle for our spin probe with T_1e = 6.2 μs (41). The repetition rate was limited by the maximum allowed duty cycle of a power amplifier. Full CYCLOPS phase cycling was used. Gradients were generated on a three dimensional rectangular grid 11×21×11. The number of projections is approximately equal to:

$$N\approx \frac{\pi }{6}\prod N_i,$$ [3]

where N_i are the three image dimensions. The coefficient of π/6 in Equation [3] originates from the ratio of volumes between sphere and cube with equal diameter and side since measurements were performed only for the elements of the grid that satisfy the inequality $\mid \overrightarrow{G}\mid \le G_{\max }$. For the dimensions mentioned above, 1007 gradients were sampled. The number of measurements can be further decreased by factor of one half utilizing the symmetry relation between measurements with gradients $\overrightarrow{G}$ and $\overrightarrow{G}\prime =-\overrightarrow{G}$, however we have found that this reduction negatively affects image quality. To produce an image the 11×21×11 experimental data were zero padded to obtain a 22×42×22 matrix and Fourier transformed. No additional digital filters were applied.

Measurements and Algorithms

Main coil and gradient coils settling times

The gradient and main field coils in any setup for in vivo imaging have considerable inductance and therefore substantial time is required to achieve the desired magnetic field in these coils. For linear current supplies the settling time of a coil is approximately proportional to the magnetic field or gradient step (here expressed in seconds per Tesla or seconds per T/m). The settling time of our main DC field coil is 45 s/T. The settling times of X-, Y- and Z- gradient coils are 0.6 s*m/T, 1.8 s*m/T and 2.8 s*m/T, respectively.

For the SPI experiment with a gradient interval of ±15 mT/m and 11×21×11 image dimensions the maximum gradient step is about 15 mT/m*2/11 = 2.73 mT/m, which requires about 8 ms for the slowest Z-gradient coil. For ESE imaging with the same maximum gradient and a 14×14 protocol the gradient jump will be about 10 mT/m·2/14 = 1.4 mT/m and will take about 4 ms (5 ms was used). To avoid gradient jumps higher than those described above the gradient table was sorted into optimal order (see (24) for SPI and (39) for ESE). For the baseline correction, traces were recorded with the magnetic field 0.9 mT lower than the resonance condition. To ensure that magnetic field had reached its equilibrium value we set a time of 100 ms to settle the off-resonance field step and 250 ms to settle once back on-resonance.

Receiver arm bandwidth

The bandwidth of the receiver arm of the imager was measured using a network analyzer HP8752ES (Agilent Technologies, Inc., Santa Clara, CA 95051, USA). The excitation arm of the analyzer (output power of −35 dBm) attenuated by 40 dB was connected to the resonator port of the circulator {11}. The power arm port of the circulator was terminated with 50 Ohm. The Network analyzer was phase-locked to the HP8662A source {1}. The desired range of frequencies of the network analyzer was swept using computer control. The oscillatory time traces at each frequency value acquired by the Acqiris AP235 board (in single shot mode, trace length 4 μs) were Fourier transformed to obtain the signal amplitude and this, plotted versus frequency gave the dependence of signal amplitude on excitation frequency and hence the amplifiers bandwidth.

Imager frequency characteristic

To measure the cumulative imager profile a 1 mM OX063H phantom was placed into the resonator and FIDs (for SPI) or spin echoes (for ESE) were recorded as a function of the stepped magnetic field and then Fourier transformed. This gave the dependence of the FID and echo signal amplitudes and phases on magnetic field position. Since the natural inhomogeneous line width of the OX063H, 16 μT, is sufficient to produce an echo no imaging gradients were applied.

Measurement of T_2e and spatial resolution

The performance of ESE imaging was characterized by the T_2e and spatial resolution. For the measurement of the T_2e resolution, only voxels of the homogeneous phantom with amplitudes greater than 20% of the maximum were selected. We defined the T_2e resolution as the standard deviation of the T_2e from all of the voxels in the homogeneous phantom with one outer layer eroded. The spatial resolution of an image can be quantified by the response of an image to an abrupt step function change in sample density, viz. no sample at one side and constant sample density on the other side of the boundary of a homogeneous phantom (40). The change of image signal intensity obtained along a line perpendicular to this edge was fitted with the Gauss error function $erf(x∕\sigma \sqrt{2})$. The width of this error function (σ) gives an estimate of the spatial resolution. The σ value is an average of 75 measurements distributed on the surface of the sample adjacent to the wall of the bottle. The spatial resolution of the ESE images was measured from an images obtained with τ = 0.63 μs.

T_2e measurements under non-imaging conditions

Phase relaxation was measured using a two-pulse sequence. The π/2– and π – pulses had the same amplitude, and durations of 35 ns and 70 ns respectively. Eight step phase cycling was used and τ was varied from 0.63 μs to 20 μs (120 points logarithmically spaced). The repetition time was 80 μs. Gradients were not applied during the measurement. The falling portion of the echo was integrated to obtain the amplitude.

RESULTS AND DISCUSSION

Receiver arm bandwidth

The pulse imager acquires the complete signal line shape all-at-once and therefore its receiver arm frequency bandwidth has to be sufficient to accommodate the whole spectrum of signal frequencies. The bandwidth of the receiving arm of the pulse bridge was measured to be about 37 MHz (see Figure 2). This bandwidth should be in principle sufficiently flat to perform imaging of 3 cm cubic object with an applied gradient of up to 30 mT/m (0.03 m · √3 · 30 mT/m · 28.02 MHz/mT = 35.6 MHz) although in practice other factors limit the useful bandwidth - vide infra.

Figure 2.

The imager receiver arm frequency response profile.

Frequency profile correction

The collective distortion of the signal frequency profile introduced by the imager is a complicated function of the receiver arm frequency response profile, the resonator bandwidth and the frequency spectrum of applied RF pulses. One can significantly improve the quality of the image by correcting all the acquired projections using this function. Since the response of the spin system is not linear with power and RF pulses have a non-ideal shape, it is very hard to calculate a correction function from the first principles. The alternative is to determine the function experimentally for a given instrument, quality of the cavity (Q) and duration of the RF pulses (tⁱ_p). An example of such a function for an ESE pulse sequence is presented in the Figure 3. As one can see the cumulative profile (7.1 MHz) is considerably narrower than the bandwidth of the resonator (250 MHz/17 ≈ 14.7 MHz) and the pulses (1/70ns ≈ 14 MHz, 1/35ns ≈ 29 MHz). The cumulative bandwidth of the imager can be roughly estimated by the relation:

Figure 3.

The cumulative frequency profile of the imager as determined using a two pulse echo signal. The profile was measured with the resonator Q set to 17 (equivalent bandwidth 14.7 MHz) and an ESE sequence with 35 ns and 70 ns π/2- and π- pulses (equivalent bandwidths of 28.6 MHz and 14.3 MHz, respectively).

$$BW\approx 1/\left(\frac{1}{B{W}_R}+\sum \frac{1}{B{W}_p^i}\right)\approx 1/\left(\frac{Q}{v}+\sum t_p^i\right)\approx 5.8\mathrm{MHz}.$$ [4]

Here BW_R and BWⁱ_p are the bandwidths of resonator and RF pulses, respectively; ν is the imager frequency. The direct consequence of Equation [4] is that for the SPI pulse sequence, that consists of a single 29 MHz-wide π/2-pulse, the cumulative bandwidth will be always broader than the ESE bandwidth. Using Equation [4] we can estimate the largest possible bandwidth of our instrument to be about 19 MHz for ESE and 27 MHz for SPI. These estimates assume that the shortest RF pulses our instrument can generate are 16 ns and that the minimum feasible resonator Q is five. These experiments will require RF power on the order of 1 kW. This power level is achievable by the power amplifier used but exceeds the maximum allowed power of the present receiver protection circuitry.

Baseline correction

Considerable improvement of image quality was obtained when off-resonance time traces were subtracted from the on-resonance data traces. This procedure removed virtually all image artifacts due to RF reflections, circulator spurious “echoes” and resonator ring down. Figure 4 shows axial cross-section of the phantom. The meniscus can clearly be seen. However it can be noticed that image reconstructed from projections corrected using just one baseline trace recorded prior to the experiment has an obvious “zero” artifact (marked by an arrow in Figure 4A). This artifact is independent of imaging modality and is located in the center of the image, at the point where all the gradients coincide with zero value. We believe that the major source of this artifact is ambient frequency pick-up. This is not surprising considering the high sensitivity of the instrument. We found that the best suppression of the “zero” artifact was achieved when off-resonance time traces were acquired immediately after every data trace. This mode of operation was very time consuming because of the amount of on-off field stepping involved. Therefore we acquired off-resonance time traces less frequently and generated the missing off-resonance traces using cubic spline interpolation for every point of the time trace. It was found empirically that a baseline acquisition for every fourth trace was sufficient for a high quality ESE image (see Figure 4B). For SPI baseline acquisition for every ninth trace was satisfactory.

Figure 4.

Influence of the baseline correction on the quality of image obtained with the ESE-III protocol. Images were reconstructed from the projections corrected using: one base line acquired prior to the experiment (A) and baselines acquired for every fourth projection (B). The area of the largest artifact (marked by the arrow in Figure 4A) corresponds to the three gradients zero crossover point of the imager. An axial cross section of the phantom is presented.

Acquisition speed

An image's overall acquisition time depends both on the imaging parameters (e.g. the number of projections, base line traces, averages etc) and on the performance of the imager itself. The efficiency of an instrument can be characterized by the performance overhead - the excess of the actual experimental time over and above the “ideal” calculated data acquisition time (simply the total number of acquired traces times the repetition time per trace): Overhead = (t_exp - t_ideal)/t_ideal*100%. The smaller the overhead the more efficiently the imager can acquire the data. The overhead of the imager results from the additional time necessary (i) to send appropriate commands to the imager components and to transfer acquired data from analog to digital converters to the computer; (ii) to settle the currents in the main field and gradient coils.

During the imaging a number of different sequences are generated and corresponding data acquired as shown in Table 1. For the SPI pulse sequence there are four phase cycle steps and for the ESE sequence an eight-step phase cycle and five measurements with different τ (all together 40 different sequences). The pulse programmer (PulseBlasterESR) has an on-board memory sufficient to store about 500 different single-pulse or ESE sequences. The Acqiris ADC board has the capability to average multiple traces in a single programming cycle (up to 65535 averages per trace). The board equipped with 24 Mbytes of on-board memory can store more than 500 two-thousand-point time traces per channel. Therefore all pulse sequences required for a particular gradient setting can be generated and acquired during one programming cycle. Phase cycling performs best when all steps of the phase cycling are done first in the inner cycle and, then, repeated number-of-averages times. For ESE the optimal way is to place the phase cycling into the innermost cycle, change to different τ values in the intermediate cycle and average data in the outer cycle. Below we demonstrate that this mode of programming is favorable not only from the experimental point of view but considerably reduces the overhead. The timings for ESE and SPI pulse sequences with different phase cycling schemes are presented in the Tables 2 and 3. The data are given for the very fast imaging experiments ESE-I and SPI-I that have only 1000 averages per projection and zero gradient settling time. The programming of all sequences at once allows one to reduce the overhead time by a factor of three to five compared to separate programming. In addition one can see that experiments with different phase cycling schemes have very little difference in performance overhead. All listed strategies are built into the SpecMan4EPR software.

Table 2.

Dependence of the single projection acquisition time for single τ ESE imaging and SPI on the number of phase cycles. The acquisition times are averages obtained from 1000 measurements.

Protocol	Acquisition time	“Ideal” imaging timea	Overhead
ESE-I, all phase cycling steps programmed at once
8 steps	18 ms	15 ms	20%
4 steps	18 ms		20%
2 steps	17 ms		13%
ESE-I, phase cycling steps programmed separately
8 steps	26 ms	15 ms	73%
1 step	17 ms		13%
SPI-I, all phase cycling steps programmed at once
4 steps	8 ms	7 ms	14%
SPI-I, phase cycling steps programmed separately
4 step	11ms	7 ms	57%
1 step	8 ms		14%

^aThe “ideal” imaging time includes only the pure acquisition time.

Table 3.

Dependence of the acquisition time for ESE imaging on programming type. The acquisition times are averages obtained from 200 measurements.

Protocol	Acquisition time	“Ideal” imaging time	Overhead
ESE-Ia, sequences with different τ programmed separately.	135 ms	75 ms	80%
ESE-Ia, sequences with different τ programmed at once.	85 ms		13%

Due to the limited SNR, the imaging protocols applied for in vivo imaging typically have a higher number of averages. The overhead of these protocols due to the factors described above will be smaller the larger the number of averages. For example the overhead for the scheme with five 1000-averages sequences (Table 3, sequences with different τ programmed at once) of 13 % will decrease below 2 % for measurements with 8000 averages.

Examples

Figure 5 presents selected saggital slices of ESE and SPI 3D images of the homogeneous 1 mM OX063H. The white frame marks the boundary of the resonator. The bottom of the phantom is aligned with the left edge of the resonator so that vial extends to the right beyond the resonator's right hand edge. The first two images (Figure 5A and 5B) were obtained using ESE and their acquisition parameters are summarized in the Table 4. Acquisition times in these examples refer to the full acquisition time including overhead. The fast, 32 second acquisition time, ESE-II image in the Figure 5A presents the capabilities of our instrument for rapid imaging. Due to a low number of projections this image contains minor artifacts and some amplitude non-uniformity. The decrease of the intensity towards the image edges is due to the magnetic field B₁ non-uniformity outside the resonator. The length of the resonator is 15 mm, correspondingly areas of the sample more than ±7.5 mm from the center are located in the fringe field. The spatial resolution of the image is 2.0 mm. Significant improvement is observed in the “quality” image obtained using the 4 min 20 second long ESE-III protocol (Figure 5B). Because of the 50 % higher gradient and five times more projections, the resolution of this image is substantially better - 1.4 mm. The SPI image presented in the Figure 5C has 1.4 mm resolution. The phase encoding protocol of the spin probe spatial distribution in SPI makes the resolution of an SPI image equal to the voxel size. Using the prior knowledge of the phantom and resonator dimensions it is more efficient to use an asymmetric imaging procedure (11 steps along the XZ directions perpendicular to the long axis of resonator and 21 steps along the resonator Y axis). Thus the SPI image in Figure 5C is smaller in the vertical dimension. Nevertheless, the imaged region is sufficient to include the phantom completely. The results of the imaging of SPI and ESE are identical for the inner resonator volume, outlined by the frames in Figures 5A and 5B and vertical lines in Figure 5C. One can notice that the SPI image is much more sensitive to the fringe fields. The right hand edge of our phantom extends far beyond the inner resonator volume on one side of the resonator (right side of the images in Fig. 5). The SPI image has considerable intensity out to 12.5 mm from the center of the resonator, 5 mm outside the physical dimensions of the resonator. In contrast, the ESE image intensity is negligible at 10 mm to the right from the resonator center, 2.5 mm from the right-hand edge of the resonator. The reason for this difference is that the ESE has stronger dependence of signal intensity on RF pulse turning angle than FID signal (42). The turning angle of an RF pulse is proportional to the strength of RF field that is highest in the inner volume of the resonator and gradually decreases outside resonator.

Figure 5.

Selected saggital slices of 3D images of the homogeneous 1mM OX063H phantom. The white frame marks the boundary of the resonator. The bottom of the phantom is aligned with the left edge of the resonator while the rest of the phantom extends to the right beyond the resonator sensitive volume. A. “Fast” image obtained using the ESE-II protocol, imaging time 32 sec. B. “Quality” image obtained using the ESE-III protocol, imaging time 4 min 20 sec. C. SPI image obtained using the SPI-II protocol, imaging time 2 min 54 sec.

Table 4.

EPRI protocols and image parameters.

Protocol and gradient	Projections /base lines	“Ideal” imaging time	Imaging time (overhead)	Spatial resolution, σ	Standard deviation of T2e
“Fast” ESE protocols
ESE-II (spatial only)	126 / 33	19 sec	32 sec (30%)	2.0 mm
ESE-IIa (3D T2 image)	126 / 33	1 min 35 sec	1 min 48 sec (15%)	2.0 mm	0.76 μs
“Quality” ESE protocols
ESE-III (spatial only)	654 / 165	3 min 17 sec	4 min 20 sec (32%)	1.4 mm
ESE-IIIa (3D T2 image)	654 / 165	16 min 23 sec	17 min 35 sec (7%)	1.4 mm	0.41 μs
SPI protocol
SPI-II (spatial only)	1007/ 113	2 min 05 sec	2 min 54 sec (39%)	1.4 mm

The distributions of the T_2e values obtained for the “fast”, ESE-IIa, and the “quality”, ESE-IIIa, ESE imaging protocols are presented in the Figures 6. The means of both distributions (4.43 μs and 4.54 μs, for the “fast” and “quality” images, respectively) are not statistically different from the average T_2e of 4.8 μs measured in a non-imaging experiment. The standard deviations of T_2e of the “fast” and “quality” images were found to be 0.76 μs and 0.41 μs respectively. The reduction in standard deviation can be attributed to the better SNR of the “quality” image. In terms of pO₂ these standard deviations result in 4 torr and 2 torr precision, respectively.

Figure 6.

The distribution of T_2e in the image of the homogeneous 1mM OX063H phantom obtained using 5-echo ESE imaging. “Fast” ESE-IIa image: imaging time 1 min 48 sec, mean T_2e value 4.43 μs, standard T_2e deviation 0.76 μs. “Quality” ESE-IIIa image: imaging time 17 min 35 sec, mean T_2e value 4.54 μs, standard T_2e deviation 0.41 μs.

The relaxation parameter that can be directly determined from SPI is T_2e*. Besides the true T_2e that is dependent on oxygen concentration, the observed relaxation time has other contributions (see e.g. (21)). An elaborate calibration procedure is required to obtain pO₂ from an SPI image and as our aim was simply to demonstrate that we could efficiently obtain both SPI and ESE data in the same instrument, we did not determine the SPI derived pO₂ standard deviation in this work.

The need to record the traces for baseline subtraction results in an increase of the experiment time. For example, the “quality” ESE-III protocol has a 63 second overhead arising from 654 gradient settling steps of five milliseconds and 165 off-/on- resonance main field jumps of 350 milliseconds duration, taking approximately 3.3 seconds and 58 seconds respectively. We are aiming for improvements to the imager's stability that should reduce the need to do such baseline corrections and consequently reduce the experiment time.

The overhead of the SPI-II protocol exceeds that for ESE-IIa and ESE-IIIa (see Table 4). Comparing this overhead with the SPI-I experimental overhead (see Table 2), we see that major contribution to overhead are gradient and, especially, field settling times. The large linear volume (a sphere of 150 mm diameter) gradient system of our magnet was designed for CW EPR imaging and has relatively high inductance and requires long settling times. An imager that has field and gradient coils with lower inductance will perform considerably faster. For example an SPI imager equipped with high performance MRI-type coils demonstrated a ~20% overhead in a similar experiment (43). From these results we conclude that for imagers with slow, high inductance gradient coils, the ESE imaging protocols that contain less gradient steps are more efficient. Imagers with fast, low inductance field and gradient coils will perform equally well using either methodology.

CONCLUSION

The pulse EPR imager presented in this work satisfies all requirements of a modern instrument. It combines high SNR and acquisition speed with versatility that allows the use of this instrument for different imaging modalities.