High fidelity triangular sweep of the magnetic field for millisecond scan EPR imaging

Abstract

Linearity of the magnetic field sweep is important for high resolution continuous wave EPR imaging. Driving the field with triangular wave function is the most efficient way to scan EPR projections. However, the magnetic field sweep profile can be significantly distorted during fast millisecond projection scan. In this work, we introduce a method to generate highly linear and properly symmetrical triangular sweeps of the magnetic field using calibrated harmonics of the triangular wave function. First, the frequency response function of the EPR magnet and its power circuitry was obtained. For this, the field sweeping coil was driven with sinusoidal signals of different frequencies and the actual magnetic field inside the magnet was recorded. To cover wide range of frequencies, the measurements were carried out independently using gaussmeter, Hall-effect linear sensor integrated circuit, and an inductance coil. For each frequency, the system gain and the phase delay were determined. These data were used to adjust the amplitudes and the phases of individual harmonics of the triangular wave function. After the calibration, the maximum deviation of the magnetic field from the linear function was 0.05% of sweep width for 4 ms scan. The maximum discrepancy between the forward and the reverse scan was less than 0.04%. Sweep overhead time for changing the scan direction was 5%. The proposed approach allows generation of high fidelity triangular magnetic field sweeps with accuracy better than 0.1% for the range of the magnetic field sweep widths up to 48 G and scan duration from 10 s down to 1 ms.

Keywords: Continuous wave; EPR imaging; Electron paramagnetic resonance; Fast scan; Frequency response function; High resolution; Linear time-invariant system; Magnetic field; Sweep linearity.

Figure 1:

(A) Singular period of the triangular wave function and its approximations. Red line: the approximation computed by adding up the first 47 harmonics of the Eq. 8; blue line: the approximation computed using the Eq. 9 with the Gaussian relaxation factor σ = 16. In both cases H(ω) is assumed to be a constant. (B) The difference between the triangular wave function and its approximations. A possible data acquisition window is indicated with the dashed lines.

Figure 2:

Root-power spectral density of (A) reference sine wave signal 330 Hz from function generator; (B) the resultant magnetic field inside the EPR magnet measured using Lakeshore MNA-1904-VH Hall probe and (C) by Honeywell SS495A1 Hall-effect linear sensor integrated circuit.

Figure 3:

Frequency response function of the EPR magnet measured at the static magnetic field of 440 G. (A) Relative amplitude of the magnetic field sweep measured using gaussmeter (green crosses), Honeywell magnetic sensor (blue circles), and the inductance coil (red plus signs). The amplitude of the signal from the current monitor of the power supply is also shown (magenta diamonds). (B) Magnetic field sweep delay with respect to the reference signal from the function generator. Colors and signs have the same meaning as in (A). Signal delay for the current monitor was about 65 μs in the whole frequency range and is not shown for the clarity of the figure.

Figure 4:

Difference between the measured magnetic field inside the EPR magnet and the triangular function. (A) Field sweep coil was driven with uncorrected triangular wave function; (B) sweep profile was generated using Eq. 9 and interpolated data from the frequency response function from Fig. 3; (C) the same as (B) but the harmonics of the sweep function were manually fine-tuned for better accuracy of the field scan. Blue lines show forward scans, red lines show the flipped reverse scans. The magnetic field was measured using Honeywell Hall-effect magnetic sensor. In all cases the central magnetic field was 440 G, sweep width 48 G, scan duration 4 ms. The magnetic field data were accumulated for 24576 scans. EPR data acquisition window is indicated by dashed lines. Overhead time for changing the scan direction is 0.2 ms or 5% of total scan duration.

Figure 5:

Difference between the measured magnetic field inside the EPR magnet and the triangular function for 20 ms (A), 4 ms (B) and 1 ms (C) scans with the sweep width of 48 G. In all cases the field sweep profile was generated using Eq. 9 and interpolated data for the frequency response function of the magnet. All other parameters were the same as in Fig. 4.

Figure 6:

Left panel: EPR spectra of 2 mL 0.5 mM TEMPONE radical solution acquired with 100, 20 and 4 ms scans using direct triangular field sweeps. Right panel: the same sample measured with 20, 4 and 1 ms scans and the sweep profile generated using Eq. 9 and interpolated data of the frequency response function of the magnet. Scans 100, 20 and 4 ms were recorded using lock-in amplifier and magnetic field modulation 0.25 G; scans 1 ms were obtained directly digitizing signal from the microwave bridge without using field modulation. Spectra accumulation time in all cases was 16 s, incident microwave power 20 mW. Blue lines show spectra acquired with forward scan direction; red lines correspond to the reverse scans.

Figure 7:

3D spectral-spatial EPR images of the labyrinth phantom sample. The sample has two isolated compartments filled with 2 mM oxygen-free and 3 mM air-saturated solutions of Finland triarylmethyl radical (dFT). (A) and (B) Integral signal intensity and the Lorentzian width of the observed EPR line, respectively, obtained with the corrected field sweep profile. (D) and (E) The same sample measured with the direct triangular field sweep. (C) and (F) Histograms of the Lorentzian line width data from (B) and (E), respectively. Blue bars represent data for deoxygenated solution, red bars are air-saturated solution. EPR images were obtained from 16384 experimental projections with the maximum field gradient of 12 G/cm. Single scan duration was 20 ms, sweep width 24 G. Each projection was scanned twice, total image acquisition time, 11 min. Magnetic field modulation 40 mG at 95.5 kHz, incident microwave power 10 mW.