Ruben Pellicer-Guridi^{1}, Michael W. Vogel^{1}, Rainer Körber^{2}, Jan-Hendrik Storm^{2}, Jiasheng Su^{1}, David C. Reutens^{1}, and Viktor Vegh^{1}

Ultra-low field MR detector coils experience long dead-times which reduce acquisition efficiency. We present a simple low insertion loss Q-damping scheme and a post-processing method that, combined, allow earlier signal acquisition. Proposed methods have been empirically verified with a cylindrical detector at 2.5 kHz. This approach can improve imaging efficiency for ULF MR considerably, promoting the use of inexpensive resistive coils for low-cost, portable ULF MR instruments.

**Synopsis**

*Frequency
increase Q-damping*: Optimal coil de-energizing follows an exponential decay
with a time constant ( dependent on the resonant frequency of
the detector (*f _{0}*) such
that . We propose
to accelerate this dissipation by temporarily re-tuning the circuit to a higher
frequency, which is achieved by reducing the capacitance of the resonant
circuit. We have opted to use the coil’s natural resonant frequency of 85kHz,
which offers a 34 fold acceleration compared to the 2.5kHz acquisition
frequency. Component switching and pre-amplifier protection are achieved by a
set of 3 reed relays (Fig.1).

*Software ring-down attenuation*: The long ring-down re-induced by
switching Q-damping relays is
attenuated by subtracting estimated re-ringing from the signal. Three re-ringing
estimation algorithms have been tested:

- Mono-exponential
fitting: A mono-exponential oscillatory decay has been fitted to the section
where the re-ringing is dominant over the signal following Equation(1). Circuit
resonant frequency (
*f*) and decay time (_{0}*τ*) were estimated from an averaged NMR signal free re-ringing. Equation(1) is then used to estimate the phase (*Φ*) and amplitude (*A*) of the re-ringing overlapped with the MR signal._{rd}

$$V_rd=A_{rd}e^{-t\over τ_{rd}}cos(2\pi f_0t+\phi).\space\space\space\space(1)$$

- Rigid recorded ring-down: A recorded NMR signal free re-ringing is averaged and subtracted from the signal.
- Adaptive recorded ring-down: The phase and magnitude of the recorded averaged re-ringing is adjusted and subtracted individually for each acquisition. To estimate the phase and amplitude, a sinusoidal lobe is fitted to one of the first re-ringing lobes where the re-ringing dominates over the MR signal.

*NMR
experiment*: Test
coil parameters: 25.6Ω AC resistance at 1kHz, 52.6mH, 29mm inner diameter,
48.1mm outer diameter and 34mm height. Signals from a 20ml water sample and an
in-vivo human thumb were acquired (Fig.4).

**Results**

Experimental acquisitions show that the coil was de-energized from a 180° Rf pulse in less than 2ms. The corresponding estimated decay time is 1.9μs (critically damped with 20kΩ). The switching of the mechanical relays generate a re-ringing which decays to noise floor level in 20 ms, and is highly reproducible regardless of the preceding Rf pulse intensity (0°, 90° or 180°)(Fig.2).

*All three software ring-down attenuation methods improved
the spectrum(Fig.3-4). Directly subtracting the averaged ring-down had the poorest
performance, reducing ring-down effects by about 60%. The exponential fitting
and adaptive recorded ring-down subtraction methods attenuated ring-down by 80%,
reducing sensor dead-time to 4ms.*

**Discussion**

Switching the resonant frequency to higher frequencies has allowed us to completely dissipate energy within 2ms, which is remarkably fast considering employed relays have a 0.2ms response time. The characteristics of the re-ringing are independent of employed Rf power, which confirms the efficacy of the proposed damping approach.

Software ring-down attenuation reduces acquisition dead-time significantly. The limited attenuation efficiency of the direct subtraction of the averaged recorded ring-down implies that the reproducibility of re-ringing is limited; likely due to the use of electromechanical switches. Hence, adjusting the amplitude and phase of the averaged ring-down improves ring-down attenuation. The exponential fitting method can attenuate the ring-down with minimal noise insertion but is more sensitive to imprecision in estimation of re-ringing.

**Conclusion**

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Circuit
diagram of the Q-damping.

Visualization
of four re-ringing signals. The re-ringings are similar with some variation in
phase and amplitude.

Residual
re-ringing signal after processed with proposed algorithms. The averaged
ring-down is also plotted as a reference. The residual after employing the
exponential fitting algorithm is shown in (A). Note the second harmonic at 5kHz dominates the residual. Direct subtraction of averaged ring-down shows
considerably higher residual (B) unless compensated in phase and magnitude (C).

Visualization
of tested re-ringing attenuation methods on human in-vivo thumb and water experiments
for different dead-times, represented in the legend in seconds. The first
column shows the original signal without corrections for water (A) and thumb
(E). The
exponential fitting (B & F) and adaptive recorded re-ringing (D & J)
methods reach similar results. The rigid re-ringing subtraction (C & G)
method shows the weakest attenuation.