### 3488

Reduced Eddy Current induced image distortions and Peripheral Nerve Stimulation based on the Optimal Diffusion-weighting Gradient Waveform Design (ODGD) formulation
Óscar Peña-Nogales1, Yuxin Zhang2,3, Rodrigo de Luis-Garcia1, Santiago Aja-Fernández1, James H. Holmes3, and Diego Hernando4

### Synopsis

Diffusion-Weighted MRI (DW-MRI) often suffers from signal attenuation due to long TE, motion-related artefacts, dephasing due to concomitant gradients (CGs), and image distortions due to eddy currents (ECs). Further, the application of rapidly switching gradients may cause peripheral nerve stimulation (PNS). These challenges hinder the progress, application and interpretability of DW-MRI. Therefore, based on the Optimized Diffusion-weighting Gradient waveforms Design (ODGD) formulation, in this work we design optimal (minimum TE) nth-order moment-nulling diffusion-weighting gradient waveforms with or without CG-nulling able to reduce EC induced distortions and PNS-effects. We assessed the feasibility of these waveforms in simulations and phantom experiments.

### Introduction

Diffusion-Weighted MRI (DW-MRI) has a unique ability to probe tissue microstructure through the application of strong switching diffusion-weighting gradients. However, the application of these gradients results in significant challenges including 1) signal attenuation[1], 2) motion-related artifacts[2,3], 3) signal dephasing due to concomitant gradients (CGs)[4,5], 4) image distortions (shearing and scaling) due to eddy currents (ECs)[6,7,8], and 5) might cause peripheral nerve stimulation (PNS)[9,10].

Particularly, ECs and PNS appear when the gradient amplifiers are switched fast to drive large gradient intensities. Firstly, switching gradients result in current inductions that persist after the gradients are switched off[6,7]. Although, ECs are usually tackled through pre-emphasis and post-processing, there are also suboptimal (long TE) diffusion-weighting waveforms (e.g., BIPOLAR[11]) that achieve intravoxel rephasing and EC-nulling. Secondly, they cause an electric depolarization that may lead to PNS[9]. PNS is usually diminished by limiting the maximum slew rate of the waveform resulting in sub-optimal waveforms.

For these reasons, there is an unmet need for optimized diffusion-weighting waveforms able to overcome these challenges. Recently, a nonlinear constrained optimization formulation for the design of high-order moment-nulled and/or CG-nulled waveforms, termed Optimized Diffusion-weighting Gradient waveform Design (ODGD)[12], has shown great potential in-vivo DW-MRI. Therefore, the purpose of this work is to design optimized waveforms (minimum TE) based on the ODGD formulation that achieve EC- and PNS-nulling, while preserving previous properties.

### Methods

The ECs impulse response is given by $e(t,\tau)=H(t)\sum_\text{n}\alpha_\text{n}\exp{\left(-\frac{t}{\tau_\text{n}}\right)}$, where $\tau_\text{n}$,$\alpha_\text{n}$, n and H(t) are a characteristic time constant, amplitude, number of induced currents, and the step function, respectively. Thus, we can reduce EC induced distortions (EC-nulling) for a set of time constants ($\tau$) by adding the linear constraints $g(t,\tau)=-\frac{dG(t)}{dt}\circledast~e(t,\tau)\Bigr\rvert_{t=\text{T}_\text{Diff}}=0$ to the formulation[6,8].

A conservative nerve impulse response is given by[10,13] $n(t)=\frac{αc}{r(c+t)^2}$, where the gradient-coil specific constants $\alpha$, r, and c are the effective coil length, rheobase, and chronaxie time, respectively. Thus, for waveforms designs with the maximum slew rate supported by the MRI unit we can reduce the nerve stimulation (PNS-nulling) by adding the linear constraints $R(t)=\frac{dG(t)}{dt}\circledast~n(t)<Plimit=1$, where the PNS limit ($\text{P}_\text{Limit}$) is established by the International Electrotechnical Commission (IEC 60601-2-33). For the sake of clarity, Table 1 summarizes all constraints of the extended ODGD formulation.

In this work, MONO[12], BIPOLAR, MOCO[12] and nth-order moment-nulled ODGD waveforms without and with EC- and PNS-nulling were designed for b-values=100-2000s/mm², and TEPI (EPI readout time to the center of the k-space) of 16.4-46.4ms.

A 7.5L cylindrical water phantom doped with NaCl and NiCl2[14] was scanned at a 3T unit (GE Healthcare, Waukesha, WI) using a spin echo DW-EPI sequence to assess EC induced image distortions for several diffusion-weighting waveforms without and with EC-nulling, and to assess the implementation feasibility and SNR of PNS-nulling waveforms. Acquisition parameters were TR=4s, slice thickness=5mm, FOV=24x24cm, in-plane resolution=1.88x1.88mm, full k-space, six diffusion-weighting directions (±A/P,±R/L,±S/I), and b-values(averages)=[0(1),100(2),1000(4)]s/mm2. SNR maps were computed following Ref[15].

### Results

Figure 1 shows examples of various waveforms designed for the experiments. Figure 2 shows the TE dependence on the b-value of MONO, BIPOLAR, MOCO and various ODGD waveforms, and the TE reduction achieved using ODGD-M1-CG compared to ODGD-M1-CG-EC, and ODGD-M1-EC without and with CG-nulling compared to BIPOLAR. ODGD-M1-CG results in TE reductions between 3.8-14.7% compared to ODGD-M1-CG-EC. Relative to BIPOLAR, ODGD-M1-EC and ODGD-M1-CG-EC result in TE reductions between 1.9-27.9%, and -7-11.22%, respectively.

Figure 3 and 4 show the difference between DW images of opposite diffusion-weighting polarity, and their distribution, respectively. MONO is visually severely affected by EC induced distortions showing strong mismatch between opposite DW images. BIPOLAR, and ODGD-M1-EC are slightly more homogeneous than ODGD-M1. This is clearly visible at the phantom’s border where the shearing and scaling effects are apparent when showing the difference between opposite DW images. Further, BIPOLAR, and ODGD-M1-EC have tight confidence intervals with no bias on the phantom’s border.

Slew rate of ODGD-Mn-PNS are slightly different to ODGD-Mn (Figure 1.e)) resulting in TE reductions between 0-0.94%, 0-0.74%, and 0-0.75% for M0, M1, and M2 respectively. Further, there is no SNR difference between ODGD-M0 and ODGD-M0-PNS, neither between ODGD-M1 and ODGD-M1-PNS (results not shown).

### Discussion

We implemented and assessed the feasibility of the extended ODGD formulation[12] in phantom experiments. ODGD-Mn waveforms, where n=1,2, without and with EC-nulling have promising performance to reduce EC-effects. Nevertheless, this formulation needs to be further validated in-vivo studies (note that PNS-effects only appear on in-vivo experiments). Extension of the formulation to optimize the imaging gradients in addition to the diffusion gradients is also desirable[13].

### Conclusion

ODGD provides optimized motion-compensated, CG-, EC- and/or PNS-nulled diffusion-weighting gradient waveforms, and have the potential to improve image quality compared to state-of-the-art DW-MRI methods.

### Acknowledgements

The authors acknowledge the Consejería de Educación of Junta de Castilla y León and the Fondo Social Europeo for the predoctoral grant of the first author. The authors also thank the National Institute of Health, NIDDK Wisconsin Multidisciplinary K12 Urologic Research Center Development Program K12DK100022. Finally, the authors would like to acknowledge research support from GE Healthcare.

### References

[1] Taouli B, et al. Diffusion-weighted MR Imaging of the Liver1. Radiology. 2009;254(1):47-66

[2] Norris DG. Implications of bulk motion for diffusion-weighted imaging experiments: Effects, mechanisms, and solutions. J Magn Reson Imaging. 2001;13:486-495.

[3] Murphy P, et al. Error Model for reduction of cardiac and respiratory motion effects in quantiative liver DW-MRI. Magn Reson Med. 2013;70(50):1460-1469.

[4] Baron C, et al. The effect of concomitant gradient fields on diffusion tensor imaging. Magn Reson Med. 2012;68:1190-1201.

[5] Bernstein MA, et al. Concomitant Gradient Terms in Phase Contrast MR: Analysis and Correction. Magn Reson Med. 1998;39(2):300-308.

[6] Bernstein, M. A, et al. Handbook of MRI pulse sequences. Elsevier, 2004.[7] Jezzard P, et al. Characterization of and correction for eddy current artifacts in echo planar diffusion imaging. Magn Reson Med. 1998;39(5), 801-812.

[7] Jezzard P, et al. Characterization of and correction for eddy current artifacts in echo planar diffusion imaging. Magn Reson Med. 1998;39(5), 801-812.

[8] Aliotta E, et al. Eddy Current-Nulled Convex Optimized Diffusion Encoding (EN-CODE) for Distortion-Free Diffusion Tensor Imaging With Short Echo Times. Magn Reson Med. 2018;79(2), 663-672.

[9] Reilly J. P, Peripheral nerve stimulation by induced electric currents: exposure to time-varying magnetic fields. Medical and Biological Engineering and Computing. 1989;27.2:101.

[10] Den Boer J. A, et al. Generalization to complex stimulus shape of the nerve stimulation threshold based on existing knowledge of its relation to stimulus duration for rectangular stimuli. In Proc Int Soc Magn Reson Med. 1989;7:108.

[11] Alexander A. L, et al. Elimination of eddy current artifacts in diffusion‐weighted echo‐planar images: the use of bipolar gradients. Magn Reson Med. 1997;38(6), 1016-1021.

[12] Peña-Nogales Ó, et al. Optimized Diffusion-Weighting Gradient Waveform Design (ODGD) formulation for motion compensated and concomitant gradient nulling. Magn Reson Med. 2018;00: 1-15.

[13] Schulte R. F, et al. Peripheral nerve stimulation‐optimal gradient waveform design. Magn Reson Med. 2015;74(2):518-522.

[14] Imaging B. 150028 USA Instruments INC. SNR Phantom for GE MRI. https://parts.blockimaging.com/150028-USA-Instruments--INC.-SNR-Phantom-for-GE-MRI-for-GE--Closed-MRI/. [Online; accessed 30-October-2018].

[15] Aja-Fernández, et al. Spatially Variant Noise Estimation in MRI: A Homomorphic Approach. Medical Image Analysis. 2015;20184-197.

### Figures

Table_1. Optimized Diffusion-weighted Gradient waveform Design (ODGD) formulation. GMax and SRMax are the maximum gradient intensity and slew rate respectively, TRF-90 and TRF-180 the excitation and refocusing radiofrequency pulses, TEPI the time required by the EPI readout to reach the center of the k-space, TDiff the end of the diffusion-weighting gradients, A1 and A2 the time periods before and after TRF-180, and G(t) is the optimal diffusion-weighting gradient waveform. In this work, GMax=70mT/m, and TRF-90=TRF-180=5.5ms. Waveforms without PNS-nulling were computed with SRMax=100T/m/s (limit usually used to avoid PNS-effects) and with PNS-nulling with SRMax=150T/m/s (hardware limit), respectively.

Figure_1.Traditional waveforms (a), first-order moment-nulled (M1) Optimized Diffusion-weighted Gradient waveform Designs (ODGD-M1) without and with CG-nulling[12] (b), ODGD-M1 waveforms with EC-nulling for a time constant of τ=10ms without and with CG-nulling (c), ODGD-M0 waveforms and their slew rate without and with PNS-nulling (d) and (e), respectively. (a-c) waveform designs were computed with a time resolution of 0.5ms and (d-e) with 0.04ms. All waveforms were designed for b-value=1000s/mm2 and TEPI of 24.6ms. ODGD-M0 and ODGD-M0-PNS were computed with SRMax of 100T/m/s (limit used to avoid PNS-effects) and 150T/m/s (hardware limit), respectively. Note the different slew rate of ODGD-M0-PNS compared to ODGD-M0.

Figure_2.Minimum TE achieved for a range of b-values 100-200s/mm2 and TEPI=26.4ms for ODGD-Mn, ODGD-Mn-CG, ODGD-Mn-EC, ODGD-Mn-CG-EC, and the traditional waveforms (MONO, BIPOLAR, and MOCO) for M0, M1, and M2 moment constraint, respectively (a). TE reductions (ΔTE) achieved using ODGD-M1-CG compared to ODGD-M1-CG-EC, and ODGD-M1-EC and ODGD-M1-CG-EC compared to BIPOLAR for the same range of b-values and TEPI in the range of 16.4-46.4ms (b). EC-nulling waveforms were designed to null time constants of τ=10ms. ODGD waveforms with EC-nulling achieve higher minimum TE than the corresponding ODGD waveform without EC-nulling. In these cases, ΔTE is larger for higher b-values and lower TEPI.

Figure_3. Difference between diffusion-weighted images acquired with opposite diffusion-weighting polarity (±A/P), b-value=1000s/mm2, and TEPI=11ms with waveforms MONO, ODGD-M1, BIPOLAR, and ODGD-M1-EC of the phantom experiment (a). Masks for ROI analysis (b). MONO is severely affected by eddy currents induced distortions showing strong mismatch between opposite DW images. At the phantom’s border, ODGD-M1 is slightly affected by EC induced distortions. ODGD-M1, BIPOLAR, and ODGD-M1-EC show more homogeneous difference between opposite DW images than MONO. Compared to ODGD-M1, BIPOLAR and ODGD-M1-EC show similar variability between opposite DW images despite their longer TE.

Figure_4.Distribution of the difference between diffusion-weighted images acquired with three opposite diffusion-weighting directions (±A/P,±R/L,±S/I) for waveforms of Figure 3. Red and black boxes show the distribution of the phantom and border masks, respectively, shown in Figure 3. Both masks of ODGD-M1, BIPOLAR, and ODGD-M1-EC show less variation between opposite DW images (tighter confidence interval and lower height) proving better EC performance than MONO. Compared to ODGD-M1, BIPOLAR and ODGD-M1-EC show similar variability between opposite DW images (width of the phantom mask) despite their longer TE, and no bias on the border mask (height of the boxplot) showing better EC performance.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
3488