Engineering clinical translation of OGSE diffusion MRI

Abstract

Oscillating gradient spin echo (OGSE) diffusion MRI (dMRI) can probe the diffusive dynamics on short time scales $\lesssim 10\text{ms}$, which translates into the sensitivity to tissue microstructure at the short length scales $\lesssim 10\mu \text{m}$. OGSE-based tissue microstructure imaging techniques able to characterize the cell diameter and cellular density have been established in pre-clinical studies. The unique image contrast of OGSE dMRI has been shown to differentiate tumor types and malignancies, enable early diagnosis of treatment effectiveness, and reveal different pathophysiology of lesions in stroke and neurological diseases. Recent innovations in high-performance gradient human MRI systems provide an opportunity to translate OGSE research findings in pre-clinical studies to human research and the clinic. The implementation of OGSE dMRI in human studies has the promise to advance our understanding of human brain microstructure and improve patient care. Compared to the clinical standard (pulsed gradient spin echo), engineering OGSE diffusion encoding for human imaging is more challenging. This review summarizes the impact of hardware and human biophysical safety considerations on the waveform design, imaging parameter space, and image quality of OGSE dMRI. Here we discuss the effects of the gradient amplitude, slew rate, peripheral nerve stimulation, cardiac stimulation, gradient driver, acoustic noise and mechanical vibration, eddy currents, gradient nonlinearity, concomitant gradient, motion and flow, and signal-to-noise ratio. We believe that targeted engineering for safe, high-quality, and reproducible imaging will enable the translation of OGSE dMRI techniques into the clinic.

1 |. OVERVIEW OF OGSE METHODOLOGY

1.1 |. Which tissue building blocks would we like to become sensitive to?

Cytoarchitecture and its alternation provide fundamental information about disease identification, progression, and response to treatment.¹ In oncology, the cellular size, shape, density, and composition of tissues at the length scale of $\gtrsim 1\mu \text{m}$ are the biomarkers for tumor staging and evaluation of treatment response.^2–4 For example, immune cells (such as T cells) have relatively small average radii of 2–5 μm;⁵ glioma cells have average radii of 4–7 μm;^6–10 and cells in breast tumor,¹¹ prostate epithelium¹² and hepatocytes¹³ have relatively large average radii ≥6 μm (Figure 1). After treatment, cell size shrinkage (e.g., glioma radii reduction from 6 μm to ~4 μm^14,15) and low tumor cell density are typical features of treatment-induced necrosis and apoptosis.¹⁶

FIGURE 1.

The length scales that pre-clinical, human high-performance gradient and clinical whole-body diffusion MRI are sensitive to, compared with the cell radii of different human tumors.

In neurological and neurodegenerative diseases, the integrity and density of axons, neuronal cell bodies, and dendrites are altered.^17–21 For example, axonal beading (blebbing or varicosities) along the axon length,^22,23 which occurs already in normal axons,^24,25 becomes more pronounced in axonal injury.^20,21,23 Dendritic swelling and beading have also been observed in ischemic stroke.¹⁸ These morphological changes of axons and dendrites are associated with underlying pathology such as microtubules damage in stretched nerve fibers²⁰ and ischemia.¹⁷ Average varicosity spacing along axons has been reported to be 3–5 μm.^19,23–25 Therefore, capturing abnormal beading (amplitude or spacing) at the micrometer range may identify the focal and/or global regions of tissue damages in the brain, which is a challenge in traumatic brain injury²³ and other brain diseases.

With excellent soft tissue contrast that can reflect structural, functional, and molecular information, MRI is indispensable for assessing spatially heterogeneous lesions. In the clinic, the size of an MR image voxel is a few millimeters, about 100–1000 times coarser than the characteristic length scales of the relevant tissue microstructure mentioned above. Therefore, MRI contrast reflects massive averaging over water molecules experiencing different cellular environments. This is the inherent mismatch between MRI and biopsy/histopathology analysis of relatively small samples. Remarkably, water diffusion, ubiquitous in tissues, allows us to tune MRI sensitivity to micrometer-level tissue building blocks, by varying the diffusion time and weighting.^26–30

1.2 |. Why is OGSE optimal to probe short diffusion times?

The fundamental relation between the diffusion length ${\ell }_D$ (root mean squared molecular displacement) and the diffusion time $t$ in $d$ spatial dimensions serves as a basis for probing length scales by varying the diffusion time:

$${\ell }_D\left(t\right)\equiv \sqrt{⟨x^2\left(t\right)⟩}=\sqrt{2dD\left(t\right)t}.$$ (1)

In simple liquids, diffusion is Gaussian, and $D$ is time-independent constant; for example, $D=3\mu {\text{m}}^2/\text{ms}$ for water at 37°C. In tissues, microstructural complexity makes diffusion non-Gaussian, and the mean squared displacement $⟨x^2\left(t\right)⟩$ does not in general grow linearly with $t$. Therefore, the diffusion coefficient becomes a function of the diffusion time $t$. In the diffusion MRI (dMRI) literature, the cumulative diffusion coefficient $D\left(t\right)=⟨x^2\left(t\right)⟩/2dt$ is most commonly used, following Equation (1); alternatively, one can define an instantaneous $D_{\text{inst}}\left(t\right)={\partial }_t⟨x^2\left(t\right)⟩/2d$. In any case, the diffusion time $t$, as the time of the evolution of the mean squared displacement, exists irrespective of an MRI sequence. As we will discuss below, different diffusion measurements may be seen as filters imposed on the “ideal” objective diffusive dynamics of spin-carrying molecules in a given medium.

Qualitatively speaking, the characteristic scale ${\ell }_c$ of tissue structures that cause diffusion restriction or hindrance (e.g., cell size, the correlation length of cell packing or of axonal beading, etc) are best sensed when ${\ell }_c$ is matched by the diffusion length, ${\ell }_D\left(t_c\right)~{\ell }_c$. This equation defines the time scale $t~t_c$ to be attained for resolving tissue structure at the length scale ${\ell }_c$. A more rigorous picture is that of the gradual coarse-graining of the tissue microstructure by the increasing diffusion length (Equation 1), washing out structural details finer than ${\ell }_D\left(t\right)$.^28,31

The classic way to measure time-dependent $D\left(t\right)$ is to employ pulsed gradient spin echo (PGSE)³² dMRI with narrow pulses (Figure 2A,C). In an ideal, narrow-pulse PGSE measurement, one assumes negligible displacement during the pulse duration $\delta$, and the diffusion time $t\simeq \Delta$ is just the interval between the front lobes of the two pulses. Finite $\delta$ sets the precision for our ability to define the diffusion time. The corresponding PGSE signal attenuation $\text{ln}\left(S/S_0\right)=-b_{\text{PG}}D\left(t\right)+𝒪\left(b_{\text{PG}}^2\right)$ involves the diffusion weighting

$$b_{\text{PG}}=(g\delta {)}^2\left(\Delta -\frac{1}{3}\delta \right),g=\gamma G.$$ (2)

The overall scale of diffusion weighting is determined by the Larmor frequency gradient $g$, related to the field gradient $G$ by the gyromagnetic ratio $\gamma$. A useful number to keep in mind is $g=0.0214(\mu \text{m}\cdot \text{ms}{)}^{-1}$ for $G=80\text{mT}/\text{m}$, a maximal single-axis gradient for a state-of-the-art clinical scanner. The smallness of such nominally “strong” gradient $g$ in the microstructure units, and the fact that $b~g^2$, explain why it is challenging to create appreciable signal attenuation if one wishes to probe the scales below $\lesssim 10\mu \text{m}$. Indeed, to obtain a moderate $b_{\text{PG}}~1\text{ms}/\mu {\text{m}}^2=1000\text{s}/{\text{mm}}^2$ (for a desired attenuation $b_{PG}\cdot D\left(t\right)~1$ with $D\left(t\right)~1\mu {\text{m}}^2/\text{ms}$ in tissues, to ensure adequate precision in estimating the diffusion tensor), one has to employ sufficiently long timings $\delta$ and $\Delta$. In our example, $b_{\text{PG}}\approx 1\text{ms}/\mu {\text{m}}^2$ can be reached, for example, for $\delta =7\text{ms}$ and $\Delta =50\text{ms}$. Making $\delta$ longer decreases the precision in defining the diffusion time, whereas increasing $\Delta$ makes us less sensitive to small structures. In particular, based on Equation (1), probing displacements $\lesssim 10\mu \text{m}$ (the cell sizes relevant to clinical questions) at this $t\simeq \Delta =50\text{ms}$ is already beyond reach.

FIGURE 2.

(A) and (B) show the schematic of PGSE and trapezoidal-modulated OGSE waveforms, respectively. (C–G) show PGSE waveform and different OGSE waveforms with the polarity of post-180 diffusion pulse reversed, the anti-derivative $q\left(t\right)$ of the gradient, and its spectrum $q\left(\omega \right)$. OGSE waveforms can achieve higher $b$-values with multiple oscillating periods (E vs. D) while maintaining the same diffusion time (or OGSE frequency), for example, at $f=60\text{Hz}$. (F) and (G) show the cosine and sine OGSE waveforms, respectively, at the same $b$-value and frequency ranges.

Stronger gradients enable shortening both $\delta$ and $\Delta$. For example, a gradient amplitude of 200 mT/m can achieve $\delta$ and $\Delta ~10\text{ms}$, allowing probing displacements ~ 10 μm. However, PGSE dMRI remains inefficient for achieving shorter diffusion times $\lesssim 10\text{ms}$ even as the gradient performance increases. Since $\Delta$ cannot fall below $\delta$, the diffusion weighting for the shortest possible diffusion times $\Delta \gtrsim \delta$ scales as $b_{\text{PG}}~g^2{\delta }^3$. This rather unfortunate ${\delta }^3$ scaling makes it challenging to attain appreciable diffusion weightings at short times.

Oscillating gradient spin echo (OGSE)^33,34—a train of periodically changing $g\left(t\right)$ with frequency $f$—saves the day by decoupling the diffusion time (of the order of the oscillation period $1/f$) from the total waveform duration $T=N/f$ of $N$ oscillations (Figure 2B). In this way, the diffusion weighting^28,35,36

$$b_{\text{OG}}=N\cdot b_1,b_1~g^2/f^3$$ (3)

is accumulated over $N$ periods, where the single-period weighting $b_1$ is akin to that for PGSE with $\delta ~\Delta ~1/f$. With $N\gg 1$ periods, we probe the diffusive dynamics at the shortest time scale $~1/f$ yet enjoy an $N$-fold increased attenuation (Equation 3), cf. examples shown in Figure 2D,E. The number $N$, practically limited by the $T_2$ relaxation, separates the time scales $1/f$ and $T$, thereby setting the precision of defining the oscillation frequency $f=\omega /2\pi$.

Trapezoid-cosine OGSE waveform³⁷ (Figure 2D) has been commonly used, for its frequency selection around the designed frequency and higher $b$-value, as compared to pure cosine waveform (Figure 2F) and pure sine waveform (Figure 2G), with the latter causing the admixture^28,38 of the long-time PGSE $D\left(T\right)$, further complicating the analysis. Furthermore, the effective OGSE frequency of a certain waveform has been calculated in two approaches: (1) the peak frequency of the spectrum $q\left(\omega \right)$ of $q\left(t\right)={\int }_0^t\text{d}{t}^{\prime }g\left(t^{\prime }\right)$, the anti-derivative of the gradient waveform; (2) the centroid of the spectrum $q\left(\omega \right)$ (Equation 7 in Reference [39]). In this review, we refer to the peak frequency when reporting the numerical value.

1.3 |. How to select the OGSE frequency range for probing specific tissue microstructure?

A practically important question is how to select the OGSE frequency given the characteristic scale ${\ell }_c$ of tissue structures we would like to probe. An order of magnitude estimate for the diffusion time $t~t_c$ can be made based on the discussion after Equation (1). Our intuition then suggests to choose OGSE frequency $\omega ~1/t_c$. However, as we discuss below, the nonlocal relation between the OGSE-measured $D_{\text{OG}}\left(\omega \right)$ and the PGSE-measured time-dependent diffusion coefficient $D\left(t\right)$ means that $D_{\text{OG}}\left(\omega \right)$ cannot in general be interpreted as ${\left.D\left(t\right)\right|}_{t~1/\omega }$. Below, we will give a few biologically relevant examples (tumors, neurodegenerative disorders), where an explicit conversion between PGSE and OGSE is possible.

We note from the outset, that $D\left(t\right)$ and $D_{OG}\left(\omega \right)$ measured for all $t$ and $\omega$, carry exactly the same information about the diffusion process. However, this information gets “distributed” across $t$ or $\omega$ differently in either quantity. PGSE measures the mean squared displacement $⟨x^2\left(t\right)⟩$ accumulated over the entire time interval from 0 to $t$. Hence, the cumulative $D\left(t\right)$ accumulates all the history of the random walker’s (water molecule) displacement. In comparison, OGSE captures the diffusive dynamics at a set time scale $~1/\omega$ (assuming the transient processes have died out during a large number $N$ of oscillations). In this regard, $D_{\text{OG}}\left(\omega \right)$ is closer to the instantaneous $D_{\text{inst}}\left(t\right)$.

To formalize this intuition, we recall^28,40 that both $D\left(t\right)$ and $D_{OG}\left(\omega \right)$ are different facets of the dispersive diffusivity $D\left(\omega \right)$, which relates the Fourier components of the diffusive flux and the density gradient, $j\left(\omega \right)=-𝒟\left(\omega \right)\nabla \psi \left(\omega \right)$, generalizing the Fick’s law. Technically, $𝒟\left(\omega \right)$ is a Fourier transform of the retarded velocity autocorrelation function $𝒟\left(t\right)=\theta \left(t\right)⟨v\left(t\right)v\left(0\right)⟩$ of a random walker, where the unit step function $\theta \left(t\right)=1$ at $t>0$ and $\theta \left(t\right)=0$ otherwise. Applying any gradient waveform $g\left(t\right)\equiv \text{d}q\left(t\right)/\text{d}t$, the diffusion signal attenuation (up to $𝒪\left(g^2\right)$) reads^26,28

$$\text{ln}\frac{S\left[q\right(t\left)\right]}{S_0}=-\int \frac{\text{d}\omega }{2\pi }q(-\omega )𝒟\left(\omega \right)q\left(\omega \right)+𝒪\left(q^4\right),$$ (4)

where $q\left(\omega \right)$ is the Fourier transform of $q\left(t\right)$. In other words, the signal $S\left[q\right(t\left)\right]$ is a functional of the gradient waveform $g\left(t\right)$, that is, a mapping of a function to a number. One can view Equation (4) as that $g\left(t\right)$ imposes a filter of the shape $q(-\omega )q\left(\omega \right)\equiv \left|q\right(\omega ){|}^2$ on the actual $𝒟\left(\omega \right)$.

• In OGSE encoding in the limit $N\to \infty ,{\left|q_{\text{OG}}\left(\omega \right)\right|}^2$ becomes a delta function at the frequency of oscillation (Figure 2E), thereby yielding ${\left.D_{\text{OG}}\left(\omega \right)\right|}_{N\to \infty }=\text{Re}𝒟\left(\omega \right)$, the real part of $𝒟\left(\omega \right)$.²⁸

• In PGSE encoding with narrow pulse, $q_{\text{PG}}\left(\omega \right)~1/(-i\omega )$ (Figure 2C), such that

$$D\left(t\right)=\frac{1}{t}\int \frac{\text{d}\omega }{2\pi }{e}^{-i\omega t}\frac{D\left(\omega \right)}{[-i(\omega +i0){]}^2}.$$ (5)

Equation (5) and the relations between differently defined time- or frequency-dependent diffusion coefficients are summarized in Figure 6 and Section 2.2.2 of Reference [28].

FIGURE 6.

The maximum $b$-value of trapezoid-cosine OGSE achieved at TE’s and frequencies using the gradient and slew rate constrained by both MRI system limits in Figure 4 and CS threshold of whole-body gradient coils. As an example, the CS threshold of the whole-body gradient coil is characterized with $\Delta G_{\text{min}}=113\text{mT}/\text{m}$ and ${SR}_{\text{min}}=62.5\text{T}/\text{m}/\text{s}$.

The manifestly nonlocal in time/frequency relation between the ideal $D_{\text{OG}}\left(\omega \right)=\text{Re}D\left(\omega \right)$ and $D\left(t\right)$ (Equation 5) makes converting between $t$ in PGSE and $\omega$ in OGSE challenging. In particular, while $D\left(t\right)$ and $D_{\text{OG}}\left(\omega \right)$ carry exactly the same information, one needs to know $D_{\text{OG}}\left(\omega \right)$ for all $\omega$ to recover $D\left(t\right)$ for any $t$—and vice-versa, one needs to know $D\left(t\right)$ for all $t$ to recover $D_{\text{OG}}\left(\omega \right)$ for any $\omega$.

In biological systems, explicit conversion between $t$ in PGSE and $\omega$ in OGSE is feasible for geometries for which the functional forms of the time-dependent diffusion are known. Specifically:

• Short-time surface-to-volume (S/V) limit^36,38,41: $t=(9/64)\cdot 2\pi /\omega$,^28,38 as recently observed in a fiber phantom on a clinical scanner.⁴² Being in a short-time limit requires the diffusion length $~\sqrt{D/\omega }$ much smaller than the cell size. In in vivo MRI, Reynaud et al.⁷ observed the $1/\sqrt{\omega }$ functional form, a signature of the S/V limit, in a mouse glioma model with OGSE frequency up to 225 Hz, where the tumor cell radii ≥ 5 μm.

• Long-time power-law approach^28,43,44: $D\left(t\right)-D_{\infty }~t^{-\vartheta }$ towards the bulk diffusivity ${\left.D_{\infty }\equiv D\left(t\right)\right|}_{t\to \infty }$ due to coarse-graining over the structural disorder corresponds to the dispersive contribution $𝒟\left(\omega \right)-D_{\infty }~{\omega }^{\vartheta }$, with $\omega ~1/t$ dependent on the disorder exponent $\vartheta$, cf. Equation 48 in Reference [28]. In particular, the power law tail $1/\sqrt{t}~\sqrt{\omega }$ was identified⁴³ as coming from one-dimensional structurally disordered ($\vartheta =1/2$) neurites in the normal and globally ischemic rat brain.³⁵ The increase in this specific dispersive contribution in ischemia was interpreted as the sensitivity to the increase of the structural disorder (e.g., beading) along neurites in stroke.⁴³ This behavior has been subsequently identified in human brain OGSE dMRI studies.^39,45

• Fully confined pores: The low-frequency functional forms are $D_{\text{OG}}\left(\omega \right)~{\omega }^2{R}^4/D_0$ (first observed by Stepisnik et al.⁴⁶) and $D\left(t\right)~R^2/t$, where $R$ is the pore size. This is an example where $D_{\text{OG}}\left(\omega \right)$ and $D\left(t\right)$ are qualitatively different in terms of $\omega ~1/t$. OGSE in tumor cells assumed as impermeable spheres should exhibit this functional form.⁷ In this review, we use this functional form when correlating OGSE frequency and tumor cell size to illustrate the sensitivity of OGSE to tissue length scale, with $D_0=2\mu {\text{m}}^2/\text{ms}$.

To summarize, while our intuition suggests that OGSE at frequency $\omega$ should correspond to PGSE at the time scale $t~1/\omega$, the essentially nonlocal relation (Equation 5) makes this correspondence non-universal (model-dependent). When we know what kind of biological system we are studying (e.g., tumor, axonal beading), it is possible to explicitly select the frequency range in OGSE and the corresponding diffusion time range in PGSE depending on the tissue length scale we want to probe.

1.4 |. From gradient performance to pre-clinical, clinical, and human research findings of OGSE dMRI

High-performance gradient is essential to OGSE dMRI.^6,47 OGSE waveforms with high maximum gradient amplitude ($G_{\text{max}}$) and slew rate ($S{R}_{\text{max}}$) are necessary to maximize the $b$-value, especially at high OGSE frequency. Therefore, a shorter echo time (TE) and a higher signal-to-noise ratio (SNR) can be achieved.

Figure 1 shows the sensitivity of OGSE dMRI to tissue length scale at different gradient strengths. Operating at ≥400 mT/m and ≥1 000 T/m/s, OGSE dMRI in pre-clinical scanners can achieve high frequency $f\ge 200$ Hz and the sensitivity to tissue length scales as small as 1 μm.^13,48 The accuracy of OGSE dMRI has been well studied in animal models that evaluate MRI-measured cell size and cellularity of different tumor types validated with pathology.^{6–11,48–50} High accuracy has been shown in detecting cell sizes in treatment-naïve gliomas,^7,10 as well as cell shrinkage after treatment.⁵¹ Furthermore, the unique image contrast of OGSE dMRI has also been shown to indicate brain pathologies including axonal beading^35,43,52 and demyelination.^53,54

Current clinical standard whole-body MRI systems operate at $G_{\text{max}}$ of 33–80 mT/m and $S{R}_{\text{max}}$ of 120–200 T/m/s. They allow a maximum of 40–50 Hz OGSE frequencies,^{11,12,39,55–57} corresponding to a length scale limit of about 6 μm. OGSE dMRI has emerged for imaging cancer,^{11–13,55–59} stroke,^52,60 brain maturation,⁶¹ and pediatrics.⁶² A thorough review of the applications can be found in Reynaud et al.,⁶ and Xu.⁶³ The limited gradient performance of current clinical MRI systems may not achieve high sensitivity to short tissue length scales. Indeed, multiple studies^49,50 have reported an overestimated glioma cell radii of 8–15 μm in patients.

Human high-performance gradient MRI systems operating at $G_{\text{max}}$ of 200–500 mT/m and $S{R}_{\text{max}}$ of 200–900 T/m/s^64–69 have been introduced by multiple MRI vendors and academic sites. Recent studies^45,70,71 have demonstrated achieving high $b$-value and high OGSE frequency at short TE (Figure 3) in human brain. For example, Zhu et al.⁷¹ and Michael et al.⁷⁰ both showed achieving OGSE frequency ≥100 Hz, theoretically providing sensitivity to tissue length scale as small as 4 μm.^72–74 These systems may best address the need for probing tissue microstructures relevant to tumors⁷¹ and brain diseases and disorders.^23,25,43

FIGURE 3.

Example of human brain OGSE dMRI at different gradient configurations, including $G_{\text{max}}$ of 80 mT/m and $S{R}_{\text{max}}$ of 200 T/m/s; $G_{\text{max}}$ of 200 mT/m and $S{R}_{\text{max}}$ of 500 T/m/s; and $G_{\text{max}}$ of 300 mT/m and $S{R}_{\text{max}}$ of 750 T/m/s. Images were acquired within peripheral nerve stimulation and cardiac stimulation limits in a head-only high-performance gradient MRI system.

In summary, recent system hardware innovations meet the need for high-performance gradient for OGSE dMRI in human studies. These provide opportunities to translate pre-clinical research findings to human research and the clinic. Indeed, preliminary studies have shown new image contrasts that potentially reveal tissue microstructures including cellular density, restricted tissue size, and water exchange rate in tumor patients,⁷¹ stroke patients,⁵² and healthy human brain.^45,70,75,76 In this review, we emphasize the unique engineering challenges of OGSE dMRI when translating the technique from pre-clinical studies to human studies, and discuss the approaches to advance the translation.

2 |. IMPACTS OF SYSTEM ENGINEERING ON OGSE DMRI

Although the biophysics of OGSE dMRI has been validated in pre-clinical MRI systems, the clinical adoption of OGSE dMRI needs to address unique engineering challenges, as summarized in Table 1. In pre-clinical MRI, high image quality and accuracy in diffusion MRI measurements are achieved with high SNR, high spatial resolution, and high accuracy of magnetic gradient field. This is because the small field-of-view (FOV) of 15–40 mm makes it much easier to increase $G_{\text{max}}$ and $S{R}_{\text{max}}$ for a given accuracy tolerance on the gradient field, as well as to ensure relatively low power consumption and high duty cycle.

TABLE 1.

Engineering challenges of human OGSE dMRI, comparing to pre-clinical OGSE dMRI and clinical whole-body PGSE dMRI.

	Section	Engineering	MRI system and diffusion encoding technique				Effect on image
			Pre-clinical, OGSE	Clinical whole-body, PGSE	Human whole-body, OGSE	Human head-only, OGSE
MRI system limitation		Main magnetic field	4.7T, 7T, 11T	3T	3T, 7T	3T, 7T, 10.5T
		Imaging FOV	1.5–4 cm	20–50 cm	20–50 cm	20–30 cm
	2.1	Gradient	> 400 mT/m	50–200 mT/m	50–200 mT/m	200–500 mT/m
	2.4	Power electronics	—	High power at high b-value	High power at low b-value for high $f$	HIgh power at low b-value for high $f$	Imaging parameter space
	2.5	Acoustic noise and mechanical vibration	Frequency dependent	—	Frequency dependent	Frequency dependent
	2.6	Eddy current	—	Linear 0th & 1st order terms	Nonlinear 0th & 1st order termsa	Nonlinear 0th & 1st order terms	Image quality and accuracy of quantification
	2.7	Gradient nonlinearity	Neglectable	Unneglectable for large FOV	Unneglectable for large FOV	Higher in 26-cm FOVa
	2.8	Concomitant gradient	Neglectable	Even terms only	Even terms only	Odd & even terms; 5–40X highera
	2.9	Motion and flow	1st & 2nd moment nulled	Not motion-compensated	1st & 2nd moment nulled	1st & 2nd moment nulled
	2.10	SNR	High	Medium	Low	Medium
Biophysical safety requirement	2.2	PNS threshold	Unconstrained	Whole-body coil PNS threshold		2–5X highera	Imaging parameter space
	2.3	CS threshold	Unconstrained	Whole-body coil CS threshold		> 2.5X higher at 300 mT/ma

Abbreviations: CS, Cardiac stimulation; FOV, Field-of-view; PNS, Peripheral nerve stimulation; SNR, Signal-to-noise ratio.

^aIn comparision to whole-body, PGSE.

In human MRI, however, the MRI system limit and biophysical safety constraints affect the usable MRI parameters, such as TE, $b$-value, OGSE frequency, and TR. We illustrate MRI system limits in the following sections including gradient performance (Section 2.1), power electronics (Section 2.4), and acoustic noise and mechanical vibration (Section 2.5). We further discuss biophysical safety constraints including peripheral nerve stimulation (PNS) (Section 2.2) and cardiac stimulation (CS) (Section 2.3). Furthermore, imaging in the ~ 10× gradient coil size inevitably leads to challenges from relatively large gradient nonlinearity, high concomitant gradient field, and high power consumption. If unaddressed, these effects compromise image quality and scan efficiency. We discuss them in the sections on eddy currents (Section 2.6), gradient nonlinearity (Section 2.7), concomitant gradient (Section 2.8), motion and flow (Section 2.9), and SNR (Section 2.10). Different engineering requirements for human versus pre-clinical MRI systems, as well as those between OGSE and PGSE, are discussed.

2.1 |. Imaging parameter space at maximum gradient performance

Recent developments of highly efficient gradient coils and high-power electronics have advanced $G_{\text{max}}$ and $S{R}_{\text{max}}$ in human MRI systems (Table 2). In whole-body MRI systems with a bore diameter ≥ 60 cm, the majority of high-end clinical systems operate at $G_{\text{max}}=80\text{mT}/\text{m}$ and $S{R}_{\text{max}}=200\text{T}/\text{m}/\text{s}$. Whole-body MRI systems operating at $G_{\text{max}}=100-200\text{mT}/\text{m}$ and $S{R}_{\text{max}}=200\text{T}/\text{m}/\text{s}$ have been achieved, which were first introduced by the Human Connectome Project.^77,78 Due to limited coil efficiency, the large-bore whole-body gradient coils need very high input current ≥ 900 A and voltage ≥ 2 000 V to reach high $G_{\text{max}}$ and $S{R}_{\text{max}}$.⁷⁹ Therefore, whole-body high-performance gradient MRI systems are enabled by high-power electronic devices. As a variety of new systems at 3T^80–83 and 5T⁸⁴ are becoming clinically available, whole-body high-performance gradient MRI systems will become more widely accessible to patients.

TABLE 2.

Representative human high-performance gradient MRI systems with human in vivo images published.

Whole-body MRI system	Field strength (Tesla)	Bore size (cm)	${\mathbf{G}}_{\text{max}}$ (mT/m)	${\mathbf{S}\mathbf{R}}_{\text{max}}$ (T/m/s)
Prismaa (S.)	3	60	80	200
Premiera (G.)	3	70	80	200
UHP 3T (G.)	3	60	113	260
Jupiter (U.)	5	60	120	200
Cima.X (S.)	3	60	200	200
Connectome 1.0 (S.)	3	56	300	200
Head-only MRI system	Field strength (Tesla)	Gradient coil size (cm)	${\mathbf{G}}_{\text{max}}$ (mT/m)	${\mathbf{S}\mathbf{R}}_{\text{max}}$ (T/m/s)
Magnetom 7T Plusa (S.)	7	40	80	350
LH7 (A.)	10.5	41	117	900
MAGNUS† (G.)	3	42	200	500
IMPULSE (S.)	7	44	200	900
Achieva HPGa (P.)	3	33	200	600
MAGNUS 2.0a (G.)	3	42	300	750
Connectome 2.0 (S.)	3	44	500	600
Neuro Frontier (U.)	3	39	650	600

Note: Clinical products: Siemens Prisma, GE HealthCare Premier, Siemens Cima.X, United Imaging Jupiter; Research prototypes from Siemens: Connectome 1.0, Magnetom 7T Plus, IMPULSE, Connectome 2.0; Research prototypes from GE HealthCare: UHP 3T, MAGNUS, MAGNUS 2.0; Research prototypes from Philips: Achieva HPG (high-performance gradient); Research prototypes from United Imaging: Neuro Frontier; Research prototypes from the academia: LH7. S.: Siemens; G.: GE HealthCare; U.: United Imaging; A.: The academia; P.: Philips.

^aOGSE images published in journal papers/abstracts.

Gradient coils with a smaller diameter of 33–44 cm but high coil efficiency have been developed and installed at 3T,^64–66,69 7T,⁶⁷ and 10.5T⁶⁸ MRI systems. These systems can achieve up to 650 mT/m with 7 MVA input power per axis (Table 2). The small-bore gradient coils are dedicated to human brain imaging. Feasibility of human prostate imaging in these small-bore systems⁸⁵ has also been demonstrated.

Figure 4 shows the maximum $b$-values of conventional trapezoid-cosine OGSE waveforms at different TE’s and OGSE frequencies using the $G_{\text{max}}$ and $S{R}_{\text{max}}$ of different MRI systems. The calculation is detailed in Supplementary Material S1. As $G_{\text{max}}$ increases from 80 mT/m (Figure 4A) to 200 mT/m (Figure 4C) in the whole-body MRI systems, the maximum $b$-value at a fixed TE and OGSE frequency greatly increases. At 200 mT/m and 200 T/m/s, the relatively long ramp time prohibits operating at high OGSE frequencies $f\ge 140\text{Hz}$ (Figure 4C, Supplementary Figure S3). The higher $S{R}_{\text{max}}$ of head-only gradient MRI systems enable higher OGSE frequencies (Figure 4D). By further pushing $G_{\text{max}}$ to 300–500 mT/m and $S{R}_{\text{max}}$ to 600–750 mT/m, simultaneously high $b$-value, short TE, and high OGSE frequency are achieved (Figure 4E,F).

FIGURE 4.

The maximum $b$-value of trapezoid-cosine OGSE achieved at varying TE’s and frequencies, using simultaneous $G_{\text{max}}$ and $S{R}_{\text{max}}$ of whole-body MRI systems (A–C) and head-only MRI systems (D–F). The calculation is detailed in Supplementary Material S1. At a fixed frequency, the maximum $b$-value shows discontinuity at certain TE, which is due to the use of different numbers of OGSE waveform periods, as shown in Supplementary Figure S2. Other system constraints are not imposed.

The imaging parameter space at maximum gradient performance can be accessed in phantom and animal studies where the physiological risk due to the fast-switching magnetic field is absent or considered negligible.

2.2 |. Peripheral nerve stimulation

In human MRI, the operation of the gradient field is subject to biophysical safety constraints. Fast-switching magnetic fields that are generated by gradient coils induce electric fields, which can trigger uncomfortable sensations through PNS in humans. PNS constraint⁸⁶ is implemented to protect human biophysical safety in MRI scans. The linear gradient field threshold curve⁸⁶ is described as $\Delta G\left(\tau \right)=S{R}_{\text{min}}\cdot \tau +\Delta G_{\text{min}}$, where $S{R}_{\text{min}}$ is the minimum slew rate to cause nerve stimulation at infinitely long ramp time, $\Delta G_{\text{min}}$ is the minimum gradient amplitude to cause nerve stimulation at infinitely high slew rate, and $\tau$ is the ramp time.

Head-only gradient coils allow a higher (~ 5×) PNS threshold^87–89 compared to whole-body gradient coils. At high-gradient amplitude that is desired for diffusion encoding (e.g., 200 mT/m), the maximum slew rate applicable to human imaging is reduced to ~200 T/m/s in head-only gradient coils and 70–90 T/m/s in whole-body gradient coils due to PNS thresholds.

Figure 5 shows the maximum $b$-values of trapezoid-cosine OGSE waveforms at different TEs and OGSE frequencies using the gradient and slew rate constrained by both MRI system limits and PNS threshold of gradient coils. The actual used gradient amplitude and slew rate are shown in Supplementary Figure S4. The PNS threshold reduces the maximum $b$-value at a fixed OGSE frequency and TE (Figure 5), compared to the $b$-value without the PNS threshold (Figure 4).

FIGURE 5.

The maximum $b$-value of trapezoid-cosine OGSE achieved at TE’s and frequencies using the gradient and slew rate constrained by both MRI system limits in Figure 4 and PNS threshold of gradient coils. As an example in this review, the head-only gradient coils are characterized with $\Delta G_{\text{min}}=39.5\text{mT}/\text{m}$ and ${SR}_{\text{min}}=185.6\text{T}/\text{m}/\text{s}$, in the linear gradient field threshold curve of bipolar gradients. As an example in this review, the whole-body gradient coil is characterized with $\Delta G_{\text{min}}=19.7\text{mT}/\text{m}$ and ${SR}_{\text{min}}=84.8\text{T}/\text{m}/\text{s}$.

The PNS threshold has a high impact on the OGSE imaging space at high OGSE frequencies, which requires simultaneously high-gradient amplitude (to achieve adequate $b$-value) and high slew rate (to achieve high frequency). At high-gradient amplitude, the slew rate within the PNS threshold is reduced, leading to a long ramp time and prohibiting high OGSE frequency. Reducing the gradient amplitude and increasing the slew rate allow OGSE gradient waveforms with high frequencies (Figure 5C), as detailed in Supplementary Figure S5. However, the achievable $b$-value is smaller (Figure 5C vs. Figure 4C).

The high PNS thresholds of head-only gradient coils greatly expand the achievable imaging parameter space of OGSE dMRI. For example, $b\ge 500\text{s}/{\text{mm}}^2$ can still be achieved at $f=100\text{Hz}$ and TE= 121 ms (Figure 5D) in the head-only gradient coil with 200 mT/m and 231 T/m/s (Supplementary Figure S4D). In comparison, the $b$-value is reduced to ≤ 200 s/mm² at $f=100\text{Hz}$ and TE= 149 ms in whole-body gradient coil (Figure 5C) with same 200 mT/m but a lower slew rate of 89 T/m/s due to PNS (Supplementary Figure S4C). At $G_{\text{max}}=300-500\text{mT}/\text{m}$, the PNS thresholds of existing head-only gradient coils eventually limit minimum TE at high OGSE frequency $f\ge 100\text{Hz}$ and $b\ge 1000\text{s}/{\text{mm}}^2$ (Figures 5E,F and S4E,F).

2.3 |. Cardiac stimulation

Cardiac stimulation (CS) is another biophysical safety constraint that limits the slew rate at high-gradient amplitudes. In the clinical whole-body MRI systems with $G_{\text{max}}\le 80\text{mT}/\text{m}$, CS is not a concern. However, it becomes an important consideration in higher-performance gradient systems.

For whole-body gradient systems, the electromagnetic field in the chest and heart of a human is typically the highest at the brain imaging position.⁹⁰ Through electromagnetic simulation, the chronaxie of CS has been approximated to be about one order of magnitude longer than that of PNS.⁹¹ Depending on the scan position, the CS threshold can be lower than the PNS threshold at high-gradient amplitude in whole-body systems. For example, the slew rates limited by PNS and CS in the whole-body gradient Connectome 1.0 system were estimated to be ~88 T/m/s and ~77 T/m/s at 300 mT/m, respectively (estimated from Figure 2 in Reference [91]). In other words, besides PNS, the CS threshold of whole-body gradient coils may further limit the usable slew rate when high-gradient amplitude is needed, such as in OGSE. Figure 6 shows the maximum $b$-value at each TE and OGSE frequency using the gradient and slew rate constrained by both MRI system limits and the CS threshold of whole-body gradient coils. At low gradient amplitude (Figure 6A,B), the maximum $b$-value is larger compared to that constrained by the PNS threshold (Figure 5A,B). At high-gradient amplitude (Figure 6C), the maximum $b$-value at 60 Hz and TE of 96 ms becomes smaller compared to that constrained by the PNS threshold (Figure 5C), indicating that the CS threshold becomes the dominant factor limiting the maximum achievable $b$-value.

For imaging the brain in the head-only gradient systems, the electromagnetic field in the chest and heart is greatly reduced compared to whole-body MRI systems at the brain imaging position.^90,92 This is beneficial not only for the PNS threshold but also for the CS threshold, which was demonstrated by Klein et al.⁹³ in animal experiments. The recent electromagnetic simulation by Hua et al.⁹⁴ indicated that the maximum electric fields that can be generated by the MAGNUS X, Y, Z coils, individually and in three-axes combined mode, at 300 mT/m and 750 T/m/s are below the IEC 60601–2-33 CS limit. This study suggested that the CS threshold at the brain imaging position in head-only gradient systems with ≤ 300 mT/m and ≤ 750 T/m/s is higher than the PNS threshold. Therefore, the CS threshold does not further limit the OGSE dMRI parameter space beyond the PNS limitation. At higher gradient performance and/or other imaging positions, the CS threshold and its impact on OGSE dMRI need to be re-evaluated. Further studies using both animal and human body models⁹⁵ are ongoing to improve our understanding of the bioelectromagnetic safety in high-performance whole-body and head-only gradient systems. With better knowledge, OGSE imaging parameter space for safe human studies may be further expanded.

2.4 |. Gradient driver

The high power consumption of diffusion MRI is a limiting factor to both the imaging parameter space and scan efficiency. The gradient field is determined by gradient coils with input currents, $I\left(t\right)$, which are delivered by power electronic devices including a gradient power amplifier (GPA) and a power supply (PS) for each physical gradient axis. Ohmic heating in the gradient coil and losses in the power electronic devices are summarized as gradient heating. Excessive heat must be transported away from the gradient coil and power electronic devices to avoid potential hardware damage. The removal of heating in the gradient chain is detailed in Supplementary Material S2. Therefore, it is important to illuminate the gradient heating generated by OGSE waveforms, its impact on imaging acquisition, and existing mitigation approaches.

Losses in the PS and GPA are not purely Ohmic, and the gradient coil also has frequency-dependent impedances. However, a simple resistive circuit is commonly used to approximate the Ohmic losses $P\left(t\right)=I^2\left(t\right)R$ in the gradient system, where $R$ is the resistance of the gradient coil. The current $I\left(t\right)$ is proportional to the gradient amplitude $G\left(t\right)$. Consequently, the dissipated energy during the playout period $T$ of a gradient waveform scales as

$$E\propto {\int }_0^T{G}^2\left(t\right)\text{d}t.$$ (6)

The high-gradient amplitude and long duration of the OGSE waveforms require much higher power input, compared to that of PGSE at the same $b$-value. For example, at $b=800\text{s}/{\text{mm}}^2$, an OGSE waveform at 66 Hz (Figure 7D) and 100 Hz (Figure 7E) requires 2.6× and 6.0× higher energy consumption of the PGSE waveform at $b=800\text{s}/{\text{mm}}^2$ (Figure 7A).

FIGURE 7.

Energy over the diffusion encoding waveforms of OGSE and PGSE.

The power consumption and heating of OGSE are more problematic in whole-body gradient systems with a larger bore size. Power is proportional to $d^5$, where $d$ is the gradient coil diameter.⁷⁹ For example, the same OGSE waveform at $f=66\text{Hz}$ and $b=800\text{s}/{\text{mm}}^2$ in a 70-cm diameter bore whole-body gradient system and a 60-cm gradient system require 12.9× and 5.95× higher power, compared to that in a 42-cm diameter head-only gradient system.

A common approach to reducing the energy consumption in PGSE is to reduce the gradient amplitude and increase the waveform duration $\delta$ and the mixing time $\Delta$ (Figure 7C) to achieve the $b$-value (Equation 2). The energy consumption is reduced and the TE is moderately prolonged. Unfortunately, this approach does not work in OGSE as the width of the diffusion lobes is fixed at a given frequency. Lowering the gradient amplitude quadratically reduces the energy consumption but it also quadratically reduces the $b$-value (Equation 3). To match the $b$-value, more periods of OGSE diffusion lobes need to be added (Equation 3), which may contribute to even more energy consumption, as examined in Figure 7F.

To manage the energy consumption and thermal heating in OGSE dMRI, we consider a short heating time constant in the range of tens of milliseconds (e.g., GPA and PS) and a long heating time constant in the range of minutes (e.g., gradient coil, cold plates). First, the energy consumption of an OGSE waveform on a single physical axis may exceed the peak load limits of the PS and GPA. Therefore, it is not possible to run these waveforms by adding dead time after the acquisition of each slice. One mitigation approach is to distribute the amplitude of OGSE gradients on multiple physical axes, for example, using tetrahedral diffusion encoding.⁹⁶ This will reduce the peak load of a single GPA and PS, assuming one GPA and PS per physical axis. A disadvantage is the reduced flexibility for the diffusion encoding directions. Furthermore, longer heating time constants can be addressed by a load-balanced order of the diffusion encoding volumes. For example, a low-frequency OGSE volume with a smaller energy consumption and a high-frequency OGSE volume with a higher energy consumption can be interleaved. In cases when the heating time constant of PS and/or GPA is shorter than the acquisition time of a 3D volume, the diffusion encoding waveforms can also be interleaved on a per-slice level.^97,98

In addition, hardware improvements may also mitigate the heating limitation. For example, hardware designs include higher-rated power modules and components, larger baseplate components that have more contact area to the cold plate to remove heat, and improved cold plate (pin fins) that have more surface area in contact with heat-generated components. These will result in lower thermal resistance on heat-components to help efficiently remove excessive heat, to ensure high OGSE gradient amplitude and short TR per slice.

In summary, the energy consumption and gradient driver heating are more challenging for OGSE dMRI, compared to PGSE dMRI. Other advanced dMRI pulse sequences that need high current for a long duration have similar issues.⁹⁹ As the energy consumption and gradient driver heating are associated with the current, an effective way to achieve high-gradient OGSE dMRI without demanding high current input is to increase the gradient coil efficiency. Therefore, OGSE dMRI in whole-body MRI systems is more challenging, compared to the power-efficient head-only MRI systems.

2.5 |. Acoustic noise and mechanical vibration

Acoustic noise and mechanical vibration, caused by Lorentz force when the current runs in the gradient coil at the strong main magnetic field, affect human scan safety and patient comfort. Lorentz’s force is proportional to the main magnetic field and the gradient current. For a given gradient performance, acoustic noise and mechanical vibration tend to be weaker in MRI systems with a high coil efficiency, as the required current is lower for a given gradient amplitude. The amplitudes of both the acoustic noise and mechanical vibration have frequency dependence. Their frequency transfer functions are system hardware characteristics. In the acoustic noise transmission pathway of current–gradient coil vibration–air–subject, the primary frequency range of the acoustic noise perceived by subjects is between several hundred hertz to a few kilohertz. In the mechanical vibration transfer pathway of current–gradient coil vibration–surrounding components–subject, the primary frequency range of the mechanical vibration felt by subjects is between tens to hundreds of hertz range.

Due to the use of high current for diffusion encoding and fast-switching current for EPI readout, dMRI is one of the most challenging pulse sequences for acoustic noise and mechanical vibration. For example, the mechanical vibration has been shown to introduce signal dephasing in DTI^100–102 and diffusion-weighted MR spectroscopy.^103,104 In OGSE dMRI, even higher current and oscillation at up to 120 Hz exacerbate the acoustic noise level and mechanical vibration. The oscillation frequency of trapezoidal OGSE waveforms does not directly reach the kilohertz range like typical EPI readout gradients. But, the high amplitude of the OGSE diffusion gradient disperses considerable energy into higher harmonics in the kilohertz range. Chen et al.¹⁰⁵ reported that this feature could lead to higher acoustic noise contributed by the OGSE diffusion gradient, potentially surpassing the noise contributed by the EPI readout.

Since the oscillation frequencies of OGSE sequences typically are in the tens to hundreds of hertz range, which can coincide with the mechanical vibration resonance frequencies of MRI systems, OGSE can significantly increase mechanical vibration perceived by subjects. High-frequency and $b$-value OGSE sequences are accompanied by more pronounced mechanical vibration compared to typical PGSE diffusion gradients. Such vibration can lead to discomfort for subjects and may affect the imaging results. Wu et al.¹⁰⁶ reported patient discomfort due to mechanical vibration in a 3T whole-body MRI system. In a 4.7T pre-clinical MRI system, Xu et al.¹⁰⁷ reported mechanical vibration-induced bias on apparent diffusion coefficient (ADC) at an OGSE frequency of 150 Hz in a free water phantom.

To follow the acoustic noise standard^108,109 and mitigate mechanical vibration, system hardware modifications^110,111 and gradient waveform optimization have been employed and proven effective. For example, the engineering of the patient table and its connection (or lack of connection) with the vibrating scanner has shown less sensation of vibration by human subjects in the Connectome 1.0 MRI system.⁷⁷ Furthermore, specific to OGSE pulse sequence, Chen et al.¹⁰⁵ optimized the gradient waveforms to suppress the frequency components at the resonant peaks in the acoustic noise spectrum of a certain MRI system.

In summary, since the OGSE pulse sequence often pushes the hardware capabilities of MR systems to their limits, its application often brings about increased acoustic noise and mechanical vibration. These issues can lead to discomfort for subjects and potentially degrade image quality. By optimizing the system design and OGSE pulse sequence with knowledge of system characteristics in mechanical vibration and acoustic noise generation, we can mitigate these challenges to ensure human scan safety and improve patient comfort, facilitating the clinical application of OGSE dMRI.

2.6 |. Eddy currents

High-gradient amplitudes of OGSE waveforms introduce a strong eddy current. The difference in the diffusion waveform shapes between PGSE and OGSE differentiates their respective eddy current behaviors and their effect on $k$-space encoding and image quality.

PGSE diffusion gradients have been shown to commonly introduce the 0th and 1st spatial order phase errors, leading to image shift, scaling, and shearing in echo-planar acquisition.¹¹² Pulse sequence modifications including bipolar diffusion gradient waveforms¹¹³ and twice-refocused spin echo,¹¹⁴ as well as post-processing correction including FMRIB Software Library (FSL) EDDY¹¹⁵ have shown success in eliminating the effect of diffusion gradient-induced eddy current on image quality. High-order eddy currents caused by PGSE diffusion gradients have also been characterized by using field camera at 3T¹¹⁶ and 7T.^117,118 Integrating the actual magnetic field evolution in the image reconstruction from the $k$-space data has shown to improve image quality of brain DTI.^116,118

The characteristics of oscillating gradient-induced eddy currents have not been fully investigated in a variety of MRI systems. However, the oscillating gradient at high amplitude may introduce additional spatial high-order or temporal oscillatory field responses due to joint effects of eddy currents, amplifier response, and mechanical vibrations. In a 7T head-only gradient MRI system, Valsamis et al.¹¹⁷ reported time-varying phase errors with a nonlinear time dependence introduced by oscillating gradients at 40 Hz, measured with a field camera. It resulted in image blurring in the echo-planar acquisition, which can be corrected by modeling the eddy currents as a combination of constant and exponentially decaying $k$-space offsets during post-processing.¹¹⁷

Figure 8 compares the measured maximum phase accrual overtime on a 100-mm radius sphere after playing out different diffusion gradient waveforms on the three physical gradient axes, measured with a field camera in a 3T head-only gradient MRI system.⁶⁶ In agreement with Valsamis et al.,¹¹⁷ the 0^th and 1^st order eddy currents of PGSE (Figure 8A, PG) exhibit long time constants, resulting in approximately linear phase accrual. In comparison, the commonly used trapezoid-cosine OGSE waveform (Figure 8A, OG1) and a modified “gap-filled” OGSE waveform¹¹⁹ (Figure 8A, OG2) both exhibit additional components with shorter time constants, resulting in nonlinear phase accrual. Stronger overall eddy currents were observed for OG1 than for PG. Interestingly, however, OG2 had reduced 0th, 2nd, and 3rd order eddy currents compared to those of PG. No oscillatory field response was observed for either OGSE waveform in this system. Furthermore, in another 3T head-only MRI system, Dai et al.⁷⁵ applied FSL EDDY¹¹⁵ to correct for eddy current in DTI acquisitions with trapezoid-cosine OGSE gradients at 0–47.5 Hz in a 3T head-only MRI system. It showed effective elimination of OGSE-induced eddy currents without modeling oscillator terms.

FIGURE 8.

(A) Pulsed (PG), trapezoid-cosine oscillating (OG1 at 33 Hz), and a modified oscillating (OG2 at 35 Hz) diffusion waveforms, and (B) the eddy currents resulting from them for different axes of diffusion encoding measured by a field camera in a 3T high-performance head-only gradient MRI system. In (B), all subplots show the temporally evolving phase accrual (in radians) during a subsequent EPI readout, resulting from the application of diffusion gradients. These evolutions are given in terms of coefficients of spherical harmonic basis functions of different orders (denoted in legend), with scaling that reflects the maximum phase accrual on a sphere of radius 100 mm. The contributions resulting from diffusion encoding were isolated by taking differences between the coefficients of dMRI acquisitions and corresponding $\text{b}=0s/{mm}^2$ acquisitions. Note that vertical scaling is consistent within rows except for the first row (zeroth-order eddy currents), for which the vertical scale is much larger for diffusion encoding along the SI axis than for diffusion encoding along the LR and AP axes. LR: Left-right; AP: Anterior-posterior; SI: Superior-inferior.

Pre-emphasis-based compensation for linear and constant eddy currents, as well as high-order eddy current mitigation,¹²⁰ are commonly implemented in MRI systems. They are calibrated once at the system installation and upgrad by measuring the eddy current-induced phase error when applying a single trapezoidal gradient. The calibration is protocol-independent. However, the compensation terms depend on both the calibration parameters and the applied gradient waveforms. For example, Xu et al.¹²⁰ formulated the high-order eddy current compensation terms for PGSE dMRI. For successful clinical translation of OGSE dMRI, a similar formula would need to be provided for OGSE dMRI, implemented, and tested in both clinical and research MRI systems.

In summary, OGSE-induced eddy currents have been shown to introduce different image artifacts in echo-planar acquisitions in different MRI systems.^75,117 The varying design of OGSE waveforms may further complicate the behavior and effect of eddy currents. The measurement of phase errors using the field camera will be useful for a comprehensive evaluation of OGSE-induced eddy currents. For correction of image artifacts, corrections of phase errors up to third-order spherical harmonics using the field camera measurement have been shown to achieve good image quality in both echo-planar acquisition¹¹⁷ and spiral acquisition.⁷⁰ Correction approaches without using the field camera measurement^75,117 have also been demonstrated.

2.7 |. Gradient nonlinearity

The actual magnetic gradient field deviates from the ideal value due to the gradient nonlinearity^121,122 (Figure 9A), resulting in spatially varying $b$-values and inaccurate estimation of diffusion parameters when unaccounted for.^123–125 Errors of 10–20% in diffusion measurements in clinical MRI systems¹²¹ and up to 30% in ultra-strong gradient MRI systems¹²⁶ have been reported. As the small-bore head-only gradient coils target a smaller diameter spherical volume of ≤30 cm for imaging, the gradient nonlinearity is relatively larger in the same-sized sphere compared to whole-body gradient systems. For example, the gradient nonlinearity of head-only gradient systems was reported to range from 6% to 10% in 20-cm diameter spherical volume,^67,77 20% in 22 × 22 × 20 cm³ volume,⁶⁶ and ≤17% in 26-cm diameter spherical volume.⁶⁴

FIGURE 9.

(A) The nonlinear gradient field results in spatially varying $b$-value when the diffusion encoding gradient is played along the physical $X,Y$, and $Z$ axis, for example, in the 10-cm diameter sphere. (B) ADC is incorrectly estimated without correcting the gradient nonlinearity effect on the $b$-value. For example, in the fluid-filled resected cavity of a glioblastoma patient after surgery, ADC was overestimated, compared to the ADC of the cerebrospinal cord. After correction, the ADC of the fluid-filled resected cavity was close to the ADC of the cerebrospinal cord. (C) Simulation of the effect of gradient nonlinearity on non-Gaussian diffusion measurements, for example, $\frac{ADC\left(60Hz\right)}{ADC\left(0Hz\right)}$, in a tumor model with a cell radius of 5 μm and different intra-tumoral volume fraction. The retrospective gradient nonlinearity correction largely reduces the bias on ADC(60 Hz) and ADC(0 Hz). However, the bias on $\frac{ADC\left(60Hz\right)}{ADC\left(0Hz\right)}$ cannot be corrected.

In whole-body MRI systems, the effect of gradient nonlinearity along the physical $Z$ axis can be ameliorated by moving the volume of interest to the iso-center where gradient nonlinearity is neglectable. This approach cannot mitigate the effect when the volume of interest is off-center along X or Y. In head-only systems, the small-bore size of 33–44 cm in diameter prohibits inferior brain regions from being scanned at the iso-center. Therefore, the gradient nonlinearity may have more effect on regions including the cerebellum, brainstem, cervical spine, etc.

In the estimation of diffusion parameters, corrections for nonlinear gradient have been implemented by calculating the actual gradient fields in each voxel and applying them in the diffusion parametric estimation¹²¹ (Figure 9B). These methods have been mostly applied and validated in PGSE DWI and DTI, demonstrating improved accuracy and reproducibility of breast DWI¹²³ and brain DTI¹²⁷ in multicenter studies.

Compared to PGSE DWI and DTI, time-dependent dMRI probes high-order diffusion parameters that reflect the non-Gaussian diffusion process. The effect of gradient nonlinearity on high-order diffusion parameters can also be appreciated in PGSE diffusional kurtosis imaging (DKI). Several studies on both phantom and human brain^75,124,128 have shown that DKI parameters have smaller percent errors due to gradient nonlinearity, compared to DTI parameters. Mesri et al.¹²⁴ showed that the effect of gradient nonlinearity is less prominent at low SNR levels. As DKI is acquired at a high $b$-value and long TE in whole-body MRI systems, the effect of gradient nonlinearity on DKI is overwhelmed by the noise. At a shortened TE and high SNR enabled by the high-performance gradients, the gradient nonlinearity can be problematic for high-order diffusion parameters in both PGSE DKI and OGSE dMRI (Figure 9C). Both the characterization and correction¹²⁹ are needed to ensure accurate interpretation of tissue microstructure from OGSE dMRI measurements.

In summary, applying OGSE dMRI to probe high-order diffusion parameters is more challenging in regions suffering from high gradient nonlinearity, for example, in the inferior brain scanned in a head-only MRI system, since a high-gradient field is needed for achieving sensitivity to non-Gaussian diffusion. Approaches for correcting gradient nonlinearity effect on non-Gaussian diffusion MRI need further investigation and validation.

2.8 |. Concomitant gradients

When a linear gradient field is generated, it is accompanied by spatially dependent concomitant gradient fields, which are also referred to as Maxwell terms.^130,131 The strength of the concomitant gradient field is proportional to the square of the applied linear gradient strength, and inversely proportional to the main magnetic field $B_0$. Therefore, the effect of concomitant gradient field can be 5–40× higher at high-performance gradient MRI systems (Table 1), compared to clinical whole-body MRI systems. Moreover, asymmetric design of high-performance gradient coils^64–69 present both odd and even order concomitant gradient fields,¹³² whereas the symmetric gradient systems only present even order terms. Therefore, the concomitant gradient effect is much higher in high-performance asymmetric gradient systems. Across different main magnetic fields (Table 1), 7T and 10.5T are less affected by the concomitant gradient field, compared to 3T.

Concomitant gradient fields affect both the gradient-induced image contrast, for example, in dMRI^133–135 and phase-contrast MRI,¹³¹ and the $k$-space encoding.¹³⁶ To mitigate the effect of concomitant fields, the 0^th and 1^st order concomitant field terms can be calibrated and corrected through RF modulation and gradient pre-emphasis.^132,137 However, the higher order terms that exist in both symmetric and asymmetric gradient systems, require high-order gradient coils for correction,¹³⁸ which may not be widely accessible.

In diffusion with asymmetric gradient waveforms on each side of the refocusing pulse, the concomitant gradient has been shown to introduce spatially varying diffusivity measurements.^133–135 Since most of the OGSE waveforms used in human studies have a symmetric design, the concomitant gradients are not expected to affect the $k$-space encoding. However, OGSE-induced concomitant gradient fields can cancel the crusher gradient,¹³⁹ resulting in image artifacts (Supplementary Material S3 and Figure S6). Increased crusher gradient is therefore more important in OGSE dMRI, compared to PGSE dMRI.

2.9 |. Motion and flow

Diffusion-encoding gradients render MR signals sensitive to other forms of motion aside from diffusion, for example, non-rigid motion of organs and perfusion at low $b$-values. This unintentional sensitivity confounds the quantification of ADC if unaccounted for, which may lead to incorrect clinical diagnosis when using DWI and ADC. For example, the non-rigid motion of the liver caused by cardiac motion has been shown to dephase diffusion signals, resulting in overestimation of ADC.^134,140 Furthermore, the effect of intravoxel incoherent motion (IVIM),¹⁴¹ that is, microcirculatory flows in the capillary bed, has been observed at low $b$-values in prostate and liver, confounding ADC measurements when it is not modeled. As more clinical OGSE dMRI studies are done in the body, it is important to consider motion-compensation to ensure motion-robust, repeatable time-dependent diffusion measurements.

The effects of non-rigid tissue motion on dMRI can be reduced when the moments of diffusion gradient waveforms are nulled.^{134,140,142,143} In OGSE, trapezoid-cosine waveforms are most commonly used, which are typically designed to have first-order moments nulled.^{37,70,144,145} This feature is often achieved by modifying the timing of the quarter-period gradient lobes. Second-order moments of these waveforms can also be nulled.¹⁴⁶

The motion compensation of OGSE waveforms is beneficial to many applications where various motions confound diffusion estimates. Jiang et al. used OGSE to perform motion-robust, time-dependent diffusion measurements in the human liver.¹³ Furthermore, the insensitivity of OGSE to motion-induced phase accumulation benefits OGSE dMRI with multi-shot acquisitions, for which shot-to-shot phase differences corrupt images. Michael et al.¹⁴⁶ reported that using oscillating gradients with a high-performance gradient system enabled artifact-free multi-shot diffusion acquisitions in the human brain.

In IVIM, motion-compensated OGSE diffusion encoding also suppresses ballistic flow signals.¹⁴⁷ However, another form of IVIM signal—pseudo-diffusive flow—cannot be suppressed by flow-compensated waveform design alone. However, Wu and Zhang¹⁴⁸ showed that these signals can be disentangled from OGSE ADC estimates by playing out pulsed gradients orthogonally to oscillating gradients and comparing the signal acquired with pulsed gradients only. This approach is particularly useful when using the low $b$-values ($b<300\text{s}/{\text{mm}}^2$) at which the IVIM effect is most pronounced. It can be practically necessary for MRI systems with relatively low gradient strength where high $b$-values ($b>300\text{s}/{\text{mm}}^2$) cannot be achieved at high OGSE frequencies.

In summary, the typical motion-compensated nature of OGSE mitigates several forms of errors stemming from non-diffusive motion. Specific OGSE waveform parameterization varies across sites and such compensation must be designed for. When it is performed, robust image quality in body and brain applications can be achieved.

2.10 |. Signal-to-noise ratio

The long diffusion encoding of OGSE waveforms results in long TE≥ 100 ms, and low SNR per acquisition. To boost SNR, large voxel sizes of 20–51 mm³ at 3T,^{12,51,57–59} 10 mm³ at 4.7T,^52,61 and 19 mm³ at 7T³⁹ systems have been used in OGSE dMRI acquisitions. These resolutions are relatively low compared to a voxel size of 10 mm³ in clinical DWI at 3T.

Acquisitions strategies have been proposed to improve upon the SNR of standard 2D echo-planar readout in OGSE dMRI. For example, spiral acquisition can reduce TE and increase SNR. In OGSE dMRI, Michael et al.⁷⁰ reported a TE reduction from 128 ms in echo-planar acquisition to 95 ms in spiral acquisition in a 3T head-only high-performance gradient MRI system. Furthermore, Wu et al.¹⁴⁹ applied an oscillating gradient diffusion-prepared 3D gradient spin-echo sequence which has shown an SNR increment of 1.7–2.3 times compared to 2D echo-planar acquisition in a whole-body clinical 3T MRI system. In addition, this 3D acquisition was shown to effectively reduce the duty cycle and reduce the scan time for whole-brain coverage.

Moreover, OGSE waveform designs with shortened duration have been proposed to reduce TE and increase SNR. For example, Borsos et al.¹⁴⁵ used a frequency-tuned bipolar oscillating gradient at 7T. The TE at 23 Hz and $b=2500\text{s}/{\text{mm}}^2$ was reduced to 91 ms, compared to a TE of 128 ms using trapezoid-cosine OGSE at the same frequency and $b$-value. The shortened TE enabled achieving adequate SNR for OGSE-based DKI analysis in the human brain at 75 mT/m.

In summary, SNR is a major challenge to the clinical translation of OGSE dMRI, due to the relatively long TE’s. High-performance gradient MRI shortens the TE and improves SNR. OGSE diffusion encoding with other k-space acquisition approaches, including spiral and 3D gradient spin-echo, as well as the optimized OGSE waveforms, have also been shown to improve SNR.

3 |. DISCUSSION AND CONCLUSIONS

Emerging human high-performance gradient MRI systems undeniably advance dMRI techniques. OGSE dMRI is a technique that greatly benefits from high-performance gradient, enabling the translation from pre-clinical research findings to human research. Effective clinical translation of OGSE dMRI calls for engineering on multiple fronts including MRI system hardware, software calibration and compensation, and pulse sequence design, along with advances in clinical applications.

First, MRI system hardware innovations including high-power gradient driver and power-efficient gradient coils are fundamental to the dissemination of OGSE dMRI in the clinic. Whole-body and head-only MRI systems at remarkably high $G_{\text{max}}\ge 200\text{mT}/\text{m}$ and $S{R}_{\text{max}}\ge 200\text{mT}/\text{m}$ are becoming commercially available. The high-performance gradient greatly expands the achievable imaging parameter space of OGSE dMRI of a single image. To enable highly time-efficient acquisition of OGSE dMRI of a 3D volume, power electronic systems need to deliver not only high peak power in a single TR (e.g., ~ 100 ms), but also high average power in the range of seconds to several minutes. Therefore, a highly efficient gradient amplifier is needed to achieve gradient performance without significantly increasing the burden on a site’s power and cooling infrastructure. For example, the use of semiconductor substrates with wider bandgaps in power transistors of the gradient drivers has been shown to have lower power losses,¹⁵⁰ allowing higher current and voltage output from the gradient drivers without expensive upgrades of site electrical power infrastructure. Therefore, the developments of power electronics provide a pathway for the drop-in electronic upgrade of existing clinical whole-body MRI systems to high-performance gradient systems, which may enable wide adoption of OGSE dMRI in the clinic.

As the gradient strength and slew rate of MRI system hardware become higher, biophysical safety constraints such as PNS and CS eventually become a bottleneck limiting the usable imaging parameter space of OGSE dMRI in humans. To mitigate such constraints, PNS-optimized gradient coils through electromagnetic field analysis have been conceptualized and produced.^89,151 Potential future development of both PNS and CS-optimized large-bore gradient coils, or specialty gradient coils for body anatomies, will further expand the imaging capability of OGSE dMRI. Furthermore, PNS-optimized diffusion encoding waveform design¹⁵² may also be useful for improving the imaging parameter space of OGSE dMRI in the existing MRI systems.

Other engineering challenges including eddy current, gradient nonlinearity, concomitant gradient, acoustic noise, and mechanical vibration can also be addressed by either incorporating them in the gradient coil design and/or through modification of other MRI subsystems,^110,111 or pulse sequence optimization. With a better understanding of the requirements on individual performance specifications, future development of MRI system hardware and OGSE diffusion encoding waveforms can be accelerated.

In humans, OGSE dMRI has been predominantly studied at 3T, with a few studies demonstrating the feasibility of OGSE dMRI at 7T in human brain.³⁹ Relatively low gradient performance and SNR of 1.5T clinical MRI systems may limit the clinical translation of OGSE dMRI at low fields. However, the advances in gradient coils at low fields and denoising techniques may allow the investigation of OGSE dMRI at low fields in the future. At ultra-high fields, the head-only high-performance gradient coils have been introduced to both 7T⁶⁷ and 10.5T.⁶⁸ In these systems, the SNR of OGSE dMRI can benefit from both a short TE and a high main magnetic field. However, the $T_2$ shortening effects at high fields counteract the benefit of high SNR, requiring shorter TE and higher gradient performance for dMRI. In addition, operating high-performance gradient coils at high fields has increased challenges including mechanical stability and motional eddy current. However, the lower concomitant gradient fields at high main magnetic fields benefit dMRI with spiral acquisitions, which shortens TE and boosts SNR. Therefore, continued progress in both hardware engineering and sequence development to address specific challenges at high-field environments will fuel more interest in using advanced dMRI such as OGSE to study the human brain at ultra-high fields.

With high-power efficiency and high PNS and CS thresholds, head-only gradient coil^64,66–69 may also accelerate clinical translation of OGSE dMRI for human neuroimaging. These gradient coils not only advance OGSE dMRI in human brain imaging, but also empower other MRI techniques including other advanced dMRI,⁷⁶ diffusion-relaxation MRI,^153–155 functional MRI,¹⁵⁶ high-resolution anatomical imaging, and myelin mapping.¹⁵⁷ Techniques like these may advance our understanding of brain structure, connectivity, and functions in neurodegenerative diseases, disorders, and brain oncology. Ultimately, they may help meet the need to develop non-invasive radiographic methods and tools in the clinical management of these patients.

Clinical translation of OGSE dMRI necessitates demonstration of its unique value in clinical applications, compared to other MRI techniques that may not require high-performance gradient coils. For example, several OGSE dMRI clinical studies^{12,55–58,71} have demonstrated improved diagnostic performance in tumor grading and identifying tumor recurrences in oncological applications, compared to clinical DWI and ADC. Chemical exchange saturation transfer (CEST)¹⁵⁸ has also shown promise in oncological imaging. Comparing or combining OGSE dMRI with other promising techniques in large studies of tumor patients will be useful for shaping future clinical MRI techniques in oncology. Furthermore, developing new OGSE dMRI-based biomarkers for neurodegenerative disease and disorders that have been validated in animal studies, for example, axonal beading^{23,25,35,43,52} and demyelination in stroke, may further accelerate clinical adoption of OGSE dMRI.

It is also worth studying the capability of time-dependent DKI versus time-dependent DWI and DTI in characterizing tissue microstructures in clinical studies. Time-dependent DKI with OGSE diffusion encoding has shown unique image contrast that may differentiate restriction cell size and water exchange rate, which may reveal pathological alternations in gray and white matter.^54,159 Recent studies have demonstrated the feasibility of OGSE DKI in the human brain.^75,145 However, lower maximum frequencies and longer TE were obtained in OGSE DKI at the high $b\ge 2000\text{s}/{\text{mm}}^2$ (Figures 4–6). In addition, OGSE DKI is accompanied by reduced scan efficiency due to its high power consumption, as well as higher acoustic noise level and mechanical vibration. Improvements in gradient waveform design and MRI system hardware modifications are more critical for the use of OGSE DKI in patient studies.

In summary, growing evidence demonstrates the unique capability of OGSE dMRI in addressing clinically significant problems. We have identified specific engineering challenges facing OGSE dMRI applied to humans. We believe that continued progress in addressing these challenges will ultimately make the clinical adoption of OGSE dMRI feasible soon.