Magnetic gradient fields are essential in magnetic resonance imaging to encode the spatial distribution of the magnetization. Furthermore, strong gradients are usually used to obtain information about diffusion processes within a sample noninvasively [1]. As a consequence of Maxwell's equations, these linear gradient fields are always accompanied by so-called concomitant or Maxwell fields. These magnetic fields scale with the applied gradient amplitude and the distance from the gradient isocenter. Their malign impact results from the introduction of an additional phase on transverse magnetization [2,3], which can manifest as artifacts such as signal dropouts [4], degradation of the signal-to-noise ratio (SNR), or, for example, corrupted T2* relaxometry measurements [5]. Concomitant fields are also known to impede proper evaluation of quantitative diffusion metrics such as the apparent diffusion coefficient (ADC), which may exhibit spatially dependent variations [6]. Since the strength of the concomitant field is inversely proportional to the main magnetic field, special caution is required on low magnetic field systems [7,8], where recent advances also enable diffusion-weighted experiments [9].

Double diffusion encoding (DDE) [10] pulse sequences apply two diffusion weightings in one experiment. These sequences have raised attention due to their wide range of possible applications [[11], [12], [13]]. The fractional anisotropy (FA), which can be estimated using diffusion-tensor imaging [14,15], cannot differentiate between microscopically isotropic diffusion and an isotropic distribution of anisotropic diffusion compartments within an image voxel [16]. Metrics such as microscopic anisotropy [[17], [18], [19]] and fractional eccentricity [20] overcome this ambiguity and can be inferred from a particular DDE gradient scheme, where two subsequent diffusion weightings with different angle between the directions are separated by a refocusing radiofrequency (RF) pulse allowing for an adequate mixing time [21], often referred to as double-pulsed-field-gradient (d-PFG) experiments. In contrast to the well-known single-refocused Stejskal-Tanner diffusion experiment [22], these diffusion sensing sequences are generally not intrinsically compensated for unwanted effects due to concomitant fields because the diffusion weightings are often realized as two pairs of bipolar gradients to avoid echo time increase and signal loss when using additional refocusing pulses.

Depending on the considered problem, various compensation strategies for concomitant fields have been developed. These include redesigning the pulse sequence for fast spin-echo imaging [3], “prewarping” the accumulated concomitant phase [23], real-time gradient pre-emphasis to account for first-order concomitant fields on asymmetric gradient systems [24], additional constraints in optimized waveform design [25,26], and reconstruction-based corrections for spiral-ring turbo spin-echo imaging [27].

In this study, we propose a method for concomitant field compensation in the context of DDE in sequences with arbitrary pairs of bipolar diffusion gradients on each axis enclosing a refocusing RF pulse. Provided that the bipolar gradients probe different diffusion directions, the sequence is prone to concomitant field-induced artifacts. However, the different amplitudes on the physical gradient axes before and after the refocusing RF pulse allow for modifications in the gradient amplitude and thus give room for optimization of the temporal gradient waveforms to reduce concomitant field-induced signal loss.

We show in both simulations and measurements that – by controlled addition of oscillating gradients to the original waveform – the effect of the concomitant gradients on a clinical MR system is reduced while the original sequence characteristics are only slightly changed, leading to a measurable SNR increase.