To develop a novel method for DWI which enables utilization of the MRI-phase for encoding the diffusion of water molecules.

Diffusion Weighted Imaging (DWI) in MRI uses the loss of phase coherence within the imaging voxel – induced by the random walk of the spins under the influence of a linear gradient – to deduce micro-structural information. Since diffusion is typically dyadic (i.e. equal # of spins moving in opposed directions), the entire spin ensemble within the imaging voxel does not experience a net phase accrual, but only a loss in total signal magnitude due to dephasing. Hence, classical DWI cannot utilize the MRI-phase information per se.

DWI² is based upon the idea that a diffusing spin in a 2^nd order magnetic field (i.e. B(z)=β*z²) will experience only positive phase accrual independent of the direction of motion. Thus, DWI² can explore the MRI-phase information. Furthermore, the absence of a linear component (i.e. B(z)=α*z) in the proximity around z=0 leads to minimal loss in signal magnitude. Thus, in DWI² the SNR remains minimally altered when imaging at this preferred position. This opens the gateway to entirely new concepts for diffusion weighted imaging, in particular to elevated sensitivity to micro-architectural complexity currently hidden due to limited SNR [1].

Experiments used a classical spin-echo sequence with TE=50ms and TR=500ms at 3T (Philips Medical Systems). As shown in the figure, a water sample (a) was placed along the z-symmetry axis of two Helmholtz coils (inner ∅=10mm, # 150 windings for each coil, length of each coil=10mm, separation of 8.6mm between coils, ∅0.3mm for copper wire) which could be operated in linear or quadratic mode. Imaging was done at z=0 with transverse image orientation to explore the effect of the linear or quadratic field on the diffusion of the water molecules. One single sinusoidal gradient pulse was applied after the π/2-pulse and before the π-pulse at ν=100Hz with a current of 1A. Pre-emphasis of the gradient pulse was adjusted to ensure a net pulse area of zero. A magnetostatic field simulation (FEMM 4.2) of the quadratic coil configuration yields β=5300T/m² at z=0. Analytic calculus predicts a net phase-change φ=γDβ/(2ν²) = (-)0.16 [rad] (with D the water diffusion coefficient and γ the gyromagnetic ratio). Monte Carlo simulations (Camino software [2], #100000 particles, pure water, β=7560T/m², ν=30Hz) were performed to investigate the correctness of the analytic calculus.The resulting images of the MR-magnitude and MR-phase for both coil configurations (linear, quadratic) are shown in (b) without (0A) and with application of a current (1A). The linear coil configuration leads – as expected – to a significant reduction in magnitude (c) without any statistically significant phase change (d). This is corroborated by analytic calculus. On the contrary, the quadratic coil configuration leads to no statistically significant loss in magnitude (as expected), while a statistically significant negative phase drift is measured. The measure phase shift of (-)0.24±0.11rad agrees within errors with the theoretically expected of (-)0.16rad. Monte Carlo simulations (e) confirmed the net phase shift for the quadratic field configuration (φ^AVG=-1.44rad) with excellent agreement to the analytic expression (φ^theory=-1.45rad). Classical DWI is a powerful method for gaining insight into tissue microstructure. Its diagnostic value is currently explored for various applications, from diagnosis over response to therapy to prediction of outcome. Intrinsically, DWI uses the decrease of the MR-magnitude signal as a function of b-value for extracting the mono-exponential or bi-exponential ADC value(s). More complex diffusion information are obtained via stretched exponentials [3], or ADC-values at shorter diffusion time scales via oscillating gradients [4]. Still, all those methods utilize the MR-magnitude information. The inevitable loss in signal often limits DWI to low b-values and hence restricts the potential of the method for characterizing microstructure. DWI² overcomes this limitation by using 2^nd order spatial field changes for encoding the diffusion information. As expected from theory – and experimentally demonstrated – a quadratic field gradient leads to a minimal loss in signal magnitude in combination with a net shift in phase when operating in close proximity of z=0 for B(z)=βz². Monte Carlo simulations of freely diffusing water molecules show excellent agreement between theory and simulation results, further demonstrating the validity of the proposed method. The essential conservation of signal for DWI² leads therefore to a paradigm shift for DWI as currently inaccessible domains can now be explored.