Encoding Diffusion: Basics
Amy Howard1
1University of Oxford, United Kingdom

Synopsis

This talk will introduce the basic concepts behind diffusion encoding and how, by mapping the microscopic motion of water molecules through tissue, we can infer microstructural information in vivo. Specifically, we will discuss how diffusion weighting is achieved through the use of time-varying magnetic field gradients, and how we can manipulate the encoding to provide sensitivity to different aspects of the microstructure (e.g. the size and shape of cells, or fibre orientations in the white matter). Here we will focus on three methods: single diffusion encoding, double diffusion encoding and the use of oscillating gradients.

Single diffusion encoding (SDE)

Introduced by Stejskal and Tanner in mid 1960s1, the commonly used Pulsed Gradient Spin Echo (PGSE) sequence combines spin echo imaging with a single pair of diffusion-sensitising gradients defined by three parameters: the gradient amplitude, $$$|G|$$$, duration, $$$\delta$$$, and the time between the pulses i.e. the diffusion time, $$$\Delta$$$. The gradients occur after the $$$90^\circ$$$ RF ‘excitation’ pulse, and sit either side of the $$$180^\circ$$$ RF ‘refocussing’ pulse. The first diffusion gradient imparts a spatial pattern of phase modulation across the sample which, in the absence of diffusion, is perfectly undone by the second gradient. In the presence of diffusion, spin displacement along the orientation of the gradient results in net phase accrual (dephasing) and an attenuation of the MR signal. For Gaussian diffusion, the signal exhibits mono-exponential decay $$$S_b = S_0 exp(-bD)$$$, where $$$D$$$ is the apparent diffusion coefficient, $$$b$$$ describes the sensitivity to diffusion and is given by time dependent integral of the diffusion gradient, and $$$S_0$$$ is the signal at $$$b=0$$$. Deviations from mono-exponential signal decay may indicate more complex microenvironments with restricted diffusion or multiple compartments.

By manipulating the encoding parameters ($$$G, \delta, \Delta$$$) and/or acquiring data along multiple orientations, we can sensitise our signal to different length scales or examine the time- and orientational-dependence of diffusion – all of which can inform us about the underlying tissue microstructure. For example, in the long diffusion time regime, multi-shell acquisitions can be used to estimate the density and shape of multiple compartments (intra-cellular, extra-cellular and CSF)2, whilst high b-value data can provide more distinct crossing fibres when mapping the structural connectome3, or isolate the signal from the intra-axonal space4. Short diffusion times provide information about the size and shape of cells5, whilst multi-$$$\Delta$$$ multi-$$$b$$$ data can differentiate exchange from cell soma contributions in the grey matter6.

SDE acquisitions are not restricted to the standard PGSE sequence. One example is the stimulated echo acquisition mode (STEAM)7,8 when probing diffusion times which are long compared to the T2 (e.g. for imaging at 7T). Here, the $$$180^\circ$$$ RF pulse is replaced by two $$$90^\circ$$$ pulses, separated by some mixing time $$$t$$$, which determines the diffusion time. Consequently, the encoded signal is stored in the longitudinal axis, before being placed in the transverse plane just prior to imaging. Since the longitudinal axis is subject to T1 relaxation rather than the faster T2 of the transverse plane, STEAM facilitates relatively high SNR imaging at long diffusion times, when compared to PGSE.

Whilst SDE is still the workhorse of many diffusion studies, its ability to measure certain tissue features, such as small compartments, may be limited. Consequently, certain applications may benefit from alternative encoding methods9.

Double diffusion encoding (DDE)

Double diffusion encoding consists of two pairs of pulsed-field gradients that are separated by some mixing time $$$t$$$10,11. DDE consequently provides two additional tuneable parameters: the orientation of the gradient pairs with respect to one another, and the mixing time. Data acquired with gradients along the same orientation but with varying $$$t$$$ can be used to estimate molecular exchange between two compartments with fast and slow diffusion (e.g. extra- versus intra-cellular water)12. Here the first gradient set acts as a low-pass filter, preferentially attenuating the fast compartment. During mixing time $$$t$$$, molecular exchange takes place, whereby MR visible water returns to the fast diffusion compartment. The second set of gradients then measure the apparent diffusion coefficient of both compartments. At short $$$t$$$, the ADC resembles that of the slow compartment, whilst at long $$$t$$$, the ADC is equal to the weighted sum from both compartments. The rate at which the ADC returns equilibrium thus informs on the rate of exchange. Alternatively, the mixing time $$$t$$$ may be fixed and the orientation of the gradient sets varied to measure diffusion anisotropy13, whilst blocks with opposite orientations and a short mixing time can provide information about compartment size14.

Oscillating gradients

Oscillating gradients, i.e. a series of pulsed gradients with alternate polarity, are typically used to probe very short diffusion times (<10ms) with sufficient diffusion weighting15. As each set of bi-polar gradients are close together, the diffusion time is short. Since the b-value scales as a function of the number of gradient sets, considerable diffusion weighting can be achieved when compared to the SDE sequence. Consequently, oscillating gradients facilitate estimation of small pores (cells) with highly restricted diffusion16 whilst dampening signal from water with high diffusivity (e.g. from water diffusing along disperse axons17).

Acknowledgements

AFDH is supported by the Wellcome Trust (grants WT202788/Z/16/A, WT221933/Z/20/Z and WT215573/Z/19/Z). The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z).

References

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Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)