Links between measured signal, the temporal profile of the diffusion-encoding gradients and spatial features of the measured probes will be explained. Among others, the temporal gradient profiles "short-short", "long-long", "long-short", and gradient profiles with multiple gradient pulses will be discussed.
Two gradient pulses 1: short-short
Diffusion encoding is achieved by application of two gradient pulses of opposite polarity that are played out so quickly that particle motion is effectively “frozen” during their application. Consequently, only the particle motion in the time interval $$$\Delta$$$ between the gradient pulses is of relevance (1,2).
Two gradient pulses 2: long-long
In reality, the application of short gradient pulses is challenging due to limited available gradient amplitude. Thus, diffusion encoding is achieved by “long” gradients of a non-zero duration $$$\delta$$$ and separation $$$\Delta-\delta$$$ . Particle motion during the gradient pulse must be taken into account (3).
Two gradient pulses 3: long-short
The first gradient pulse is long and the second gradient pulse is short (4). Their durations and amplitudes must meet the following condition: $$$ \delta_{long}G_{long}=\delta_{short}G_{short}$$$.
Three or more short gradient pulses
Diffusion encoding is achieved by three or more short gradient pulses (5-7).
Further temporal gradient profiles
In general, basically any temporal profile $$$G(t)$$$ can be used for diffusion encoding (8). Several temporal profiles that have been described in the literature will be shortly presented.
Two gradient pulses 1: short-short
For two gradient pulses in the short pulse approximation, the measured signal equals the Fourier transform of the volume-averaged diffusion propagator. This makes possible the measurement of many propagator-derived metrics such as the time-dependent diffusion coefficient $$$D(t)$$$ and the diffusional kurtosis $$$K(t)$$$ (9). The behavior of diffusion propagator, $$$D(t)$$$, and $$$K(t)$$$ will be discussed for open and closed domains. Moreover it will be discussed that the magnitude of the form factor of the domain can be retrieved (10,11).
Two gradient pulses 2: long-long
For two long gradient pulses, the measured signal equals the Fourier transform of the volume-averaged center of mass (COM) propagator (3). Here, “COM” refers to the COMs $$$x_{com,1}$$$ and $$$x_{com,2}$$$ of the particle trajectories during first and second gradient, i.e. $$$x_{com,1}=\frac{1}{\delta}\int_0^\delta x(t)dt$$$ and $$$x_{com,2}=\frac{1}{\delta}\int_\Delta^{\Delta+\delta} x(t)dt$$$ . Several effects that occur with long gradient pulses will be discussed including edge enhancement (12). Differences between closed and open domains will be explained and it will be discussed to which extent long-long can be regarded as an approximation for short-short (13).
Two gradient pulses 3: long-short
The same mathematical framework as for long-long can be used. It will be discussed how the average shape of an ensemble of closed pores or cells can be detected by means of long-short gradient pulses making possible to perform diffusion pore imaging (14).
Three or more short gradient pulses
Dividing the signal obtained with short-short-short and short-short gradient profiles can be used to estimate the shape of point-symmetric pores (15). By means of a recursive reconstruction, the shape of arbitrary domains (16) and of periodic lattices can be retrieved (17). Differences between the pore imaging techniques relying on multiple short gradient pulses and on long-narrow gradient pulses will be discussed.
Further temporal gradient profiles
Some properties of further temporal gradient profiles will be summarized and discussed.
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