Target audience: Researchers interested in the characterization of perfusion using contrast-free methods, such as measuring intravoxel incoherent motion using diffusion-weighted MRI.
Participants will develop a deep understanding of the effects of applied magnetic field gradients on the transverse magnetization of particles undergoing motion / flow and the implications on the magnitude and phase of the measured MRI signal. Topics include gradient moments, velocity encoding (VENC), the intravoxel incoherent motion (IVIM) model, the Gaussian phase approximation, flow-compensation / higher order moment nulling and oscillating gradients / temporal diffusion spectroscopy.
Participants will develop a deep understanding of:
As a result, they will be able to select the most appropriate technique to answer their research question, avoid pitfalls and be aware of confounding effects, which might affect the correct interpretation of their results.
Gradient moments are a concept, which enables us to understand the sensitivity of an applied gradient waveform to different aspects of particle motion. It arises naturally from the equation for the phase φ that is acquired by a spin packet travelling along the trajectory x(t) while the gradient g(t) is active1. Taylor expansion around t = 0 yields: $$\phi(t)=\gamma\int_0^t\mathbf{x}(t)\cdot\mathbf{g}(t)dt=\mathbf{m}_0(t)\cdot\mathbf{x}_0+\mathbf{m}_1(t)\cdot\mathbf{v}_0+... .$$ The zeroth order moment is directly related to the k-space position, yielding the Imaging Condition $$$m_0(TE)=0$$$, which is mandatory for any motion-sensitizing gradient waveform.
The first order moment is directly related to the velocity encoding (VENC). To measure flow velocities based on the phase of the MRI signal, the VENC, which determines the waveform's sensitivity needs to be chosen appropriately to avoid velocity aliasing.
Designing waveforms compensated (nulled) for higher-order moments can be beneficial, for example in the case of cardiac diffusion-weighted MRI2. Frameworks have been developed to design compensated gradient waveforms, which additionally minimize eddy currents3 or concomitant fields4. The nulling of moments does however come at a price: typically the achievable diffusion-encoding strength (b-value) or the SNR (increase echo time) are reduced.
Considering the possibility of having different flow directions within a voxel or region of interest naturally leads to the concept of intravoxel incoherent motion5. To separate the effects of diffusion and perfusion, a two-compartment model is commonly applied, with the blood compartment contributing the perfusion fraction f to the unweighted signal6: $$S(b)=S(0)\left[(1-f)e^{-bD}+f{e}^{-bD_b}F(b)\right].$$ The measured diffusion of the tissue fraction (D) could shown non-Gaussian (Kurtosis) effects at higher b-values due to restricted motion and thus a dependence on the applied gradient waveform. The same was found for the self-diffusion coefficient of blood (Db), which becomes relevant in the context of motion-compensated encoding7.
For the signal attenuation F(b) of the perfusion (blood) compartment analytical expressions are only available for the border cases of:
The range of motion in between those limits can be explored using the concept of normalized phase distributions, which highlights the benefits of flow-compensation to characterize the vascular network8.
There are pitfalls related to the separation of diffusion and perfusion, such as the well-known echo time dependence of the perfusion fraction9 and observed dependences of the IVIM parameters on the cardiac cycle10.
Using oscillating gradients (temporal diffusion spectroscopy11) enables shortening of the effective diffusion time, which shifts the signal attenuation from the pseudo-diffusion limit towards the straight flow limit. There are connections to the concept of moment nulling: cosine gradients can be implemented flow-compensated, while sine gradients have a non-zero first gradient moment.
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4. Peña‐Nogales Ó, Zhang Y, Wang X, de Luis‐Garcia R, Aja‐Fernández S, Holmes JH, et al. Optimized Diffusion‐Weighting Gradient Waveform Design (ODGD) formulation for motion compensation and concomitant gradient nulling. Magn Reson Med 2019;81:989–1003.
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