Target audience

Students and scientists interested in learning about tissue microstructure imaging with diffusion. Some prior knowledge of diffusion and diffusion MRI, corresponding e.g. to what was covered in the preceding lectures of the course, is assumed.

Methods

Lecture and exercises. Bring paper and pencil.

Contents

Starting from some general considerations about modeling diffusion in tissue as a sum of Gaussian compartments, we will introduce the so-called ”Standard Model”, an overarching framework widely used to describe water diffusion in the brain. The Gaussian compartments of this model correspond to axons or neurites and extra axonal space, and is described in terms of the diffusivities of the compartments as well as the orientation distribution of axons. Notably, axons in this picture are approximated as having zero radius (sticks), due to the insensitivity of typical diffusion sequences to their small radii (~1 μm). Distances on such a small scale requires correspondingly large gradients to achieve sufficient signal attenuation from intra-axonal spins. We will discuss the conditions under which it can be expected to hold, such as long diffusion times, and present evidence for its validity. Difficulties with estimating model parameters from typical data will be explained, due to an inherent model degeneracy at low b values, as well as potential strategies to overcome them. Among promising strategies are extensions of the classical Stejskal-Tanner diffusion pulse sequence, such as double diffusion encoding and free waveforms. Double diffusion encoding, for example, extends the conventional pulse designed by adding an additional independent diffusion encoding block, substantially increasing the degrees of freedom of the sequence. In this context, we will highlight the nature of the new information achievable from such sequences, such as diffusion covariance tensors, microscopic anisotropy and more. Other strategies (orthogonal measurements) include sampling data along additional dimensions such as diffusion time and echo time. Finally, we will discuss various scenarios leading to deviations from the standard model. Depending on the diffusion time, such properties could include deviations from stick geometry of neurites caused e.g. by axonal undulation, beading, spines, branching/curvature, finite radii. There could also be a substantial contribution from additional compartments such as cell bodies and other cell types, as well as heterogeneity in e.g. axonal populations reflected in distributions of T₂ values and diffusivities. The basic compartmental assumption could be compromised by exchange between compartments.

Acknowledgements

The authors would like to thank Dmitry Novikov and Els Fieremans for discussions, and for hospitality during a sabbatical at CBI/NYU for SJ. SJ acknowledges funding from Aarhus University Research Foundation (AUFF), the Lundbeck foundation, and Augustinus Fonden.