Microstructure Models, Part I
Valerij G. Kiselev1 and Sune N. Jespersen2

1Medical Physics, Dpt. of Radiology, Faculty of Medicine, University of Freiburg, Germany, 2CFIN, University of Aarhus, Aarhus, Denmark

Synopsis

We discuss the principles of accessing the tissue microstructure using diffusion MRI. This challenge is decomposed into the forward and inverse problems: the biophysical modeling of the diffusion-weighted MRI signal, and the model parameter estimation, respectively. We focus on the former and briefly discuss the latter. The central phenomenon for the biophysical modeling is the course-graning of the structural details by diffusion. It will be discussed for the regimes of short times (when diffusion reveals the interface surface per unit volume) to long times (when diffusion becomes sensitive to the overall structural organization of tissues). The case of impermeable compartments will be treated separately to clarify the sensitivity of diffusion measurements to the size of small cells

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

The goal of accessing tissue microstructure using diffusion MRI poses two major challenges. The first is to predict the observed signal given a tissue microstructure, which is referred to as the forward problem. It belongs to the realm of physics in which similar problems has been considered since the nineteenth century. In the context of diffusion MRI, the problem further splits in finding the properties of water diffusion in such complex media as biological tissues and how these properties are imprinted in diffusion MRI signal. We start with an overview of water diffusion in complex media for increasing diffusion time. The focus will be on the coarse-graining effect of diffusion, which is the averaging of the local cellular features, the more efficient the longer the diffusion time is. We explain how this phenomenon leads to the picture of Gaussian compartments for long diffusion times. We further consider the measurement procedure that adds the gradient waveform to the parameters affecting the measured signal. We discuss a “road map” of diffusion MRI to classify different measurement regimes. The second challenge is the determination of the microstructure properties given the measured signal (the inverse problem). Responding to this challenge requires the synergy of practically all disciplines composing our community: Physics as represented by the solution to the forward problem, engineering for the design of hardware and pulse sequences, statistics and data processing technologies from computer science. It is also important to realize the difference between microstructure models and signal representation. Using the simplest examples, we explain the origin of the “remarkably unremarkable” signal obtained using the commonly used diffusion measurements.

Acknowledgements

The authors would like to thank Dmitry Novikov and Els Fieremans for discussions. SJ acknowledges funding from Aarhus University Research Foundation (AUFF), the Lundbeck foundation, and Augustinus Fonden.

References

Kiselev, V.G., 2017. Fundamentals of diffusion MRI physics. NMR Biomed 30, e3602-n/a.

Novikov, D.S., Fieremans, E., Jespersen, S.N., Kiselev, V.G., 2018a. Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. NMR in Biomedicine 0, e3998.

Novikov, D.S., Kiselev, V.G., Jespersen, S.N., 2018b. On modeling. Magnetic Resonance in Medicine 79, 3172-3193.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)