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.