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Microstructure with Magnetic Resonance - 1st Edition - ISBN: 9780128224694

Microstructure with Magnetic Resonance, Volume 4

1st Edition

Problems and Solutions

Authors: Valerij Kiselev Dmitry Novikov
Paperback ISBN: 9780128224694
Imprint: Academic Press
Published Date: 1st November 2021
Page Count: 250
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Table of Contents

1. Diffusion basics
2. First touch of microstructure
3. Describing randomness: Correlation functions
4. The induced field and spin phase
5. Transverse relaxation
6. Physics of diffusion measurement
7. The cumulant expansion and velocity autocorrelation function
8. Beyond the Gaussian approximation
9. Transverse relaxation in dilute suspensions
10. Diffusion in three dimensions
11. Multiple Gaussian compartments
12. Diffusion and Bloch – Torrey equations
13. Impermeable interfaces and porous media
14. Permeable interfaces and heterogeneous media
15. Advanced diffusion encoding
Appendices: The aftermath (Math facts, tricks and hacks)


Microstructure with Magnetic Resonance: Problems and Solutions responds to the challenge of how to see the invisible with magnetic resonance imaging. Technically, the goal is to quantify cellular-level properties of biological tissues and microarchitecture of porous media orders of magnitude below the achievable resolution of MR. While the interest in this area has grown exponentially, current research involves physics outside the scope of standard NMR and MRI textbooks. Microstructure with Magnetic Resonance: Problems and Solutions introduces readers to methods of describing complex media in statistical terms, and covers the effects of complex microenvironments on the MR signal phase, on the transverse relaxation, and on different facets of the diffusion-weighted signal.

The book presents the material as a set of problems with detailed solutions, that build on each other, stimulating a hands-on approach to learning. Each chapter begins with a short introduction to the topic, followed by problems, solutions, and a summary of key points. The problems start from the basics, and bring the reader step-by-step to the frontier of current knowledge. The overall focus is on gaining physical insight, by drawing on simple physical analogies and dimensional analysis, which help to reproduce the essence of the results obtained in classical and recent studies. The necessary mathematics is collected in dedicated appendices.

With this book the reader will:

• Understand the classic and current literature on microstructure mapping with NMR and MRI;

• Become familiar with the modern trends in microstructure MR;

• Be able to design new experiments using MR based on a solid theoretical foundation.

Key Features

• Explains physics necessary to understand how the microscopic structure of biological tissues and porous media manifests itself in different magnetic resonance contrasts (phase, relaxation, diffusion).
• Uses a unique problem/solution structure to provide for efficient learning from the basics to the frontiers of knowledge.
• Tested through numerous teaching courses for trainees.


Researchers working in the field of in vivo Magnetic Resonance Imaging (MRI) who wish to extend their skills to tissue microstructure mapping using diffusion MRI, as well as researchers in NMR in material science


No. of pages:
© Academic Press 2021
1st November 2021
Academic Press
Paperback ISBN:

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About the Authors

Valerij Kiselev

Dr. Kiselev joined the field of MRI with a decade-long research experience in quantum field theory including authoring a textbook on this subject. His current focus is on understanding how the microstructure of biological tissues is imprinted in the observable MRI signal obtained with dedicated MRI techniques. His contributions include quantification of perfusion measurements using DSC MRI, vessel size imaging, and the effective medium approach to transverse relaxation and diffusion with the goal to quantify the cellular tissue microarchitecture. He has organized numerous educational events on diffusion and perfusion MRI, where he introduced the problem-solving approach.

Affiliations and Expertise

Medical Physics, Department of Radiology, University Medical Center Freiburg, Freiburg, Germany

Dmitry Novikov

Dr. Novikov brings a decade of experience in theoretical condensed matter physics to the biomedical MRI. He is developing analytical tools and parameter estimation methods to quantify cellular-level tissue structure and its changes in disease based on various MRI contrasts. His contributions include the effective medium approach for diffusion and relaxation to quantify cell density, their packing arrangement, membrane permeability and other related metrics, with the goal to identify quantitative disease biomarkers in neurodegenerative diseases, tumors and myopathies. He introduced the problem-solving approach to the ISMRM educational sessions.

Affiliations and Expertise

Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA