A Fractional Langevin Equation Approach to Diffusion Magnetic Resonance Imaging

  1. Stuart A. Rice2,3 and
  2. Aaron R. Dinner2,3
  1. Jennie Cooke

Published Online: 8 NOV 2011

DOI: 10.1002/9781118135242.ch5

Advances in Chemical Physics, Volume 147

Advances in Chemical Physics, Volume 147

How to Cite

Cooke, J. (2011) A Fractional Langevin Equation Approach to Diffusion Magnetic Resonance Imaging, in Advances in Chemical Physics, Volume 147 (eds S. A. Rice and A. R. Dinner), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118135242.ch5

Editor Information

  1. 2

    Department of Chemistry, The University of Chicago, Chicago, Illinois, USA

  2. 3

    The James Franck Institute, The University of Chicago, Chicago, Illinois, USA

Author Information

  1. The School of Medicine, Faculty of Health Sciences, Trinity College Dublin, Ireland

Publication History

  1. Published Online: 8 NOV 2011
  2. Published Print: 2 DEC 2011

ISBN Information

Print ISBN: 9781118122341

Online ISBN: 9781118135242

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Keywords:

  • fractional Langevin approach, diffusion MRI;
  • DWMRI in treatment planning;
  • DWI applications, DW–MRI in vivo

Summary

This chapter contains sections titled:

  • Overview

  • Phase Diffusion and Brownian Motion

  • A Langevin Equation Approach to Normal Diffusion

  • Fractional Diffusion: Possible Explanations of the Stretched Exponential Behavior Using the Fractional Langevin Equation

  • Magnetic Resonance Imaging Methods

  • Results of Experimental Investigation

  • Discussion

  • Acknowledgments

  • Appendix A

  • Appendix B

  • References