Cumulant expansion with localization
Maryam Afzali1,2, Tomasz Pieciak3, Derek K Jones2, Jürgen Schneider4,5, and Evren Özarslan6,7
1Leeds Institute of Cardiovascular and Metabolic Medicine, University of Leeds, Leeds, United Kingdom, 2Cardiff University Brain Research Imaging Centre (CUBRIC), School of Psychology, Cardiff University, Cardiff, United Kingdom, 3LPI, ETSI Telecomunicación, Universidad de Valladolid, Valladolid, Spain, 4Leeds Institute of Cardiovascular and Metabolic Medicine, Leeds, United Kingdom, 5Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, Oxford, United Kingdom, 6Department of Biomedical Engineering, Linköping University, Linköping, Sweden, 7Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden
Diffusion MR is sensitive to the microstructural features of a sample. Fine-scale characteristics can be probed by employing strong diffusion gradients while the small gradient regime is determined by the cumulants of the distribution of particle displacements. However, the cumulant expansion suffers from a finite convergence radius and cannot represent the ‘localization regime’ that emerges at higher gradient strengths characterized by a stretched exponential dependence. Here, we propose a new representation for the diffusion MR signal. Our method provides not only a robust estimate of the first few cumulants but also a meaningful extrapolation of the signal decay.
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