A unique analytical solution of the white matter standard model using linear and planar encodings
Open accessAbstract
Purpose: It is known that white matter modeling based on commonly used linear diffusion encoding is an ill‐posed problem. We analyze the additional information gained from a double pulsed diffusion encoding. Methods: Zeroth (spherical means) and second‐order (harmonic powers) rotation invariant signal features are used to factor micro‐ and mesoscopic contributions. The b‐value dependency up to second‐order of the features form 6 nonlinear equations, which are analyzed. Results: The 6 derived equations can be uniquely solved for all relevant biophysical parameters. No assumptions about the form of the mesoscopic contribution (fiber dispersion) is necessary. Under certain conditions the solution still shows a certain degeneracy which is inherent to model. It is further shown that a combination of second‐order information from single and spherical diffusion encoding is not enough to solve the problem. Conclusions: A combination of single and double pulsed diffusion encodings is sufficient to solve the full 3 compartment white matter model uniquely.
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The data may not uniquely support the biological interpretation one wishes to make, though subsequent theoretical work has characterized this degeneracy and shown that the model parameters can be distinguished with sufficiently informative acquisition protocols or additional measurements.
“In other words, the data may not uniquely support the biological interpretation one wishes to make, though subsequent theoretical work has characterized this degeneracy and shown that the model parameters can be distinguished with sufficiently informative acquisition protocols or additional measurements (Coelho et al., 2019; Reisert et al., 2019).”
From 40 Years of diffusion MRI in the brain: From history to emerging frontiers (2026) · cites this paper as Reisert et al., 2019
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NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain
Zhang, H., Schneider, T., Wheeler-Kingshott, C. A., & Alexander, D. C. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2012.03.072 · Cited by 3,288 · see citing works
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Kamiya, K., Hori, M., & Aoki, S. (2020) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2020.108908 · Cited by 283 · see citing works
Jelescu, I. O., de Skowronski, A., Geffroy, F., Palombo, M., & Novikov, D. S. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119277 · Cited by 177 · see citing works
Diffusion time dependence, power‐law scaling, and exchange in gray matter
Olesen, J. L., Østergaard, L., Shemesh, N., & Jespersen, S. N. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.118976 · Cited by 125 · see citing works
Lampinen, B., Szczepankiewicz, F., Lätt, J., Knutsson, L., Mårtensson, J., Björkman-Burtscher, I. M., van Westen, D., Sundgren, P. C., Ståhlberg, F., & Nilsson, M. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120338 · Cited by 38 · see citing works
40 Years of diffusion MRI in the brain: From history to emerging frontiers
Le Bihan, D. (2026) · Imaging Neuroscience · doi:10.1162/imag.a.1365
“…biological interpretation one wishes to make, though subsequent theoretical work has characterized this degeneracy and shown that the model parameters can be distinguished with sufficiently informative acquisition protocols or additional measurements ( Coelho et al., 2019; Reisert et al., 2019).”
- Authors
- Reisert, M., Kiselev, V. G., & Dhital, B.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Reisert, Marco
- Venue
- Magnetic Resonance in Medicine
- Publisher
- Wiley
- Published
- 2019-02-27
- Volume
- 81
- Issue
- 6
- Pages
- 3819-3825
- ISSN
- 0740-3194 (ISSN-L)
- 1522-2594
- OpenAlex
- W2916784958
- Cited by
- 46
- References
- 1
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 4 · 2023: 2 · 2022: 7 · 2021: 5 · 2020: 15 · 2019: 5
- FWCI
- 5.29
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Magnetic Resonance in Medicine (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › NMR spectroscopy and applications
- Keywords
- white matter microstructure, spherical means, harmonic power, b-value dependence, ill-posed inverse problems, analytical solution, fiber dispersion, biophysical parameter estimation, degeneracy
- MeSH terms
- Humans, Image Processing, Computer-Assisted, Signal Processing, Computer-Assisted, Diffusion Magnetic Resonance Imaging, White Matter
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