arxiv: 2604.08092 · v1 · submitted 2026-04-09 · ⚛️ physics.med-ph

Recognition: 2 theorem links

· Lean Theorem

Predicting Mesoscopic Larmor Frequency Shifts in Ex Vivo Porcine Optic Nerve

Anders Dyhr Sandgaard , Andr\'e Pampel , Roland M\"uller , Niklas Wallstein , Toralf Mildner , Carsten J\"ager , Markus Morawski , Aage Kristian Olsen Alstrup

show 2 more authors

Harald E. M\"oller Sune N{\o}rh{\o}j Jespersen

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:51 UTC · model grok-4.3

classification ⚛️ physics.med-ph

keywords optic nerveLarmor frequency shiftsquantitative susceptibility mappingwhite matter microstructuremesoscopic fieldshollow cylinder modelex vivo porcinemyelin susceptibility

0 comments

The pith

Microstructure-informed QSM accurately predicts orientation-dependent Larmor frequency shifts in white matter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether a model of white matter as dispersed hollow cylinders for axons and spherical inclusions can predict sub-voxel Larmor frequency shifts measured in ex vivo pig optic nerves at different orientations to the magnetic field. Using diffusion-weighted and multi-gradient echo imaging on a 3T scanner, the authors compare the measured shifts to predictions from microstructure-informed quantitative susceptibility mapping. The close match supports that these shifts arise from mesoscopic perturbations due to uniformly magnetized axons, with little contribution from iron as shown by de-ironing experiments. This matters because clinical QSM voxels average over these microscopic variations, so accounting for them improves susceptibility estimates.

Core claim

Microstructure-informed Quantitative Susceptibility Mapping (μQSM), which models axons as orientationally dispersed hollow cylinders and other inclusions as spheres, accurately reproduces the observed orientation dependence of Larmor frequency shifts in ex vivo porcine optic nerve. The estimated sub-voxel frequency shifts matched the μQSM predictions, consistent with mesoscopic field perturbations from uniformly magnetized axons, and de-ironing had minimal effect indicating negligible iron contribution.

What carries the argument

Microstructure-informed Quantitative Susceptibility Mapping (μQSM) using a model of orientationally dispersed hollow cylinders for axons plus spherical inclusions.

Load-bearing premise

The optic nerve can be adequately represented by orientationally dispersed hollow cylinders for axons plus spherical inclusions, and the imaging protocols isolate orientation-dependent mesoscopic shifts without significant confounding from diffusion or other effects.

What would settle it

A significant mismatch between measured frequency shifts and μQSM predictions in additional nerve orientations or after de-ironing, beyond measurement uncertainty, would falsify the claim.

read the original abstract

Larmor frequency shifts in white matter (WM) vary with fiber orientation due to anisotropic microstructure. Since clinical voxels are significantly larger than these microscopic frequency variations, the measured signal represents a bulk average of local shifts. Accurate estimation of magnetic susceptibility therefore requires accounting for these underlying frequency distributions that exist below the imaging resolution. We evaluated whether Microstructure-informed Quantitative Susceptibility Mapping ({\mu}QSM) can predict orientation-dependent sub-voxel frequency shifts from orientationally dispersed hollow cylinders and spherical inclusions. Diffusion-weighted and multi-gradient-echo images were acquired from ex vivo pig optic nerves at multiple orientations relative to the main magnetic field using a 3T Siemens Connectom scanner. We also analyzed de-ironed optic nerves to try and separate the effects of myelin and iron on susceptibility. The estimated sub-voxel frequency shifts closely matched {\mu}QSM predictions, consistent with mesoscopic field perturbations generated by uniformly magnetized axons. De-ironing had minimal effect on the frequency shifts, indicating negligible iron contribution. {\mu}QSM accurately reproduces the orientation dependence of Larmor frequency shifts in optic nerve WM, providing new insight into their microstructural origin and supporting improved estimation of tissue magnetic susceptibility in Quantitative Susceptibility Mapping.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This validates μQSM predictions on ex vivo optic nerve with a de-ironing control, but the multi-GRE data may mix in diffusion dephasing effects.

read the letter

The main point is that their μQSM model, built on dispersed hollow cylinders plus spheres, matches the measured orientation-dependent frequency shifts in these pig optic nerves, and de-ironing barely moved the numbers. That lines up with myelin as the main driver rather than iron. They did the work on a 3T Connectom scanner with multi-orientation and diffusion-weighted scans, which is a reasonable setup for testing the sub-voxel averaging idea in white matter. The de-ironing step is a useful addition because it gives an independent check on what is actually producing the susceptibility contrast. The match they report is consistent with the model assumptions and adds a concrete data point that prior papers on μQSM lacked for this tissue. The experimental control over orientation in ex vivo samples is a strength here, since it lets them isolate the angular dependence without the usual in vivo complications. On the downside, the multi-gradient-echo protocol at 3 T is vulnerable to diffusion dephasing from internal gradients, and the abstract gives no sign they corrected for echo-time dependence or used very short TEs to separate static shifts from dynamic effects. If the full methods do not show that the observed orientation pattern survives such controls, part of the agreement could be artifactual rather than a clean test of the mesoscopic field map. The lack of visible error bars or statistical detail in the summary also makes it hard to judge how close the match really is. This is targeted work for people already using or building microstructure-informed QSM models in neuroimaging. It will not rewrite the broader field but gives a practical check that readers in that niche can use to gauge the framework's reliability. The experimental design is sound enough on its own terms to warrant referee time, even if revisions are needed on the diffusion isolation question. I would send it for peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript reports multi-orientation 3T MRI experiments on ex vivo porcine optic nerves using diffusion-weighted and multi-gradient-echo sequences. It tests whether the μQSM model—representing axons as orientationally dispersed hollow cylinders with myelin susceptibility contrast plus spherical inclusions—predicts the measured sub-voxel Larmor frequency shifts. The authors report close agreement between estimates and model predictions, with de-ironing producing minimal change, and conclude that the shifts originate from mesoscopic perturbations by uniformly magnetized axons with negligible iron contribution.

Significance. If the quantitative match holds, the work supplies direct experimental grounding for microstructure-informed QSM in white matter by using independent multi-orientation measurements to test predictions from a physically motivated cylinder-plus-sphere model. The de-ironing control is a useful addition for separating myelin versus iron effects. This would support improved susceptibility estimation in anisotropic tissue and clarify the microstructural basis of orientation-dependent frequency shifts.

major comments (2)

[Results] Results section (comparison of measured vs. predicted shifts): the claim of 'close agreement' is presented without error bars on the estimated frequency shifts, without reported quantitative metrics (R², RMSE, or p-values), and without details on how the sub-voxel shifts were extracted from the multi-GRE data. This makes it impossible to judge the robustness of the central match.
[Methods] Methods (imaging protocol and data analysis): the multi-gradient-echo parameters and any correction for diffusion dephasing arising from susceptibility-induced internal gradients are not described in sufficient detail. Because the μQSM model assumes static mesoscopic field maps, the observed orientation dependence could partly reflect TE-dependent diffusion weighting rather than the static perturbations being tested.

minor comments (2)

[Abstract] Abstract: the term 'de-ironed' is used without a one-sentence description of the chemical procedure or reference to the methods.
[Figures] Figure legends: axis labels and units for the frequency-shift plots should be stated explicitly rather than relying on the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us identify areas where the manuscript can be clarified and strengthened. We address each major comment below and will revise the manuscript to incorporate the requested improvements.

read point-by-point responses

Referee: [Results] Results section (comparison of measured vs. predicted shifts): the claim of 'close agreement' is presented without error bars on the estimated frequency shifts, without reported quantitative metrics (R², RMSE, or p-values), and without details on how the sub-voxel shifts were extracted from the multi-GRE data. This makes it impossible to judge the robustness of the central match.

Authors: We agree that quantitative support for the 'close agreement' claim was insufficient in the original submission. In the revised manuscript we will add error bars to all reported frequency shift estimates, include R² and RMSE values (and, where appropriate, p-values) for the comparison between measured and μQSM-predicted shifts, and provide a complete description of the sub-voxel frequency extraction procedure, including the multi-echo fitting model, phase unwrapping steps, and any regularization applied to the multi-GRE data. revision: yes
Referee: [Methods] Methods (imaging protocol and data analysis): the multi-gradient-echo parameters and any correction for diffusion dephasing arising from susceptibility-induced internal gradients are not described in sufficient detail. Because the μQSM model assumes static mesoscopic field maps, the observed orientation dependence could partly reflect TE-dependent diffusion weighting rather than the static perturbations being tested.

Authors: We acknowledge that the multi-gradient-echo acquisition parameters were not reported at the level of detail required. The revised Methods section will list all relevant parameters (echo times, number of echoes, TR, flip angle, bandwidth, etc.). With respect to diffusion dephasing, the experiments used chemically fixed ex vivo tissue, which markedly lowers diffusivity relative to in vivo conditions, and employed short echo times. In the revision we will explicitly discuss this potential confound, provide the rationale for why TE-dependent diffusion weighting is expected to be negligible, and, if the raw data permit, include a supplementary simulation or analysis confirming that the observed orientation dependence is dominated by the static mesoscopic field perturbations assumed by the μQSM model. revision: partial

Circularity Check

0 steps flagged

No significant circularity: model predictions tested on independent multi-orientation data

full rationale

The paper's core chain generates μQSM predictions of sub-voxel Larmor shifts from a microstructural model (dispersed hollow cylinders plus spheres) and compares them directly to experimental frequency estimates extracted from multi-gradient-echo acquisitions at multiple orientations in ex vivo porcine optic nerves. This is an external validation step rather than a derivation that reduces to its own inputs. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations that close the loop are present in the reported workflow. The match to data provides independent grounding, and de-ironing experiments further separate contributions without circular reuse of the same measurements.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions about axon geometry and magnetization; no new entities are postulated. Free parameters such as cylinder radii, susceptibility values, and dispersion angles are likely present in the μQSM implementation but not quantified here.

free parameters (2)

axon radius and orientation dispersion
Geometric parameters in the hollow-cylinder model that determine the predicted frequency shift distribution.
susceptibility contrast of myelin
Value used to scale the magnetized cylinder contribution.

axioms (2)

domain assumption Axons behave as uniformly magnetized hollow cylinders
Invoked to generate the mesoscopic field perturbations in the μQSM forward model.
domain assumption Other susceptibility sources can be treated as spherical inclusions
Used to complete the sub-voxel frequency distribution calculation.

pith-pipeline@v0.9.0 · 5571 in / 1440 out tokens · 48092 ms · 2026-05-10T17:51:35.993223+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

µQSM model: fMeso = −2πγB0(χC−λSχS)½(T̂B̂−⅓) + bother inside tissue (Eq. 5); hollow cylinders + spheres; fODF from FBI
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Residual frequency shift δf matches µQSM predictions; de-ironing minimal effect; QSM bias ~20% vs µQSM ~1%

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

56 extracted references · 54 canonical work pages

[1]

sub- voxel

Magnetic susceptibility, 2) Larmor frequency, 3) Modelling, 4) QSM, 5) µQSM 2 Conflict of interest The authors declare no conflict of interest. 1 | Abstract Purpose Larmor frequency shifts in white matter (WM) vary with fiber orientation due to anisotropic microstructure. Since clinical voxels are significantly larger than these microscopic frequency vari...

work page doi:10.46540/3103-00144b 2010
[2]

MR susceptibility imaging

Duyn J. MR susceptibility imaging. J Magn Reson. 2013;229:198-207. doi:10.1016/j.jmr.2012.11.013

work page doi:10.1016/j.jmr.2012.11.013 2013
[3]

Biophysical mechanisms of MRI signal frequency contrast in multiple sclerosis

Yablonskiy DA, Luo J, Sukstanskii AL, Iyer A, Cross AH. Biophysical mechanisms of MRI signal frequency contrast in multiple sclerosis. Proc Natl Acad Sci U S A. 2012;109(35):14212-14217. doi:10.1073/pnas.1206037109

work page doi:10.1073/pnas.1206037109 2012
[4]

Clinical quantitative susceptibility mapping (QSM): Biometal imaging and its emerging roles in patient care

Wang Y, Spincemaille P, Liu Z, et al. Clinical quantitative susceptibility mapping (QSM): Biometal imaging and its emerging roles in patient care. J Magn Reson Imaging. 2017;46(4):951-971. doi:10.1002/jmri.25693

work page doi:10.1002/jmri.25693 2017
[5]

Biophysical mechanisms of phase contrast in gradient echo MRI

He X, Yablonskiy DA. Biophysical mechanisms of phase contrast in gradient echo MRI. Proc Natl Acad Sci U S A. 2009;106(32):13558-13563. doi:10.1073/pnas.0904899106

work page doi:10.1073/pnas.0904899106 2009
[6]

Generalized Lorentzian Tensor Approach (GLTA) as a biophysical background for quantitative susceptibility mapping

Yablonskiy DA, Sukstanskii AL. Generalized Lorentzian Tensor Approach (GLTA) as a biophysical background for quantitative susceptibility mapping. Magn Reson Med. 2015;73(2):757-764. doi:10.1002/mrm.25538

work page doi:10.1002/mrm.25538 2015
[7]

Observation of magnetic structural universality using transverse NMR relaxation

Ruh A, Emerich P, Scherer H, Novikov DS, Kiselev VG. Observation of magnetic structural universality using transverse NMR relaxation. J Magn Reson. 2018;353:107476. doi:10.48550/arxiv.1810.04847

work page doi:10.48550/arxiv.1810.04847 2018
[8]

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution

Sandgaard AD, Shemesh N, Kiselev VG, Jespersen SN. Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution. NMR Biomed. 2023;36(3):e4859. doi:10.1002/nbm.4859

work page doi:10.1002/nbm.4859 2023
[9]

Larmor frequency in heterogeneous media

Kiselev VG. Larmor frequency in heterogeneous media. J Magn Reson. 2019;299:168-175. doi:10.1016/j.jmr.2018.12.008

work page doi:10.1016/j.jmr.2018.12.008 2019
[10]

Quantitative Susceptibility Mapping: Concepts and Applications

Reichenbach JR, Schweser F, Serres B, Deistung A. Quantitative Susceptibility Mapping: Concepts and Applications. Clin Neuroradiol. 2015;25(2):225-230. doi:10.1007/s00062-015- 0432-9

work page doi:10.1007/s00062-015- 2015
[11]

The contribution of myelin to magnetic susceptibility- weighted contrasts in high-field MRI of the brain

Lee J, Shmueli K, Kang BT, et al. The contribution of myelin to magnetic susceptibility- weighted contrasts in high-field MRI of the brain. Neuroimage. 2012;59(4):3967-3975. doi:10.1016/j.neuroimage.2011.10.076

work page doi:10.1016/j.neuroimage.2011.10.076 2012
[12]

Layer-specific variation of iron content in 27 cerebral cortex as a source of MRI contrast

Fukunaga M, Li TQ, Van Gelderen P, et al. Layer-specific variation of iron content in 27 cerebral cortex as a source of MRI contrast. Proc Natl Acad Sci U S A. 2010;107(8):3834-

2010
[13]

doi:10.1073/pnas.0911177107

work page doi:10.1073/pnas.0911177107
[14]

Superficial white matter imaging: Contrast mechanisms and whole-brain in vivo mapping

Kirilina E, Helbling S, Morawski M, et al. Superficial white matter imaging: Contrast mechanisms and whole-brain in vivo mapping. Sci Adv. 2020;6(41). doi:10.1126/sciadv.aaz9281

work page doi:10.1126/sciadv.aaz9281 2020
[15]

On the contribution of deoxy-hemoglobin to MRI gray-white matter phase contrast at high field

Lee J, Hirano Y, Fukunaga M, Silva AC, Duyn JH. On the contribution of deoxy-hemoglobin to MRI gray-white matter phase contrast at high field. Neuroimage. 2010;49(1):193-198. doi:10.1016/j.neuroimage.2009.07.017

work page doi:10.1016/j.neuroimage.2009.07.017 2010
[16]

The clinical utility of QSM: disease diagnosis, medical management, and surgical planning

Eskreis-Winkler S, Zhang Y, Zhang J, et al. The clinical utility of QSM: disease diagnosis, medical management, and surgical planning. NMR Biomed. 2017;30(4). doi:10.1002/nbm.3668

work page doi:10.1002/nbm.3668 2017
[17]

Iron, Myelin, and the Brain: Neuroimaging Meets Neurobiology

Möller HE, Bossoni L, Connor JR, et al. Iron, Myelin, and the Brain: Neuroimaging Meets Neurobiology. Trends Neurosci. 2019;42(6):384-401. doi:10.1016/j.tins.2019.03.009

work page doi:10.1016/j.tins.2019.03.009 2019
[18]

Lorentz sphere versus generalized Lorentzian approach: What would lorentz say about it? Magn Reson Med

Yablonskiy DA, He X, Luo J, Sukstanskii AL. Lorentz sphere versus generalized Lorentzian approach: What would lorentz say about it? Magn Reson Med. 2014;72(1):4-7. doi:10.1002/mrm.25230

work page doi:10.1002/mrm.25230 2014
[19]

3D fiber tractography with susceptibility tensor imaging

Liu C, Li W, Wu B, Jiang Y, Johnson GA. 3D fiber tractography with susceptibility tensor imaging. Neuroimage. 2012;59(2):1290-1298. doi:10.1016/j.neuroimage.2011.07.096

work page doi:10.1016/j.neuroimage.2011.07.096 2012
[20]

Effects of white matter microstructure on phase and susceptibility maps

Wharton S, Bowtell R. Effects of white matter microstructure on phase and susceptibility maps. Magn Reson Med. 2015;73(3):1258-1269. doi:10.1002/mrm.25189

work page doi:10.1002/mrm.25189 2015
[21]

How far away from anisotropic microstructure do you need to be for QSM to be faithful? In: Proceedings of the 32nd Annual Meeting of ISMRM

Sandgaard AD, Jespersen S. How far away from anisotropic microstructure do you need to be for QSM to be faithful? In: Proceedings of the 32nd Annual Meeting of ISMRM. ; 2024:#2464. doi:10.58530/2024/2464

work page doi:10.58530/2024/2464 2024
[22]

Magnetic susceptibility induced white matter MR signal frequency shifts - Experimental comparison between Lorentzian sphere and generalized Lorentzian approaches

Luo J, He X, Yablonskiy DA. Magnetic susceptibility induced white matter MR signal frequency shifts - Experimental comparison between Lorentzian sphere and generalized Lorentzian approaches. Magn Reson Med. 2014;71(3):1251-1263. doi:10.1002/mrm.24762

work page doi:10.1002/mrm.24762 2014
[23]

Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex vivo 28 mouse brain

Sandgaard AD, Kiselev VG, Henriques RN, Shemesh N, Jespersen SN. Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex vivo 28 mouse brain. Magn Reson Med. 2024;91(2):699-715. doi:10.1002/mrm.29867

work page doi:10.1002/mrm.29867 2024
[24]

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources

Sandgaard AD, Shemesh N, Østergaard L, Kiselev VG, Jespersen SN. The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources. NMR Biomed. 2024;37(8):e5150. doi:10.1002/nbm.5150

work page doi:10.1002/nbm.5150 2024
[25]

Fiber ball imaging

Jensen JH, Russell Glenn G, Helpern JA. Fiber ball imaging. Neuroimage. 2016;124(Pt A):824-833. doi:10.1016/j.neuroimage.2015.09.049

work page doi:10.1016/j.neuroimage.2015.09.049 2016
[26]

Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution

Tournier JD, Calamante F, Gadian DG, Connelly A. Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. Neuroimage. 2004;23(3):1176-1185. doi:10.1016/j.neuroimage.2004.07.037

work page doi:10.1016/j.neuroimage.2004.07.037 2004
[27]

Modeling dendrite density from magnetic resonance diffusion measurements

Jespersen SN, Kroenke CD, Østergaard L, Ackerman JJH, Yablonskiy DA. Modeling dendrite density from magnetic resonance diffusion measurements. Neuroimage. 2007;34(4):1473-1486. doi:10.1016/j.neuroimage.2006.10.037

work page doi:10.1016/j.neuroimage.2006.10.037 2007
[28]

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

Novikov DS, Fieremans E, Jespersen SN, Kiselev VG. Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. NMR Biomed. 2019;32(4):e3998. doi:10.1002/nbm.3998

work page doi:10.1002/nbm.3998 2019
[29]

Predicting Mesoscopic Larmor Frequency Shifts in White Matter With Diffusion MRI—A Monte Carlo Study in Axonal Phantoms

Sandgaard AD, Jespersen SN. Predicting Mesoscopic Larmor Frequency Shifts in White Matter With Diffusion MRI—A Monte Carlo Study in Axonal Phantoms. NMR Biomed . 2025;38(3):e70004. doi:10.1002/nbm.70004

work page doi:10.1002/nbm.70004 2025
[30]

DeepACSON automated segmentation of white matter in 3D electron microscopy

Abdollahzadeh A, Belevich I, Jokitalo E, Sierra A, Tohka J. DeepACSON automated segmentation of white matter in 3D electron microscopy. Commun Biol. 2021;4(1):1-14. doi:10.1038/s42003-021-01699-w

work page doi:10.1038/s42003-021-01699-w 2021
[31]

Automated 3D Axonal Morphometry of White Matter

Abdollahzadeh A, Belevich I, Jokitalo E, Tohka J, Sierra A. Automated 3D Axonal Morphometry of White Matter. Sci Rep. 2019;9(1):1-16. doi:10.1038/s41598-019-42648-2

work page doi:10.1038/s41598-019-42648-2 2019
[32]

Cellular and subcellular localizations of nonheme ferric and ferrous iron in the rat brain: A light and electron microscopic study by the perfusion-Perls and -Turnbull methods

Meguro R, Asano Y, Odagiri S, Li C, Shoumura K. Cellular and subcellular localizations of nonheme ferric and ferrous iron in the rat brain: A light and electron microscopic study by the perfusion-Perls and -Turnbull methods. Arch Histol Cytol. 2008;71(4):205-222. doi:10.1679/aohc.71.205

work page doi:10.1679/aohc.71.205 2008
[33]

Med J Aust

The Principles of Humane Experimental Technique. Med J Aust. 1960;1(13):500-500. 29 doi:10.5694/j.1326-5377.1960.tb73127.x

work page doi:10.5694/j.1326-5377.1960.tb73127.x 1960
[34]

Aldehyde fixative solutions alter the water relaxation and diffusion properties of nervous tissue

Shepherd TM, Thelwall PE, Stanisz GJ, Blackband SJ. Aldehyde fixative solutions alter the water relaxation and diffusion properties of nervous tissue. Magn Reson Med. 2009;62(1):26-

2009
[35]

doi:10.1002/MRM.21977

work page doi:10.1002/mrm.21977
[36]

Considerations and recommendations from the ISMRM diffusion study group for preclinical diffusion MRI: Part 2—Ex vivo imaging: Added value and acquisition

Schilling KG, Grussu F, Ianus A, et al. Considerations and recommendations from the ISMRM diffusion study group for preclinical diffusion MRI: Part 2—Ex vivo imaging: Added value and acquisition. Magn Reson Med. 2025;93(6):2535-2560. doi:10.1002/MRM.30435

work page doi:10.1002/mrm.30435 2025
[37]

Effects of formalin fixation and temperature on MR relaxation times in the human brain

Birkl C, Langkammer C, Golob-Schwarzl N, et al. Effects of formalin fixation and temperature on MR relaxation times in the human brain. NMR Biomed. 2016;29(4):458-465. doi:10.1002/nbm.3477

work page doi:10.1002/nbm.3477 2016
[38]

Optic nerve-associated connective tissue structures revisited: A histological study using human fetuses and adult cadavers

Cho KH, Takahashi A, Yamamoto M, et al. Optic nerve-associated connective tissue structures revisited: A histological study using human fetuses and adult cadavers. Anat Rec. 2022;305(12):3516-3531. doi:10.1002/AR.24925

work page doi:10.1002/ar.24925 2022
[39]

Measuring the iron content of dopaminergic neurons in substantia nigra with MRI relaxometry

Brammerloh M, Morawski M, Friedrich I, et al. Measuring the iron content of dopaminergic neurons in substantia nigra with MRI relaxometry. Neuroimage. 2021;239:118255. doi:10.1016/j.neuroimage.2021.118255

work page doi:10.1016/j.neuroimage.2021.118255 2021
[40]

Radiation damping at clinical field strength: Characterization and compensation in quantitative measurements

Wallstein N, Müller R, Pampel A, Möller HE. Radiation damping at clinical field strength: Characterization and compensation in quantitative measurements. Magn Reson Med. 2024;91(3):1239-1253. doi:10.1002/mrm.29934

work page doi:10.1002/mrm.29934 2024
[41]

Denoising of diffusion MRI using random matrix theory

Veraart J, Novikov DS, Christiaens D, Ades-aron B, Sijbers J, Fieremans E. Denoising of diffusion MRI using random matrix theory. Neuroimage. 2016;142:394-406. doi:10.1016/j.neuroimage.2016.08.016

work page doi:10.1016/j.neuroimage.2016.08.016 2016
[42]

Gibbs-ringing artifact removal based on local subvoxel-shifts

Kellner E, Dhital B, Kiselev VG, Reisert M. Gibbs-ringing artifact removal based on local subvoxel-shifts. Magn Reson Med. 2016;76(5):1574-1581. doi:10.1002/mrm.26054

work page doi:10.1002/mrm.26054 2016
[43]

SEGUE: A Speedy rEgion-Growing Algorithm for Unwrapping Estimated Phase

Karsa A, Shmueli K. SEGUE: A Speedy rEgion-Growing Algorithm for Unwrapping Estimated Phase. IEEE Trans Med Imaging. 2019;38(6):1347-1357. doi:10.1109/TMI.2018.2884093 30

work page doi:10.1109/tmi.2018.2884093 2019
[44]

Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: An approach to in vivo brain iron metabolism? Neuroimage

Schweser F, Deistung A, Lehr BW, Reichenbach JR. Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: An approach to in vivo brain iron metabolism? Neuroimage. 2011;54(4):2789-2807. doi:10.1016/j.neuroimage.2010.10.070

work page doi:10.1016/j.neuroimage.2010.10.070 2011
[45]

A novel background field removal method for MRI using projection onto dipole fields (PDF)

Liu T, Khalidov I, de Rochefort L, et al. A novel background field removal method for MRI using projection onto dipole fields (PDF). NMR Biomed. 2011;24(9):1129-1136. doi:10.1002/nbm.1670

work page doi:10.1002/nbm.1670 2011
[46]

Increased sensitivity and signal-to-noise ratio in diffusion-weighted MRI using multi-echo acquisitions

Eichner C, Paquette M, Mildner T, et al. Increased sensitivity and signal-to-noise ratio in diffusion-weighted MRI using multi-echo acquisitions. Neuroimage. 2020;221:117172. doi:10.1016/j.neuroimage.2020.117172

work page doi:10.1016/j.neuroimage.2020.117172 2020
[47]

Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging

Jones DK, Horsfield MA, Simmons A. Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging. Magn Reson Med. 1999;42(3):515-525. doi:10.1002/(SICI)1522-2594(199909)42:3<515::AID-MRM14>3.0.CO;2-Q

work page doi:10.1002/(sici)1522-2594(199909)42:3 1999
[48]

Statistical Analysis of Spherical Data

Fisher NI, Lewis T, Embleton BJJ. Statistical Analysis of Spherical Data. Cambridge University Press; 1993. doi:10.2307/3556167

work page doi:10.2307/3556167 1993
[49]

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

Novikov DS, Veraart J, Jelescu IO, Fieremans E. Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI. Neuroimage. 2018;174:518-538. doi:10.1016/j.neuroimage.2018.03.006

work page doi:10.1016/j.neuroimage.2018.03.006 2018
[50]

Protein-induced water 1H MR frequency shifts: Contributions from magnetic susceptibility and exchange effects

Luo J, He X, d’Avignon DA, Ackerman JJH, Yablonskiy DA. Protein-induced water 1H MR frequency shifts: Contributions from magnetic susceptibility and exchange effects. J Magn Reson. 2010;202(1):102-108. doi:10.1016/j.jmr.2009.10.005

work page doi:10.1016/j.jmr.2009.10.005 2010
[51]

The effect of formalin fixation on the levels of brain transition metals in archived samples

Schrag M, Dickson A, Jiffry A, Kirsch D, Vinters H V., Kirsch W. The effect of formalin fixation on the levels of brain transition metals in archived samples. BioMetals. 2010;23(6):1123-1127. doi:10.1007/S10534-010-9359-4/TABLES/1

work page doi:10.1007/s10534-010-9359-4/tables/1 2010
[52]

Investigating time- and orientation-dependent transverse relaxation from magnetic susceptibility of white matter microstructure

Sandgaard AD, Henriques RN, Shemesh N, Jespersen SN. Investigating time- and orientation-dependent transverse relaxation from magnetic susceptibility of white matter microstructure. Published online September 30, 2025. Accessed October 15, 2025. http://arxiv.org/abs/2509.26267

work page arXiv 2025
[53]

An unconstrained four pool model analysis of proton relaxation and magnetization transfer in ex vivo white matter

Wallstein N, Pampel A, Müller R, Jäger C, Morawski M, Möller HE. An unconstrained four pool model analysis of proton relaxation and magnetization transfer in ex vivo white matter. 31 Sci Rep. 2025;15(1):1-19. doi:10.1038/s41598-025-87362-4

work page doi:10.1038/s41598-025-87362-4 2025
[54]

Histological and Histochemical Methods - Theory and Practice

Malatesta M, Kiernan JA. Histological and Histochemical Methods - Theory and Practice. Vol 60. 4th ed. Scion; 2016. doi:10.4081/ejh.2016.2639

work page doi:10.4081/ejh.2016.2639 2016
[55]

The behaviour of various glutaraldehydes on Sephadex G-10 and some implications for fixation

Hopwood D. The behaviour of various glutaraldehydes on Sephadex G-10 and some implications for fixation. Histochemie. 1967;11(4):289-295. doi:10.1007/BF00305805/METRICS

work page doi:10.1007/bf00305805/metrics 1967
[56]

Sodium pentobarbital dosages for exsanguination affect biochemical, molecular and histological measurements in rats

Mohamed AS, Hosney M, Bassiony H, et al. Sodium pentobarbital dosages for exsanguination affect biochemical, molecular and histological measurements in rats. Sci Reports 2020 101. 2020;10(1):378-. doi:10.1038/s41598-019-57252-7 Supplementary Materials Predicting Mesoscopic Larmor Frequency Shifts in Ex Vivo Porcine Optic Nerve Anders Dyhr Sandgaard1,2, An...

work page doi:10.1038/s41598-019-57252-7 2020