arxiv: 2605.01819 · v1 · submitted 2026-05-03 · 🧬 q-bio.QM

Recognition: unknown

Longitudinal QSM: Enhancing consistency of multiple time point susceptibility maps via simultaneous reconstruction

Eunseon Jeong, Hwihun Jeong, Jinhee Jang, Jiye Kim, Jongho Lee, Taechang Kim, Yangsean Choi

Pith reviewed 2026-05-09 15:49 UTC · model grok-4.3

classification 🧬 q-bio.QM

keywords quantitative susceptibility mappinglongitudinal QSMbrain ironmultiple sclerosisstroke imagingtemporal sparsity regularizationreconstruction consistency

0 comments

The pith

Longitudinal QSM jointly reconstructs brain susceptibility maps across time points to cut inter-scan variability.

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

The paper introduces Longitudinal QSM, a method that reconstructs quantitative susceptibility maps from several scans at once instead of separately. It adds a penalty that forces most temporal changes to be zero except in small regions, addressing issues like head movement and noise that make repeated scans inconsistent. Simulations showed the approach lowered differences between scans and still found the added artificial lesions. Tests on actual data from stroke and multiple sclerosis patients confirmed that normal brain areas became more stable while changes inside lesions stayed visible. This consistency matters for studies that follow iron or myelin shifts over time in aging and neurodegeneration.

Core claim

Longitudinal QSM performs simultaneous reconstruction of susceptibility maps at multiple time points by enforcing spatial sparsity of temporal changes through regularization, which reduces inter-scan variability compared to conventional independent reconstructions while accurately recovering simulated focal changes and preserving lesion-related temporal alterations in patient data.

What carries the argument

The joint estimation framework that minimizes a combined data fidelity term across time points plus a regularization term promoting spatial sparsity in the temporal difference maps.

If this is right

Inter-scan variability in susceptibility measurements is reduced in repeated scans of the same subject.
Simulated focal changes in susceptibility are recovered accurately without excessive smoothing.
Non-lesion brain regions show stabilized susceptibility values over time in stroke and MS patients.
Lesion-related temporal changes remain detectable and are not suppressed by the regularization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the sparsity assumption holds for a given disease, the method could enable earlier detection of subtle progression in neurodegenerative conditions.
Similar joint reconstruction might benefit other longitudinal quantitative MRI modalities facing registration and noise issues.
Diffuse changes across large brain areas could be underestimated if the spatial sparsity prior is too strong.

Load-bearing premise

Temporal changes in brain susceptibility occur only in spatially sparse locations rather than being widespread or diffuse.

What would settle it

Observing that the joint method fails to detect known diffuse susceptibility changes in a controlled longitudinal experiment or shows no reduction in variability for healthy subjects with no true changes.

read the original abstract

Quantitative susceptibility mapping (QSM) has been increasingly applied in longitudinal studies of neurodegenerative diseases and aging to assess temporal alterations in brain iron and myelin. The accuracy of such investigations depends on the repeatability and sensitivity of measurements. However, the ill-posed nature of the QSM processing steps makes the reconstruction vulnerable to background field changes, head orientation changes, noise, and imperfect registration, which compromise repeatability and sensitivity and hinder reliable detection of true changes. To address these limitations, we propose Longitudinal QSM, a simultaneous reconstruction framework that jointly estimates susceptibility maps across time points while enforcing spatial sparsity of temporal changes. The method was evaluated through simulations and in-vivo experiments and compared with conventional reconstruction methods. Longitudinal QSM consistently reduced inter-scan variability and accurately recovered simulated lesion changes. Application to stroke patient and multiple sclerosis patient data further demonstrated that the framework stabilizes non-lesion variability while preserving lesion-related temporal changes. This approach offers a promising tool for monitoring subtle temporal changes in brain iron and myelin in various neurodegenerative diseases as well as throughout aging and development.

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

Joint reconstruction with sparsity on temporal differences lowers QSM variability in focal cases but the tests leave open whether it damps real diffuse changes.

read the letter

The paper's main move is to reconstruct susceptibility maps from all time points together and add a term that penalizes non-sparse spatial patterns in the differences between them. This is a clear departure from the usual independent per-scan QSM pipeline. In the simulations it recovers the added focal lesions while cutting background variability, and the stroke and MS patient examples show the same pattern: stabilized non-lesion regions with lesion signals left intact. That is useful where the biology really is focal and the main problem is reconstruction noise from orientation, registration, and field changes. The joint formulation is internally consistent and directly targets the repeatability issue the abstract describes. The evaluations line up with the model assumptions on the data they used. The soft spot is the sparsity prior itself. All reported tests use focal lesions or focal pathology, so the method has not been checked against gradual, widespread susceptibility shifts such as those expected in normal aging or some neurodegenerative processes. If those diffuse signals exist, the regularization will attenuate them, and the claim that genuine temporal changes are preserved would not hold for the broader applications mentioned. The regularization weight is also a free parameter whose selection and sensitivity are not fully detailed in the available description. This work is for groups already running longitudinal QSM on patients with localized brain changes and looking for a practical way to reduce scan-to-scan scatter. Readers focused on MRI method development will see the value in the framework. The thinking is coherent and the results are reproducible on the tested cases, so the paper deserves a serious referee who can request expanded simulations on diffuse change and clearer reporting on parameter choice.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes Longitudinal QSM, a simultaneous reconstruction framework for quantitative susceptibility maps across multiple time points. It jointly estimates susceptibility while enforcing spatial sparsity of temporal differences via regularization, aiming to reduce inter-scan variability from noise, registration errors, background fields, and orientation changes. The method is evaluated in simulations with focal lesions and in-vivo data from stroke and multiple sclerosis patients, claiming reduced variability, accurate recovery of simulated lesion changes, and stabilization of non-lesion regions while preserving lesion-related temporal alterations. This is positioned as improving repeatability and sensitivity for longitudinal studies of brain iron and myelin in neurodegenerative diseases and aging.

Significance. If the central claims hold under broader validation, the approach could meaningfully advance longitudinal QSM by providing a practical way to improve consistency without separate post-processing corrections. The joint optimization with an explicit temporal sparsity prior is a clear technical contribution over independent per-time-point reconstructions. However, the significance is tempered by the narrow scope of the reported evaluations, which focus on focal pathology; broader impact on diffuse changes in aging or other diseases would require additional evidence that the regularization does not suppress genuine signals.

major comments (1)

[Abstract and in-vivo experiments] The core claim that the framework 'stabilizes non-lesion variability while preserving lesion-related temporal changes' (Abstract) rests on the modeling choice of spatial sparsity regularization for temporal differences. This assumption is load-bearing for the stated applicability to 'various neurodegenerative diseases as well as throughout aging and development,' yet all reported evaluations (simulations and in-vivo stroke/MS data) use only focal lesions. No tests inject or measure diffuse, widespread susceptibility shifts (e.g., global iron accumulation), leaving open the risk that the sparsity penalty attenuates biologically relevant non-focal signals.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The major comment highlights an important limitation in the scope of our evaluations, which we address point-by-point below. We agree that additional analysis is warranted to support broader claims.

read point-by-point responses

Referee: [Abstract and in-vivo experiments] The core claim that the framework 'stabilizes non-lesion variability while preserving lesion-related temporal changes' (Abstract) rests on the modeling choice of spatial sparsity regularization for temporal differences. This assumption is load-bearing for the stated applicability to 'various neurodegenerative diseases as well as throughout aging and development,' yet all reported evaluations (simulations and in-vivo stroke/MS data) use only focal lesions. No tests inject or measure diffuse, widespread susceptibility shifts (e.g., global iron accumulation), leaving open the risk that the sparsity penalty attenuates biologically relevant non-focal signals.

Authors: We agree that the spatial sparsity assumption on temporal differences is central to the method and that our current evaluations are restricted to focal lesions, consistent with the stroke and MS patient data. This choice reflects the typical presentation of focal pathology in the datasets used. For diffuse changes (e.g., gradual global iron accumulation), the temporal difference map would lack spatial sparsity, and strong regularization could indeed suppress genuine signals. The regularization parameter can be tuned to mitigate this, but the risk remains. To strengthen the manuscript, we will add a new simulation experiment injecting diffuse susceptibility shifts across brain regions and report the resulting bias and variability. We will also revise the abstract and discussion to explicitly qualify the applicability to focal versus diffuse changes and note this as a limitation for future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; joint reconstruction is an explicit modeling choice

full rationale

The paper proposes a simultaneous multi-timepoint QSM reconstruction that adds an explicit regularization term enforcing spatial sparsity on temporal susceptibility differences. This is presented as a design choice to improve consistency, not as a derived result that reduces to the input data or to a self-citation by construction. No equations are shown that fit parameters on a subset and then relabel the output as an independent prediction, nor is a uniqueness theorem imported from prior self-work to force the formulation. The evaluations (simulations with focal lesions plus stroke/MS patient data) are separate from the method definition and do not create a closed loop where the reported reduction in inter-scan variability is mathematically guaranteed by the same quantities used to define the regularizer. The central claim therefore remains non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on a domain assumption about the spatial sparsity of temporal susceptibility changes and an implicit regularization parameter whose value is not specified in the abstract.

free parameters (1)

temporal sparsity regularization weight
The strength of the sparsity penalty on temporal differences is a tunable hyperparameter required for the joint optimization but not quantified in the abstract.

axioms (1)

domain assumption Temporal changes in brain susceptibility are spatially sparse
This modeling premise underpins the joint reconstruction and is invoked to stabilize the ill-posed inverse problem across time points.

pith-pipeline@v0.9.0 · 5503 in / 1329 out tokens · 40429 ms · 2026-05-09T15:49:12.591622+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

[1]

Multiple sclerosis,

A. Compston and A. Coles, “Multiple sclerosis,” The Lancet, vol. 372, no. 9648, pp. 1502–1517, 2008, doi: 10.1016/s0140-6736(08)61620-7

work page doi:10.1016/s0140-6736(08)61620-7 2008
[2]

Iron, brain ageing and neurodegenerative disorders,

L. Zecca, M. B. H. Youdim, P. Riederer, J. R. Connor, and R. R. Crichton, “Iron, brain ageing and neurodegenerative disorders,” Nature Reviews Neuroscience, vol. 5, no. 11, pp. 863–873, 2004, doi: 10.1038/nrn1537

work page doi:10.1038/nrn1537 2004
[3]

Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field,

L. D. Rochefort, R. Brown, M. R. Prince, and Y. Wang, “Quantitative MR susceptibility mapping using piece-wise constant regularized inversion of the magnetic field,” Magnetic Resonance in Medicine, vol. 60, no. 4, pp. 1003–1009, 2008, doi: 10.1002/mrm.21710

work page doi:10.1002/mrm.21710 2008
[4]

Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data,

K. Shmueli, J. A. D. Zwart, P. V. Gelderen, T. Q. Li, S. J. Dodd, and J. H. Duyn, “Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data,” Magnetic Resonance in Medicine, vol. 62, no. 6, pp. 1510–1522, 2009, doi: 10.1002/mrm.22135

work page doi:10.1002/mrm.22135 2009
[5]

Quantitative Susceptibility Mapping in Multiple Sclerosis,

C. Langkammer et al., “Quantitative Susceptibility Mapping in Multiple Sclerosis,” Radiology, vol. 267, no. 2, pp. 551–559, 2013, doi: 10.1148/radiol.12120707

work page doi:10.1148/radiol.12120707 2013
[6]

High resolution magnetic susceptibility mapping of the substantia nigra in Parkinson’s disease,

A. K. Lotfipour et al., “High resolution magnetic susceptibility mapping of the substantia nigra in Parkinson’s disease,” J. Magn. Reson. Imaging, vol. 35, no. 1, pp. 48–55, 2012, doi: 10.1002/jmri.22752

work page doi:10.1002/jmri.22752 2012
[7]

χ-Separation Imaging for Diagnosis of Multiple Sclerosis versus Neuromyelitis Optica Spectrum Disorder.,

W. Kim et al., “χ-Separation Imaging for Diagnosis of Multiple Sclerosis versus Neuromyelitis Optica Spectrum Disorder.,” Radiology, vol. 307, no. 1, p. e220941, 2022, doi: 10.1148/radiol.220941

work page doi:10.1148/radiol.220941 2022
[8]

Comparison between R2′‐based and R2*‐based χ‐separation methods: A clinical evaluation in individuals with multiple sclerosis,

S. Ji et al., “Comparison between R2′‐based and R2*‐based χ‐separation methods: A clinical evaluation in individuals with multiple sclerosis,” NMR Biomed., p. e5167, 2024, doi: 10.1002/nbm.5167

work page doi:10.1002/nbm.5167 2024
[9]

Exploring the links among brain iron accumulation, cognitive performance, and dietary intake in older adults: A longitudinal MRI study,

V. Zachariou, C. Pappas, C. E. Bauer, E. R. Seago, and B. T. Gold, “Exploring the links among brain iron accumulation, cognitive performance, and dietary intake in older adults: A longitudinal MRI study,” Neurobiol. Aging, vol. 145, pp. 1–12, 2025, doi: 10.1016/j.neurobiolaging.2024.10.006

work page doi:10.1016/j.neurobiolaging.2024.10.006 2025
[10]

Longitudinal Associations of Magnetic Susceptibility with Clinical Severity in Parkinson’s Disease,

G. E. C. Thomas, N. Hannaway, A. Zarkali, K. Shmueli, and R. S. Weil, “Longitudinal Associations of Magnetic Susceptibility with Clinical Severity in Parkinson’s Disease,” Mov. Disord., vol. 39, no. 3, pp. 546–559, 2024, doi: 10.1002/mds.29702

work page doi:10.1002/mds.29702 2024
[11]

Longitudinal change in magnetic susceptibility of new enhanced multiple sclerosis (MS) lesions measured on serial quantitative susceptibility mapping (QSM),

Y. Zhang et al., “Longitudinal change in magnetic susceptibility of new enhanced multiple sclerosis (MS) lesions measured on serial quantitative susceptibility mapping (QSM),” J. Magn. Reson. Imaging, vol. 44, no. 2, pp. 426–432, 2016, doi: 10.1002/jmri.25144

work page doi:10.1002/jmri.25144 2016
[12]

Evolution of Brain Iron Levels in Multiple Sclerosis: A 2-Year Longitudinal Quantitative Susceptibility Mapping Study at 3T (P4.163),

J. Hagemeier et al., “Evolution of Brain Iron Levels in Multiple Sclerosis: A 2-Year Longitudinal Quantitative Susceptibility Mapping Study at 3T (P4.163),” Neurology, vol. 86, no. 16_supplement, 2016, doi: 10.1212/wnl.86.16_supplement.p4.163

work page doi:10.1212/wnl.86.16_supplement.p4.163 2016
[13]

Association of iron deposition in MS lesion with remyelination capacity using susceptibility source separation MRI,

H.-G. Shin et al., “Association of iron deposition in MS lesion with remyelination capacity using susceptibility source separation MRI,” NeuroImage : Clin., vol. 45, p. 103748, 2025, doi: 10.1016/j.nicl.2025.103748

work page doi:10.1016/j.nicl.2025.103748 2025
[14]

Quantifying Remyelination Using χ-Separation in White Matter and Cortical Multiple Sclerosis Lesions,

J. Müller et al., “Quantifying Remyelination Using χ-Separation in White Matter and Cortical Multiple Sclerosis Lesions,” Neurology, vol. 103, no. 6, p. e209604, 2024, doi: 10.1212/wnl.0000000000209604

work page doi:10.1212/wnl.0000000000209604 2024
[15]

Reproducibility of quantitative susceptibility mapping in the brain at two field strengths from two vendors,

K. Deh et al., “Reproducibility of quantitative susceptibility mapping in the brain at two field strengths from two vendors,” J. Magn. Reson. Imaging, vol. 42, no. 6, pp. 1592–1600, 2015, doi: 10.1002/jmri.24943

work page doi:10.1002/jmri.24943 2015
[16]

Multi-centre and multi-vendor reproducibility of a standardized protocol for quantitative susceptibility Mapping of the human brain at 3T,

M. Lancione et al., “Multi-centre and multi-vendor reproducibility of a standardized protocol for quantitative susceptibility Mapping of the human brain at 3T,” Physica Medica, vol. 103, pp. 37–45, 2022, doi: 10.1016/j.ejmp.2022.09.012

work page doi:10.1016/j.ejmp.2022.09.012 2022
[17]

Multi-centre, multi-vendor reproducibility of 7T QSM and R2* in the human brain: Results from the UK7T study,

C. Rua et al., “Multi-centre, multi-vendor reproducibility of 7T QSM and R2* in the human brain: Results from the UK7T study,” Neuroimage, vol. 223, p. 117358, 2020, doi: 10.1016/j.neuroimage.2020.117358

work page doi:10.1016/j.neuroimage.2020.117358 2020
[18]

Investigating the effect of oblique image acquisition on the accuracy of QSM and a robust tilt correction method,

O. C. Kiersnowski, A. Karsa, S. J. Wastling, J. S. Thornton, and K. Shmueli, “Investigating the effect of oblique image acquisition on the accuracy of QSM and a robust tilt correction method,” Magn. Reson. Med., vol. 89, no. 5, pp. 1791–1808, 2023, doi: 10.1002/mrm.29550

work page doi:10.1002/mrm.29550 2023
[19]

MEDI+0: Morphology enabled dipole inversion with automatic uniform cerebrospinal fluid zero reference for quantitative susceptibility mapping,

Z. Liu, P. Spincemaille, Y. Yao, Y. Zhang, and Y. Wang, “MEDI+0: Morphology enabled dipole inversion with automatic uniform cerebrospinal fluid zero reference for quantitative susceptibility mapping,” Magnetic Resonance in Medicine, vol. 79, no. 5, pp. 2795–2803, 2018, doi: 10.1002/mrm.26946

work page doi:10.1002/mrm.26946 2018
[20]

Vessel segmentation for χ$$ \chi $$‐separation in quantitative susceptibility mapping,

T. Kim et al., “Vessel segmentation for χ$$ \chi $$‐separation in quantitative susceptibility mapping,” Magn. Reson. Med., 2025, doi: 10.1002/mrm.70054

work page doi:10.1002/mrm.70054 2025
[21]

Morphology enabled dipole inversion (MEDI) from a single‐angle acquisition: Comparison with COSMOS in human brain imaging,

T. Liu et al., “Morphology enabled dipole inversion (MEDI) from a single‐angle acquisition: Comparison with COSMOS in human brain imaging,” Magn. Reson. Med., vol. 66, no. 3, pp. 777–783, 2011, doi: 10.1002/mrm.22816

work page doi:10.1002/mrm.22816 2011
[22]

Iteratively reweighted least squares minimization for sparse recovery,

I. Daubechies, R. DeVore, M. Fornasier, and C. S. Güntürk, “Iteratively reweighted least squares minimization for sparse recovery,” Commun. Pure Appl. Math., vol. 63, no. 1, pp. 1–38, 2010, doi: 10.1002/cpa.20303

work page doi:10.1002/cpa.20303 2010
[23]

T. Liu, P. Spincemaille, L. de Rochefort, B. Kressler, and Y. Wang, “Calculation of susceptibility through multiple orientation sampling (COSMOS): A method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI,” Magn. Reson. Med., vol. 61, no. 1, pp. 196–204, 2009, doi: 10.1002/mrm.21828

work page doi:10.1002/mrm.21828 2009
[24]

χ‐sepnet: Deep Neural Network for Magnetic Susceptibility Source Separation,

M. Kim et al., “χ‐sepnet: Deep Neural Network for Magnetic Susceptibility Source Separation,” Hum. Brain Mapp., vol. 46, no. 2, p. e70136, 2025, doi: 10.1002/hbm.70136

work page doi:10.1002/hbm.70136 2025
[25]

and Behrens, Timothy E.J

M. Jenkinson, C. F. Beckmann, T. E. J. Behrens, M. W. Woolrich, and S. M. Smith, “FSL,” NeuroImage, vol. 62, no. 2, pp. 782–790, 2012, doi: 10.1016/j.neuroimage.2011.09.015

work page doi:10.1016/j.neuroimage.2011.09.015 2012
[26]

Dymerska, K

B. Dymerska et al., “Phase unwrapping with a rapid opensource minimum spanning tree algorithm (ROMEO),” Magn. Reson. Med., vol. 85, no. 4, pp. 2294–2308, 2021, doi: 10.1002/mrm.28563

work page doi:10.1002/mrm.28563 2021
[27]

Fast and tissue-optimized mapping of magnetic susceptibility and T2* with multi-echo and multi-shot spirals,

Wu, W. Li, A. V. Avram, S.-M. Gho, and C. Liu, “Fast and tissue-optimized mapping of magnetic susceptibility and T2* with multi-echo and multi-shot spirals,” NeuroImage, vol. 59, no. 1, pp. 297–305, 2012, doi: 10.1016/j.neuroimage.2011.07.019

work page doi:10.1016/j.neuroimage.2011.07.019 2012
[28]

A method for estimating and removing streaking artifacts in quantitative susceptibility mapping,

W. Li et al., “A method for estimating and removing streaking artifacts in quantitative susceptibility mapping,” NeuroImage, vol. 108, pp. 111–122, 2015, doi: 10.1016/j.neuroimage.2014.12.043

work page doi:10.1016/j.neuroimage.2014.12.043 2015
[29]

A human brain atlas of χ‐separation for normative iron and myelin distributions,

K. Min et al., “A human brain atlas of χ‐separation for normative iron and myelin distributions,” NMR Biomed., p. e5226, 2024, doi: 10.1002/nbm.5226

work page doi:10.1002/nbm.5226 2024
[30]

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

F. Schweser, A. Deistung, B. W. Lehr, and J. R. Reichenbach, “Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: An approach to in vivo brain iron metabolism?,” NeuroImage, vol. 54, no. 4, pp. 2789–2807, 2011, doi: 10.1016/j.neuroimage.2010.10.070

work page doi:10.1016/j.neuroimage.2010.10.070 2011
[31]

Whole brain susceptibility mapping using compressed sensing,

Wu, W. Li, A. Guidon, and C. Liu, “Whole brain susceptibility mapping using compressed sensing,” Magnetic Resonance in Medicine, vol. 67, no. 1, pp. 137–147, 2012, doi: 10.1002/mrm.23000

work page doi:10.1002/mrm.23000 2012
[32]

Quantitative susceptibility mapping using deep neural network: QSMnet,

J. Yoon et al., “Quantitative susceptibility mapping using deep neural network: QSMnet,” NeuroImage, vol. 179, pp. 199–206, 2018, doi: 10.1016/j.neuroimage.2018.06.030

work page doi:10.1016/j.neuroimage.2018.06.030 2018
[33]

Sensitivity of MRI resonance frequency to the orientation of brain tissue microstructure,

J. Lee et al., “Sensitivity of MRI resonance frequency to the orientation of brain tissue microstructure,” Proceedings of the National Academy of Sciences of the United States of America, vol. 107, no. 11, pp. 5130–5135, 2010, doi: 10.1073/pnas.0910222107

work page doi:10.1073/pnas.0910222107 2010
[34]

An R2* model of white matter for fiber orientation and myelin concentration,

J. Lee, H.-G. Shin, W. Jung, Y. Nam, S.-H. Oh, and J. Lee, “An R2* model of white matter for fiber orientation and myelin concentration,” NeuroImage, vol. 162, pp. 269–275, 2017, doi: 10.1016/j.neuroimage.2017.08.050

work page doi:10.1016/j.neuroimage.2017.08.050 2017