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Retrospective macromolecular pool fraction mapping from conventional clinical MRI: a physics-guided self-supervised deep learning framework

Jelmer van Lune, Miha Fuderer, Oscar van der Heide, Matteo Maspero, Martin B. Schilder, Jan Willem Dankbaar, Stefano Mandija, Alessandro Sbrizzi

arXiv:2610.37213v1physics.med-phcs.CVcs.LG

TL;DR

MPF mapping relies on dedicated prospective qMT acquisitions, limiting its availability in large collections of conventional clinical scans. A physics-guided self-supervised framework estimates MPF from routine T1w, T2w, and FLAIR by embedding an analytical MT signal model and conditioning network features on acquisition parameters. Across the clinical test set, estimated MPF was consistently higher in WM (0.182 ± 0.007) than in GM (0.144 ± 0.009).

  • Problem

    MPF mapping relies on dedicated prospective qMT acquisitions, limiting its availability in large collections of conventional clinical scans.

    Source: §1 · p. 2

  • Method

    A physics-guided self-supervised framework estimates MPF from routine T1w, T2w, and FLAIR by embedding an analytical MT signal model and conditioning network features on acquisition parameters.

    Source: §1 · p. 2, §3.2 · p. 7, §3.2.1 · p. 7

  • Results

    Across the clinical test set, estimated MPF was consistently higher in WM (0.182 ± 0.007) than in GM (0.144 ± 0.009).

    Source: §5 · p. 13

  • Takeaways & Limitations

    The framework may support large-scale biomarker research using existing clinical archives and prospective MPF mapping from conventional MRI without dedicated qMT acquisition or additional scan time.

    Source: §6 · p. 17

    Absolute MPF accuracy is difficult to establish because no universally accepted qMT reference standard exists, and qMT methods can yield systematic differences.

    Source: §5.1 · p. 16

Abstract

from arXiv · show

Macromolecular pool fraction (MPF) is a quantitative imaging biomarker sensitive to myelin integrity and other changes in tissue macromolecular content, but specialized acquisitions and reconstruction methods limit its use in large-scale studies. We present a physics-guided, self-supervised deep learning framework for retrospectively estimating MPF directly from conventional clinical brain MRI ($T_1$-weighted, $T_2$-weighted, and fluid-attenuated inversion recovery [FLAIR]) without paired quantitative reference scans. The framework embeds an analytical two-pool magnetization transfer signal model that related sequence-averaged radiofrequency transmit power to apparent longitudinal relaxation. To accommodate heterogeneous clinical protocols, the network conditions intermediate features on acquisition parameters via adaptive instance normalization. It was trained and evaluated on a multisite, multivendor, multiprotocol dataset of 7,705 MRI sessions (3 T). Across 1,237 test sessions, mean MPF was $0.182 \pm 0.007$ in white matter and $0.144 \pm 0.009$ in gray matter, with limited variation across vendor-by-protocol groups (between-group coefficient of variation: 2.65% and 5.63%, respectively). In 70 sessions with demyelinating-disease labels, MPF was 35.6% lower in segmented lesions than in normal-appearing white matter. MPF maps from two different clinical protocols acquired in a healthy volunteer showed a mean voxel-wise absolute percentage difference of 7.7% and a concordance correlation coefficient of $0.888$, indicating good cross-protocol consistency. These results suggest that magnetization transfer-informed self-supervised learning enables stable MPF mapping from conventional clinical MRI, providing a scalable approach to investigate demyelinating pathology in both existing imaging archives and prospectively acquired conventional clinical scans without dedicated qMT acquisitions.

1 Introduction

MPF is a quantitative marker of macromolecular content with particular relevance to myelin integrity and demyelinating pathology. Dedicated qMT acquisitions limit its availability in clinical archives, motivating retrospective estimation from routine MRI.

1 Introduction

  • MPF is sensitive to myelin content, reduced in MS lesions, and associated in post-mortem studies with histopathological evidence of demyelination.It has been used to investigate spatial heterogeneity in demyelination and lesion evolution over time.Source: §1 · p. 2
  • Dedicated qMT methods require additional acquisition time, are prospective-only, and cannot recover MPF from existing conventional clinical scans.These limits restrict access to MPF maps and impede large-scale biomarker studies and clinical translation.Source: §1 · p. 2
  • Routine contrast ratios and empirical fits offer accessible proxies for myelin-related measures but yield relative intensity-based indices rather than quantitative physical parameters.These approaches include T1w/T2w and T1w/FLAIR ratios.Source: §1 · p. 2
  • Existing physics-guided self-supervised frameworks estimate relaxometry and PD from routine T1w, T2w, and FLAIR without paired references, but not quantitative MT parameters such as MPF.This work introduces MT-informed MPF estimation from those routine contrasts without paired qMT reference data, using a model relating apparent longitudinal relaxation to MPF and protocol-dependent average RF power.Source: §1 · p. 2

2 Theory

The theory models magnetization transfer with free-water and semisolid pools, then approximates sequence RF saturation to connect protocol-specific power with apparent longitudinal relaxation. That relaxation is incorporated into a closed-form signal model for conventional acquisitions.

2.1 Two-pool magnetization transfer model

  • MPF is the semisolid pool’s fraction of total equilibrium magnetization, while free and semisolid pools exchange longitudinal magnetization through rate constants expressed using a single exchange rate and MPF.The semisolid pool is not directly observable with conventional MRI because its transverse relaxation time is on the order of microseconds.Source: §2.1 · pp. 2–3

2.2 Sequence-averaged RF saturation approximation

  • The semisolid saturation rate is modeled from sequence-averaged RF power and an absorption lineshape, treating the clinical pulse train as continuous irradiation when its combined pulse rate is high relative to relaxation, exchange, and saturation rates.The model assumes a Gaussian lineshape and near-resonance irradiation, approximating the lineshape by its peak value.Source: §2.2 · p. 3

2.3 MT-informed forward signal modeling

  • The continuous-wave-equivalent two-pool reduction yields an apparent longitudinal relaxation rate coupled to sequence-specific RF power and MPF, which is inserted into Bloch-based signal models.Expected signal depends on tissue parameters PD, free-pool T1 and T2, and MPF, plus TR, TE, TI, flip angle, and sequence-averaged B1,rms.Source: §2.3 · p. 3
  • The model computes apparent relaxation for each sequence using its B1,rms while fixing semisolid relaxation and exchange parameters; for gradient-echo acquisitions, free-pool T2 approximates T2*.Although the reduction also yields sequence-dependent apparent equilibrium magnetization, the signal model represents its role with a single sequence-independent relative PD map, so MT effects enter only through apparent relaxation.Source: §2.3 · p. 4

3 Methods

The methods extend self-supervised physics-guided mapping to estimate MPF alongside other tissue maps from routine clinical MRI, using acquisition-conditioned features and a magnetization-transfer signal model. The study uses a multisite clinical dataset and evaluates tissue values, demyelinating lesions, cross-protocol reproducibility, and the contribution of acquisition conditioning.

3.2 Model

  • The framework estimates voxel-wise free-pool T1 and T2, proton density, and MPF from routine T1w, T2w, and FLAIR scans without quantitative reference maps.The dataset combined 7,705 3 T sessions from UMCU and MR-RATE; subject-level partitioning yielded 6,084 training, 384 validation, and 1,237 test sessions.Source: §3.1.1 · pp. 4–5, §3.2 · p. 7

3.2.1 Network architecture

  • Acquisition-conditioned AdaIN modulates encoder features using contrast type and sequence timing, while attention-based fusion combines the three contrasts in a shared-weight 2D U-Net.The output layer generates four maps, with sigmoid-constrained outputs scaled to specified physical ranges.Source: §3.2.1 · p. 7

3.2.2 Self-supervised physics-guided objective

  • The self-supervised objective enforces consistency between acquired scans and synthetic contrasts generated from predicted tissue maps and acquisition parameters.The forward model uses fixed semisolid-pool and exchange parameters from qMT literature and includes effective-TE corrections for TSE acquisitions.Source: §3.2.2 · pp. 7–8
  • A white-matter T1 prior and soft proton-density lower bound constrain an ill-posed estimation problem in which T1 and MPF can produce identical contrast at fixed B1,rms.Synthesized images are globally rescaled to normalized inputs, with the scale constrained using representative white-matter parameters.Source: §3.2.2 · p. 8

3.2.3 Training procedure and implementation details

  • Training used 6,084 sessions for 20 epochs, with model selection based on validation loss and physiologically expected white- and gray-matter ranges.The final model used a learning rate of 1 × 10^-5, batch size 16 slices, and approximately 12 hours of training on one GPU.Source: §3.1.1 · p. 5, §3.2.3 · p. 8

3.3.1 Macromolecular pool fraction in white matter and gray matter

  • Protocol robustness was assessed across 1,237 test sessions by comparing tissue-specific mean MPF across three vendor-by-protocol groups defined by T1w sequence.The groups were Philips Spoiled GRE, Philips MPRAGE, and Siemens MPRAGE; robustness was quantified with the between-group coefficient of variation.Source: §3.3.1 · p. 9

3.3.2 Demyelinating pathology

  • Demyelinating pathology analyses compared lesion MPF with NAWM and NAGM in labeled test sessions and assessed joint lesion-level variation in MPF and free-pool longitudinal relaxation rate.Lesion components with fewer than 10 voxels were excluded; 70 MR-RATE sessions had report-derived labels, alongside four UMCU sessions with confirmed MS.Source: §3.1.1 · p. 5, §3.3.2 · p. 9

3.3.3 Prospective volunteer reproducibility

  • Cross-protocol reproducibility was assessed in one healthy volunteer scanned consecutively with two clinical protocols differing primarily in T1w sequence.An AdaIN ablation replaced its layers with standard instance normalization and compared reconstruction error, vendor-by-protocol tissue MPF variation, and volunteer cross-protocol agreement.Source: §3.3.3 · p. 9, §3.3.4 · p. 9

4 Results

Across the clinical test set, MPF was higher in white than gray matter, and segmented demyelinating lesions had lower MPF than normal-appearing white matter. Maps showed cross-protocol agreement, while removing acquisition-conditioned AdaIN increased protocol-group variation, reconstruction error, and cross-protocol map differences.

4.1 Macromolecular pool fraction in white matter and gray matter

  • MPF averaged 0.182 ± 0.007 in white matter and 0.144 ± 0.009 in gray matter across 1,237 test sessions, with between-group CVs of 2.65% and 5.63%, respectively.Table 3 summarizes estimated MPF across tissue types and vendor-by-protocol groups.Source: §4.1 · p. 9, Table 3 · p. 10

4.2 Demyelinating pathology

  • Lesion MPF was 35.6% lower than in normal-appearing white matter in 70 labeled sessions, and representative maps showed lesion reductions across scanner vendors and T1w protocols.Mean lesion MPF was 0.113 ± 0.015; examples are shown for MR-RATE and UMCU subjects.Source: §4.2 · p. 10, Figure 3 · p. 11, Figure 4 · p. 12

4.3 Prospective volunteer reproducibility

  • Two protocols produced similar tissue MPF means: 0.171 ± 0.026 in white matter and 0.135 ± 0.027 in gray matter for Spoiled GRE, versus 0.171 ± 0.021 and 0.134 ± 0.023 for MPRAGE.The voxel-wise mean absolute percentage difference was 7.7%, with Pearson r = 0.895 and CCC = 0.888.Source: §4.3 · pp. 10–11

4.4 Impact of acquisition-conditioned AdaIN

  • Without acquisition-conditioned AdaIN, between-group MPF CV rose from 2.65% to 10.27% in white matter and from 5.63% to 10.37% in gray matter.The mean total L1 reconstruction error increased by 22.3%, from 0.0466 ± 0.0177 to 0.0570 ± 0.0171 (p < 0.001).Source: §4.4 · pp. 11–12
  • Without AdaIN, the volunteer cross-protocol MPF difference rose from 7.7% to 15.3%, while voxel-wise CCC fell from 0.888 to 0.672.The comparison was conducted in the prospective volunteer experiment.Source: §4.4 · p. 12

5 Discussion

The framework estimates MPF retrospectively from conventional brain MRI using a two-pool magnetization-transfer model and acquisition-conditioned features. It produced higher MPF in white than gray matter, while the separation was smaller than reported in prospective qMT studies.

5 Discussion

  • The framework estimates MPF from conventional T1w, T2w, and FLAIR images without paired qMT references, using a two-pool model and acquisition-conditioned AdaIN.The model relates apparent longitudinal relaxation to MPF and sequence-averaged RF power.Source: §5 · p. 13
  • 0.182 ± 0.007 in white matter and 0.144 ± 0.009 in gray matter; estimated MPF was higher in white matter across the clinical test set.The estimates fell within reported qMT ranges, though absolute values depend on model assumptions and fitting strategy.Source: §5 · p. 13
  • The gray-to-white matter MPF ratio was approximately 0.79, versus ratios closer to 0.5 in prospective qMT studies.The authors suggest model simplifications, fixed pool and exchange parameters, the white-matter T_f1 prior, and partial-volume effects may contribute to the reduced contrast.Source: §5 · p. 13

Spoiled GRE MPRAGE

The maps showed cross-protocol consistency and lower MPF in demyelinating lesions, while model, evaluation, and training-coverage constraints limit how broadly to interpret or deploy them. The authors describe potential retrospective and prospective uses without dedicated qMT acquisitions.

Spoiled GRE MPRAGE

  • 35.6% lower MPF in segmented lesions than in NAWM was observed in the MR-RATE demyelinating-disease subset.The four UMCU subjects with confirmed MS showed reductions of 23.5–34.2%.Source: Spoiled GRE MPRAGE · p. 14
  • 2.65% in white matter and 5.63% in gray matter were the between-group coefficients of variation; cross-protocol maps had CCC = 0.888 and a mean absolute percentage difference of 7.7%.The within-subject comparison used consecutive Spoiled GRE and MPRAGE scans; Figures 6 and 7 show the maps, voxel-wise differences, and agreement.Source: Spoiled GRE MPRAGE · pp. 14–15, Figure 6 · p. 14, Figure 7 · p. 15
  • Replacing acquisition-conditioned AdaIN with standard instance normalization increased between-group MPF variation and reduced prospective cross-protocol CCC from 0.888 to 0.672.Protocol hold-out experiments also showed limited generalization to sequence types absent from training.Source: Spoiled GRE MPRAGE · p. 15
  • The model estimates four maps from three image contrasts, using a white-matter T_f1 prior and a soft PD lower bound to constrain an ill-posed estimation problem.Ablations indicated that these regularizers improved stability, while fixed healthy-white-matter tissue parameters and selected regularization settings may bias or constrain estimates.Source: Spoiled GRE MPRAGE · p. 15, §5.1 · p. 16

5.1 Limitations

  • The analytical MT model and Bloch-based signal equations omit effects including B1 inhomogeneity and detailed echo-train dynamics.More comprehensive models may describe these effects more accurately but generally require detailed sequence information often unavailable in retrospective archives.Source: §5.1 · p. 16
  • Registering contrasts to the 2D T2w geometry and resampling to 1 × 1 mm in-plane resolution reduced through-plane detail from 3D T1w and FLAIR images.Registration errors, partial-volume effects, and slice-wise processing without adjacent-slice information may also affect the maps.Source: §5.1 · p. 16
  • Absolute MPF accuracy remains difficult to establish without a universally accepted qMT reference, and report-derived diagnoses and clinical segmentations may affect lesion and tissue analyses.The four clinically confirmed MS cases were not a systematic validation cohort.Source: §5.1 · p. 16
  • The study evaluated 3 T scans, with protocol diversity concentrated mainly in T1w acquisitions; generalization beyond represented systems and protocols remains unestablished.Unseen T1w sequence types showed substantial parameter shifts, and the prospective reproducibility experiment included one healthy volunteer.Source: §5.1 · p. 16

6 Conclusion

Physics-guided self-supervised learning estimates MPF from conventional clinical brain MRI without paired qMT references. The resulting maps showed consistency across heterogeneous protocols and marked lesion MPF reductions, supporting their potential for biomarker research in existing archives and prospective conventional scans.

6 Conclusion

  • The framework estimates MPF maps from conventional clinical brain MRI without paired qMT reference data, with good consistency across heterogeneous protocols and marked MPF reductions in demyelinating-disease lesions.The authors describe potential large-scale research using existing archives and prospective mapping without a dedicated qMT acquisition or additional scan time.Source: §6 · p. 17

Data availability

The UMCU data are restricted, while MR-RATE and the code and model weights have stated online access routes.

Data availability

  • The UMCU data cannot be shared because of privacy and institutional restrictions.MR-RATE is available through Hugging Face subject to its access conditions and terms of use.Source: Data availability · p. 17
  • Code and model weights are available on GitHub.Source: Data availability · p. 17

A MT signal model assumptions

This section further justifies the sequence-averaged RF saturation and near-resonance approximations and explains why the forward model omits sequence-dependent apparent equilibrium magnetization.

A MT signal model assumptions

  • The section provides further justification for two signal-model approximations and explains the omission of sequence-dependent apparent equilibrium magnetization.Source: A MT signal model assumptions · p. 18

A.1 Sequence-averaged RF saturation

The formulation averages cumulative RF power across all pulses over the acquisition, assuming their combined rate is high relative to modeled relaxation, exchange, and saturation rates.

A.1 Sequence-averaged RF saturation

  • The formulation extends single-repetition averaging to cumulative RF power from excitation, inversion, and refocusing pulses over the entire acquisition.Source: §A.1 · p. 18
  • Combined RF pulse rates are on the order of 10^2 s^-1, exceeding modeled longitudinal relaxation and exchange rates below 15 s^-1.Source: §A.1 · p. 18
  • For B1,rms = 2.3 µT and T s 2 = 12.5 µs, the modeled semisolid-pool saturation rate is approximately 6 s^-1, below the combined pulse rate.Source: §A.1 · p. 18

A.2 Near-resonance assumption and apparent equilibrium magnetization

The model assumes Gaussian absorption and near-resonance irradiation, then uses a sequence-independent proton-density parameter in place of sequence-dependent apparent equilibrium magnetization.

A.2 Near-resonance assumption and apparent equilibrium magnetization

  • The semisolid-pool absorption lineshape is assumed Gaussian, and near-resonance irradiation permits approximating it by its peak value.Source: §A.2 · p. 18
  • The near-resonance approximation is generally satisfied for 3D acquisitions but less valid for multislice 2D T2w, and is applied throughout for efficient self-supervised training.Explicitly modeling off-resonant contributions would require pulse timing, waveforms, and slice-selection information typically unavailable in retrospective archives.Source: §A.2 · p. 18
  • The continuous-wave-equivalent model represents two-pool longitudinal dynamics with an effective single-pool model characterized by apparent relaxation and sequence-dependent equilibrium magnetization.Source: §A.2 · p. 18
  • The forward signal models replace sequence-dependent apparent equilibrium magnetization with a sequence-independent relative PD map, neglecting its modulation by semisolid-pool saturation.Source: §A.2 · p. 18
  • For multislice 2D T2w acquisitions, uncertain saturation modeling could affect signal amplitude and estimated MPF maps, motivating omission of explicit apparent-equilibrium modulation.Source: §A.2 · pp. 18–19
  • Long T2w repetition times make recovery nearly complete, limiting saturation-rate uncertainty through recovery; estimated PD is effective and sequence-independent, not free-pool or apparent equilibrium magnetization.Source: §A.2 · p. 19

SUPPLEMENTARY MATERIALS OF: "RETROSPECTIVE

The supplied passage is a supplementary-material heading for macromolecular pool fraction mapping.

SUPPLEMENTARY MATERIALS OF: "RETROSPECTIVE

S1 Characteristics of the UMCU multiple sclerosis subset

The supplementary analyses characterize the MS subset and acquisition handling, assess quantitative-map reproducibility and regularization, and test whether estimates generalize to protocols withheld from training. Withholding a protocol shifted estimates substantially, while the reported reproducibility and ablation analyses identify conditions associated with more stable estimates.

S1 Characteristics of the UMCU multiple sclerosis subset

  • The MS subset table covers four clinically confirmed UMCU test-set subjects, all scanned on Philips 3 T systems.Subjects A–D correspond to rows in Figure 4; the table lists demographic and acquisition parameters.Source: Table S1.1 · p. 25

S2 TSE echo time correction

  • For TSE acquisitions, the forward models replace nominal echo time with an effective echo time to account for stimulated-echo contributions.The effective echo time is calculated as TEeff = cTE TEnom.Source: S2 TSE echo time correction · p. 26

S3 Hyperparameter tuning

  • Hyperparameter tuning evaluated a search grid to identify the optimal model configuration, but the supplied passages do not report the selected values.The search space and explored values are referenced in Table S3.1.Source: S3 Hyperparameter tuning · p. 27, Table S3.1 · p. 27

S4 Prospective volunteer acquisition parameters

  • The prospective volunteer acquisition table compares Spoiled GRE and MPRAGE protocols on a Philips Ingenia 3 T system.The protocols are designated by their respective T1w sequence.Source: Table S4.1 · p. 28

S5 Quantitative results for all estimated maps

  • 7.7% was the mean absolute percentage difference for MPF maps between the Spoiled GRE and MPRAGE protocols in the prospective volunteer.The corresponding differences were 7.7% for free-pool T1, 4.8% for free-pool T2, and 4.8% for PD.Source: S5 Quantitative results for all… · p. 31

S6 Impact of acquisition conditioning

  • Removing acquisition-conditioned AdaIN reduced cross-protocol reproducibility, as reflected by a lower concordance correlation coefficient.The comparison used an otherwise identical unconditioned baseline and maps from a healthy volunteer scanned with Spoiled GRE and MPRAGE.Source: Table S6.1 · p. 32, Figure S6.1 · p. 33

S7 Ablation of the regularization terms

  • Removing either regularization term worsened its associated estimates or agreement; omitting both also produced substantially lower free-pool T1 values than the full model.Removing the T1 prior primarily affected T1 and MPF, while removing the PD constraint primarily affected PD and T2; simultaneous omission showed similar trends.Source: S7 Ablation of the regularization terms · p. 34, Table S7.1 · p. 35, Table S7.2 · p. 36

S8 Generalization to unseen T1w protocols

  • Withholding either T1w protocol shifted estimates in the corresponding out-of-domain group, increasing white-matter MPF between-group CV to 19.71% or 11.06%.The MPRAGE-only model estimated 0.126 in the unseen Philips Spoiled GRE group; the Spoiled-GRE-only model estimated approximately 0.15 in unseen MPRAGE groups.Source: S8 Generalization to unseen T1w… · p. 37

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