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

physics.med-phOct 27, 2026

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

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

Organizations: Computational Imaging Group for MRI Therapy & Diagnostics, University Medical Center Utrecht, Utrecht, The Netherlands · Department of Radiology, University Medical Center Utrecht, Utrecht, The Netherlands

Abstract

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.

Figures & tables

Figure 1: Theoretical behavior of apparent longitudinal relaxation time (

T_{1}^{\mathrm{app}}=1/R_{1}^{\mathrm{app}}

) as a function of sequence-averaged RF amplitude (

B_{1,\mathrm{rms}}

) across varying macromolecular pool fractions (

m_{0}^{\mathrm{s}}\in[0,0.25]

) according to Eq. ( 4 ). Fixed representative white matter parameters:

T_{1}^{\mathrm{f}}=2000~\mathrm{ms}

T_{1}^{\mathrm{s}}=300~\mathrm{ms}

T_{2}^{\mathrm{s}}=12.5~\mu\mathrm{s}

, and

R_{x}=13.6~\mathrm{s}^{-1}

. The dashed line indicates the free-water longitudinal relaxation time (

T_{1}^{\mathrm{f}}

) in the absence of MT (

m_{0}^{\mathrm{s}}=0

	$\boldsymbol{T_{1}\mathrm{w}}$		$\boldsymbol{T_{2}\mathrm{w}}$	FLAIR
Sequence	3D Spoiled GRE	3D MPRAGE	2D TSE	3D TSE (IR)
Sessions ( $n$ )	4,168	1,144	5,312	5,312
TR [ms]	5.26 [5.03–5.40]	2500	4063 [2779–4918]	4800
TE [ms]	2.38 [2.25–2.49]	3.94 [3.53–4.09]	80	314.5 [275.0–370.3]
TI [ms]	NA	1004	NA	1650
FA [ ∘ ]	10	8	90	90

Table 1: Acquisition parameters for the UMCU and MR-RATE clinical datasets (training, validation, and test sets combined). Values denote median [min–max]; single values indicate dataset-wide constants. GRE: Spoiled Gradient-Echo; MPRAGE: Magnetization-Prepared Rapid Gradient-Echo; TSE: Turbo Spin Echo; IR: Inversion Recovery; NA: Not Applicable; FA: Flip Angle; ETL: Echo Train Length; BW: Pixel Bandwidth.

Dataset	Level	Training (80%)	Validation (5%)	Test (15%)	Total
UMCU (Philips)	Sessions	4,173	265	874	5,312
UMCU (Philips)	Subjects	1,755	110	327	2,192
MR-RATE (Siemens)	Sessions	1,911	119	363	2,393
MR-RATE (Siemens)	Subjects	1,840	115	342	2,297
Combined	Sessions	6,084	384	1,237	7,705
Combined	Subjects	3,595	225	669	4,489

Table 2: Subject-level partitioning of the UMCU, MR-RATE, and combined clinical datasets. Each source dataset was independently partitioned using an 80/5/15% training, validation, and test split.

		Philips (UMCU)		Siemens (MR-RATE)
Tissue	Total	Spoiled GRE	MPRAGE	MPRAGE
	( $n=1,237$ )	( $n=653$ )	( $n=221$ )	( $n=363$ )
WM	$0.182\pm 0.007$	$0.186\pm 0.006$	$0.179\pm 0.004$	$0.177\pm 0.006$
GM	$0.144\pm 0.009$	$0.149\pm 0.005$	$0.147\pm 0.005$	$0.134\pm 0.006$

Table 3: Mean estimated macromolecular pool fraction (

m_{0}^{\mathrm{s}}

; MPF) in white matter (WM) and gray matter (GM) across the full clinical test set and the three vendor-by-protocol groups. Values represent mean

\pm

standard deviation across MRI sessions.

Figure 2: Distribution of estimated macromolecular pool fraction (

m_{0}^{\mathrm{s}}

; MPF) values in white matter (WM) and gray matter (GM) for the three vendor-by-protocol groups in the clinical test set. Solid lines show the mean density across MRI sessions and shaded regions indicate one standard deviation.

Figure 3: Representative MPF maps from the MR-RATE test set (Siemens MPRAGE). Each of the four rows shows a distinct, randomly selected subject with a report-derived demyelinating-disease diagnosis. Columns show the input $T_{1}$ -weighted, $T_{2}$ -weighted, and FLAIR images together with the generated $m_{0}^{\mathrm{s}}$ map. White boxes indicate regions enlarged in the zoom panels.

Figure 4: Representative MPF maps from the four subjects with MS identified in the UMCU test set. Rows A and B correspond to the Philips Spoiled GRE vendor-by-protocol group, whereas rows C and D correspond to the Philips MPRAGE vendor-by-protocol group. Columns show the input $T_{1}$ -weighted, $T_{2}$ -weighted, and FLAIR images together with the generated $m_{0}^{\mathrm{s}}$ map. White boxes indicate regions enlarged in the zoom panels.

Figure 5: Relationship between lesion-wise free-pool longitudinal relaxation rate ( $R_{1}^{\mathrm{f}}$ ) and macromolecular pool fraction ( $m_{0}^{\mathrm{s}}$ ; MPF) in the MR-RATE demyelinating-disease subset ( $n=70$ MRI sessions, 673 unique lesions). Each point represents the median $R_{1}^{\mathrm{f}}$ and $m_{0}^{\mathrm{s}}$ value within a single demyelinating lesion. Black arrows indicate the principal-component eigenvectors and are scaled to one standard deviation along each component.

Figure 6: Prospective within-subject reproducibility in a healthy volunteer scanned with two different clinical protocols. Top row: estimated macromolecular pool fraction ( $m_{0}^{\mathrm{s}}$ ; MPF) map from the Spoiled GRE protocol. Middle row: corresponding MPF map from the MPRAGE protocol. Bottom row: voxel-wise percentage difference maps between the two generated MPF maps.

Figure 7: Voxel-wise agreement between macromolecular pool fraction ( $m_{0}^{\mathrm{s}}$ ; MPF) maps estimated from the Spoiled GRE and MPRAGE protocols in a healthy volunteer. Each point represents a brain parenchymal voxel, colored by local voxel density (log scale). The solid line denotes identity and the dotted line the reduced major axis (RMA) fit. Pearson’s $r$ and the concordance correlation coefficient (CCC) are shown in the top left.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Demographics & Hardware
	Spoiled GRE Protocol		MPRAGE Protocol
Parameter	Subject A	Subject B	Subject C	Subject D
Age [years]	35	51	13	49
Sex	Male	Male	Male	Female
Scanner model	Ingenia	Ingenia Elition X	Ingenia	Ingenia CX
$\boldsymbol{T_{1}\mathrm{w}}$ Sequence

Appendix

Table S1.1: Demographic and acquisition parameters for the four subjects with clinically confirmed MS in the UMCU test set. Subjects A–D correspond to Rows A–D in Figure 4 in the main manuscript. All examinations were performed on Philips 3 T systems. GRE: Gradient-Echo; TSE: Turbo Spin Echo; IR: Inversion Recovery; MPRAGE: Magnetization-Prepared Rapid Gradient-Echo; NA: Not Applicable; BW: Pixel Bandwidth; FA: Flip Angle; ETL: Echo Train Length.

Hyperparameter	Explored values
Learning rate	[ $10^{-6}$ , $10^{-5}$ , $10^{-4}$ , $10^{-3}$ , $10^{-2}$ ]
$\lambda_{\mathrm{PD\text{-}constraint}}$	[0.1, 0.2, 0.25, 0.50, 0.75, 1.0, 2.0]
$\lambda_{T_{1}\text{-}\mathrm{prior}}$	[0.0001, 0.001, 0.002, 0.0025, 0.005, 0.01]

Appendix

Table S3.1: Hyperparameter search space and range of values evaluated during the optimization process.

	Spoiled GRE Protocol			MPRAGE Protocol
Parameter	$\boldsymbol{T_{1}\mathrm{w}}$	$\boldsymbol{T_{2}\mathrm{w}}$	FLAIR	$\boldsymbol{T_{1}\mathrm{w}}$	$\boldsymbol{T_{2}\mathrm{w}}$	FLAIR
Sequence	3D Spoiled GRE	2D TSE	3D TSE (IR)	3D MPRAGE	2D TSE	3D TSE (IR)
TR [ms]	5.07	4340	4800	2500	4990	4800
TE [ms]	2.27	80	336	3.79	80	337
TI [ms]	NA	NA	1650	1004	NA	1650
FA [ ∘ ]	10	90	90	8	90	90

Appendix

Table S4.1: Acquisition parameters for the two clinical protocols evaluated in the prospective healthy volunteer on a 3 T Philips Ingenia system. Protocols are designated by their respective

T_{1}\mathrm{w}

sequence (Spoiled GRE protocol vs. MPRAGE protocol). GRE: Spoiled Gradient-Echo; TSE: Turbo Spin Echo; IR: Inversion Recovery; NA: Not Applicable; BW: Pixel Bandwidth; FA: Flip Angle; ETL: Echo Train Length.

White Matter (WM)
		Philips (UMCU)		Siemens (MR-RATE)
Metric	Total	Spoiled GRE	MPRAGE	MPRAGE	Between-group
	( $n=1{,}237$ )	( $n=653$ )	( $n=221$ )	( $n=363$ )	CV (%)
$m_{0}^{\mathrm{s}}$	$0.182\pm 0.007$	$0.186\pm 0.006$	$0.179\pm 0.004$	$0.177\pm 0.006$	$2.65$
$T_{1}^{\mathrm{f}}$ [ms]	$1982\pm 58$	$1967\pm 60$	$2017\pm 64$	$1987\pm 40$	$1.26$
$T_{2}^{\mathrm{f}}$ [ms]	$76.6\pm 13.1$	$73.8\pm 13.7$	$80.9\pm 18.9$	$78.8\pm 1.2$	$4.68$

Appendix

Table S5.1: Quantitative parameter estimates in white matter (WM) and gray matter (GM) across the clinical test set (

n=1{,}237

MRI sessions), stratified by the three vendor-by-protocol groups. Values represent mean

\pm

standard deviation across MRI sessions. The between-group coefficient of variation (CV) was calculated from the three vendor-by-protocol group means (Philips Spoiled GRE, Philips MPRAGE, and Siemens MPRAGE).

Metric	NAWM	NAGM	Lesion	$\Delta$ vs. NAWM (%)	$\Delta$ vs. NAGM (%)
$m_{0}^{\mathrm{s}}$	$0.176\pm 0.005$	$0.133\pm 0.005$	$0.113\pm 0.015$	$-35.6\%$	$-15.2\%$
$T_{1}^{\mathrm{f}}$ [ms]	$1981\pm 38$	$2182\pm 59$	$2369\pm 209$	$+19.6\%$	$+8.6\%$
$T_{2}^{\mathrm{f}}$ [ms]	$78.5\pm 0.8$	$86.5\pm 2.1$	$105.8\pm 16.2$	$+34.8\%$	$+22.3\%$
$\mathrm{PD}$ [a.u.]	$0.678\pm 0.015$	$0.736\pm 0.018$	$0.842\pm 0.045$	$+24.2\%$	$+14.4\%$

Appendix

Table S5.2: Quantitative parameter estimates in demyelinating WM lesions, normal-appearing white matter (NAWM), and normal-appearing gray matter (NAGM) for the MR-RATE demyelinating-disease test subset (

n=70

MRI sessions; Siemens Magnetom Vida 3 T). Values represent mean

\pm

standard deviation across MRI sessions. Relative percentage differences were calculated as

\Delta=(\mu_{\mathrm{lesion}}-\mu_{\mathrm{tissue}})/\mu_{\mathrm{tissue}}\times 100\%

, where the reference tissue was either NAWM or NAGM.

Subject	Protocol	Compartment	$m_{0}^{\mathrm{s}}$	$T_{1}^{\mathrm{f}}$ [ms]	$T_{2}^{\mathrm{f}}$ [ms]	$\mathrm{PD}$ [a.u.]
Subject A	Spoiled GRE	NAWM	$0.193\pm 0.026$	$1922\pm 191$	$69.0\pm 6.6$	$0.656\pm 0.051$
		NAGM	$0.150\pm 0.036$	$2245\pm 430$	$82.8\pm 21.5$	$0.703\pm 0.090$
		Lesion	$0.127\pm 0.036$	$2447\pm 580$	$114.6\pm 57.6$	$0.769\pm 0.090$
		$\Delta$ vs. NAWM (%)	$-34.2\%$	$+27.3\%$	$+66.1\%$	$+17.2\%$
		$\Delta$ vs. NAGM (%)	$-15.3\%$	$+9.0\%$	$+38.4\%$	$+9.4\%$
Subject B	Spoiled GRE	NAWM	$0.182\pm 0.023$	$1949\pm 180$	$68.1\pm 4.5$	$0.671\pm 0.048$

Appendix

Table S5.3: Subject-level quantitative parameter estimates in normal-appearing white matter (NAWM), normal-appearing gray matter (NAGM), and demyelinating WM lesions for the four clinically confirmed multiple sclerosis subjects in the UMCU test set acquired on Philips 3 T systems. Values represent voxel-wise mean

\pm

standard deviation within each tissue compartment for each subject. Subjects A–D correspond to Rows A–D in Figure 4 and Supplementary Table S1.1 . Relative differences were calculated separately for each subject as

\Delta=(\mu_{\mathrm{lesion}}-\mu_{\mathrm{tissue}})/\mu_{\mathrm{tissue}}\times 100\%

, where the reference tissue was either NAWM or NAGM.

Figure S5.1: Prospective within-subject reproducibility in a healthy volunteer scanned with two different clinical protocols. Columns show the generated macromolecular pool fraction ( $m_{0}^{\mathrm{s}}$ ; MPF), free-pool longitudinal relaxation time ( $T_{1}^{\mathrm{f}}$ ), free-pool transverse relaxation time ( $T_{2}^{\mathrm{f}}$ ), and relative proton density ( $\mathrm{PD}$ ) maps. The top row corresponds to the Spoiled GRE protocol, the middle row to the MPRAGE protocol, and the bottom row shows voxel-wise percentage difference maps between the two generated quantitative maps. Mean absolute percentage differences across brain parenchyma (WM+GM) were 7.7% for $m_{0}^{\mathrm{s}}$ , 7.7% for $T_{1}^{\mathrm{f}}$ , 4.8% for $T_{2}^{\mathrm{f}}$ , and 4.8% for $\mathrm{PD}$ .

Figure S5.2: Voxel-wise agreement between quantitative maps estimated from the Spoiled GRE and MPRAGE protocols in a healthy volunteer. From left to right, panels show the macromolecular pool fraction ( $m_{0}^{\mathrm{s}}$ ; MPF), free-pool longitudinal relaxation time ( $T_{1}^{\mathrm{f}}$ ), free-pool transverse relaxation time ( $T_{2}^{\mathrm{f}}$ ), and relative proton density ( $\mathrm{PD}$ ). Each point represents a brain parenchymal voxel (WM+GM), colored by local voxel density on a logarithmic scale shared by all panels. The solid line denotes identity and the dotted line the reduced major axis (RMA) fit. Pearson correlation coefficients ( $r$ ) and concordance correlation coefficients (CCC) are reported for each quantitative map to assess cross-protocol reproducibility.

			Philips (UMCU)		Siemens (MR-RATE)
Parameter	Conditioning	Total	Spoiled GRE	MPRAGE	MPRAGE	Between-group
		( $n=1{,}237$ )	( $n=653$ )	( $n=221$ )	( $n=363$ )	CV (%)
White Matter (WM)
$m_{0}^{\mathrm{s}}$	AdaIN	$0.182\pm 0.007$	$0.186\pm 0.006$	$0.179\pm 0.004$	$0.177\pm 0.006$	2.65
	No AdaIN	$0.189\pm 0.018$	$0.205\pm 0.008$	$0.174\pm 0.004$	$0.171\pm 0.004$	10.27
$T_{1}^{\mathrm{f}}$ [ms]	AdaIN	$1982\pm 58$	$1967\pm 60$	$2017\pm 64$	$1987\pm 40$	1.26

Appendix

Table S6.1: Ablation study evaluating the impact of acquisition-conditioned adaptive instance normalization (AdaIN) on quantitative parameter estimates across the multicenter clinical test set (

n=1{,}237

MRI sessions). Values represent mean

\pm

standard deviation across MRI sessions for white matter (WM) and gray matter (GM). Results are shown for the proposed acquisition-conditioned model (AdaIN) and an otherwise identical unconditioned baseline model (No AdaIN). Group-specific estimates are reported for the three vendor-by-protocol groups (Philips Spoiled GRE, Philips MPRAGE, and Siemens MPRAGE). The between-group coefficient of variation (CV) was calculated from the corresponding groups.

Figure S6.1: Impact of acquisition conditioning on cross-protocol reproducibility of the generated macromolecular pool fraction ( $m_{0}^{\mathrm{s}}$ ; MPF) maps in the prospective healthy volunteer. Voxel-wise agreement between MPF maps estimated from the Spoiled GRE and MPRAGE protocols is shown for the proposed acquisition-conditioned model (AdaIN; left) and an otherwise identical unconditioned baseline model (No AdaIN; right). Each point represents a brain parenchymal voxel (WM+GM), colored by local voxel density on a logarithmic scale; both panels share the same axis ranges and color scale. The solid line denotes identity and the dotted line the reduced major axis (RMA) fit. Pearson correlation coefficients ( $r$ ) and concordance correlation coefficients (CCC) quantify cross-protocol agreement. Removal of acquisition conditioning reduced reproducibility, resulting in a lower CCC.

			Philips (UMCU)		Siemens (MR-RATE)
Parameter	Configuration	Total	Spoiled GRE	MPRAGE	MPRAGE	Between-group
		( $n=1{,}237$ )	( $n=653$ )	( $n=221$ )	( $n=363$ )	CV (%)
White Matter (WM)
$m_{0}^{\mathrm{s}}$	Full model	$0.182\pm 0.007$	$0.186\pm 0.006$	$0.179\pm 0.004$	$0.177\pm 0.006$	2.65
	No $T_{1}^{\mathrm{f}}$ prior	$0.177\pm 0.013$	$0.165\pm 0.005$	$0.187\pm 0.003$	$0.192\pm 0.004$	7.96
	No PD constraint	$0.236\pm 0.012$	$0.230\pm 0.011$	$0.239\pm 0.009$	$0.245\pm 0.009$	3.26

Appendix

Table S7.1: Regularization ablation: quantitative parameter estimates in white matter (WM) and gray matter (GM) across the clinical test set (

n=1{,}237

MRI sessions) for models trained with and without the

\mathrm{PD}

constraint (

\lambda_{\mathrm{PD\text{-}constraint}}\in\{0.5,0\}

) and white-matter

T_{1}^{\mathrm{f}}

prior (

\lambda_{T_{1}\text{-}\mathrm{prior}}\in\{0.0025,0\}

). Values denote mean

\pm

standard deviation across sessions. Between-group coefficient of variation (CV) quantifies variation across the three vendor-by-protocol group means (Philips Spoiled GRE, Philips MPRAGE, and Siemens MPRAGE).

Parameter	Configuration	MPD (%)	CCC	$r$
$m_{0}^{\mathrm{s}}$	Full model	7.67	0.888	0.895
	No $T_{1}^{\mathrm{f}}$ prior	14.60	0.473	0.793
	No PD constraint	9.56	0.881	0.892
	Neither	12.14	0.419	0.805
$T_{1}^{\mathrm{f}}$ [ms]	Full model	7.70	0.673	0.776
	No $T_{1}^{\mathrm{f}}$ prior	19.57	0.722	0.898

Appendix

Table S7.2: Regularization ablation: prospective cross-protocol reproducibility of quantitative maps in a healthy volunteer scanned with the Spoiled GRE and MPRAGE protocols. Metrics evaluate voxel-wise agreement across brain parenchyma (WM+GM). MPD: mean absolute percentage difference; CCC: concordance correlation coefficient;

r

: Pearson correlation coefficient.

Configuration	Withheld protocol	Included protocol(s)	Training sessions
Pooled (full model)	None	Spoiled GRE + MPRAGE	6,084
MPRAGE-only	Spoiled GRE	MPRAGE	2,773
Spoiled GRE-only	MPRAGE	Spoiled GRE	3,311

Appendix

Table S8.1: Overview of training subsets evaluated in the protocol hold-out experiments. All models were evaluated on the complete clinical test set (

n=1{,}237

sessions).

		Philips (UMCU)		Siemens (MR-RATE)
Parameter	Training data	Spoiled GRE ( $n=653$ )	MPRAGE ( $n=221$ )	MPRAGE ( $n=363$ )	Between-group
					CV (%)
White Matter (WM)
$m_{0}^{\mathrm{s}}$	Pooled (full model)	$0.186\pm 0.006$	$0.179\pm 0.004$	$0.177\pm 0.006$	2.65
	MPRAGE only	$0.126\pm 0.004^{\dagger}$	$0.182\pm 0.005$	$0.183\pm 0.006$	19.71
	Spoiled GRE only	$0.177\pm 0.007$	$0.146\pm 0.007^{\dagger}$	$0.148\pm 0.008^{\dagger}$	11.06

Appendix

Table S8.2: Quantitative parameter estimates in white matter (WM) and gray matter (GM) across the clinical test set (

n=1{,}237

MRI sessions) for models trained on protocol-restricted subsets. Values denote mean

\pm

standard deviation across sessions. † indicates an out-of-domain evaluation where the corresponding protocol was withheld from the training set. Between-group coefficient of variation (CV) was calculated across the three vendor-by-protocol group means.

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