DeepPV-MRF: End-to-End Partial-Volume Fraction Estimation from MR Fingerprinting Time Series

Tianyi Ding; Yang Gao; Zhuang Xiong; Feng Liu; Martijn A. Cloos; Jin Jin; Hongfu Sun

eess.SPOct 14, 2026

DeepPV-MRF: End-to-End Partial-Volume Fraction Estimation from MR Fingerprinting Time Series

Authors: Tianyi Ding, Yang Gao, Zhuang Xiong, Feng Liu, Martijn A. Cloos, Jin Jin, Hongfu Sun

Organizations: School of Electrical Engineering and Computer Science, University of Queensland, QLD 4072, Australia · School of Computer Science and Engineering, Central South University, Changsha 410083, China · Image X Institute, Sydney School of Health Sciences, Faculty of Medicine and Health, University of Sydney, NSW 2006, Australia · Donders Institute for Brain Cognition and Behaviour, Radboud University, Nijmegen, Netherlands ·

Abstract

Background: Estimating subvoxel tissue fractions from magnetic resonance fingerprinting (MRF) is challenging. Conventional dictionary matching and segmentation pipelines can propagate errors from intermediate parametric maps into tissue fraction estimates. Purpose: We introduce DeepPV-MRF, a deep learning framework that directly estimates voxel-wise tissue fractions from raw MRF signals. Methods: A cascaded spatial-temporal network was trained on subject-derived Bloch simulations with radial k-space undersampling. The network combines temporal encoding and spatial U-Net refinement to estimate cerebrospinal fluid (CSF), gray matter (GM), and white matter (WM) fractions without intermediate T1/T2 maps. We compared DeepPV-MRF with partial-volume dictionary matching (PV-DM) and pseudoinverse estimation (PV-Pinv) using simulated and in vivo data. Results: DeepPV-MRF outperformed both methods across acquisition settings. In single-shot simulations, CSF/WM/GM mean absolute errors were 0.0418/0.0744/0.0757, versus 0.1281/0.2443/0.2958 for PV-DM and 0.2021/0.2793/0.2630 for PV-Pinv. Corresponding structural similarity values were 0.960/0.916/0.922. In vivo results showed sharper anatomical boundaries and smoother tissue transitions, while cross-shot analysis indicated improved consistency across volunteers. Conclusions: DeepPV-MRF enables accurate and efficient direct tissue fraction estimation from MRF signals, particularly with limited shots. Further validation is needed before clinical deployment.

Figures & tables

Figure 1: (a) Overview of the DeepPV-MRF framework, including real and imaginary input channels and tissue-fraction (TF) prediction. (b) U-Net encoder structure with channel depths and block functions (left), and decoder structure for TF prediction (right).

Figure 2: (a) Synthetic data generation pipeline, (b) inversion recovery balanced steady-state free precession sequence, (c) radial subsampling trajectory, (d) random cropping, and (e) examples of the first four real and imaginary channels of the training input data.

Figure 3: Qualitative comparison of tissue fraction maps for cerebrospinal fluid (CSF), white matter (WM), and gray matter (GM) under single-shot, three-shot, and six-shot acquisitions in the synthetic test set. For each tissue type and acquisition setting, four methods are compared: Reference Label, partial volume dictionary matching (PV-DM), partial volume pseudoinverse (PV-Pinv), and the proposed DeepPV-MRF. Corresponding absolute difference maps are shown in the second row for each acquisition setting to visualize voxel-wise reconstruction errors. All maps are displayed using a common intensity window of [0, 1] for tissue fractions and [0, 0.2] for difference maps.

	Tissue	Method	MAE ( $\times 10^{3}$ ) ( $\downarrow$ )	PSNR ( $\uparrow$ )	SSIM ( $\uparrow$ )	$\mathbf{r}_{\text{weighted}}$ ( $\uparrow$ )
Single-Shot	CSF	DeepPV-MRF	41.76 $\pm$ 5.39	30.81 $\pm$ 1.37	0.960 $\pm$ 0.014	0.957 $\pm$ 0.013
		PV-DM	128.07 $\pm$ 28.60	19.93 $\pm$ 1.72	0.643 $\pm$ 0.081	0.71 $\pm$ 0.103
		PV-Pinv	202.10 $\pm$ 35.96	15.22 $\pm$ 1.27	0.396 $\pm$ 0.076	0.338 $\pm$ 0.314
	WM	DeepPV-MRF	74.39 $\pm$ 10.65	24.80 $\pm$ 1.38	0.916 $\pm$ 0.018	0.846 $\pm$ 0.034
		PV-DM	244.25 $\pm$ 35.03	12.57 $\pm$ 1.22	0.527 $\pm$ 0.039	0.414 $\pm$ 0.096
		PV-Pinv	279.27 $\pm$ 26.89	11.76 $\pm$ 0.79	0.448 $\pm$ 0.047	0.346 $\pm$ 0.105

Table 1: Performance comparison of different tissue fraction estimation methods under different shot numbers using simulated magnetic resonance fingerprinting (MRF) signals. Quantitative results are reported as mean

\pm

standard deviation across all synthetic test slices pooled from the 3 unseen test subjects.

Figure 4: Scatter plots comparing DeepPV-MRF predicted tissue fraction values against reference FSL-FAST labels for cerebrospinal fluid (CSF), white matter (WM), and gray matter (GM) across single-shot (top row), three-shot (middle row), and six-shot (bottom row) acquisition settings. Each plot displays voxel-wise predictions (y-axis) versus corresponding reference values (x-axis). Quantitative metrics include Pearson correlation coefficient, MAE, coefficient of determination ( $R^{2}$ ), and the slope of the fitted regression line. The red dashed line indicates the line of perfect agreement.

Figure 5: Comparison of predicted tissue fraction maps for cerebrospinal fluid (CSF), white matter (WM), and gray matter (GM) across single-shot, three-shot, and six-shot in vivo MRF acquisitions for sub 01. For each tissue type, results from three methods—partial volume dictionary matching (PV-DM), partial volume pseudoinverse (PV-Pinv), and the proposed DeepPV-MRF—are shown from left to right. Each row corresponds to a different acquisition setting, with intensity values mapped from 0 to 1.

Figure 6: Representative in vivo partial-volume maps from two volunteers (sub 02 and sub 03) reconstructed using the proposed DeepPV-MRF model under 1-shot, 3-shot, and 6-shot acquisitions. For each volunteer, the same anatomical slice is shown across shot settings to qualitatively assess consistency across acquisition schemes. Separate maps are shown for CSF, WM, and GM tissue fractions. All maps are displayed on the same scale from 0 to 1.

Tissue	Subject	1-shot vs. 6-shot	3-shot vs. 6-shot	Improvement (%)
CSF	sub01	0.164	0.138	15.9
	sub02	0.131	0.126	3.5
	sub03	0.130	0.109	16.5
WM	sub01	0.245	0.179	27.1
	sub02	0.227	0.194	14.8
	sub03	0.191	0.181	5.1

Table 2: Cross-shot consistency of DeepPV-MRF in the three in vivo volunteers, using the six-shot prediction as an internal high-shot reference. Lower mean absolute error (MAE) indicates greater agreement between the lower-shot and six-shot predictions. The six-shot prediction is used only as an internal consistency reference and should not be interpreted as in vivo ground truth.

Figure 7: In vivo noise-sensitivity analysis for the single-shot setting across the three volunteers. The input MRF signals were perturbed with complex Gaussian noise over signal-to-noise ratio (SNR) levels from 10 dB to 40 dB. Rows correspond to sub01, sub02, and sub03, and columns show cerebrospinal fluid (CSF), white matter (WM), and gray matter (GM). The plotted values represent the mean absolute error (MAE) between predictions from noisy inputs and the corresponding clean-input predictions. Solid lines indicate the mean across slices, and shaded regions denote the 95% confidence intervals.

Core ablations
Family	Setting	CSF MAE	WM MAE	GM MAE	Avg. MAE	Avg. PSNR	Avg. SSIM
	Full model	41.76	74.39	75.69	63.95	26.48	0.933
	With B0/PD heads	43.42	77.70	78.51	66.55	26.14	0.922
	Temporal encoder only	52.12	110.25	106.26	89.54	23.95	0.890
	No spatial gradient loss	44.45	77.69	79.55	67.23	26.05	0.925
Latent dimension sweep

Table 3: Ablation study on the external 1-shot simulation test set. Mean absolute error (MAE) denotes tissue-wise

\mathrm{MAE}_{\mathrm{tissue}}

and is reported in

\times 10^{3}

. Macro-averaged Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) are unweighted averages across cerebrospinal fluid (CSF), white matter (WM), and gray matter (GM). The best value for each metric within each ablation family is shown in bold, with lower MAE and higher PSNR/SSIM indicating better performance. The full model denotes the architecture used for the main results; the B0/PD-head row adds auxiliary heads to this model.

Figure 8: in vivo comparison of T1 and T2 maps from MRF-Mixer (left) and composite maps derived from DeepPV-MRF (middle), with their absolute difference shown on the right. The composite maps combine estimated tissue fractions with pure-tissue relaxation values. The difference maps confirm that the largest discrepancies are concentrated at tissue boundaries, consistent with partial volume effects.

Shot setting	Tissue	Metric	Friedman $p_{\mathrm{Holm}}$	$\Delta$ vs PV-DM	$\Delta$ vs PV-Pinv
Single-shot	CSF	MAE ( $\times 10^{3}$ )	$2.78\times 10^{-52}$	$-0.094$	$-0.153$
		PSNR	$2.78\times 10^{-52}$	$11.434$	$16.549$
		SSIM	$1.37\times 10^{-52}$	$0.332$	$0.554$
		$r_{\mathrm{weighted}}$	$1.37\times 10^{-52}$	$0.259$	$0.477$
	WM	MAE ( $\times 10^{3}$ )	$6.01\times 10^{-51}$	$-0.165$	$-0.209$
		PSNR	$1.93\times 10^{-48}$	$12.611$	$13.350$

Supplementary Table 1: Paired statistical analysis using the same simulation slices as in main manuscript Table 1. For each shot setting, tissue, and metric, we report the Holm-adjusted Friedman

p

-value across the three methods and the median paired difference (

\Delta

) of DeepPV-MRF relative to each baseline. For MAE, negative values indicate lower error; for PSNR, SSIM, and

r_{\mathrm{weighted}}

, positive values indicate improved performance. Across all post-hoc paired Wilcoxon signed-rank tests, the Holm-adjusted

p

-value was

6.83\times 10^{-20}

Shot setting	Tissue	MAE ( $\times 10^{3}$ ) ( $\downarrow$ )	RMSE ( $\times 10^{3}$ ) ( $\downarrow$ )
Single-shot	CSF	19.25 $\pm$ 3.62	43.35 $\pm$ 7.50
	WM	38.98 $\pm$ 7.53	83.00 $\pm$ 13.41
	GM	55.34 $\pm$ 10.12	95.24 $\pm$ 15.34
Three-shot	CSF	12.56 $\pm$ 3.26	28.90 $\pm$ 7.57
	WM	29.23 $\pm$ 5.24	59.49 $\pm$ 9.15
	GM	39.88 $\pm$ 8.06	69.26 $\pm$ 12.51

Supplementary Table 2: Whole-brain error metrics for the DeepPV-MRF model under different shot settings. Metrics were computed over all voxels within the brain mask across the same 123 external synthetic test slices used for the main simulation evaluation. Values are reported as mean

\pm

standard deviation.

Magnetic Resonance Imaging

Magnetic resonance imaging uses magnetic fields and radio waves to create images of anatomy and tissue function for research and clinical care.

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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+4

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

Magnetic Resonance Imaging Brain MRI Physics-Informed ML Self-Supervised Learning

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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.

Abstract

Magnetic Resonance Imaging

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