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 · Australian Institute for Bioengineering and Nanotechnology, University of Queensland, St Lucia, QLD, Australia · Siemens Healthineers Pty Ltd, Brisbane, Queensland, Australia · School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia
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 ( ×103 ) ( ↓ )
PSNR ( ↑ )
SSIM ( ↑ )
rweighted ( ↑ )
Single-Shot
CSF
DeepPV-MRF
41.76 ± 5.39
30.81 ± 1.37
0.960 ± 0.014
0.957 ± 0.013
PV-DM
128.07 ± 28.60
19.93 ± 1.72
0.643 ± 0.081
0.71 ± 0.103
PV-Pinv
202.10 ± 35.96
15.22 ± 1.27
0.396 ± 0.076
0.338 ± 0.314
WM
DeepPV-MRF
74.39 ± 10.65
24.80 ± 1.38
0.916 ± 0.018
0.846 ± 0.034
PV-DM
244.25 ± 35.03
12.57 ± 1.22
0.527 ± 0.039
0.414 ± 0.096
PV-Pinv
279.27 ± 26.89
11.76 ± 0.79
0.448 ± 0.047
0.346 ± 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 ± 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 ( R2 ), 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.
Family
Setting
CSF MAE
WM MAE
GM MAE
Avg. MAE
Avg. PSNR
Avg. SSIM
Core ablations
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 MAEtissue and is reported in ×103 . 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 pHolm
Δ vs PV-DM
Δ vs PV-Pinv
Single-shot
CSF
MAE ( ×103 )
2.78×10−52
−0.094
−0.153
PSNR
2.78×10−52
11.434
16.549
SSIM
1.37×10−52
0.332
0.554
rweighted
1.37×10−52
0.259
0.477
WM
MAE ( ×103 )
6.01×10−51
−0.165
−0.209
PSNR
1.93×10−48
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 ( Δ ) of DeepPV-MRF relative to each baseline. For MAE, negative values indicate lower error; for PSNR, SSIM, and rweighted , positive values indicate improved performance. Across all post-hoc paired Wilcoxon signed-rank tests, the Holm-adjusted p -value was 6.83×10−20 .
Shot setting
Tissue
MAE ( ×103 ) ( ↓ )
RMSE ( ×103 ) ( ↓ )
Single-shot
CSF
19.25 ± 3.62
43.35 ± 7.50
WM
38.98 ± 7.53
83.00 ± 13.41
GM
55.34 ± 10.12
95.24 ± 15.34
Three-shot
CSF
12.56 ± 3.26
28.90 ± 7.57
WM
29.23 ± 5.24
59.49 ± 9.15
GM
39.88 ± 8.06
69.26 ± 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 ± standard deviation.
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 (T1-weighted, T2-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±0.007 in white matter and 0.144±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.
Jelmer van Lune, Miha Fuderer, Oscar van der Heide +5
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 Fingerprinting (MRF) and other highly accelerated transient-state parameter mapping techniques enable simultaneous quantification of multiple tissue properties, but often suffer from aliasing artifacts due to compressed sampling. Incorporating spatial image priors can mitigate these artifacts, and deep learning has shown strong potential when large training datasets are available. However, extending this paradigm to MRF-type sequences remains challenging due to the scarcity of quantitative imaging data for training. Can this limitation be overcome by leveraging sources of training data from clinically-routine weighted MRI images? To this end, we introduce MRI2Qmap, a plug-and-play quantitative reconstruction framework that integrates the physical acquisition model with priors learned from deep denoising autoencoders pretrained on large multimodal weighted-MRI datasets. MRI2Qmap demonstrates that spatial-domain structural priors learned from independently acquired datasets of routine weighted-MRI images can be effectively used for quantitative MRI reconstruction. The proposed method is validated on highly accelerated 3D whole-brain MRF data from both in-vivo and simulated acquisitions, achieving competitive or superior performance relative to existing baselines without requiring ground-truth quantitative imaging data for training. By decoupling quantitative reconstruction from the need for ground-truth MRF training data, this framework points toward a scalable paradigm for quantitative MRI that can capitalize on the large and growing repositories of routine clinical MRI.
Mohammad Golbabaee, Matteo Cencini, Carolin Pirkl +3
University of Bristol · IRCCS Fondazione Stella Maris · GE Healthcare +2
Quantitative imaging methods, such as magnetic resonance fingerprinting (MRF), aim to extract interpretable pathology biomarkers by estimating biophysical tissue parameters from signal evolutions. However, the pattern-matching algorithms or neural networks used in such inverse problems often lack principled uncertainty quantification, which limits the trustworthiness and transparency, required for clinical acceptance. Here, we describe a physics-structured variational autoencoder (PS-VAE) designed for rapid extraction of voxelwise multi-parameter posterior distributions. Our approach integrates a differentiable spin physics simulator with self-supervised learning, and provides a full covariance that captures the inter-parameter correlations of the latent biophysical space. The method was validated in a multi-proton pool chemical exchange saturation transfer (CEST) and semisolid magnetization transfer (MT) molecular MRF study, across in-vitro phantoms, tumor-bearing mice, healthy human volunteers, and a subject with glioblastoma. The resulting multi-parametric posteriors are in good agreement with those calculated using a brute-force Bayesian analysis, while providing an orders-of-magnitude acceleration in whole brain quantification. In addition, we demonstrate how monitoring the multi-parameter posterior dynamics across progressively acquired signals provides practical insights for protocol optimization and may facilitate real-time adaptive acquisition.
Alex Finkelstein, Ron Moneta, Or Zohar +4
School of Biomedical Engineering, Tel-Aviv University, Tel-Aviv, Israel · Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, Israel · School of Biochemistry, Neurobiology, and Biophysics, Tel-Aviv University, Tel-Aviv, Israel +1