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Improved three component IVIM fitting using physics-informed neural network with multimodal spatial prior

Nhat Hoang, Abrar Faiyaz, Emmanuel A. Mensah, Md Nasir Uddin, Jianhui Zhong, Giovanni Schifitto

arXiv:2610.28873v1eess.IV

TL;DR

Three-component IVIM fitting is challenged by parameter degeneracy, with different parameter combinations producing near-identical signals. PACE integrates IVIM signals with T1w and FLAIR anatomy through cross attention and selective spatial gating, with an anatomy-weighted spatial prior. The reported results show improved parameter reconstruction, while in-vivo parameter RMSE remains uncertain without ground truth.

  • Problem

    Different IVIM parameter combinations can produce near-identical signals, making parameter estimation an ill-posed inverse problem.

    Source: Introduction · p. 3

  • Method

    PACE combines IVIM signals with T1w and FLAIR anatomical context through cross attention and selective spatial integration, with an anatomy-weighted prior constraining signal reconstruction from similar neighbors.

    Source: Introduction · p. 4, §2.6 · p. 7

  • Results

    PACE improved IVIM parameter reconstruction accuracy compared with DNNs and conventional models, while the spatial prior enhanced reconstruction across all five parameters at a moderate cost to perfusion and interstitial lesion contrast.

    Source: CONCLUSION · p. 15

  • Takeaways & Limitations

    The findings support anatomically guided, physics-informed approaches as a proof of concept for future IVIM research.

    Source: CONCLUSION · p. 15

    In-vivo parameter RMSE remains uncertain because signal RMSE is a surrogate benchmark in the absence of ground truth.

    Source: §4.4 · p. 14

Abstract

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Purpose: To mitigate parameter degeneracy and improve robustness of IVIM fitting, a multimodal physics-informed neural network was developed to leverage anatomical information through the combined use of cross attention, selective spatial gating, and anatomy-weighted spatial prior. Methods: T1w and FLAIR anatomical images were co-registered to IVIM signal in native space and segmented by tissue type. The proposed Physics-Anchored Cross-attention Embedding network (PACE) encoded IVIM signals and their anatomical features in parallel branches, then integrated them via cross attention and spatial gating. An anatomy-weighted spatial prior further constrained signal reconstruction using anatomically similar neighboring voxels. PACE and its prior-guided variant were compared with two baseline deep neural networks (DNN and IVIM3C), least squares, non-negative least squares, and maximum a posteriori fitting models. All models were evaluated on signal and parameter reconstruction accuracy and lesion contrast fidelity using data generated from subjects drawn from the University of Rochester COVID cohort. Results: PACE variants demonstrated lower RMSE for all IVIM parameters except for Dmv. The anatomy-weighted spatial prior further reduced RMSE across all five parameters relative to the default PACE, with modest reductions in lesion contrast accuracy for fmv and fint. For in-vivo evaluation, PACE with spatial prior also showed the best signal reconstruction across all noise levels while maintaining good to excellent ICC. Conclusion: Multimodal anatomical information improved IVIM fitting accuracy and robustness, with selective spatial integration via cross attention, gating, and anatomy-weighted spatial prior. Keywords: intravoxel incoherent motion, physics-informed deep learning, diffusion MRI, multimodality fusion, attention mechanism

Introduction

Three-component IVIM fitting is an ill-posed problem: distinct parameter combinations can yield nearly identical signals, and noise further destabilizes estimates. PACE combines T1w and FLAIR anatomy with IVIM signals to address this degeneracy.

Introduction

  • Three-component IVIM adds parameters to an already ill-posed inverse problem, making precise fitting especially challenging at low SNR.Different parameter combinations can produce near-identical signal profiles, and noise can destabilize perfusion estimates.Source: Introduction · p. 3
  • Deep neural networks can improve scalability and noise resilience over traditional IVIM fitting, but unsupervised models may overfit noise and supervised models may be biased toward training populations.These architecture and training concerns motivate additional context for fitting.Source: Introduction · p. 3
  • Multimodal diffusion MRI can improve reconstruction robustness and diagnostic accuracy, but how to integrate anatomical context for IVIM fitting remains unknown.Tissue subtypes may have distinct T1w and FLAIR profiles that help distinguish similar IVIM attenuations.Source: Introduction · pp. 3–4
  • PACE combines IVIM signals with T1w and FLAIR context, using cross attention, selective spatial integration, and an anatomy-weighted prior to improve reconstruction accuracy and tissue-contrast fidelity.The prior regularizes signal reconstruction using anatomically similar neighboring voxels.Source: Introduction · p. 4

Methods

The methods use a 120-subject cohort and construct synthetic and in-vivo data for three-component IVIM fitting. Synthetic examples include tissue-matched spatial context, while in-vivo fitting uses co-registered anatomical images and local neighborhoods.

2.1 Study Population

  • The study population comprised 120 subjects from a long-COVID neurological sequelae study, including 100 with varying white matter hyperintensity severity.The cohort mean age was 69.3 ± 5.1 years; 69 were female and 51 male.Source: §2.1 · p. 4

2.2 MRI acquisition

  • MRI acquisition used a 3T Siemens Prisma Fit scanner, with 1 mm isotropic T1w and FLAIR images and 2.4 mm isotropic IVIM diffusion-weighted imaging.The IVIM sequence used spin-echo EPI at TR/TE = 6800/84 ms; the supplied acquisition passage also lists b-values through 700 and 1000 s/mm².Source: §2.2 · p. 4

2.3 IVIM models

  • The three-component IVIM model represents normalized signal decay using parenchymal, intermediate, and microvascular diffusivities and signal fractions.The parenchymal fraction is constrained by the intermediate and microvascular fractions.Source: §2.3 · pp. 4–5

2.4.1 Synthetic patch creation

  • Synthetic training data used tissue-specific parameter ranges estimated from LSQ fits to about 2.2 million voxels, with one-fifth of patches planted as cross-tissue degenerate pairs.The final split contained 570k training voxels and 38k each for validation and testing, with no voxel overlap across splits.Source: §2.4.1 · p. 5

2.4.2 In-vivo patch creation

  • For synthetic voxels, tissue-matched 3x3 and 5x5 anatomical and IVIM neighborhoods supplied spatial context; in-vivo inference used co-registered T1w and FLAIR images with 3x3 neighborhoods.The in-vivo patches also included b0 and neighborhood IVIM signals.Source: §2.4.1 · p. 5, §2.4.2 · p. 5

2.5 Neural Network Architecture

PACE encodes the center-voxel IVIM signal and T1w/FLAIR neighborhood patches in separate branches, then integrates anatomical context through cross attention. Parameter-specific gates regulate that context before prediction.

2.5 Neural Network Architecture

  • PACE uses a primary center-signal encoder and separate T1w and FLAIR neighborhood encoders, then integrates their features through cross attention and parameter-specific gating.Training uses IVIM signal reconstruction and tissue-classification losses.Source: §2.5 · p. 5

2.5.1 Modality representations

  • The IVIM branch maps the normalized target-voxel signal to a latent vector, while two CNN branches encode T1w and FLAIR neighborhood patches as spatial tokens.Each anatomical encoder uses a two-layer CNN block before flattening and projection.Source: §2.5.1 · p. 6

2.5.2 Cross-attention and spatial context integration

  • Cross attention uses the IVIM representation as query and the T1w/FLAIR latent vectors as keys and values to integrate multimodal spatial context.The query uses a gradient-isolated IVIM representation, so spatial information does not update the IVIM encoder.Source: §2.5.2 · p. 6

2.5.3 IVIM parameter gating mechanism

  • Individualized gates regulate how much attention-derived spatial information is added to each IVIM parameter representation.The gates are initialized to σ(−2), and the parameter fractions are constrained to sum to one after spatial gating.Source: §2.5.3 · pp. 6–7

2.6 Anatomy-weighted spatial prior

The anatomy-weighted spatial prior uses anatomical similarity among neighboring voxels to constrain center-voxel signal reconstruction. Its objective compares the predicted signal with an anatomy-weighted neighborhood signal.

2.6 Anatomy-weighted spatial prior

  • The anatomy-weighted prior constrains the predicted center-voxel signal using anatomically similar neighboring voxels.It targets signal degeneracy without directly constraining IVIM parameters.Source: §2.6 · p. 7
  • Neighbor weights are based on anatomical similarity, and the weighted neighborhood signal supplies the target for the spatial-prior loss.The decay of weights with anatomical dissimilarity is modulated by h = 0.5.Source: §2.6 · p. 7
  • The spatial-prior objective is a mean squared error between the predicted signal and the anatomy-weighted neighborhood signal.This regularizes signal reconstruction rather than directly imposing parameter constraints.Source: §2.6 · p. 7

2.7 Training Objective

The training objective combines IVIM signal reconstruction with auxiliary tissue-classification and spatial losses. Tissue classification is used to encourage discriminative spatial features, while the classifier output and tissue labels do not enter the attention or spatial pathways.

2.7 Training Objective

  • ℒIVIM is the mean squared error between predicted and normalized ground-truth IVIM signals.Source: §2.7 · p. 7
  • Weighted cross-entropy penalizes tissue-classification errors to encourage tissue-discriminative spatial features, while a separate classifier keeps its labels and output out of the attention and spatial pathways.Source: §2.7 · pp. 7–8
  • The total loss adds the IVIM, cross-entropy, and spatial-prior losses, with auxiliary-loss strengths set by tuning coefficients.Source: §2.7 · pp. 7–8

2.8 Model Training Procedure

Synthetic training exposed PACE, DNN, and IVIM-3C to multiple simulated noise levels, and synthetic-trained networks were tested on independent in-vivo data without adaptation. Conventional fitting methods provided additional comparison models.

2.8.1 Synthetic Training

  • PACE, DNN, and IVIM-3C were trained on synthetic signals at 20, 25, 30, and 35 dB, with Rician noise added to synthetic signals.PACE and DNN shared settings except for spatial configuration; tissue labels and the spatial prior were used only during training when enabled.Source: §2.8.1 · p. 8

2.8.2 In-vivo evaluation

  • Networks trained synthetically at 25 SNR were applied to independent in-vivo test data without retraining or fine-tuning.IVIM signals were median-b0 normalized, and T1w/FLAIR intensities were clipped to their 1st–99th percentile range and scaled to [0, 1].Source: §2.8.2 · p. 8

2.8.3 Conventional Models

  • Conventional comparisons included segmented LSQ, NNLS, and MAP fitting, using shared parameter bounds.LSQ first estimated Dpar from b ≥ 200 s/mm2 signals before bounded nonlinear fitting; NNLS used a 200-point logarithmic diffusion spectrum, and MAP used empirical priors from initial LSQ estimates.Source: §2.8.3 · pp. 8–9

2.9 Evaluation Metrics

Evaluation covered reconstruction accuracy, lesion-contrast fidelity, and in-vivo inference stability. The ablation study isolated spatial inputs, fusion, gating, and auxiliary-loss contributions, prioritizing parameter RMSE.

2.9.1 Reconstruction Accuracy

  • Parameter RMSE against synthetic ground truth measured estimation accuracy, while signal RMSE against ground truth measured reconstruction fidelity in synthetic and in-vivo tests.Source: §2.9.1 · p. 9

2.9.2 Lesion Contrast Fidelity

  • Lesion contrast fidelity was quantified as WMH–NAWM contrast-to-noise ratio for each IVIM parameter, using each tissue class’s parameter mean and standard deviation.Source: §2.9.2 · p. 9

2.9.3 Intraclass Correlation Coefficient

  • Inference stability used two-way mixed, single-measurement ICC across five seed initializations, noise levels, and 38 in-vivo subjects; ICC above 0.90 was rated excellent.Source: §2.9.3 · p. 9

2.10 Ablation Study

  • The ablation study removed spatial inputs, attention fusion, gating, or auxiliary losses one at a time and compared parameter RMSE, using lesion CNR secondarily when RMSE was comparable.Source: §2.10 · p. 9

2. 11.1 Synthetic Comparison

Synthetic comparisons assessed parameter RMSE and lesion-contrast fidelity across seven models and four noise levels. Separate hybrid-brain and in-vivo evaluations used distinct ground-truth and reconstruction strategies.

2. 11.1 Synthetic Comparison

  • Seven models were compared for parameter RMSE at 20, 25, 30, and 35 dB, with lesion CNR RMSE and predicted-versus-ground-truth WMH distributions also assessed.Source: §2 · p. 10

2.11.2 Hybrid brain and WMH burden

  • The hybrid brain template retained one high-WMH subject’s T1w, FLAIR, and b0 data, assigned synthetic IVIM parameters sampled from LSQ tissue-class distributions, and evaluated maps at 25 dB.Source: §2.11.2 · p. 10

2.11.3 In-vivo Comparison

  • Because in-vivo parameter ground truth was unavailable, signal RMSE was measured against acquired signals in stratified voxel samples, with WMH voxels included for each subject.Noise levels were varied and signal RMSE and ICC recomputed to assess reproducibility and noise resilience.Source: §2.11.3 · p. 10

Result

PACE with its anatomy-weighted spatial prior generally improved IVIM parameter fitting, while lesion-contrast effects varied by parameter. Across in-vivo noise levels it achieved the lowest signal RMSE, and hybrid-brain results favored it on four of five parameter RMSEs.

3.1 Ablation Results

  • At SNR 25 dB, no ablation consistently improved default PACE; adding b0 or neighboring IVIM inputs raised parameter RMSE, especially for fint and Dpar.Adding b0 raised all five parameter RMSEs; neighboring IVIM signals raised four of five.Source: §3.1 · p. 10
  • Replacing cross-attention with concatenation raised fint RMSE 9.6%; closing gating raised Dpar RMSE 9.7% and fint RMSE 11.4%, while switching off LCE had no noticeable RMSE effect.Increasing the neighborhood from 3 × 3 to 5 × 5 raised all five RMSEs; Dpar and fint were consistently most sensitive to spatial-architecture changes.Source: §3.1 · pp. 10–11

3.2 Anatomy-Weighted Spatial Prior

  • The 3 × 3 anatomy-weighted prior reduced RMSE across all five IVIM metrics, with the largest reductions for Dpar (0.206 × 10^-3 to 0.166 × 10^-3 mm2/s), fint (0.132 to 0.121), and fmv (0.0238 to 0.0202).Smaller improvements occurred for Dint (0.702 × 10^-3 to 0.694 × 10^-3 mm2/s) and Dmv (0.0680 to 0.0636).Source: §3.2 · p. 11
  • Spatial-prior CNR error fell for Dpar (0.229 to 0.0988) and Dint (0.0957 to 0.0758) but rose for Dmv (0.112 to 0.120) and fint (0.0715 to 0.0963); 5 × 5 neighborhoods lowered RMSE for Dpar, Dmv, and fmv but raised Dint and fint.The 5 × 5 neighborhood also produced a pronounced shift in the WMH distribution for fint.Source: §3.2 · p. 11

3.3.1 Synthetic Comparison

  • PACE with spatial prior had the lowest averaged RMSE for Dpar (0.175 × 10^-3 mm2/s), Dint (0.669 × 10^-3 mm2/s), fint (0.126), and fmv (0.0201); IVIM-3C led Dmv (56.1 × 10^-3 mm2/s).Default PACE was a close second for the four parameters; the spatial-prior model ranked second for Dmv.Source: §3.3.1 · p. 11
  • Lesion CNR had no clear winner: MAP led Dpar, NNLS Dint, LSQ Dmv and fmv, and default PACE fint; spatial priors helped Dpar, Dint, and Dmv but reduced fint and fmv fidelity.The prior also shifted Dint and fint distributions closer to ground-truth profiles.Source: §3.3.1 · p. 12

3.3.2 In-vivo comparison

  • PACE with spatial prior had the lowest in-vivo signal RMSE across tissue types and noise levels: 0.0639 at 20 dB and 0.0529 at 35 dB; its advantage was most noticeable at lower SNR.All three evaluated methods had ICC above 0.8 for every parameter; DNN was most consistent except for fint (0.841 versus PACE’s 0.969).Source: §3.3.2 · p. 12

3.3.3 Hybrid brain

  • In the hybrid-brain comparison, PACE with spatial prior had the lowest RMSE for four of five parameters, while IVIM-3C led Dmv RMSE (58.0 × 10^-3 mm2/s) and overall signal RMSE (0.0231).PACE with prior’s largest relative improvements over DNN were Dpar (0.155 × 10^-3 versus 0.237 × 10^-3 mm2/s) and fint (0.111 versus 0.207).Source: §3.3.3 · p. 12

Discussion

The discussion attributes improved three-component IVIM fitting to selective use of anatomical context and an anatomy-weighted spatial prior. It also emphasizes trade-offs in lesion contrast and limits on interpreting in-vivo results.

Discussion

  • Integrating spatial inputs and priors improved IVIM parameter reconstruction accuracy, while lesion contrast fidelity showed moderate trade-offs.The discussion presents anatomy-weighted signal as an approach to address IVIM degeneracy.Source: Discussion · p. 12

4.1 IVIM degeneracy and parameter identifiability for the intermediate component

  • The intermediate component is underdetermined when all three exponential contributions coexist, and PACE variants had lower Dint and fint RMSE than non-PACE models in synthetic evaluation.Sparse sampling in intermediate b-value regimes compounds the identifiability challenge.Source: §4.1 · p. 13

4.2 Architectural ablation and spatial context filtering

  • PACE benefited from selective spatial integration: adding neighboring IVIM signals or removing attention weighting or gating reduced fitting performance.T1w and FLAIR supplied complementary context, and a 3x3 neighborhood appeared sufficient; larger windows did not improve fitting.Source: §4.2 · p. 13

4.3 The Effect of Anatomy-Weighted Spatial Prior

  • The 3x3 anatomy-weighted spatial prior reduced RMSE for all five parameters versus default PACE, but moderately worsened fint and fmv lesion contrast agreement.The 5x5 variant had mixed performance, consistent with larger neighborhoods incorporating less relevant local information.Source: §4.3 · p. 14

4.4 Hybrid Brain and In-vivo Performance

  • On the hybrid brain test, PACE with spatial prior had the lowest RMSE for four of five parameters despite IVIM-3C having the lowest brain-averaged signal RMSE.In vivo, spatial-prior PACE had the lowest signal RMSE across tested noise levels, especially at lower SNR, but signal RMSE was only a surrogate without ground truth; ICC remained good to excellent and generally below DNN.Source: §4.4 · pp. 14–15

4.5 Limitations

  • The study was limited to one cohort and acquisition protocol, depended on accurate segmentation and registration, and did not account for partial-volume effects.Performance may depend on input resolution and on how anatomical contrast relates to IVIM parameter distributions; interactions between the spatial prior and other PACE ablations were not assessed.Source: §4.5 · p. 15

CONCLUSION

  • PACE with the anatomy-weighted spatial prior reduced RMSE across all five IVIM parameters, with a moderate cost to perfusion and interstitial lesion contrast.The conclusion frames these findings as a proof of concept for anatomically guided, physics-informed IVIM fitting.Source: CONCLUSION · p. 15
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