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Abstract

Physics-informed neural networks (PINNs) have shown promise in addressing the ill-posed deconvolution problem in computed tomography perfusion (CTP) imaging for acute ischemic stroke assessment. However, existing PINN-based approaches remain deterministic and do not quantify uncertainty associated with violations of physics constraints, limiting reliability assessment. We propose Evidential Perfusion Physics-Informed Neural Networks (EPPINN), a framework that integrates evidential deep learning with physics-informed modeling to enable uncertainty-aware perfusion parameter estimation. EPPINN models arterial input, tissue concentration, and perfusion parameters using coordinate-based networks, and places a Normal–Inverse–Gamma distribution over the physics residual to characterize voxel-wise aleatoric and epistemic uncertainty in physics consistency without requiring Bayesian sampling or ensemble inference. The framework further incorporates physiologically constrained parameterization and stabilization strategies to promote robust per-case optimization. We evaluate EPPINN on digital phantom data, the ISLES 2018 benchmark, and a clinical cohort. On the evaluated datasets, EPPINN achieves lower normalized mean absolute error than classical deconvolution and PINN baselines, particularly under sparse temporal sampling and low signal-to-noise conditions, while providing conservative uncertainty estimates with high empirical coverage. On clinical data, EPPINN attains the highest voxel-level and case-level infarct-core detection sensitivity. These results suggest that evidential physics-informed learning can improve both accuracy and reliability of CTP analysis for time-critical stroke assessment. Source code is available at https://github.com/jhlee0619/EPPINN.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/3341_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/jhlee0619/EPPINN

Link to the Dataset(s)

ISLES 2018 benchmark: https://www.isles-challenge.org/ Digital brain perfusion phantom (Aichert/Riordan): https://www5.informatik.uni-erlangen.de/research/data/digital-brain-perfusion-phantom/index.html

BibTex

@InProceedings{LeeJun_Evidential_MICCAI2026,
        author = { Lee, Junhyeok AND Choi, Minseo AND Jang, Han AND Jeon, Young Hun AND Eum, Heeseong AND Jang, Joon AND Sohn, Chul-Ho AND Choi, Kyu Sung},
        title = { { Evidential Perfusion Physics-Informed Neural Networks with Residual Uncertainty Quantification } },
        booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
        year = {2026},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 16882},
        month = {September},
        page = {pending}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    This work addresses uncertainty quantification in PINNs for stroke perfusion imaging. The main contribution is the proposal of an evidential deep-learning approach to characterize aleatoric and epistemic uncertainty that outperforms conventional perfusion imaging strategies (SVD and PINN-based ones)

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
    • This work represents a novel revisiting of uncertainty quantification in stroke perfusion PINNs via evidential deep learning.
    • The method proves competitive when comparing it against conventional perfusion approaches and PINN-based ones.
  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    • Authors claim benefits of the proposed methods over Bayesian/ensembling uncertainty quantification approaches. However, a direct comparison against such approaches is missing. How do all these methods compare in speed, uncertainty quantification, and parameter fitting performance?

    • Do authors use a time-invariant SVD algorithm? If not, being the clinical standard, it should be included as a baseline.

  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not provide sufficient information for reproducibility.

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    -

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html

    • Including threshold-free metrics in Table 1 (e. g. ROC-AUC, or PR-AUC) is very relevant to understand the clinical utility of EPINN parameter maps compared with baseline ones. Please include.

    • Table 1- What ‘Det’ means, and how is it calculated?

    • In Fig. 3, authors disregarded SVD-based methods. This is very relevant, as represents the clinical reference. Please include.

    • There is no information on how the AIF network is fit. Where do ground-truth AIF comes from? Do authors annotate them? How? Please provide details.

    • How r(t,x) parametrizes the NIG? A smoother transition in the explanation of this section would help readability. How is C(a,v) defined/obtained?

    • There is no information at all about the code reproducibility of this work.

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    There is some novelty in the evidential deep learning uncertainty quantification proposed approach; however, the lack of baseline comparison with other uncertainty quantification methods, as well as some minor ambiguities in the paper (see other comments) discourage a clear acceptance.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Review #2

  • Please describe the contribution of the paper

    The authors present EPPINN, a physics-informed neural network for inverse modeling in CT perfusion that augments output predictions with evidential uncertainty estimates. They use a three network approach where one network fits the arterial input function (AIF), a second network fits the tissue concentration curve, and a third network outputs target parameters of the inverse problem and uncertainty estimation. They evaluate their framework on three dataset including a synthetic brain phantom, the ISLES 2018 benchmark, and a third retrospective clinical dataset. They compare their method to several baselines included two variants of SVD, a nonlinear regression model, and two alternative PINN frameworks. Their method consistently outperforms the baselines in accuracy on the phantom set and shows some evidence of desirable properties on clinical data, though evaluation of uncertainty is limited.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
    • Well-motivated clinical application and clear attention to key issues of identifiability and uncertainty in ill-posed inverse problems.
    • Interesting modeling approach involving residual uncertainty. Key idea of modeling uncertainty in the physical residual rather the predictions is conceptually attractive when combining with messy data and incomplete physics.
    • Thorough evaluations on both phantom and clinical datasets with comparison to several baselines with varying levels of complexity and similarity to the proposed method.
    • Includes robustness and ablation analyses showing impact of noise, sparsity, and modeling choices.
    • Good application of background knowledge and practical solutions to stabilize training.
  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    • Weak justification for uncertainty estimates. The method applies the Deep Evidential Regression framework to the physical residual, which claims to decompose uncertainty into aleatoric and epistemic components. But there is little prior justification or empirical validation of this decomposition in the work. The is a result showing “high empirical coverage” on the phantom data is limited and does not investigate the epistemic/aleatoric decomposition.
    • Unclear accuracy/performance tradeoff. It is claimed that their methods requires “under 1 min per case after AIF pre-training”, which is quite surprising for training a PINN and warrants elaboration. How long does pre-training take? What is the end-to-end runtime for inversion of a single case, and how does it compare to the baselines?
    • Ablation result is unclear. The proposed model does not consistently outperform the one without “physics-informed initialization.” The authors claim this is attributable to a numerical stability/accuracy tradeoff. If there is a significant difference in data missingness in the reported results due to instability, these numbers should be included to justify the proposed initialization scheme.
    • Evaluation protocol ambiguity. No mention of hyperparameter optimization is included, and it is not mentioned if evaluation involved test data held-out from hyperparameter selection.
    • No reference to codebase and insufficient details to fully reproduce algorithm without access to code.
  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not provide sufficient information for reproducibility.

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    N/A

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The paper addresses a clinically relevant problem by incorporating uncertainty modeling into physics-informed neural networks for CT perfusion analysis. The framework is well motivated and shows promising empirical results in synthetic and clinical evaluations. However, the central methodological contribution of evidential uncertainty modeling is insufficiently justified. The interpretation of the predicted aleatoric and epistemic uncertainty quantities are not theoretically or empirically validated. The uncertainty evaluation is limited and does not establish calibration of the predicted aleatoric and epistemic uncertainty estimates. Additional concerns include unclear accuracy vs. runtime tradeoff compared to baselines, ambiguous ablation results, and unclear evaluation protocol. The approach is conceptually interesting and empirical results are good, but the core contribution of uncertainty modeling requires additional validation.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    Accept

  • [Post rebuttal] Please justify your final decision from above.

    The authors adequately resolved that outstanding concerns with the paper. Runtime and evaluation protocol were clarified, ablation inconsistency was addressed, and reproducibility was promised through future code release. The paper addresses an important problem with strong empirical results, and the rebuttal resolved sources of ambiguity.



Review #3

  • Please describe the contribution of the paper

    The paper introduces EPPINN, an uncertainty-aware physics-informed framework for CT perfusion (CTP) analysis in acute ischemic stroke. The method combines coordinate-based PINNs for arterial input and tissue concentration modeling with an evidential formulation that places a Normal–Inverse–Gamma distribution over the physics residual, allowing decomposition into aleatoric and epistemic uncertainty without Bayesian sampling or ensembles. The model also incorporates several stabilization choices, including CBV–MTT parameterization, AIF pre-training, adaptive spatial encoding, and annealed evidential loss. The paper evaluates the method on digital phantom data, ISLES 2018, and a clinical cohort, reporting improved perfusion estimation under noisy or sparse sampling settings and higher infarct-core detection sensitivity than classical deconvolution and PINN baselines.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    The paper addresses a meaningful problem in stroke imaging: CTP deconvolution is ill-posed, noise-sensitive, and clinically high-stakes, so adding uncertainty awareness to a physics-informed approach is well motivated. Methodologically, the idea is interesting and reasonably novel: instead of only producing deterministic PINN estimates, the model explicitly quantifies uncertainty in physics-constraint satisfaction in a computationally efficient way. The paper is also technically coherent. The architecture, loss formulation, and stabilization strategies are clearly described, and the visual overview in Fig. 1 helps make the design easy to follow. The empirical section is fairly broad, spanning controlled phantom experiments, ISLES, and a small clinical cohort, and the phantom results and coverage plots in Fig. 2 support the claim that the method is more robust under sparse temporal sampling and low SNR. The qualitative maps in Figs. 3 and 4 also suggest smoother and more coherent outputs than prior PINN baselines.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    The main weakness is that the paper’s empirical validation is only partially convincing despite a strong conceptual setup. The reported clinical and benchmark evaluation emphasizes sensitivity alone for infarct-core detection, with an absolute CBF threshold of 25 ml/100g/min used for binarization, but the paper provides little discussion of the tradeoff with specificity, false positives, lesion over-segmentation, or calibration of the final clinical decision map. A method can achieve high case-level sensitivity by overcalling abnormal tissue, and the manuscript does not provide enough complementary metrics to rule this out. This is especially relevant because the qualitative examples in Fig. 3 suggest visual smoothness and broad deficits, but smoothness alone does not establish superior clinical delineation.

    The second weakness is that the uncertainty story, while appealing, remains somewhat underdeveloped. The method quantifies uncertainty over the physics residual, not directly over the estimated perfusion parameters or infarct-core predictions, and the paper does not fully clarify how clinicians should interpret or use these uncertainty maps in practice. The empirical calibration check in the phantom setting is useful, but it is limited to residual uncertainty coverage under selected settings and does not establish that uncertainty is well calibrated or decision-relevant on the clinical datasets. The paper therefore argues for improved reliability, but the evidence for clinically meaningful reliability gains is still somewhat indirect.

    There are also some concerns about the fairness and completeness of the comparisons. The baselines include SVD, bcSVD, boxNLR, SPPINN, and ReSPPINN, which is sensible, but the paper does not make entirely clear whether all methods were equally tuned for each dataset and acquisition regime. Although the paper evaluates on three datasets, the real clinical validation is still limited by the relatively small clinical cohort (n = 42). In addition, the ablation table presents some results as unstable and excluded from ranking, and one row reports values of exactly 1.00 across CBF regions for “w/o Annealing,” which is unusual and would benefit from explanation. More broadly, some of the gains, particularly in the phantom ablations, seem driven by engineering choices for optimization stability rather than by the evidential formulation alone, so the paper could do more to disentangle what comes specifically from evidential learning versus what comes from careful PINN training design. While the paper is generally well written, some claims are stronger than the evidence currently supports. For instance, the conclusion suggests enhanced “accuracy and reliability,” but the reliability evidence is mostly based on conservative residual-uncertainty coverage and qualitative maps rather than a rigorous clinical uncertainty evaluation. I think the paper is still good because the problem is important, the method is thoughtful, and the results are promising, but the experimental framing and uncertainty validation are not yet fully complete.

  • Please rate the clarity and organization of this paper

    Satisfactory

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    N/A

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    I recommend a Weak Accept (4) for this paper. The main reason is that the paper addresses an important and clinically relevant problem in acute stroke imaging, and the proposed method is both technically interesting and reasonably well motivated. In particular, extending PINN-based CT perfusion modeling with an evidential formulation for uncertainty-aware residual modeling is a meaningful idea, and the paper presents a coherent framework that combines physics-informed learning, structured parameterization, and optimization stabilization in a practical per-case inference setting. The evaluation is also reasonably broad, spanning digital phantom experiments, ISLES 2018, and a clinical cohort, and the results suggest improved robustness under sparse temporal sampling and low-SNR conditions, along with stronger infarct-core detection sensitivity than the included baselines. At the same time, I did not score it higher because several parts of the empirical validation remain somewhat incomplete. The clinical evaluation emphasizes sensitivity, but provides limited analysis of specificity, false positives, over-segmentation, or broader clinical calibration, making it harder to judge the practical tradeoffs of the method. In addition, the uncertainty formulation is appealing, but the paper mainly validates uncertainty through residual coverage in phantom experiments and qualitative maps, rather than demonstrating how uncertainty improves downstream clinical decision-making. Although the evaluation includes three datasets, the real clinical validation is still limited by the relatively small clinical cohort, and the paper could do more to disentangle which gains come specifically from the evidential formulation versus the other stabilization components. Overall, I found the paper promising, but not yet strong enough for a clearer accept.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    Accept

  • [Post rebuttal] Please justify your final decision from above.

    I support acceptance because the paper makes a meaningful technical contribution by integrating evidential uncertainty quantification into a physics-informed CT perfusion framework while preserving a practical per-case runtime. The original submission was promising but had several weaknesses in evaluation and presentation. The rebuttal addressed the most important of these constructively: the authors clarified that additional specificity/precision and ROC-AUC/PR-AUC metrics will be added, provided more detail on the uncertainty decomposition and calibration behavior, explained the anomalous ablation results, and clarified the evaluation and hyper-parameter protocol. I still view some limitations as unresolved, particularly the lack of direct Bayesian/ensemble uncertainty baselines and the modest size of the clinical cohort. However, these now read as limitations of scope rather than flaws that invalidate the contribution. Overall, I believe the paper is above the acceptance threshold and recommend Accept.



Review #4

  • Please describe the contribution of the paper

    The paper proposes a method for CT perfusion parameter estimation that combines physics-informed neural networks with evidential learning. It addresses the deterministic nature of existing PINN-based methods for CTP estimation by introducing uncertainty quantification for residual estimation through evidential learning. In addition to the evaluation of estimation error, experimental validation is performed to evaluate the impact of estimated parameters on the downstream task of infarct core detection in ischemic stroke lesions.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
    • The application of evidential learning + PINN for CT perfusion estimation is novel. Evidential learning-based uncertainty estimation is proposed as a mechanism to assess the reliability of predictions in the presence of noise and violations of physics constraints.
    • The authors have demonstrated the robustness of the proposed method. They show than the estimated perfusion parameters degrade gradually with increasing noise and poor sampling conditions. This is notably better than the existing methods where the error increases drastically.
    • The authors have demonstrated the impact on the downstream task of infarct core detection in ischemic stroke lesions. Compared to baselines, the detection improves both in a benchmark dataset and a clinical cohort.
    • The ablation study across ROIs demonstrates how design choices impact performance.
  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    • One major weakness of the paper is that the proposed method is only compared against deterministic approaches. In the absence of uncertainty-aware baselines, the evaluation can assess performance only relative to having no uncertainty estimation, rather than the quality of the uncertainty quantification itself.
    • While the authors show improvement in performance of the downstream task, the evidence provided is weak. Only sensitivity scores (case-level and voxel-level) are reported. This does not sufficiently demonstrate the clinical relevance of the improvement in parameter estimation.
    • The proposed uncertainty-aware residual estimation is motivated as capturing deviations from physics constraints. However, the experimental validation is limited to matched modeling assumptions and therefore does not demonstrate the robustness of the uncertainty estimates.
  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    N/A

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (5) Accept — should be accepted, independent of rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The paper presents a novel application of evidential physics-informed neural networks for uncertainty-aware CT perfusion parameter estimation. Experimental validation supports the technical soundness of the methods. Superior robustness of the proposed method to noise and sampling intervals is demonstrated. However, there are some gaps in the evaluation which raise concerns about clinical outcomes and generalizability.

  • Reviewer confidence

    Very confident (4)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Author Feedback

We thank the reviewers and respond by theme.

A. Bayesian/ensemble UQ baselines & runtime (R1.5a, R5.5a-i, R2.5b). Stroke triage is time-critical. With ~1.9M neurons lost per minute of delay [Saver, Stroke, 2006] and reperfusion benefit decaying within 4.5-24 h, the per-case budget is tight. HMC/VI BPINN and deep ensembles require repeated optimization or sampling at >=10x per-case cost. On RTX 3090, EPPINN runs ~50 s/case (AIF ~5-6 s, joint ~42 s), comparable to SPPINN/ReSPPINN. SVD/bcSVD/boxNLR are seconds-scale. Our contribution is single-pass UQ within this budget, and we plan a direct BPINN/ensemble comparison as the next step.

B. Sensitivity, specificity, AUC (R1.10a, R4.5a, R5.5a-ii). In acute triage, missed cores preclude reperfusion and dominate risk over over-segmentation. We prioritize core-detection at the validated CBF<25 ml/100g/min threshold [Murphy, AJNR, 2007], applied uniformly so the comparison reflects map quality, not threshold engineering. Det = case with CBF/DWI core overlap. EPPINN reduces missed cases, with case-level Det 43/93 (ISLES) and 41/42 (clinical), vs 38/93 and 38/42 for boxNLR. Voxel sensitivity follows, 0.32 vs <=0.26 ISLES (+24% rel.) and 0.74 vs <=0.41 clinical (+83% rel.). A sens-spec tradeoff is inherent at any fixed threshold. We agree. Specificity and precision will be added to Table 1, and ROC-AUC/PR-AUC reported as secondary threshold-free metrics in the revised manuscript.

C. Calibration, aleatoric/epistemic split (R2.5a, R4.5b, R5.5a-iii). On the phantom data of Fig. 2, Spearman rho(sigma_r, |r|)=0.66.The 1-sigma coverage is 87.0% and 2-sigma 95.6%, conservative and monotone. By construction sigma_ale=beta/(alpha-1) and sigma_epi=sigma_ale/nu. sigma_ale dominates under low SNR, and sigma_epi is elevated near vessel and tissue boundaries where the box-residue assumption is most strained (Fig. 4 right). Rho and the per-component breakdown will be folded into Fig. 2. D. Ablation (R2.5c, R4.5d). We agree this row is anomalous. The “w/o Annealing” CBF row of 1.00 is a placeholder marking divergent training, because applying the full evidential weight from step 0 (no annealing) makes CBF training fail to converge (raw NMAE in the 5-9 range). The dagger excludes this row from ranking, and the revised caption will replace 1.00 with the raw values. “w/o Phys-init” carries the same dagger, winning on isolated ROIs but unstable across cohorts (more convergence failures, worse rank). This is the stability/accuracy tradeoff in Sec. 2.3(4).

E. HP & evaluation protocol (R2.5d). All hyperparameters (lr, lambdas, annealing, net sizes) were fixed on the digital phantom and applied without further tuning to ISLES and clinical. An identical training budget (lr, batch, iters) is used across SPPINN/ReSPPINN/EPPINN. SVD/bcSVD/boxNLR have no neural-network HPs. ISLES and the clinical cohort serve as de facto held-out tests.

F. Code release (R1.7, R2.5e, R1.10f). We will release source code (training, inference, baselines, evaluation) upon acceptance.

G. R1 specifics. [R1.5b/10c] SVD. The paper already includes both time-variant SVD [Ostergaard, MRM, 1996] and block-circulant time-invariant bcSVD [Wu, MRM, 2003]. We will add SVD/bcSVD to Fig. 3 alongside boxNLR. [R1.10d] AIF GT. Clinical AIF was extracted from manually annotated ROIs in ICA/MCA-M1.ISLES uses RAPID-derived AIF curves released with prior PINN-CTP work [de Vries, Medical Image Analysis, 2023], while the phantom uses the analytic curve, and f_AIF fits these via L1 loss. [R1.10e] NIG. f_par outputs (alpha, beta, nu) via softplus+eps. r(t,x) is the observed residual. Under NIG, variance follows Inv-Gamma(alpha, beta) and mean follows N(0, variance/nu). C(alpha, nu) gathers r-independent NLL terms.

H. Cohort n=42 (R4.5c). We acknowledge it is modest. The cohort uses a uniform protocol with paired DWI and complements ISLES (n=93) for a total of 135 cases, with multicenter validation ongoing.



Meta-Review

Meta-review #1

  • Your recommendation

    Invite for Rebuttal

  • Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.

    This paper proposes an evidential physics-informed neural network for CT perfusion analysis that models uncertainty in the physics residual.

    Reviewers agree the problem is important, and the approach is novel with promising results, but raise concerns about insufficient validation of the uncertainty formulation, missing or incomplete baseline comparisons (especially uncertainty-aware methods), and limited clinical evaluation and metric reporting. I suggest that the authors clarify these points in the rebuttal.

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation.

    The authors provided a constructive rebuttal, and there is consensus among the reviewers that the paper addresses an important problem in CT perfusion analysis with a novel and promising framework. The rebuttal clarified the main concerns regarding uncertainty calibration, runtime, evaluation protocol, ablation results, and additional clinical metrics. I therefore recommend acceptance.

    Some limitations remain, particularly the lack of direct comparison with Bayesian or ensemble-based uncertainty methods and the modest size of the clinical cohort. I encourage the authors to discuss these limitations clearly and to release the code as stated.



Meta-review #2

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation.

    agree with the reviewers



Meta-review #3

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation.

    All reviewers indicated acceptance post-rebuttal. The single-pass evidential UQ contribution is novel and the runtime justification for omitting Bayesian/ensemble baselines is reasonable.



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