{"id":"a954dca9-53bf-417f-b582-7ccc6e8e310d","arxiv_id":"2505.03382","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A PINN-based method recovers active contractility parameters and detects fibrotic scars in simulated cardiac tissue from sparse displacement and strain data, with a few percent error in homogeneous tests.","lead":"This paper tests a physics-informed neural network that estimates how strongly heart muscle tissue contracts from sparse, noisy movement data. It works on simulated heart-tissue cubes, including detection of scarred regions, but has not yet been tested on real patient data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Time-dependent scar detection relies on the untested factorization σ0(x)S1(t); regional activation delay is confounded with reduced contractility, so the central generalization is not yet supported.","rationale":"The paper is a serious in-silico methods study: the FEM forward solver is high-fidelity, the optimization pipeline is described in enough detail to reproduce (modulo missing code/seeds), losses are ablated, and multi-seed ensembles are reported. The central numerical demonstrations for the cases actually run are credible. My concern is not with internal consistency of those runs. It is that the headline generalization to 'time-dependent scenarios' with spatially-varying contractility silently imports the factorization σ0(x)S1_a(t). The authors explicitly note in §2.1.1 that Sa(t;x) is space-dependent in general, but then in §3.1.2 they exploit the decoupling without testing the case where the temporal profile itself varies. Since the ODE (2) is linear in σ0 but the control a(t) determines the waveform, a regional delay enters multiplicatively at any observation time and is therefore indistinguishable from a regional change in σ0 unless the full time course is used with a model that includes τ(x). Scar tissue is precisely where conduction and activation are altered, so this is not a remote edge case. The reader's weakest_assumption identifies exactly this point, and I agree. The recommended verdict remains CONDITIONAL: the method is promising and the reported experiments support the quasi-static heterogeneous and time-dependent homogeneous claims, but the unified central claim should be conditioned on a global activation time course (or extended to estimate or test τ(x)). Secondary issues, such as threshold selection using ground-truth-informed FPR/FNR, reinforce the need for careful claims but do not change this assessment.","tokens_in":23300,"tokens_out":6843,"duration_ms":75550,"concrete_test":"Generate a time-dependent ground truth with uniform σ0=118 kPa but a regional activation delay: replace a(t) by a(t−τ(x)) in Eq. (2), with τ(x)=40 ms inside the spherical scar volume of §3.2.1 and τ=0 elsewhere. Use the same Section 3.1.2 data protocol (displacement on five y-slices, 10,000 points, LD=0.05 noise, same Adam/BFGS schedule and hyperparameters) and run the NNσ0 pipeline exactly as described. If the estimated σ0 field contains a low-contractility region matching the delayed volume, or if the reported L1 relative error exceeds the ≈2% of Table 5 by a substantial margin, the factorization is the load-bearing limitation for time-dependent scar detection. If the recovered field is uniform within the Table 5 noise band, the concern is resolved for this regime.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In §3.1.2 the time-dependent inversion is made tractable by the factorization Sa(t;x)=σ0(x) S1_a(t), where S1_a(t) is the solution of Eq. (2) for σ0=1 with one global control a(t). Because Eq. (2) is linear in σ0, this factorization is exact only if the activation time course is the same at every material point. In cardiac tissue this need not hold: regional activation delay (dyssynchrony, slowed conduction around scars) shifts the control to a(t−τ(x)). During the systolic observation window 160–350 ms, S1_a(t) varies strongly, so a delay is mathematically confounded with an amplitude change: at any fixed t the recovered field would be σ0(x) S1_a(t−τ(x))/S1_a(t), which can create a spurious low-contractility (scar-like) region even when σ0 is uniform. The paper's time-dependent experiments treat only homogeneous σ0 (§3.1.2), while the scar reconstructions are quasi-static (§3.2), so no experiment exercises this confound. The central claim that the method estimates spatially-varying active contractility in time-dependent scenarios from displacement/strain data is therefore under-supported: it holds under the factorization assumption, but that assumption is both physiologically nontrivial and untested here.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a physics-informed neural network (PINN) methodology for estimating the active contractility of cardiac tissue from sparse, noisy displacement and strain measurements. The forward model is a three-dimensional, time-dependent hyperelastic biomechanical model with an active-stress term governed by a Bestel-Clément-Sorine ODE. The unknown maximum active stiffness σ0 is either a scalar trainable parameter or a neural-network field, and the displacement field is represented by a separate network. The reconstruction is formulated as an energy minimization with data, PDE-residual, and boundary losses, augmented with Fourier features, residual-based attention, exact Dirichlet boundary enforcement, and a complementary-weight regularization of the parameter network near the Dirichlet boundary. Experiments on an idealized 10 mm cube cover quasi-static and time-dependent homogeneous cases, and quasi-static heterogeneous cases with one or two spherical scars. The reported results show small L2 errors in displacement and parameter estimates at noise levels up to LD = 0.05, and qualitative scar reconstructions after thresholding.","tokens_in":23627,"tokens_out":7026,"duration_ms":70014,"significance":"If the results hold, the paper offers a useful step toward non-invasive scar identification from imaging-like data without stress measurements. The manuscript has concrete strengths: it systematically ablates weighting schemes (Section 2.4 and Appendix S-2), compares exact versus weak boundary enforcement (Appendix S-4), analyzes robustness to boundary-condition misspecification (Appendix S-5), and reports multi-seed runs with geometric-mean trajectories. The apparent-Pareto-front analysis for the scalar case is a practical contribution to PINN hyperparameter selection. However, the current evidence is a self-consistency check on an idealized cube geometry: the FEM ground truths are generated with the same constitutive and active-stress models used in the physics loss, and the central time-dependent spatial-parameter claim is not exercised by any experiment. The clinical relevance suggested by the Introduction and Conclusion therefore rests on additional, untested assumptions.","major_comments":[{"comment":"The parametrisation Sa(x,t)=σ0(x) S1_a(t), introduced in §2.1.1 and used throughout §3.1.2, is load-bearing for the time-dependent claim, but it is only exact if the activation time course a(t) is the same at every material point. Regional activation delays (e.g., around scars or in dyssynchrony) replace a(t) by a(t−τ(x)); because S1_a(t) varies strongly over the systolic window 160–350 ms, a delay τ(x) is confounded with an amplitude change, so a uniform σ0 could be reconstructed as a spurious low-contractility region. The time-dependent experiments in §3.1.2 treat homogeneous σ0 only, and the heterogeneous scar reconstructions in §3.2 are quasi-static, so no experiment exercises this confound. The Introduction's claim that the method 'enables the estimation of spatially-varying active contractility properties both in quasi-static and time-dependent scenarios' is therefore supported only under a physiologically non-trivial assumption that is not tested. I recommend adding a time-dependent heterogeneous test case with regional activation delay (or with different activation time courses per region) and, if the confound persists, tempering the claim accordingly.","section":"§3.1.2, Tables 3–5"},{"comment":"The robustness results are reported only for 'successful seeds' while the text states that each test case was run with ten seeds in total (e.g., Table 4: 7/10 noiseless and 6/10 noisy; Table 5: 8/10 and 9/10). Since the success criterion is not defined, the reader cannot tell whether the excluded seeds failed to converge, found a wrong local minimum, or were discarded for other reasons. Averaging over the survivors alone overstates the method's robustness and the reported uncertainty. Please define the success criterion a priori, report outcomes for all ten seeds (including failures), or provide a failure-mode analysis; this is needed to substantiate the paper's robustness claims.","section":"§3.1.2, Tables 3–5"},{"comment":"The classification threshold T for scar detection is selected by minimising the total misclassification rate on the same test cases for which classification accuracy is reported (Figures S7–S8, with T≈50 kPa). This is an in-sample hyperparameter choice, so the reported false-positive/false-negative behaviour in Figures 7 and 9 is optimistically biased and does not estimate generalisation to new scar geometries or tissue proportions; Appendix S-6 itself notes that the optimal threshold depends on the relative proportions of healthy and scarred tissue. Please evaluate the threshold on a hold-out set (or via cross-validation) and report classification metrics as a function of T on unseen cases.","section":"Appendix S-6 and §3.2.1–3.2.2"},{"comment":"Because the observation data are produced by FEM solutions of the same governing equations (Eq. (1)) and the same active-stress model (Eq. (2)) used in the PINN loss, the benchmarks are a self-consistency check rather than an external validation of the constitutive or active-stress modeling assumptions. This is an appropriate scope for a first methods paper, but the Introduction and Conclusion should state this limitation explicitly and avoid wording that suggests immediate applicability to clinical data.","section":"§3.1 and §3.2"}],"minor_comments":[{"comment":"The main text and Appendix S-6 state that the optimal classification threshold is approximately 50.00 kPa, but Figure S7's caption reports the optimal threshold as 34.3 kPa for the single-scar case. Please reconcile this inconsistency.","section":"Section 3.2 and Appendix S-6"},{"comment":"The caption of Table 3 reports an 'L1 relative error on Sa,' while Tables 1, 2, 4, and 5 do not specify the norm used; please state consistently which norm is used for each reported parameter error.","section":"Tables 1, 3, 4, 5"},{"comment":"The handling of the initial condition for the time-dependent PDE is not fully specified: 100 data points at t = 160 ms are mentioned, but Eq. (1) requires both u(0) and v0; please state whether velocity data are used and how the implicit initial condition is enforced in the loss.","section":"Section 3.1.2"},{"comment":"The main text says the modified boundary loss plus R2 regularization 'effectively reduces' the identifiability problem, while Appendix S-3 states that it mitigates the issue only 'to some extent' and that artifacts remain near the edges; please make these statements consistent.","section":"Section 2.3.2 and Appendix S-3"},{"comment":"No quantitative classification metrics (e.g., Dice coefficient, FPR/FNR) are reported in the main text for the scar cases, so the central scar-detection claim rests on qualitative figures; please add numeric metrics.","section":"Section 3.2"},{"comment":"The paper does not include a data/code availability statement. Since the study is fully in silico and uses the open-source carputils/carpentry framework, please state whether scripts and trained configurations will be released to support reproducibility.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of a computational-mechanics or machine-learning journal, and I see no evidence of misconduct. The main gap is the mismatch between the broad claims in the Introduction and Conclusion and the tested configurations: time-dependent spatial heterogeneity is not actually exercised, and the reported robustness is based on selective seed reporting. Both issues are fixable with additional experiments and revised claims, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent in-silico methods paper and it deserves a proper review, but the abstract and introduction oversell what the time-dependent experiments actually show. The genuinely new bit is the extension of the authors' earlier passive-property PINN work to active contractility, with a two-network formulation, Fourier features on the parameter network, boundary identifiability regularization, and a scar-detection post-processing step. On the cube geometry the reconstructions are clean, the error numbers are low, and the engineering comparisons — Pareto-front weight analysis, adaptive weighting versus residual-based attention, exact versus weak Dirichlet enforcement, and robustness to Robin boundary misspecification — are useful and honestly reported.\n\nThe soft spots are real, and one is load-bearing. The time-dependent claim is only tested with a homogeneous sigma0. The scar reconstructions are quasi-static. So the statement that the method estimates spatially-varying active contractility in time-dependent scenarios is not supported by the experiments. More fundamentally, the model factorizes Sa(t;x) = sigma0(x) S1_a(t), which is exact only when the activation time course is identical everywhere. Regional activation delay — relevant in dyssynchrony and around scars — would be confounded with reduced amplitude, producing scar-like artifacts. The paper does not test or acknowledge this.\n\nThree smaller issues. First, several tables report only the number of successful seeds (6–9 of 10), with no explanation of what happened to the rest; that matters for a method whose convergence is seed-dependent. Second, the classification threshold is selected on the same test cases used to evaluate misclassification, and the paper is internally inconsistent: Section 3.2 says the optimal threshold is about 50 kPa, while Figure S7's caption gives 34.3 kPa. Third, the benchmark is a self-consistency check — FEM data generated with the same constitutive and active-stress models that enter the PINN physics loss — and no baseline against classical PDE-constrained optimization or data assimilation is included.\n\nNone of this sinks the paper. For what it is — a careful in-silico demonstration on an idealized geometry — it is sound and well written. The authors should release code and data, report all seeds, fix the threshold inconsistency, and either add a time-dependent heterogeneous experiment with regional activation delay or explicitly state the factorization as a limitation. I would send it to peer review, with major revision requests along those lines.","headline":"Solid in-silico methods paper on PINN-based active contractility estimation; the central time-dependent heterogeneity claim is not yet tested because all time-dependent runs use a spatially uniform parameter and the assumed space-time factorization excludes local activation delays.","tokens_in":24125,"tokens_out":3140,"would_cite":false,"duration_ms":32409,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A physics-informed neural network can reconstruct the spatially varying contractility of heart muscle—including the location and shape of fibrotic scars—from sparse, noisy displacement and strain data alone, with no stress measurements.","keywords":["physics-informed neural networks","cardiac biomechanics","active stress estimation","inverse problems","scar detection","Fourier features","parameter estimation","time-dependent elasticity"],"falsifier":"A decisive test: simulate the same contraction model with two regions that activate at different times, feed the network only displacement and strain data, and threshold the recovered $\\sigma_0(\\mathbf{x})$ field; if the late-activating region shows up as a spurious low-contractility scar, the single-time-profile assumption marks the boundary of the method’s validity.","tokens_in":23119,"feed_emoji":"🫀","tokens_out":14078,"duration_ms":127012,"temperature":0.7,"pith_summary":"This paper tries to establish that one can infer the local strength of cardiac muscle contraction from the kind of data medical imaging actually provides: displacement and strain fields sampled at limited points, possibly on parallel slices and corrupted by noise, without ever measuring stress. It does this by fitting two neural networks—one for the displacement field and one for the contractility field—to an energy-minimisation problem that balances data misfit against the residual of the cardiac mechanics equations. If the claim holds, a single training run can produce a spatially resolved map of contractility from cine- or tagged-MRI-like data, and that map can be thresholded into healthy tissue, scar core, and grey zone. The study is in-silico: all ground truths come from finite-element simulations on a cuboid tissue sample, so the claim is about feasibility of the inversion strategy rather than clinical validation.","feed_headline":"Neural nets map heart contractility from sparse MRI-like data","feed_subtitle":"An in-silico study recovers contractility fields and scar shapes from noisy displacement and strain data.","key_machinery":"The central mechanism is the factorisation of active stress into a space-dependent amplitude and a known time profile, $S_a(t;\\mathbf{x})=\\sigma_0(\\mathbf{x})\\,S^1_a(t)$, where $S^1_a$ is the solution of the scalar active-stress rate equation with unit amplitude. Because the parameter enters linearly, the inverse problem reduces to recovering one scalar field instead of a full spatio-temporal activation history. That field is represented by a second neural network trained jointly with the displacement network; Fourier feature embeddings on the parameter network counteract spectral bias, a distance-function layer enforces the Dirichlet boundary exactly, and a gradient-based regularisation weighted away from the Dirichlet face restores identifiability of $\\sigma_0$ near that boundary. Residual-based attention on the PDE loss stabilises the resulting multi-objective optimisation.","core_discovery":"The paper claims that a physics-informed neural network, given displacement measurements (and, for heterogeneous fields, additional strain measurements) sampled on a few parallel slices of cardiac tissue, can recover the spatially varying active-stress parameter $\\sigma_0(\\mathbf{x})$ that drives contraction, in both a quasi-static approximation and the full time-dependent momentum equation. The key reduction is that the active-stress rate equation has the rescaling property $S^{\\sigma}_a(t)=\\sigma\\,S^1_a(t)$, so the temporal shape of contraction is computed once and the inverse problem becomes the estimation of the scalar field $\\sigma_0(\\mathbf{x})$. In the reported in-silico tests the field is recovered with relative errors of a few percent even at noise level $LD=0.05$, and thresholding the reconstructed field locates simulated fibrotic scars and their surrounding grey zones without stress data and without prior shape assumptions.","pith_inferences":["A natural extension the paper does not run: allow the activation timing itself to vary spatially, and try to estimate $t_{\\mathrm{sys}}(\\mathbf{x})$ as an additional field; the same two-network construction could turn the single-time-profile limitation into a diagnostic for dyssynchrony.","Because the optimal classification threshold depends on the relative proportions of healthy and scarred tissue, clinical use would likely need an adaptive threshold chosen from the reconstructed field’s histogram rather than the fixed 50 kPa value used here.","The space–time factorisation of the parameter should transfer to any constitutive parameter that enters the stress linearly with a known temporal envelope, so the approach may generalise beyond cardiac active stress to other contractile materials.","The seed-to-seed spread of the reconstructed fields, which the paper reports as trajectory-spanned areas, could be converted into a pixel-wise confidence map for scar boundaries, giving clinicians an uncertainty estimate alongside the thresholded classification."],"forward_implications":["At the tested noise levels, up to an $LD=0.05$ limiting dispersion, the contractility parameter is recovered to within roughly 1–6% relative error in both quasi-static and time-dependent cases, with displacement fields recovered to 2–5% $L^2$ error.","Simulated scars, including a core surrounded by a grey zone, are located by thresholding the reconstructed contractility field at about 50 kPa, with only minor misclassification and a slight underestimation of the scarred area.","Stress data are never needed; the heterogeneous cases use displacement plus strain, and the paper notes that strain can be obtained from tagged-MRI or derived from displacement data in post-processing.","Because the temporal activation profile is precomputed once from a scalar ODE and the architectures are tailored to the problem, the method requires fewer training points and epochs than previous PINN-based inversions in elasticity.","Exactly enforcing the Dirichlet boundary and applying the weighted gradient regularisation mitigates a known failure of active-stress identifiability near the fixed boundary, and the results are robust to mis-specification of the boundary condition as a Robin condition with an uncertain spring stiffness."],"supporting_citations":[{"why":"It supplies the quasi-static PDE-constrained formulation and the gradient-regularisation idea that the method adapts.","marker":"[8]"},{"why":"It is the prior PINN estimation of passive material properties whose training/loss setup and noise model are carried over.","marker":"[9]"},{"why":"It is the original PINN inverse-problem formulation that the two-network parameter-estimation approach extends.","marker":"[10]"},{"why":"It defines the apparent Pareto front used to analyse and choose loss weights in the scalar-parameter test case.","marker":"[13]"},{"why":"It is the active-stress constitutive law that places the sought parameter into the equilibrium equation along the fibre direction.","marker":"[17]"},{"why":"It supplies the scalar active-stress rate equation and the linear rescaling property that makes space–time factorisation possible.","marker":"[18]"},{"why":"It is the residual-based attention mechanism applied to the PDE loss in all reported test cases.","marker":"[22]"},{"why":"It is the distance-function construction used to impose the Dirichlet boundary exactly, improving identifiability near the boundary.","marker":"[23]"}],"fun_headline_variants":["PINNs map cardiac contractility from sparse MRI data","Neural nets recover heart force fields from scans","AI uncovers cardiac contractility from noisy images","Physics-informed nets pinpoint heart fibrosis","Sparse imaging data yield cardiac force fields via PINNs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes every point in the tissue follows the same known time course of contraction and differs only in one overall strength number, so the entire spatial pattern of contractility is captured by that single strength field; if contraction timing varies from region to region, the estimated field can be misleading.","fun_headline_variants_meta":{"raw":{"variants":["PINNs map cardiac contractility from sparse MRI data","Neural nets recover heart force fields from scans","AI uncovers cardiac contractility from noisy images","Physics-informed nets pinpoint heart fibrosis","Sparse imaging data yield cardiac force fields via PINNs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001137,"raw_usage":{"total_tokens":4739,"prompt_tokens":978,"completion_tokens":3761,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":594,"completion_tokens_details":{"reasoning_tokens":3690}},"tokens_in":594,"tokens_out":3761,"duration_ms":22268,"temperature":1.0,"reasoning_tokens":3690,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:53:23.591003+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test: simulate the same contraction model with two regions that activate at different times, feed the network only displacement and strain data, and threshold the recovered $\\sigma_0(\\mathbf{x})$ field; if the late-activating region shows up as a spurious low-contractility scar, the single-time-profile assumption marks the boundary of the method’s validity.","supporting_citations":[{"cited_title":"Pozzi, D","cited_arxiv_id":null,"evidence_quote":"It supplies the quasi-static PDE-constrained formulation and the gradient-regularisation idea that the method adapts."},{"cited_title":"Active stress vs","cited_arxiv_id":null,"evidence_quote":"It is the active-stress constitutive law that places the sought parameter into the equilibrium equation along the fibre direction."},{"cited_title":"A biomechanical model of muscle contraction","cited_arxiv_id":null,"evidence_quote":"It supplies the scalar active-stress rate equation and the linear rescaling property that makes space–time factorisation possible."}],"review_version":1}