{"id":"5b973b32-e384-4fa8-be27-825ecdf3ab7b","arxiv_id":"2509.19404","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"A low-dimensional ball representation of cardiac activation lets particle filters quantify uncertainty in ECGI, producing probabilistic activation maps, earliest-site likelihoods, and block-line discrimination.","lead":"The paper introduces a particle-filtering method for electrocardiographic imaging that reconstructs not just a single activation map but probabilities of activation over time and space. It also estimates whether suspected conduction roadblocks in the heart are real or artifacts, and demonstrates this on simulated data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Probabilistic outputs are not shown to be calibrated; the hand-tuned simplified model may yield overconfident or arbitrary probabilities, undermining the central UQ claim.","rationale":"The paper is a well-written methods contribution with careful experiments: separate forward/inverse meshes, deliberate conductivity mismatch, forward/backward filtering, and honest discussion of limitations. The algorithm is clear and reproducible in principle. However, the abstract's central claim is the production of 'probabilistic maps' and 'confidence' estimates, and this is where the evidence is thinnest. The reader's conditional verdict focuses on the representational assumption (ball-like fronts), which is indeed untested for complex arrhythmias. I partially agree: that misspecification would likely reveal itself in poor calibration. But a more immediate and decisive check is calibration itself, because even under the assumed representation, the posterior probabilities are not validated. The hand-tuned Σ_w and uninformative dynamics could make the probability scale arbitrary. A reliability diagram on the existing simulated cases would settle this. If calibration fails, the central 'non-deterministic' contribution is not supported; if it passes, the method is at least internally consistent for focal cases. The reader's verdict of CONDITIONAL is appropriate; my concern does not move it, but adds a specific test to the conditions.","tokens_in":18304,"tokens_out":8442,"duration_ms":72395,"concrete_test":"Re-run the SIR filter on Stim2Iso and Stim2Ani with the exact parameters of §4.1.2 (N=1000, l=3, Σr=10 mm, λ=5 mm, Σw=(0.02)^2I, width=5 mm). For every myocardial node x and each time tk, compute the posterior activation probability P̂(x,tk) = Σ_i ω_i^k 1[v_{ξ_i^k}(x)>0.5] (Eq. 16). Using the ground-truth bidomain solution v_true used to generate the BSPMs, compute the actual activation indicator I(x,tk)=1[v_true(x,tk)>0.5]. Pool all (x,tk) pairs and build a reliability diagram: sort P̂ into 10 bins of width 0.1; in each bin, compute the empirical frequency of I=1. If the curve deviates from the diagonal by more than 0.1 in any bin with at least 100 samples, or if the expected calibration error (mean |bin frequency - bin center|) exceeds 0.05, the probability maps are not calibrated. This directly tests whether the central UQ claim holds even in the paper's own simulated settings.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central novelty is not the particle filter per se but the probabilistic outputs: activation probability maps (Eq. 16), earliest-activation pseudo-probabilities (Eq. 17), and block-line mode probabilities (Eq. 18). These are posterior quantities under a highly simplified generative model: fixed smoothed-Heaviside template (Eq. 7), geodesic-ball state (Eq. 8), random-walk radii (Eq. 10) with exponential-uniform center jumps, and a Gaussian likelihood whose covariance Σ_w is hand-tuned 'by estimating the order of magnitude... and then fine-tuned' (§4.1.2). No evidence is provided that these posterior probabilities are calibrated. For a model to support statements like 'the likelihood of activation at each point over time' or 'confidence in the presence of a block,' events assigned probability p should occur with empirical frequency p. The paper reports only correlations of deterministic activation maps and shows qualitative probability images; it never computes reliability diagrams or coverage statistics. Under model misspecification (wrong conductivity, isotropic geodesics, fixed width=5 mm, simplified V), the posterior can be arbitrarily over- or under-confident. The hand-tuned Σ_w is a particularly delicate knob: it directly controls the likelihood scale and hence the spread of all reported probabilities. Absent calibration, the 'uncertainty-aware' maps may be visually informative but numerically not trustworthy, undermining the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a particle-filtering approach to electrocardiographic imaging (ECGI) in which the cardiac activation front is represented by a small number of growing geodesic balls (centers and radii), thereby reducing the state dimension enough to make sequential Monte Carlo tractable. The method outputs, in addition to deterministic activation maps, activation probability maps, pseudo-probability maps for earliest activation sites, and a discrete-mode extension that assigns probabilities to candidate conduction lines of block. The numerical study uses simulated bidomain data, including isotropic and anisotropic cases, deliberately mismodeled conductivity in the inverse model, and a separate coarser mesh to avoid inverse crime. The reported activation-map correlations exceed 0.95 in the anisotropic mismatched cases, and the block-line mode probabilities correctly favor the true block in most tested scenarios.","tokens_in":18666,"tokens_out":3471,"duration_ms":32174,"significance":"If the probabilistic outputs are taken at face value, the paper contributes a genuinely new capability to ECGI: posterior inference over activation sequences, with clinically interpretable confidence maps and a mechanism to assess whether a detected line of block is physiological or an artifact. The design is thoughtful: the low-dimensional state parameterization is the key enabling idea, the numerical experiments deliberately include model mismatch, and the paper is appropriately cautious about the heuristic nature of pseudo-probabilities. The strongest empirical results, activation correlations above 0.95 under anisotropic mismodeling, support the feasibility claim. However, the central added value is uncertainty quantification, and the paper does not yet demonstrate that the reported probabilities are calibrated or robust to the hand-tuned observation covariance. That gap prevents the current version from fully supporting the probabilistic claims.","major_comments":[{"comment":"The observation noise covariance Σ_w is fine-tuned 'to allow sufficient diversity among particles while avoiding excessive resampling.' The likelihood scale set by Σ_w directly controls the spread of every probabilistic output (Eqs. 16–18), yet no sensitivity analysis or calibration check is provided. The paper's central claim is uncertainty-aware inference; for this, the posterior probabilities should be shown to be meaningful (e.g., via reliability diagrams, coverage of activation times, or a sensitivity study over a range of Σ_w). Without such evidence, the reported probability maps may be visually suggestive but are not established as calibrated uncertainty statements.","section":"§4.1.2, Eq. (12)"},{"comment":"The block-line extension is described as letting each particle choose among 'a predefined set of geodesic distances and corresponding transfer matrix O.' However, the experimental section only states that two distance maps were provided; it never specifies how O is modified for each mode. If O is in fact identical across modes, then the mode probability (18) only compares alternative activation-front geometries under the same forward model, not the conductivity changes that a true block would induce. The paper should either document the mode-dependent O or explicitly state that only the geodesic distance varies, and justify that this is sufficient to discriminate true from artificial block lines.","section":"§4.3, Eq. (18)"},{"comment":"Several headline results are averages of forward and backward filter outputs, e.g., (P_fwd + P_bwd)/2 and the block-mode probabilities 'averaged across 50 forward and 50 backward filter outputs.' No justification is given for this averaging, and the forward and backward filters have different bias patterns (the paper itself notes the forward method is inaccurate early and the backward method is inaccurate late). A simple average is not a posterior quantity and may hide systematic disagreement. The authors should either provide a decision-theoretic justification for the combination or report forward and backward results separately, with a measure of agreement.","section":"Figures 7–8 and 11"}],"minor_comments":[{"comment":"Typos: 'a conduction lines of block' and 'a priori block' (twice). Please also check 'visulization' and 'F or' in Algorithm 1.","section":"Abstract and Conclusion"},{"comment":"The activation probability maps in Figures 4–6 would benefit from colorbars and a consistent scale across time frames and methods; currently the visual comparison is difficult.","section":"§4.2"},{"comment":"The sentence 'we ran 50 forward and 50 backward filters' is not followed by a description of how the 50 runs differ (only particle initialization randomness is implied). Please clarify whether these are independent SMC runs and how variance across runs was assessed.","section":"§4.3"},{"comment":"Reference [51] duplicates [37]; [52] is cited for SBDF2 but may be better attributed to the original method; please verify citation details.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the journal's scope as a statistical-methodology contribution to an applied inverse problem. The main revision needed is to turn the uncertainty-quantification claim from qualitative to quantitative: report calibration or at least a sensitivity analysis of the probabilistic outputs to the tuned covariance. The block-line extension also needs technical clarification. I do not see a fundamental flaw in the approach; the concerns are fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe short version: this paper deserves a serious referee. The method is a new low-dimensional parameterization of activation-sequence ECGI, using a small number of geodesic balls (centers and radii), which makes SIR particle filtering tractable. It also produces genuinely new outputs: activation probability maps, earliest-site pseudo-probability maps, and a line-of-block confidence mode. The authors are candid about limitations, and the numerical study avoids inverse crime by using different forward/inverse meshes, deliberate conductivity mismatch, and forward/backward runs.\n\nWhat's solid: the state-space construction (Eqs. 6–10) is simple and physically motivated; the likelihood (Eq. 12) is standard. Activation-map correlations stay above 0.95 even when anisotropic data are filtered through an isotropic model. The block-line experiment is a real model-selection exercise, not a fit. The pseudo-probability estimator is explicitly labelled non-normalized, which is honest. The paper also states clearly that it does not benchmark against deterministic ECGI for activation maps, keeping the contribution focused on UQ rather than chasing a better map.\n\nThe soft spots are real but not fatal. The biggest is calibration: the probability maps are posterior summaries under a heavily simplified generative model, and the paper never shows reliability diagrams or coverage statistics. The authors hand-tune Sigma_w and don't report sensitivity to Sigma_r, lambda, or the front width. So the confidence numbers should be read as relative, not absolute. The stress-test note is right about this, but it is a missing analysis, not a hidden fatal flaw. Second, the ball-shaped front assumption is tested only on focal stimulations and one block line; re-entry or fragmented fronts are out of scope, and the authors say so. Third, the forward/backward averaging is ad hoc; a principled smoothing would strengthen the claims. Fourth, no code or data is shipped, which hampers reproducibility.\n\nWho is this for? Researchers in Bayesian inverse problems and ECGI; anyone who wants to add interpretable uncertainty to activation maps. A referee should push for calibration tests, sensitivity analysis, and at least one comparison to a deterministic method on the same data. If those are added, this becomes a solid methods contribution.\n\nRecommendation: send to peer review. My own verdict is conditional acceptance: the core idea sounds sound and honestly presented, but the UQ claims need quantitative support before they can be read as calibrated confidence.","headline":"A credible proof-of-concept for particle-filtering ECGI with honest caveats; the UQ claims need calibration checks, but the low-dimensional state representation is a genuine step forward.","tokens_in":19131,"tokens_out":2926,"would_cite":true,"duration_ms":25511,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","65C05","65N21","92C55"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper makes Bayesian particle filtering tractable for electrocardiographic imaging by compressing activation fronts into a few geodesic balls, yielding probability maps rather than deterministic reconstructions.","keywords":["ECGI","particle filtering","sequential Monte Carlo","Bayesian inverse problem","activation probability","earliest activation site","conduction line of block","geodesic ball representation"],"falsifier":"Simulate or record an activation sequence whose wavefront is visibly non-ball-like — for example, a re-entrant circuit, a U-shaped block, or two fronts colliding — then run the filter on the resulting torso potentials; the central claim is falsified if the true activated regions fall outside the high-probability maps or if the reconstructed activation map misses the wavefront.","tokens_in":18149,"feed_emoji":"❤️","tokens_out":7177,"duration_ms":62248,"temperature":0.7,"pith_summary":"Electrocardiographic imaging (ECGI) reconstructs heart activation from torso potentials, but it is ill-posed and usually returns a single deterministic map. This paper argues that the activation sequence can be compressed into a few geodesic balls — each with a center and a radius — so that the hidden state has only a handful of parameters. That compression makes particle filtering computationally feasible, and the filter then returns a full posterior over activation fronts rather than one answer. From that posterior, the authors build activation maps, time-resolved activation probability maps, pseudo-probability maps for earliest activation sites, and a probability that a candidate conduction line of block is real. In simulated tests with deliberate conductivity mismatch, reconstructed activation maps remain above 0.95 correlation with reference, and the uncertainty regions stay informative.","feed_headline":"Growing-ball model makes particle filtering work for heart mapping","feed_subtitle":"Representing activation fronts as growing geodesic balls yields probability maps for every heartbeat.","key_machinery":"The load-bearing machinery is the low-dimensional state representation in Eqs. (6)-(8): the state is X_k = (c^1_k,...,c^l_k, r^1_k,...,r^l_k), where centers live on heart-mesh nodes and radii are positive reals; the transmembrane voltage is v(x) = max_i V(r_i - d(x,c_i)) with V a smoothed Heaviside and d a conductivity-weighted geodesic distance. This reduces the state dimension from the full nodal voltage vector to fewer than eight parameters, making a standard sequential importance resampling particle filter feasible, and defines the nonlinear observation map Y_k = O v_{X_k}|_{Gamma_T} + noise whose likelihood drives the particle weights.","core_discovery":"On its own terms, the paper claims that Bayesian particle filtering can solve the non-deterministic ECGI problem if the cardiac activation front is parameterized as l (typically fewer than four) growing geodesic balls on the heart mesh, each described by a center and a radius, with a smoothed-Heaviside transmembrane voltage profile. The forward map from these parameters to torso potentials is nonlinear, and the authors propagate a particle cloud through it with a deliberately simple random-walk state model. The resulting posterior supports quantities that deterministic solvers cannot provide: per-point activation probability over time, pseudo-probability of being an earliest activation site,","pith_inferences":["The same ball-and-radius state could be used as a proposal or initialization layer inside existing deterministic ECGI pipelines, since the posterior gives a natural prior over activation centers and speeds for a subsequent optimization.","The forward/backward asymmetry suggests a formal two-filter smoothing pass might yield a single calibrated posterior, rather than the averaged pseudo-probabilities the paper displays.","A natural testable extension is the low-electrode-count clinical setting (148-255 electrodes): the method's uncertainty maps should be evaluated on whether the probability regions enlarge gracefully as electrode density drops, since the paper's simulated data use around 1000 torso points.","The discrete-mode trick for lines of block generalizes beyond block detection: any discrete biophysical hypothesis (scar location, fiber orientation, or ionic model variant) could be made a competing mode in the same particle filter and scored by its posterior weight."],"forward_implications":["Activation maps no longer need to be single deterministic outputs: every point on the heart gets a time-dependent activation probability, so clinicians can see where the reconstruction is trustworthy.","Earliest activation sites, relevant for localizing premature ventricular contractions, are returned as pseudo-probability regions rather than point estimates, and the paper reports that true sites fall inside those regions in most anisotropic test cases.","Candidate lines of block from any deterministic ECGI method can be tested by giving the filter a geodesic metric with and without the block; the filter's mode probability indicates which is supported by the data.","The forward and backward filter runs can be combined to compensate for the poor early-time behavior of the forward run and the poor late-time behavior of the backward run.","Because the state stays low-dimensional, adding more activation centers or discrete model choices is computationally straightforward, which opens the door to more complex priors or fiber-aware distances when such information is available."],"fun_headline_variants":["Particle filter plus growing balls gives probabilistic heart maps","Bayesian particle filtering for uncertain cardiac activation maps","Growing geodesic balls enable particle-filtered ECGI","Probabilistic activation maps from particle-filtered ECGI","Few growing balls let particle filtering handle heart mapping"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is the Section 3.1 state parameterization: an activation front is always a union of a few growing geodesic balls with a fixed smoothed step profile; if a real front is fragmented or shaped by complex block geometry, the posterior and probability maps are misleading, and the paper itself notes in the conclusion that an unmodeled line of block will not be detected.","fun_headline_variants_meta":{"raw":{"variants":["Particle filter plus growing balls gives probabilistic heart maps","Bayesian particle filtering for uncertain cardiac activation maps","Growing geodesic balls enable particle-filtered ECGI","Probabilistic activation maps from particle-filtered ECGI","Few growing balls let particle filtering handle heart mapping"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000408,"raw_usage":{"total_tokens":1957,"prompt_tokens":751,"completion_tokens":1206,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":495,"completion_tokens_details":{"reasoning_tokens":1131}},"tokens_in":495,"tokens_out":1206,"duration_ms":8748,"temperature":1.0,"reasoning_tokens":1131,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T15:41:29.831063+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate or record an activation sequence whose wavefront is visibly non-ball-like — for example, a re-entrant circuit, a U-shaped block, or two fronts colliding — then run the filter on the resulting torso potentials; the central claim is falsified if the true activated regions fall outside the high-probability maps or if the reconstructed activation map misses the wavefront.","supporting_citations":[],"review_version":1}