{"id":"5e5e0451-dbc3-4d5c-a087-4d2c0d50c05f","arxiv_id":"2506.03869","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A new coupling term transfers the resistive valve force to the cardiac wall, making resistive valve FSI models conserve linear momentum.","lead":"This paper adds a force term to cardiac fluid-structure interaction models so that resistive valve forces are transmitted to the heart wall, restoring momentum balance. It is a practical fix that lets simplified valve models be used in beating-heart simulations without unphysical global drift.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The wall force g_k matches the resultant but not the torque of the resistive force R_k; angular momentum is therefore not conserved, so the claim that the model 'satisfies Newton's laws' is overstated.","rationale":"The reader's weakest assumption identifies exactly the gap I consider load-bearing: the construction enforces the zeroth moment of the resistive force but ignores the first moment. This is not a matter of numerical error; it is a property of the continuous equations. The paper's central advertised guarantee is Newtonian consistency, and the benchmark is designed as a clean linear-momentum test (a spherically symmetric valve with zero torque by symmetry). That the proposed force also has the right torque in that benchmark is thus no evidence of general moment balance. I independently checked the algebra: with g_k = (F_k/V_k) delta_k and R_k = K(x) delta_k where K varies with the velocity mismatch, the first moments differ unless K is constant. The concern is concrete and testable. I nonetheless stress that the paper has real merit: the linear-momentum imbalance is clearly diagnosed, the fix is simple and minimally invasive, the explicit discretization with first-order drift characterization is honest, and the idealized benchmark convincingly demonstrates that the resultant is balanced. The issue is a scope/overclaim problem, not a fundamental invalidity of the method. The right remedy is either to weaken the 'Newton's laws' wording to 'linear momentum balance' or to add a moment-matching correction (e.g., by defining g_k with the same distribution as R_k rather than a scalar multiple of delta_k). Since this is exactly the condition the reader attached, the CONDITIONAL verdict stands unchanged.","tokens_in":17832,"tokens_out":12948,"duration_ms":122998,"concrete_test":"Run a variant of the Section 3.1 spherical benchmark with the resistive plane tilted by about 15 degrees so that the valve force has a nonzero torque about the center. Track the total angular momentum of the fluid-solid system over time and repeat with halved Delta t. If angular momentum is not conserved in the Delta t -> 0 limit (equivalently, if the integrals I_R = integral x cross R_k dx and I_g = integral x cross g_k dx differ beyond discretization error), the model does not conserve angular momentum and the 'Newton's laws' claim must be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section 2.2, the attachment force is defined as g_k = (F_k/V_k) delta_k(phi_k), with F_k = integral over Omega_f of R_k dx. This fixes only the resultant: in the current configuration the torque on the solid is tau_g = (F_k/V_k) integral over Omega_s of x cross delta_k(phi_k) dx, whereas the torque exerted by the fluid on the valve is tau_R = integral over Omega_f of x cross R_k dx. Because R_k = (R_k/epsilon_k)(u-u_ALE) delta_k(phi_k), the two integrals coincide only if u-u_ALE is constant on the support of delta_k, which is generally false. Assumption 2 (valve equilibrium) is used only for the resultant; moment equilibrium of the massless valve would require tau_g = tau_R. Hence the continuous FSI model does not conserve angular momentum. The spherical benchmark cannot expose this: its azimuthal symmetry makes both torques zero. The realistic test is qualitative and does not monitor angular momentum. Thus the abstract/conclusion claim that the model 'satisfies Newton's laws' and is 'physically consistent' is too strong; only linear-momentum balance is established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes an extension of the resistive immersed implicit surface (RIIS) valve model for use in cardiac fluid-structure interaction (FSI) simulations. The authors add a distributed body force to the solid momentum equation, chosen so that its resultant equals the integral of the resistive force over the fluid domain for each valve, thereby restoring linear momentum balance to the coupled system. The modification is discretized explicitly, and numerical tests include a spherical benchmark (where center-of-mass drift is removed and the residual drift converges with the time step) and a realistic left-heart model (where valve attachment forces suppress unphysical ventricular displacements and pressure-volume loop oscillations).","tokens_in":18032,"tokens_out":11537,"duration_ms":111262,"significance":"The proposed modification addresses a real and practically important deficiency: standard RIIS, when embedded in FSI, violates linear momentum balance and can produce unphysical global motion of the heart. The spherical benchmark is well designed, and the observed first-order convergence of the residual drift with the explicit treatment is a strong consistency check. The implementation is based on the open-source lifex/deal.II stack, all parameters are reported, and no calibration is performed to obtain the physiological-looking PV loops. The main caveat is that the construction enforces only the resultant of the valve force, not the moment, so the paper's stronger claims about Newton's laws and physical consistency are not fully supported.","major_comments":[{"comment":"The proposed construction enforces only the resultant of the fluid-valve force, not its moment. With g_k = (F_k/V_k) δ_k(φ_k(x̂+d̂)) and R_k = (R_k/ε_k)(u-u_ALE) δ_k(φ_k(x)), the torque on the solid is τ_g = (F_k/V_k) ∫_{Ω_s} x × δ_k dx, whereas the torque exerted by the fluid on the valve is τ_R = ∫_{Ω_f} x × (R_k/ε_k)(u-u_ALE) δ_k dx. These coincide only if u-u_ALE is constant on the support of δ_k, which is generally not the case. Hence the total angular momentum of the coupled system is not conserved in general. The spherical benchmark of Section 3.1 cannot reveal this because its azimuthal symmetry makes both torques zero, and the realistic test of Section 3.2 does not monitor angular momentum. Since the abstract and the conclusions claim that the model 'satisfies Newton's laws' and is 'physically consistent', the claim is stronger than what is established: only linear momentum balance is demonstrated. The authors should either modify the attachment force distribution so that it also matches the torque (e.g., by taking g_k = δ_k (C_k + D_k × (x-x̄)) and fixing D_k through the torque balance) or explicitly limit the claims to linear momentum conservation.","section":"Section 2.2 (definition of C_k(t) and g_k; Eq. (3) for R_k)"},{"comment":"Assumption 3 states that the spatial distribution of bg_k is the same as in the fluid, but the implemented formula bg_k = C_k(t) δ_k(φ_k(x̂+d̂)) is not the same vector distribution as R_k ∝ (u-u_ALE) δ_k(φ_k(x)); the direction of R_k varies with the local relative velocity, while bg_k has the constant direction of C_k. The assumption is therefore a new modeling ansatz for the shape of the attachment force, not a statement of equality of distributions. Because this choice determines the torque mismatch discussed in the previous comment, it is load-bearing and should be presented and justified as such, with a discussion of its consequences.","section":"Section 2.2, Assumption 3"}],"minor_comments":[{"comment":"The phrase 'both with and withouth the newly introduced term' contains a typo: 'withouth' should be 'without'.","section":"Section 3.1, paragraph before Figure 3"},{"comment":"The word 'techinques' should be 'techniques'.","section":"Table 1 caption"},{"comment":"The row label 'computeg' should read 'compute g'.","section":"Table 2"},{"comment":"The sentence 'we valves open and close according to...' is missing a verb; it should read 'we let the valves open and close according to...'.","section":"Section 3.2, first paragraph"},{"comment":"The activation time φ in the eikonal-diffusion model uses the same symbol as the valve signed-distance functions φ_k in Section 2.1; renaming one of them (e.g., τ_act) would avoid confusion.","section":"Appendix A"},{"comment":"The Q0 entries are labeled with units 'mmHg' for initial flow rates; flow rates should have units of volume per time (e.g., mL/s) or the quantities should be defined differently.","section":"Table A.7"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: this paper fixes a real, known problem—RIIS valve models in FSI violate linear momentum because the valve forces never reach the solid—with a simple, parameter-free attachment force. The spherical benchmark is convincing that the fix works for linear momentum. But the paper overclaims when it says the model 'satisfies Newton's laws': the construction only matches the resultant of the resistive force, not its torque, so angular momentum is not conserved in general.\n\nThe new piece is the explicit formula g_k = (F_k/V_k) delta_k, with F_k the integral of the resistive term and V_k a normalization. Earlier RIIS-in-FSI work papered over the imbalance with ad hoc boundary-condition calibration. Here the term is forced by the balance condition itself, so no parameters are tuned. The ideal sphere test is well chosen: no external forces, center-of-mass drift only vanishes when the term is added, and residual drift goes as dt, consistent with explicit treatment. The cost breakdown shows the overhead is negligible. The left-heart test shows a clear qualitative improvement in displacement and pressure-volume loops.\n\nSoft spots, in proportion. The biggest is the torque issue, and it's real: the resistive force distribution on the valve generally exerts a torque, but g_k is determined only by its resultant. Assumption 2 (valve equilibrium) would require moment balance too, but only the force balance is used. The spherical benchmark has zero torque by symmetry, so it cannot expose the error. So the conclusion that the model 'satisfies Newton's laws' is too strong; what is established is linear-momentum balance. That is still a useful result, but the claim should be qualified or the method extended to match moments. Second, the spatial distribution of the attachment force is ad hoc—uniform scaling of the delta profile—with no argument that it's realistic. Third, the realistic test is qualitative; no quantitative comparison to a gold standard or sensitivity analysis. Fourth, no code or data are provided, which makes reproduction harder, though the method is simple enough to implement from the description.\n\nWho should read it: anyone doing FSI with resistive valve models, or building whole-heart digital twins. It's a modest but solid contribution. It deserves peer review; a referee should ask for the Newton's laws claim to be scaled back, a discussion of torque, and ideally release of artifacts. I'd take it.","headline":"A clean fix for a real linear-momentum imbalance in resistive valve FSI, but the 'Newton's laws' claim overreaches because only the resultant of the attachment force is balanced.","tokens_in":18574,"tokens_out":2275,"would_cite":true,"duration_ms":23143,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["65M60","74F10","76Z05","92C35"],"pacs":[],"model":"deepseek-v4-flash","headline":"Conventional resistive valve models leave the wall reaction force out of the momentum balance, so heart FSI simulations drift and oscillate; this paper adds a distributed attachment force with matching resultant and shows the artifacts…","keywords":["fluid-structure interaction","cardiac modeling","valve modeling","resistive immersed implicit surface","Newton's laws","attachment forces","left heart simulation","ALE formulation"],"falsifier":"Run the spherical benchmark with the resistive plane tilted or displaced so its fluid force has nonzero torque about the system's center of mass; if the total angular momentum changes while no external torque acts, the model is not fully Newtonian. Equivalently, compute $\\int_{\\Omega_f} (x-x_0)\\times R_k\\,dx$ and the torque of $\\hat{\\mathbf g}_k$ about the same point at peak systole in the realistic heart: a nonzero difference directly contradicts the paper's Newton-law claim.","tokens_in":17556,"feed_emoji":"🫀","tokens_out":9581,"duration_ms":97620,"temperature":0.7,"pith_summary":"Cardiac simulations that combine contracting walls with flowing blood need valves, but cheap 'resistive' valve models exert a force on the blood without passing the equal-and-opposite force to the wall that holds the valve in place. The paper argues that this omission violates Newton's laws: during isovolumetric contraction the unbalanced pressure force accelerates the whole simulated heart, producing drift in an idealized spherical benchmark and large longitudinal displacements, pulmonary-vein jets, and pressure-volume-loop oscillations in a realistic left heart. The fix is a distributed force added to the solid mechanics equation, spread over the region where each valve meets the wall and normalized so its resultant equals the force the fluid exerts on that valve. With the term included, the center of mass of the fluid-solid system stays put, the realistic traces become physiological, and the cost is small because the new term is evaluated explicitly from previous time-step data; the same correction extends to other resistive valve models.","feed_headline":"Adding valve forces stops phantom drift in heart simulations","feed_subtitle":"Without it, simulated hearts accelerate on their own; with it, they stay put and pressure-volume loops stabilize.","key_machinery":"The load-bearing object is the distributed attachment force $\\hat{\\mathbf g}_k=(F_k/V_k)\\,\\delta_k(\\varphi_k(\\hat x+\\hat d))$ added to the solid elastodynamics equation. The smoothed Dirac delta $\\delta_k$ of the signed distance function $\\varphi_k$ is the same RIIS kernel used in the fluid, so the force is spread over the valve-wall overlap region; $F_k$ is the integrated resistive force from the fluid momentum equation, and $V_k$ normalizes the distribution so its resultant equals $F_k$. Computing $\\hat{\\mathbf g}_k$ explicitly from the previous time step's velocity, pressure, and displacement keeps the added term almost free computationally while introducing a first-order error in time.","core_discovery":"The central claim is that the resistive immersed implicit surface (RIIS) valve model becomes consistent with Newton's laws in fluid-structure interaction only if the force the fluid exerts on each valve is transferred back onto the cardiac wall. The transfer is made explicit: with $R_k$ the resistive force density in the Navier-Stokes equation, the fluid force on valve $k$ is $F_k=\\int_{\\Omega_f} R_k\\,dx$, and the wall receives $\\hat{\\mathbf g}_k=(F_k/V_k)\\,\\delta_k(\\varphi_k)$, where $V_k$ is the integral of the same smoothed delta kernel over the solid domain. Matching the resultant of $\\hat{\\mathbf g}_k$ to $F_k$ restores linear momentum of the coupled fluid-solid system, and the numerical experiments confirm the consequence: no center-of-mass drift in the spherical benchmark and no unphysiological ventricular displacement, pulmonary-vein jets, or pressure-volume-loop oscillations in the realistic left heart.","pith_inferences":["The paper balances only the resultant of the fluid force on each valve, not its torque; a tilted or asymmetric valve would transmit a spurious twisting force to the wall, so angular momentum of the FSI system is not conserved in general.","A benchmark with an off-center resistive surface would expose this: if total angular momentum changes with no external torque, the model is not fully Newtonian even though it fixes the linear drift.","The near-linear relation between pressure jump and force density for closed valves could be used as a cheap surrogate for valve state in patient-specific models, since its slope encodes valve geometry.","Extending the explicit evaluation of $\\hat{\\mathbf g}_k$ to second-order extrapolation is a natural next step that should remove the residual first-order drift at essentially the same cost."],"forward_implications":["Without the attachment force, the spherical benchmark shows a clear downward acceleration of the system's center of mass; with it, the center of mass remains stationary and only a small drift remains, shrinking like $\\Delta t$ as the time step is refined.","In the realistic left heart, neglecting the force produces fast large longitudinal ventricular displacement, high atrial strains, strong pulmonary-vein jets, and sharp oscillations in pressure-volume loops, all absent when the force is included.","The pressure-volume loop of the left atrium becomes much more physiological when valve forces are included, matching the expected morphology.","The correction is not tied to RIIS specifically: the same force-balance principle extends to other resistive valve models used in FSI simulations.","The added computational cost is minor, with the linear solve dominating and the assembly of $\\hat{\\mathbf g}_k$ contributing only a small fraction of wall time."],"supporting_citations":[{"why":"Defines the resistive immersed implicit surface valve model whose fluid force is the starting point for the correction.","marker":"[24]"},{"why":"Provides the left-heart FSI model and the original RIIS application whose unphysical drift motivates the fix.","marker":"[13]"},{"why":"Supplies the monolithic ALE fluid-structure interaction scheme into which the attachment force is inserted.","marker":"[12]"},{"why":"Gives the electromechanics-driven whole-heart fluid dynamics model and valve opening/closing rule used in the realistic test.","marker":"[63]"},{"why":"Supplies the cardiac electromechanics model, fiber generation, and passive/active constitutive laws for the realistic simulations.","marker":"[25]"},{"why":"Provides the RDQ20-MF active force generation model whose strain sensitivity makes the spurious deformations consequential.","marker":"[44]"},{"why":"Introduces energy-consistent boundary conditions for electromechanics that the proposed wall-force term extends to FSI.","marker":"[43]"}],"fun_headline_variants":["Valve forces now balance heart wall, killing phantom drift","Newton's laws restored in cardiac FSI with valve forces","Fix for resistive valve models: add wall reaction forces","How to keep simulated hearts from drifting: transfer valve forces","Distributed valve forces stabilize cardiac FSI simulations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The repair assumes that transferring only the total push of the fluid on each valve to the wall is enough to restore Newton's laws; the fluid's twisting effect on the valve is never passed to the wall, so the system as a whole can still start to spin.","fun_headline_variants_meta":{"raw":{"variants":["Valve forces now balance heart wall, killing phantom drift","Newton's laws restored in cardiac FSI with valve forces","Fix for resistive valve models: add wall reaction forces","How to keep simulated hearts from drifting: transfer valve forces","Distributed valve forces stabilize cardiac FSI simulations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000246,"raw_usage":{"total_tokens":1528,"prompt_tokens":923,"completion_tokens":605,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":537}},"tokens_in":539,"tokens_out":605,"duration_ms":6309,"temperature":1.0,"reasoning_tokens":537,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:55:03.786346+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the spherical benchmark with the resistive plane tilted or displaced so its fluid force has nonzero torque about the system's center of mass; if the total angular momentum changes while no external torque acts, the model is not fully Newtonian. Equivalently, compute $\\int_{\\Omega_f} (x-x_0)\\times R_k\\,dx$ and the torque of $\\hat{\\mathbf g}_k$ about the same point at peak systole in the realistic heart: a nonzero difference directly contradicts the paper's Newton-law claim.","supporting_citations":[{"cited_title":"Fedele, E","cited_arxiv_id":null,"evidence_quote":"Defines the resistive immersed implicit surface valve model whose fluid force is the starting point for the correction."},{"cited_title":"Bucelli, A","cited_arxiv_id":null,"evidence_quote":"Provides the left-heart FSI model and the original RIIS application whose unphysical drift motivates the fix."},{"cited_title":"Bucelli, L","cited_arxiv_id":null,"evidence_quote":"Supplies the monolithic ALE fluid-structure interaction scheme into which the attachment force is inserted."},{"cited_title":"Zingaro, M","cited_arxiv_id":null,"evidence_quote":"Gives the electromechanics-driven whole-heart fluid dynamics model and valve opening/closing rule used in the realistic test."},{"cited_title":"Fedele, R","cited_arxiv_id":null,"evidence_quote":"Supplies the cardiac electromechanics model, fiber generation, and passive/active constitutive laws for the realistic simulations."},{"cited_title":"Regazzoni, L","cited_arxiv_id":null,"evidence_quote":"Provides the RDQ20-MF active force generation model whose strain sensitivity makes the spurious deformations consequential."},{"cited_title":"Piersanti, F","cited_arxiv_id":null,"evidence_quote":"Introduces energy-consistent boundary conditions for electromechanics that the proposed wall-force term extends to FSI."}],"review_version":1}