{"id":"c38138b5-acf5-4226-abc7-f3d523514f17","arxiv_id":"2505.03935","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"SWVE-Net uses a PINN embedding the Kelvin-Voigt wave equation to estimate shear modulus and viscosity from shear wave velocity fields, validated in FE simulations and ex vivo and in vivo experiments.","lead":"This paper introduces SWVE-Net, a physics-informed neural network that estimates tissue stiffness and viscosity directly from ultrasound-measured shear wave motion, without extracting dispersion curves. It may improve viscoelastic imaging of small or reflective tissues, with tests in simulations, animal organs, and two human volunteers.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The in vivo accuracy claim rests on the untested homogeneous Kelvin–Voigt assumption: with λData/λPDE=10^-4, any real-tissue model mismatch is absorbed into biased μ and η, and repeatability (SD/mean<15%) cannot detect it.","rationale":"The reader's weakest assumption correctly identifies the homogeneous Kelvin–Voigt model as the load-bearing premise, and the paper's own Discussion corroborates this by conceding that living tissues may show more complex behavior. My analysis adds specificity: the experimental loss weighting (λData/λPDE=10^-4) means that any real-tissue deviation from Eq. (8) is actively forced into the physics residual, so the inferred parameters will absorb model error as bias. Repeatability is necessary but not sufficient support, and the FE validation is an implementation check under model-perfect conditions rather than a test of the constitutive assumption. The absence of code and data prevents independent audit of the ultrasound processing, but the main scientific concern is the untested mapping from repeatable inversions to accurate parameters. A direct comparison against independent rheometry on the same specimens, or a model-mismatch FE experiment, would settle whether the concern lands. The CONDITIONAL verdict is therefore appropriate: the numerical demonstration is internally consistent, but the real-tissue accuracy claim remains unverified.","tokens_in":13065,"tokens_out":7535,"duration_ms":85003,"concrete_test":"Perform SWVE-Net inversion on fresh ex vivo liver, kidney, and brain specimens using the same ARF/ultrasound pipeline, then independently measure the viscoelastic properties of the same tissue regions with oscillatory shear rheometry or dynamic mechanical analysis, fitting a Kelvin–Voigt model to the independent data. If the SWVE-Net μ and η values differ from the independently fitted values by more than the 5% error claimed in simulation, the in vivo accuracy claim is unsupported. A complementary computational check is to generate FE data from a heterogeneous or fractional-KV model and run SWVE-Net with the current Eq. (8) loss; if the recovered parameters shift systematically from the known effective values, the model-mismatch bias is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that SWVE-Net gives high-fidelity quantitative viscoelastic parameters in living tissue requires that the wavefield in each ROI is governed by Eq. (8) with a single uniform, isotropic, incompressible Kelvin–Voigt pair (μ, η). The paper's own Discussion concedes this is an approximation: 'Living tissues may exhibit more complex viscoelastic behaviors that cannot be fully described by the KV model.' The loss weighting makes this assumption load-bearing: for experimental data λData/λPDE is set to 10^-4, so the fit is dominated by the PDE residual of the homogeneous KV equation. If the true tissue differs through heterogeneity, prestress, anisotropy, or fractional-order viscoelasticity, the optimizer can keep the PDE residual small by adjusting the unobserved pressure field p and the unmeasured component of the streamfunction, while shifting μ and η away from the true or effective values. The reported <15% SD/mean repeatability measures precision, not accuracy, and cannot reveal this systematic bias. The FE validations use exactly the same KV constitutive model that the inversion assumes, so they test correctness of the solver under model-perfect conditions, not robustness to model mismatch. The 2D-FFT comparison does not address this either because it is made on the same synthetic KV data. Thus the strongest external evidence for absolute accuracy in real tissue is the loose statement that ex vivo characteristic times are 'consistent with literature values', which is only an order-of-magnitude check.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes SWVE-Net, a physics-informed neural network (PINN) that infers the shear modulus μ and viscosity η of a homogeneous, isotropic, incompressible Kelvin–Voigt material directly from spatiotemporal vertical particle-velocity fields, bypassing dispersion-curve analysis. The method is validated on finite element (FE) simulations, including a small-scale model approximating a murine liver with strong boundary reflections, and on ex vivo and in vivo ultrasound shear-wave data from multiple organs (liver, spleen, kidney, brain, breast, biceps). The authors report FE inversion errors below 5%, a comparative 2D-FFT analysis with a +44% viscosity error on the same synthetic data, ex vivo characteristic times of order 0.1 ms, and in vivo repeatability with standard deviation-to-mean ratios below 15%.","tokens_in":13346,"tokens_out":2714,"duration_ms":29898,"significance":"If the in vivo accuracy claim could be supported, SWVE-Net would address a genuine clinical limitation: dispersion-based elastography struggles to separate viscosity-induced from structure-induced dispersion in small, reflection-prone samples. The idea of using reflected waves as multi-source data and embedding the wave equation directly in the loss is attractive and the FE demonstrations are internally consistent. The paper also provides a useful comparison showing that a standard 2D-FFT approach fails on the small-liver synthetic dataset. However, the current evidence establishes computational self-consistency and experimental repeatability, not absolute accuracy in living tissue, because no experimental ground truth is available and the FE tests use the same constitutive model in both data generation and inversion.","major_comments":[{"comment":"The in vivo accuracy claim is not supported by the evidence. For experimental data the loss weighting is set to λData/λPDE = 10^-4, so the fit is dominated by the PDE residual of the homogeneous Kelvin–Voigt equation. If real tissue differs through heterogeneity, prestress, anisotropy, or fractional-order viscoelasticity, the optimizer can keep the residual small by adjusting the unobserved pressure field and the unmeasured streamfunction components, while shifting μ and η away from their true effective values. The reported SD/mean < 15% measures precision, not accuracy. An independent validation is needed, e.g., against rheometry on tissue-mimicking phantoms with known properties, or against an established dispersion-based method on a phantom where that method is known to be accurate.","section":"Training Configuration"},{"comment":"The FE validations are consistency checks rather than external benchmarks because the same Kelvin–Voigt model, Eq. (8), is used both to generate the synthetic data and as the inversion model. The small-liver simulation (μ = 0.5 kPa, η = 0.25 Pa·s) demonstrates that the solver recovers parameters under model-perfect conditions, but it does not test robustness to model mismatch. I recommend adding numerical experiments with data generated from a different constitutive model (e.g., fractional Kelvin–Voigt or a heterogeneous spatial distribution of μ and η) to quantify the bias that real-tissue model error could introduce.","section":"Finite element simulations"},{"comment":"The claim of quantifying viscosity 'within a wide range (0.15–1.5 Pa·s)' is supported by only two FE cases, η = 0.15 and η = 1.5 Pa·s. This is an endpoint test, not a range characterization. Adding intermediate viscosity values (and possibly different shear moduli) would substantiate the stated range and would also clarify whether convergence behavior and error remain below 5% across the parameter space.","section":"Results"},{"comment":"The Discussion explicitly concedes that 'Living tissues may exhibit more complex viscoelastic behaviors that cannot be fully described by the KV model.' This limitation is load-bearing for the central claim of high-fidelity quantitative viscoelastic parameters in vivo. The paper should either temper the in vivo accuracy claims to 'KV-consistent effective parameters' or provide evidence that the KV assumption is adequate for the tissues and frequency range studied. Without such evidence, the reported ex vivo and in vivo values may be biased even when the PDE residual is small.","section":"Discussion"}],"minor_comments":[{"comment":"In the description of the two viscosity coefficients, the second is written as 'η1 = 1.5 Pa·s' but should be 'η2 = 1.5 Pa·s'.","section":"Materials and Methods (Finite element simulations)"},{"comment":"The ARF focal point is said to move 'at a speed of 40 Mach', which is physically implausible for this application and is likely a typo for 40 m/s. Please correct this.","section":"Materials and Methods (Finite element simulations)"},{"comment":"The total loss is defined as ℒ = Σ λ_PDE ℒ_PDE + Σ λ_Data ℒ_Data over M terms, but M is not defined in the main text; later the batch size is given as M = 1×10^4. Please clarify the summation index and the role of M in the loss.","section":"Results (Eq. 1)"},{"comment":"The column header 'Characteristic time / (0.1ms)' is confusing because the values appear to be multiples of 0.1 ms rather than times in seconds. Please specify the unit explicitly in the table and the text.","section":"Table 2"},{"comment":"The statement that characteristic times are 'consistent with literature values' is not quantified. Please provide the specific literature ranges or references for each organ, since this is the closest the paper comes to an external comparison for ex vivo data.","section":"Results (Ex vivo)"},{"comment":"The abstract states that SWVE-Net 'quantifies viscosity parameters within a wide range (0.15–1.5 Pa*s)', but the FE validation only uses two endpoint values; please align the abstract with the actual evidence or add intermediate cases.","section":"Abstract"},{"comment":"The Conclusion refers to 'SWE-Net' in several places where 'SWVE-Net' is intended; please correct the naming for consistency.","section":"Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable methods contribution in scope for physics.med-ph, but its clinical-translation claims outrun the validation. The FE results are self-consistent, but the lack of any independent experimental reference for absolute μ and η is the key gap. I would urge the editor to require either phantom experiments with known viscoelastic properties or a direct comparison against a validated reference method on the same samples before considering publication. I also note that no data or code availability statement is included, which is increasingly expected for PINN papers in this area."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nSWVE-Net is a real but incremental advance: the authors' own SWENet extended to infer Kelvin-Voigt viscosity, with wider organ coverage and a nice demonstration that reflected waves can be used as multi-source data rather than noise. The numerical experiments are internally consistent, the small-liver geometry is a good stress test, and the 2D-FFT comparison makes a fair point about the limits of dispersion analysis on small, reflection-heavy samples.\n\nWhat is genuinely new: the viscosity parameter η relative to SWENet, and the multi-organ ex vivo/in vivo sweep (liver, kidney, spleen, brain, muscle, breast). The FE results show <5% recovery for two viscosity levels, and that holds even in a millimeter-scale liver model with strong reflections. The repeatability numbers (SD/mean <15% in vivo) are reassuring as far as they go.\n\nThe soft spots are predictable. The title says \"high fidelity,\" but the accuracy case in real tissue is not made. The in vivo and ex vivo results demonstrate precision, not accuracy—there is no independent measurement of μ or η (no phantom with known properties, no comparison to a reference method on the same samples). The characteristic-time check against literature is only an order-of-magnitude consistency check. More importantly, the loss weighting for experimental data sets λData/λPDE = 10^-4, so the fit is dominated by the homogeneous Kelvin-Voigt PDE. Because only one particle-velocity component is measured, and the streamfunction and pressure are free fields, any real-tissue complexity (heterogeneity, anisotropy, fractional viscoelasticity) can be partly absorbed into biased μ and η while keeping the PDE residual small. The authors themselves concede in the Discussion that the KV model is a simplification. That is a genuine limitation, not a fatal one for a methods paper, but it does make \"high fidelity\" an overclaim.\n\nThe FE validation is a consistency check rather than an external benchmark: the same constitutive model generates the data and appears in the loss. That is standard practice, but it does not test robustness to model mismatch. I also would have liked an identifiability analysis for μ and η from a single velocity component, and ideally release of code and data. None is provided.\n\nNet: this is a legitimate contribution that deserves a serious referee. The right revision would soften the accuracy claims, add independent phantom or reference-method validation, and release code and data. I would send it out rather than desk-reject.\n\nBest,\n[You]","headline":"SWVE-Net is a sound, incremental extension of SWENet to viscosity inference; the numerical tests are clean, but the in vivo accuracy claim outruns the evidence.","tokens_in":13908,"tokens_out":3031,"would_cite":true,"duration_ms":30323,"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":"SWVE-Net, a physics-informed neural network, recovers the Kelvin-Voigt shear modulus and viscosity directly from measured shear-wave particle velocities, bypassing the dispersion analysis that fails on small, reflection-heavy tissue…","keywords":["shear wave elastography","viscoelasticity","physics-informed neural network","Kelvin-Voigt model","dispersion-free inversion","ultrafast ultrasound","tissue characterization","inverse problem"],"falsifier":"Run SWVE-Net on a homogeneous tissue-mimicking phantom whose stiffness and viscosity are known from independent rheometry; if the recovered pair deviates from those values by more than the reported ~5%, or if the recovered numbers drift when the region of interest is resized, the claim that the velocity field uniquely determines uniform $\\mu$ and $\\eta$ would be falsified.","tokens_in":12866,"feed_emoji":"🩺","tokens_out":10120,"duration_ms":92467,"temperature":0.7,"pith_summary":"SWVE-Net is a physics-informed neural network that turns spatiotemporal movies of shear-wave particle velocity into two viscoelastic numbers: the Kelvin-Voigt shear modulus $\\mu$ and viscosity $\\eta$. It does this by putting the viscoelastic wave equation into the network's loss function, so the network has to produce wavefields that obey physics while matching the measured data. Because it never builds a dispersion curve, it avoids the main failure mode of conventional shear-wave elastography, which cannot tell viscosity-induced dispersion apart from finite-size structural dispersion. The paper reports inversion errors below 5% in finite-element simulations, including for a few-millimeter liver model with strong reflections, and in vivo standard-deviation-to-mean ratios below 15% for breast and biceps. If correct, this would give clinicians a quantitative viscosity readout in the small, reflection-prone, heterogeneous tissues where standard methods currently fall short.","feed_headline":"Neural net recovers tissue stiffness and viscosity from shear waves","feed_subtitle":"Skips dispersion analysis, so it also works on millimeter tissue samples where reflected waves corrupt standard elastography.","key_machinery":"The carrying mechanism is a PINN whose loss consists of data mismatch plus residuals of the governing viscoelastic wave equation. Inputs are coordinates $(x_1, x_2, t)$; outputs are the stream function $\\psi$ and incremental pressure $p$, from which the vertical particle velocity $v_2$ is compared with ultrasound measurements. The unknown material parameters $\\mu$ and $\\eta$ enter only as global scalars in the PDE residual, so gradient descent on the physics loss performs the inversion. Reflections from nearby boundaries are treated not as artifacts but as additional data that constrain the parameters. The extension over the earlier elastic SWENet is the addition of the viscosity term $\\eta \\dot{v}_{i,jj}$ in the loss.","core_discovery":"The central claim is that a single measured spatiotemporal field of the vertical particle velocity $v_2$ carries enough information to identify both $\\mu$ and $\\eta$ of a homogeneous Kelvin-Voigt material, with no dispersion analysis and no training corpus beyond the one wavefield. The network outputs a stream function $\\psi$ and an incremental pressure $p$; residuals of the incompressible viscoelastic wave equation $\\rho v_{i,tt} = -p_{,i} + \\mu v_{i,jj} + \\eta \\dot{v}_{i,jj}$ are added to the data-mismatch loss. Minimizing that combined loss recovers $\\mu$ and $\\eta$ at the same time as it reconstructs the full wave field. The authors demonstrate this on finite-element data, on ex vivo liver, spleen, kidney, and brain, and on in vivo human breast and biceps. In the small-liver simulation, conventional 2D-FFT dispersion fitting returns a viscosity error of +44%, while SWVE-Net stays below 5%.","pith_inferences":["Not tested in the paper: if reflections genuinely act as extra data, inversion error should shrink as reflection density increases; this is testable in simulations with increasingly small domains.","If the same loss construction is swapped to a fractional Kelvin-Voigt or multi-relaxation model, the method could return more than one relaxation timescale; the paper only fixes one $\\eta$ per region.","A natural clinical extension is to make $\\mu$ and $\\eta$ spatially varying fields inside the ROI, which would directly map viscosity contrast across tumor or infarct boundaries instead of returning a region-average pair."],"forward_implications":["Viscoelastic parameters are inferred from one spatiotemporal particle-velocity dataset, so no large pre-collected training set is needed.","Millimeter-scale samples with strong boundary reflections become measurable; the reflections become multi-source data instead of corrupting dispersion analysis.","Viscosity estimates improve sharply over the 2D-FFT dispersion baseline: on the small-liver simulation the baseline's viscosity error is +44%, while SWVE-Net's is below 5%.","The method generalizes across organs: ex vivo liver, spleen, kidney, and brain yield characteristic times near $10^{-4}$ s, and in vivo breast and biceps repeat within 15% scatter.","Because only the PDE residual changes, the framework is stated to extend to more complex constitutive models, potentially capturing behavior beyond the single-relaxation Kelvin-Voigt form."],"supporting_citations":[{"why":"Supplies the physics-informed neural network method: PDE residuals are embedded in the loss so forward simulation and parameter inference happen in one network.","marker":"[22]"},{"why":"The authors' earlier elastic SWENet that SWVE-Net extends to viscoelasticity; it provides the architecture and training configuration.","marker":"[24]"},{"why":"Provides the incremental dynamics theory for prestressed viscoelastic solids from which the governing wave equation (Eq. 8) is derived.","marker":"[28]"},{"why":"Finite-element solver with a user-defined material subroutine that generates the synthetic ground-truth wavefields used for validation.","marker":"[23]"},{"why":"Phase-based estimator that converts ultrasound IQ data into the particle-velocity fields that form SWVE-Net's only data input.","marker":"[33]"},{"why":"The 2D-FFT dispersion-analysis baseline that fails on the small-liver case, against which SWVE-Net's viscosity accuracy is compared.","marker":"[18-20]"},{"why":"Literature values of characteristic viscoelastic times used to check the ex vivo results in Table 1.","marker":"[25-27]"}],"fun_headline_variants":["PINN elastography: no dispersion fit, works on tiny samples","Shear wave viscoelasticity from a single wavefield via PINN","No dispersion analysis: net recovers stiffness and viscosity","SWVE-Net: accurate viscoelasticity imaging on millimeter tissue","Physics-informed net maps viscosity in brain, liver, kidney"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that each region of interest is one homogeneous, isotropic, incompressible Kelvin-Voigt solid, so a single pair of numbers, stiffness $\\mu$ and viscosity $\\eta$, describes the whole region and the measured vertical velocity uniquely determines them.","fun_headline_variants_meta":{"raw":{"variants":["PINN elastography: no dispersion fit, works on tiny samples","Shear wave viscoelasticity from a single wavefield via PINN","No dispersion analysis: net recovers stiffness and viscosity","SWVE-Net: accurate viscoelasticity imaging on millimeter tissue","Physics-informed net maps viscosity in brain, liver, kidney"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00025,"raw_usage":{"total_tokens":1603,"prompt_tokens":1042,"completion_tokens":561,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":658,"completion_tokens_details":{"reasoning_tokens":472}},"tokens_in":658,"tokens_out":561,"duration_ms":5457,"temperature":1.0,"reasoning_tokens":472,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:41:45.015463+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run SWVE-Net on a homogeneous tissue-mimicking phantom whose stiffness and viscosity are known from independent rheometry; if the recovered pair deviates from those values by more than the reported ~5%, or if the recovered numbers drift when the region of interest is resized, the claim that the velocity field uniquely determines uniform $\\mu$ and $\\eta$ would be falsified.","supporting_citations":[{"cited_title":"Raissi, P","cited_arxiv_id":null,"evidence_quote":"Supplies the physics-informed neural network method: PDE residuals are embedded in the loss so forward simulation and parameter inference happen in one network."},{"cited_title":"Yin, G.-Y","cited_arxiv_id":null,"evidence_quote":"The authors' earlier elastic SWENet that SWVE-Net extends to viscoelasticity; it provides the architecture and training configuration."},{"cited_title":"Jiang, G.-Y","cited_arxiv_id":null,"evidence_quote":"Provides the incremental dynamics theory for prestressed viscoelastic solids from which the governing wave equation (Eq. 8) is derived."},{"cited_title":"http://62.108.178.35:2080/v6.14/books/sub/default.htm?startat=ch01s01asb09.html","cited_arxiv_id":null,"evidence_quote":"Finite-element solver with a user-defined material subroutine that generates the synthetic ground-truth wavefields used for validation."},{"cited_title":"Loupas, J","cited_arxiv_id":null,"evidence_quote":"Phase-based estimator that converts ultrasound IQ data into the particle-velocity fields that form SWVE-Net's only data input."}],"review_version":1}