{"id":"ad6af48d-b1e0-4645-94ff-37a063505c27","arxiv_id":"2606.24393","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"A poroelastic tendon model with crimped fibril recruitment produces slower equilibration on loading, slower relaxation on unloading, and hysteresis that decreases with higher applied load.","lead":"The paper develops a one-dimensional poroelastic model for tendons that incorporates crimped fibril recruitment into the solid skeleton. The FIB model shows slower loading dynamics, much slower unloading, and load-dependent hysteresis compared to a pure neo-Hookean skeleton.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Bespoke stress law for crimp/recruitment plus stiffness-dependent diffusivity lacks shown validation against data","rationale":"The reader's weakest_assumption already isolates the exact modeling choice that must hold for the strongest_claim to be true. No additional internal inconsistency or hidden assumption appears in the abstract description; the risk is simply that the bespoke ingredients have not yet been shown to reproduce the cited experimental phenomenology.","tokens_in":1812,"tokens_out":399,"duration_ms":18828,"concrete_test":"Re-derive the effective modulus of the FIB skeleton from the crimp geometry and neo-Hookean matrix as a function of applied stretch; insert the resulting stiffness into the diffusion coefficient; recompute the 1-D loading/unloading trajectories for the two parameter sets given in the paper; compare the predicted strain partitioning and hysteresis area to the experimental curves cited in the discussion section. A >15% mismatch in either the steady-state stretch or the hysteresis reduction with load falsifies the protection claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim (FIB model supplies a protection mechanism via extra stretch without excess fibril/NCM strain, plus loading-unloading asymmetry and hysteresis, in agreement with experiments) requires that the FIB skeleton is materially softer than NH within tendon ranges, that the diffusion coefficient's stiffness dependence produces the reported slower equilibration, and that the resulting strain partitioning matches biological observations. All three rest on the specific functional form chosen for the fibre stress (zero until crimp straightened, then load-bearing) and on how that instantaneous stiffness enters the diffusion coefficient. The abstract states the law is bespoke and that other constitutive choices could be swapped in, but supplies no derivation, no parameter fitting procedure, no sensitivity check, and no direct overlay against measured tendon curves. If the chosen law over- or under-estimates the recruitment threshold or the stiffness jump, both the softness ordering and the claimed protection effect can reverse.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript presents a one-dimensional poroelastic model for tendons in which the solid skeleton combines a soft neo-Hookean matrix with crimped fibrils that do not bear load until straightened (FIB model). Under uniaxial constant load and subsequent unloading, the FIB model is reported to be softer than a pure neo-Hookean (NH) skeleton within tendon parameter ranges, to equilibrate more slowly, to permit greater overall stretch without excessive local strain on fibrils or matrix (a claimed protection mechanism), and to exhibit loading-unloading asymmetry that produces hysteresis in the averaged stress-strain response; the diffusion coefficient in the governing equation is stated to depend on instantaneous stiffness.","tokens_in":2046,"tokens_out":484,"duration_ms":20394,"significance":"If the central claims hold after validation, the framework would supply a biologically interpretable poroelastic description of tendon recruitment that could account for observed hysteresis and strain partitioning, with the modular stress law allowing substitution of other fibril constitutive relations.","major_comments":[{"comment":"Abstract: the assertion that the FIB model is softer than NH and supplies a protection mechanism 'in agreement with experiments' is load-bearing for the central claim, yet the abstract supplies neither the explicit functional form of the bespoke stress law for crimp and recruitment, its derivation, nor any quantitative comparison to measured tendon curves or parameter-fitting procedure.","section":"Abstract"},{"comment":"Abstract: the diffusion equation is stated to have a stiffness-dependent coefficient, but no equation is written, no numerical implementation details are given, and the dependence creates a closed loop (stiffness is set by the same recruitment parameters that determine the diffusion coefficient); no sensitivity check is described to confirm that this produces the reported slower equilibration and hysteresis.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract states that other fibril constitutive laws 'can readily be considered,' but does not indicate how changes in the recruitment threshold or stiffness jump would affect the softness ordering or the protection effect.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The absence of governing equations, numerical methods, and any validation data in the provided text makes the manuscript unusually difficult to assess for a modeling paper; this may reflect an incomplete submission rather than a deliberate choice."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their constructive comments. We address each major comment below and indicate planned revisions.","responses":[{"response":"The abstract is a concise summary; the explicit piecewise stress law (zero load until crimp straightens, then neo-Hookean fibril extension) and its derivation from recruitment kinematics appear in the Methods. Agreement with experiments refers to qualitative features (greater extensibility before high local strains, load-dependent hysteresis) reported in the tendon literature, not a fitted dataset. We will revise the abstract to briefly note the stress-law form and clarify the qualitative nature of the comparison. A full quantitative fitting procedure lies outside the present scope.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the assertion that the FIB model is softer than NH and supplies a protection mechanism 'in agreement with experiments' is load-bearing for the central claim, yet the abstract supplies neither the explicit functional form of the bespoke stress law for crimp and recruitment, its derivation, nor any quantitative comparison to measured tendon curves or parameter-fitting procedure."},{"response":"The diffusion equation with instantaneous-stiffness-dependent diffusivity is written and derived in the Methods; the numerical scheme (implicit finite-difference time stepping with updated modulus at each step) is also detailed there. The coupling is not a closed loop: the effective modulus is evaluated from the current local strain and recruitment state during integration, which is standard for nonlinear poroelasticity. We agree a sensitivity study would strengthen the claims and will add one in revision to confirm the slower equilibration and hysteresis persist across the tendon parameter range.","revision_made":"partial","referee_comment":"[Abstract] Abstract: the diffusion equation is stated to have a stiffness-dependent coefficient, but no equation is written, no numerical implementation details are given, and the dependence creates a closed loop (stiffness is set by the same recruitment parameters that determine the diffusion coefficient); no sensitivity check is described to confirm that this produces the reported slower equilibration and hysteresis."}],"tokens_in":1473,"tokens_out":434,"duration_ms":27999,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main new piece here is the explicit inclusion of crimped fibril recruitment inside a poroelastic framework for tendon. Prior work had fibres but treated them as straight; this version lets the fibrils start unloaded and straighten progressively, which produces a softer overall response during loading and much slower relaxation on unloading. That asymmetry creates a hysteresis loop whose size shrinks with higher applied load, and the authors note it matches the qualitative pattern seen in experiments.\n\nThe framework itself is straightforward: a neo-Hookean matrix plus the recruitment rule, with the diffusion coefficient tied to instantaneous stiffness. The abstract is clear that the stress law is custom-built for this problem and that other fibril laws could be swapped in. That modularity is useful.\n\nThe soft spot is the lack of any quantitative check. No governing equations appear in the abstract, no parameter values or fitting procedure, and no direct comparison to measured stress-strain or fluid-flow data. The protection-mechanism claim (extra stretch without excess fibril or matrix strain) and the slower unloading both depend on the exact shape of the recruitment curve and on how stiffness feeds into diffusivity. If those functional forms are off, the ordering of FIB versus NH responses can flip. The circularity between stiffness and diffusion coefficient is acknowledged but not tested.\n\nThis is a narrow modeling contribution aimed at tendon biomechanics people who already work with poroelastic descriptions. A reader in that subfield could extract the recruitment idea and try it with their own constitutive choices. It is coherent on its own terms and shows clear thinking about the biology, so it clears the bar for serious refereeing even though the current version needs the missing validation steps filled in.","headline":"The paper adds crimped-fibre recruitment to a 1D poroelastic tendon model and shows resulting load-unload asymmetry, but the central claims rest on an unvalidated bespoke stress law with no data overlay or sensitivity checks.","tokens_in":2517,"tokens_out":428,"would_cite":false,"duration_ms":12262,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Crimped fibrils in a poroelastic tendon model allow greater stretch without high strain on fibrils or matrix, creating a protection mechanism during loading and unloading.","keywords":["poroelasticity","tendon","fibre recruitment","crimped fibrils","uniaxial loading","hysteresis","neo-Hookean matrix","diffusion equation"],"falsifier":"Direct measurement of the time required for a real tendon specimen to reach steady-state extension under a constant uniaxial load, compared against the time required for the same specimen to return to its unloaded length after load release; absence of measurable asymmetry or of load-dependent hysteresis would falsify the central claim.","tokens_in":2723,"feed_emoji":"","tokens_out":837,"duration_ms":19622,"temperature":0.7,"pith_summary":"The paper constructs a one-dimensional poroelastic model for tendon in which the solid phase consists of a neo-Hookean non-collagenous matrix plus crimped fibrils that recruit to load-bearing only after straightening. When compared with an otherwise identical model lacking fibrils, the fibril-inclusive version is softer under constant uniaxial tension and therefore reaches equilibrium more slowly; upon load release it relaxes far more slowly still because re-crimping further reduces stiffness. The resulting loading-unloading asymmetry produces a hysteresis loop in the averaged stress-strain response whose area shrinks as the applied load increases. The model thereby demonstrates how crimped-fibril recruitment lets the tissue extend farther before either fibrils or matrix experience damaging strains, consistent with experimental observations.","feed_headline":"Crimped fibrils let tendons stretch farther without high strain","feed_subtitle":"A poroelastic model shows gradual fibril recruitment slows relaxation on unloading and produces load-dependent hysteresis.","key_machinery":"The FIB model: a poroelastic solid whose neo-Hookean matrix is augmented by crimped fibrils that recruit upon straightening, governed by a diffusion equation whose coefficient depends on instantaneous stiffness.","core_discovery":"In the FIB model the solid skeleton is a soft neo-Hookean matrix reinforced by crimped fibrils that bear no load until straightened. Under constant applied tension the tissue therefore stretches farther before the fibrils or non-collagenous matrix reach high strains, furnishing a natural protection mechanism. The stiffness-dependent diffusion coefficient makes the FIB model approach steady state more slowly than the pure neo-Hookean case during loading and far more slowly during unloading, when re-crimping softens the tissue; the resulting asymmetry appears as a hysteresis loop in the stress-strain curve whose size decreases with larger applied loads.","pith_inferences":["The same recruitment mechanism may underlie the low-strain toe region observed in cyclic tendon tests in vivo.","Extending the model to spatially varying crimp angles could predict how regional differences in fibril waviness affect overall tendon compliance.","The stiffness-dependent diffusion coefficient suggests that damage-induced softening would further slow fluid flow and recovery after injury.","The framework could be used to explore how changes in fibril crimp statistics during aging or disease alter the hysteresis and protective capacity."],"forward_implications":["The FIB model reaches steady state more slowly than the neo-Hookean model during loading because the recruited fibrils keep the composite softer.","On unloading the FIB model relaxes much more slowly than the neo-Hookean model because fibril re-crimping further reduces stiffness.","The loading-unloading asymmetry produces a hysteresis loop in the averaged stress-strain curve whose area shrinks as applied load increases.","The explicit inclusion of crimped fibrils permits clearer biological interpretation and direct comparison with experimental recruitment data.","Other fibril constitutive laws can be substituted into the same poroelastic framework without altering the overall structure."],"fun_headline_variants":["Crimped fibrils protect tendon matrix in poroelastic model","Poroelastic model shows crimped fibres slow unloading relaxation","Uniaxial tendon model with fibre crimp produces load-dependent hysteresis","Crimped recruitment in poroelastic tendons explains stretch protection","Neo-Hookean poroelastic tendons with crimped fibrils yield asymmetry"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The bespoke stress law that accounts for crimp and fibril recruitment, together with the assumption that the diffusion coefficient depends on stiffness, correctly captures the mechanical response of the FIB model within typical tendon parameter ranges.","fun_headline_variants_meta":{"raw":{"variants":["Crimped fibrils protect tendon matrix in poroelastic model","Poroelastic model shows crimped fibres slow unloading relaxation","Uniaxial tendon model with fibre crimp produces load-dependent hysteresis","Crimped recruitment in poroelastic tendons explains stretch protection","Neo-Hookean poroelastic tendons with crimped fibrils yield asymmetry"]},"model":"grok-4.3","cost_usd":0.004325,"raw_usage":{"total_tokens":2239,"prompt_tokens":803,"num_sources_used":0,"completion_tokens":85,"cost_in_usd_ticks":43249500,"prompt_tokens_details":{"text_tokens":803,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1351,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":803,"tokens_out":85,"duration_ms":7741,"temperature":1.0,"reasoning_tokens":1351,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T21:47:34.028955+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct measurement of the time required for a real tendon specimen to reach steady-state extension under a constant uniaxial load, compared against the time required for the same specimen to return to its unloaded length after load release; absence of measurable asymmetry or of load-dependent hysteresis would falsify the central claim.","supporting_citations":[],"review_version":1}