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REVIEW 5 major objections 6 minor 22 references

A Reduced-Order CFD Approach for Intermediate grade Coronary Arterial Clinical Parameter Assessment

T0 review · 5 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper argues that a 1D-2D axisymmetric CFD hierarchy, fed by CT-derived geometry and non-Newtonian blood rheology, can non-invasively quantify intermediate coronary stenosis by reproducing FFR/iFR trends from above 0.92 at 40%…

desk verdict A reasonable 1D-2D coupling study whose clinical FFR/iFR claim is unsupported: the distal pressure is inherited from the 1D model, FFR/iFR are never defined, and the reported numbers are internally inconsistent. read the letter →

arxiv 2505.12485 v2 pith:56IUKYTI submitted 2025-05-18 physics.med-ph

Oeshee Roy , Priyanshu Ghosh , Sayan Karmakar , Supratim Saha This is my paper · ORCID
classification physics.med-ph
keywords coronaryarterystenosisfractionalflowreserveinstantaneouswave-freeratioreduced-orderCFD1Darterialnetwork2Daxisymmetricmodelnon-Newtonianbloodrheologylesionlength
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a reduced-order computational fluid dynamics chain — a one-dimensional model of the whole arterial tree feeding boundary conditions to a two-dimensional axisymmetric model of the narrowed segment — can turn CT-derived geometry into a non-invasive estimate of coronary stenosis severity. Fractional Flow Reserve (FFR) and instantaneous wave-free ratio (iFR), two pressure-based indices clinicians use to decide between stenting and medical therapy, both fall as stenosis severity rises: above 0.92 at 40% narrowing, down to about 0.65–0.76 at 70%, with the exact value depending on how blood's shear-thinning viscosity is modelled. The paper also reports that a 3 cm lesion produces lower FFR and iFR than a 1 cm lesion at the same percentage blockage. If the approach holds, it would offer a fast, non-invasive alternative to invasive pressure-wire measurement in the intermediate-grade grey zone where treatment decisions are hardest.

What carries the argument

The engine is the 1D-2D axisymmetric reduced-order chain. The 1D layer solves mass and momentum conservation on a 61-segment arterial tree using forward and backward characteristic variables $W_1$ and $W_2$, reconstructing cross-sectional area $A$ and velocity $u$, with a sigmoid pressure waveform at the inlet and a zero-reflection resistance model at the outlet. That layer produces the time-varying flow rate and the outlet pressure (for instance 93.303 mmHg at 70% stenosis) imposed on a 2D axisymmetric Navier-Stokes solver for the stenosed segment, which uses Newtonian, power-law, Carreau-Yasuda, or Casson viscosity to compute the local velocity and pressure fields from which FFR and iFR are derived.

What would settle it

Take the 70% stenosis case and run the 2D axisymmetric model with a coupled outflow resistance so the distal pressure is computed rather than prescribed at 93.303 mmHg; if the resulting FFR at the standard distal measurement point moves materially across the 0.75–0.80 decision zone, the higher-order model is not contributing independent clinical information.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the two-tier reduced-order model reproduces the expected physiology of intermediate stenosis while remaining cheap enough to run over one cardiac cycle. FFR and iFR decline monotonically with severity under every rheology model, FFR staying above 0.92 at 40% and reaching roughly 0.65–0.76 at 70%; the power-law fluid offers the least resistance and the highest FFR/iFR, while the Casson and Newtonian models sit at the low end. For a fixed severity, lengthening the lesion from 1 cm to 3 cm lowers both indices, evidence that lesion length should be read alongside percentage stenosis. The paper presents these trends as the basis for a non-invasive diagnostic tool that captures global flow conditions from the 1D tree and local pressure-flow detail from the 2D axisymmetric stenosis model.

Load-bearing premise

The load-bearing premise is that the 1D arterial-network pressure at the stenosis outlet is accurate enough to be imposed unchanged on the 2D model, since FFR is defined from that pressure and the 2D solver cannot independently correct the main clinical number.

Editorial extensions

If this is right

  • Clinicians could obtain FFR and iFR for intermediate lesions directly from CT data, bypassing invasive pressure-wire measurement.
  • At equal percentage stenosis, lesion length shifts the functional result: a 3 cm lesion lowers FFR and iFR relative to a 1 cm lesion, so length should enter the intervention decision.
  • The choice of blood rheology changes the clinical reading: at 70% severity the Newtonian model gives FFR about 0.68 while the power-law model gives 0.76, a spread that crosses the 0.75–0.80 decision boundary.
  • Because the 1D tree supplies the boundary conditions, the approach avoids full 3D coronary simulation and can run the local 2D model with about 200,000 elements over one cardiac cycle.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The pressure hand-off from 1D to 2D means the 2D model's FFR is largely inherited from the 1D distal pressure, so re-running the same stenosis with a self-consistently computed outlet pressure is a direct way to test how much independent information the higher-order model adds.
  • The model's monotone severity–FFR curve invites a calibration study against invasive FFR/iFR on the same CT data, which could turn these computed values into decision thresholds with confidence intervals.
  • Because the local model is axisymmetric, a natural extension is a same-patient comparison against full 3D geometry to identify the plaque shapes and curvatures where the axial symmetry assumption changes FFR by more than the grey-zone tolerance.
  • The lesion-length data could support a composite index, such as severity weighted by lesion length or pressure drop per unit length, that the paper does not define but its results suggest would sharpen the intermediate-grey-zone decision.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper proposes a reduced-order CFD approach combining a 1D arterial tree model with a 2D axisymmetric model of a stenosed coronary artery, using CT-derived geometry and non-Newtonian rheology, to estimate Fractional Flow Reserve (FFR) and instantaneous wave-free ratio (iFR) for intermediate-grade stenoses (40%, 50%, 70%). The 1D model provides global flow/pressure boundary conditions for the 2D model; FFR and iFR are reported as decreasing with severity and with longer lesion length. The authors claim the method is a reliable and non-invasive diagnostic tool for coronary stenosis evaluation.

Significance. If substantiated, a low-cost patient-specific FFR/iFR prediction tool of this type would be clinically valuable. The paper's strengths include grid-independence checks for both solvers and validation against published waveforms and steady-flow stenosis data. The 1D-to-2D hierarchical coupling is a reasonable idea in principle. However, the central claim of reliable FFR/iFR assessment is not supported: FFR is not defined or located, the 2D model inherits its outlet pressure from the 1D model, no hyperemic simulation is provided (which is standard for FFR), and there is no clinical validation against invasive FFR. The manuscript is a methodological sketch rather than a demonstrated diagnostic tool.

major comments (5)
  1. [3. Result and discussion; Table 2] FFR is never defined and the location where distal pressure is extracted is never stated. The paper reports numerical FFR values but gives no formula such as FFR = Pd/Pa and no specification of the temporal averaging (mean over the cycle, at a particular phase, etc.). This makes the headline results unreproducible. More importantly, the 2D model receives its outlet pressure as a Dirichlet boundary condition generated directly from the 1D model (Table 2). If FFR is evaluated at that outlet, its value is inherited verbatim from the 1D pressure solution, so the higher-order 2D model adds no independent information about the primary clinical index. The manuscript must define FFR/iFR precisely, state the extraction point, and show how the local 2D pressure field (if used) enters the calculation.
  2. [Table 2; 3. Result and discussion] The reported FFR values are numerically inconsistent with the imposed outlet pressures. For 70% severity, the outlet pressure is 93.303 mmHg. With an aortic pressure near 100 mmHg (as suggested by the inlet waveform), FFR at that outlet would be about 0.93, yet the text reports FFR values of 0.68 (Newtonian), 0.76 (power-law), 0.73 (Carreau), and 0.65 (Casson). If the reference aortic pressure differs from 100 mmHg, or if FFR is computed at an interior location (where pressure would be higher, not lower, than the outlet), this must be stated explicitly. As written, the reported FFR values cannot be reconciled with the stated boundary conditions.
  3. [2.1.2 Boundary conditions; 3. Result and discussion] FFR is physiologically defined under maximal hyperemia, where coronary microvascular resistance is minimized. The model applies a resting-style sigmoid pressure waveform at the inlet and a zero-reflection resistance at the outlet, with no representation of hyperemia (e.g., reduced distal resistance or adenosine-induced vasodilation). Computing FFR from a resting-state simulation therefore does not correspond to the index used clinically. The authors should either introduce a hyperemia model or explicitly argue why resting conditions are sufficient; without this, the claim that the computed values are 'FFR' is physiologically unsupported.
  4. [2.1 Computational domain] The manuscript repeatedly claims that the geometry is patient-specific and derived from 'Multi-slice CT scans', yet no details of the imaging-to-model pipeline are given: no segmentation method, no patient characteristics, no imaging parameters, and no demonstration that the analytical stenosis equation (which models area variation with axial position) matches any real patient's anatomy. The analytical equation appears to be a generic parameterization, not a patient-derived geometry. The reliability of the diagnostic prediction cannot be assessed without this information. Either provide the full patient-specific pipeline or temper the claim to 'representative stenosis geometries'.
  5. [2.2.2 Boundary Conditions] The 2D axisymmetric model imposes a single time-independent pressure value at the outlet (Table 2), while the inlet flowrate is a pulsatile waveform (Figure 5). The paper does not state whether the outlet pressure is a mean, peak, end-diastolic, or time-varying value, nor how a constant distal pressure is physically consistent with pulsatile inflow. This is not merely a presentation detail: the pressure drop computed by the 2D model (and any FFR derived from it) depends critically on the temporal nature of the outlet boundary condition. The outlet condition must be fully specified and justified.
minor comments (6)
  1. [3. Result and discussion; Conclusion] The text claims that all non-Newtonian models predict higher FFR than the Newtonian model, but the reported Casson value at 70% (0.65) is lower than the Newtonian value (0.68). The Conclusion even states that 'the Carreau and Casson models yield slightly lower values than the Newtonian model'. Please correct this inconsistency in the interpretation of the model comparison.
  2. [Figure 9] The iFR results are presented only as a qualitative description with a figure; no numerical values or a definition of the wave-free period are provided. Since iFR is a central claim of the paper, a formula and a table or precise values from the figure are needed.
  3. [Figures 8 and 11] The captions of Figures 8 and 11 are identical ('1D boundary condition given inlet to arterial tree') and do not match the content; Figure 11 appears to plot pressure drop versus severity. Please correct the captions.
  4. [2.2.1 2D Numerical details] There is a typographical error: 'Carreau Yesuda' should be 'Carreau–Yasuda'.
  5. [References] References [20] and [21] are on microfluidic particle sorting and do not appear to be relevant to the 2D stenosis validation; please cite appropriate studies for the stenotic flow validation.
  6. [3. Result and discussion] The 'grey zone' for FFR is described as 0.76–0.80, whereas the cited literature (e.g., reference [16]) commonly uses 0.75–0.80; please align the threshold with the cited sources.

Circularity Check

1 steps flagged · score 6.0 of 10

The 2D FFR/iFR predictions inherit the severity-dependent distal pressure from the 1D model; with no stated FFR extraction point, the higher-order model does not independently predict the primary clinical index.

  1. fitted input called prediction [Section 2.2.2 Boundary Conditions and Table 2; Abstract]
    "The boundary conditions for 2D axisymmetric model are generated using 1D model for flowrate and pressure conditions. At inlet, flowrate is prescribed and at the outlet, pressure is imposed. ... Fractional Flow Reserve (FFR) and instantaneous wave-free ratio (iFR) are calculated using various non-Newtonian models across different severities for higher order model."

    FFR is a pressure ratio whose numerator is distal coronary pressure. In the 2D model the only distal pressure supplied is the outlet pressure from Table 2, which is generated by the 1D model and already includes the stenosed segment (e.g., 93.303 mmHg at 70% severity). If FFR is evaluated at that outlet, it is inherited verbatim from the 1D pressure solution rather than predicted by the 2D local flow solution. The paper never states the FFR formula or the extraction point, and the reported FFR values vary with rheology even though the imposed outlet pressure is fixed, so the extraction point cannot be identified. Thus the central diagnostic result is at least partly an input boundary condition from the 1D model, not an independent 2D prediction.

full rationale

The CFD solvers themselves are validated against external literature (Low et al. for 1D waveforms; Varghese et al. for 2D stenotic flow), so the numerics are not circular. The circularity is confined to the clinical-index derivation chain: the 2D axisymmetric model receives its outlet pressure from the 1D model, and FFR/iFR are then reported for the higher-order model without a stated definition or measurement location. Because FFR is determined by distal pressure, prescribing that pressure from the 1D solution forces the severity-dependent trend and, at the outlet, the absolute value. The lesion-length and rheology comparisons still contain local 2D fluid-dynamic content, but the primary clinical parameter does not constitute an independent prediction. Score 6 reflects this partial, construction-level reduction rather than a claim that every result is predetermined.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on several unstated or literature-cited material parameters (wall stiffness beta, unstressed area, rheology coefficients, inlet waveform), an unchallenged set of physiological simplifications (laminar, Poiseuille friction, zero reflection), and the assertion that an analytical stenosis represents patient-specific anatomy. No new physical entities are introduced.

free parameters (4)
  • Wall stiffness coefficient beta per 1D segment = not reported
    Equation (3) uses beta in p = p_ext + beta(√A - √A0). Values are not given, so compliance and wave speed are unspecified; the simulation cannot be reproduced.
  • Unstressed cross-sectional area A0 per segment = not reported
    Also in Equation (3); claims patient-specific CT geometry but no actual areas or reconstruction are shown.
  • Non-Newtonian rheology parameters = not reported
    Power-law, Carreau-Yasuda, and Casson coefficients are described as taken from reference [13] but not listed; these directly set the apparent viscosity used in the 2D model and affect the resulting FFR and iFR.
  • Inlet sigmoid pressure waveform parameters = not reported
    The inlet boundary condition is described as a realistic pressure waveform created with a sigmoid function, but the amplitude, period, and shape parameters are not stated.
assumptions (6)
  • domain assumption Blood is incompressible and flow is laminar in both 1D and 2D models
    Stated in Sections 2.1 and 2.2.1; no justification for laminar assumption in stenosed coronary flow, where transitional or disturbed flow is possible.
  • domain assumption Friction in the 1D model follows steady Poiseuille flow for the given cross-sectional area
    Section 2.1.1 says friction is modeled for steady and laminar flow consistent with Poiseuille flow; pulsatile and stenosed flows may violate this.
  • domain assumption Zero reflection coefficient at all outflow boundaries
    Section 2.1.2 sets reflection coefficient to zero; this is a simplified absorbing condition that may not capture coronary bed physiology.
  • domain assumption Pressure-area relationship p = p_ext + beta(sqrt(A) - sqrt(A0)) is valid for all 61 segments including the stenosed segment
    Equation (3) is taken from literature but no validation is provided for its use in the stenosed segment; the stenosis is modeled as an area variation using the same compliance relation.
  • ad hoc to paper The analytical stenosis equation represents patient-specific coronary geometry
    Section 2.1 states stenosis is modeled using analytical equations with tapering; no CT images, segmentation, or patient data are presented, so the link to patient-specific geometry is asserted rather than demonstrated.
  • domain assumption 1D-generated flowrate and pressure waveforms are valid boundary conditions for the 2D axisymmetric model
    Section 2.2.2; the 2D model inherits its inlet flow and outlet pressure from the 1D model, so errors in the 1D solution propagate without independent correction.

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Pith. "Pith review of A Reduced-Order CFD Approach for Intermediate grade Coronary Arterial Clinical Parameter Assessment." pith.science (2026). https://pith.science/paper/56IUKYTI

@misc{pith2026250512485,
  author       = {Pith},
  title        = {Pith review of: A Reduced-Order CFD Approach for Intermediate grade Coronary Arterial Clinical Parameter Assessment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/56IUKYTI}},
  note         = {Machine review of arXiv:2505.12485}
}
read the original abstract

Coronary heart disease (CHD) remains a top reason of mortality worldwide. This study introduces a novel approach by integrating patient-specific Multi-slice CT scans into CAD models and employing a one-dimensional numerical framework to assess varying degrees of stenosis. The computational analysis encompasses the entire arterial tree, with a particular focus on stenosed coronary arteries modelled using an analytical equation. One-dimensional characteristic equations, utilizing forward and backward characteristic variables, are used to derive essential parameters such as area and velocity. A model based on resistance with reflection coefficient set to zero and realistic pressure waveform input is applied at the outflow and inflow respectively. Boundary conditions generated from the 1D model, capturing global characteristics, are subsequently used to simulate a 2D axisymmetric model, which captures local characteristics. The numerical solvers are validated against literature results, ensuring grid independence. Fractional Flow Reserve (FFR) and instantaneous wave-free ratio (iFR) are calculated using various non-Newtonian models across different severities for higher order model. Additionally, the role of lesion length in stenosed coronary arteries is investigated. Numerical simulations are performed over one cardiac cycle, covering both systole and diastole phases. The results demonstrate that FFR and iFR decrease with increasing stenosis severity. This method provides a reliable and non-invasive diagnostic tool for evaluating the functional severity of coronary artery stenosis in clinical settings, effectively capturing both global and local hemodynamic characteristics.

Figures

Figures reproduced from arXiv: 2505.12485 by the authors.

Figure 1
Figure 1. Schematic illustration of the computational domain. The computational domain for the 1D numerical simulation covers the full arterial tree with 61 segments, where the stenosed section (segment 4) is located in the left part of the coronary tree, as shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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