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Investigating the Impact of Arterial Irregularity On Clinical Parameters Using Reduced Order CFD Models In Stenosed Coronary Artery

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

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Pith's one-line read Arterial wall irregularity independently lowers FFR and iFR and raises pressure drop in stenosed coronary arteries.

desk verdict A plausible reduced-order 1D–2D workflow for coronary stenosis FFR/iFR whose headline irregularity effect rests on an unspecified geometry, making the quantitative claim irreproducible as submitted. read the letter →

arxiv 2505.13536 v1 pith:KHCR5MBK submitted 2025-05-18 physics.med-ph physics.bio-ph

Priyanshu Ghosh , Sayan Karmakar , Disha Mondal , Oeshee Roy , Supratim Saha This is my paper · ORCID
classification physics.med-phphysics.bio-ph MSC 76Z0592C35
keywords coronaryarterystenosisfractionalflowreserveinstantaneouswave-freeratiosurfaceirregularityreduced-orderCFDnon-Newtonianbloodone-dimensionalarterialtree2Daxisymmetricmodel
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

Coronary heart disease is assessed by indices such as Fractional Flow Reserve (FFR) and the instantaneous wave-free ratio (iFR), which measure whether a narrowed artery still delivers enough blood; lower values mean more severe functional blockage. This paper asks whether the roughness of the plaque, rather than just the percent narrowing, changes those indices. Using a reduced-order pipeline, a one-dimensional model of the full arterial tree that feeds boundary conditions into a two-dimensional axisymmetric model of the stenosed segment, it compares smooth and irregular blockages at 40, 50, and 70 percent severity under Newtonian and three non-Newtonian blood models. The paper reports that irregular lesions consistently yield lower FFR and iFR values and higher pressure drops than smooth lesions of the same severity. If this is right, surface irregularity acts as an independent resistance factor and should be included when interpreting non-invasive FFR and iFR estimates, because intervention decisions are often made on small differences around clinical thresholds.

What carries the argument

The load-bearing machinery is a coupled reduced-order hemodynamic pipeline. A one-dimensional model of a 61-segment arterial tree solves the mass and momentum conservation equations using forward and backward characteristic variables $W_1$ and $W_2$ (area and velocity are recovered from their sum and difference), with a pressure–area tube law $p = p_{\mathrm{ext}} + \beta(\sqrt{A}-\sqrt{A_0})$, inflow pressure from a sigmoid-shaped waveform, and an outflow resistance with zero reflection coefficient. The 1D results supply flow-rate and pressure boundary conditions for a 2D axisymmetric model of the stenosed segment, where blood is treated as Newtonian or as power-law, Carreau–Yasuda, or Casson fluid. The stenosis geometry itself is analytical, with a periodic surface irregularity whose amplitude is calibrated to height measurements from a left circumflex coronary arterial cast and whose effect is isolated by comparing with a smooth geometry of identical severity. This two-scale coupling is what lets the authors attribute changes in FFR, iFR, and pressure drop to irregularity rather than to whole-tree boundary-condition artifacts.

What would settle it

A realistic three-dimensional reconstruction of an irregular human coronary plaque at the same percent stenosis as a smooth case would settle the claim: compute FFR and iFR and see whether the smooth–irregular gap persists with true roughness geometry rather than the analytic periodic pattern.

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Extended reading notes

Core claim

The paper's central claim is that surface irregularity of a coronary stenosis is not a cosmetic detail: at the same percentage severity, an irregularly shaped plaque produces a consistently larger functional deficit than a smooth one. Across 40%, 50%, and 70% stenosis severities, the irregular arteries show lower Fractional Flow Reserve and lower instantaneous wave-free ratio, and higher pressure drop, than smooth arteries under the same rheological model. This ordering holds for Newtonian blood and for the power-law, Carreau–Yasuda, and Casson non-Newtonian models, although the magnitude of the irregularity effect varies with the model. The authors interpret the result as evidence that lesion irregularity contributes added resistance to blood flow, and therefore that non-invasive functional assessment of stenosis should not rely on severity alone. The accompanying contribution is a pipeline in which a one-dimensional model of the whole arterial tree supplies pressure and flow-rate boundary conditions to a two-dimensional axisymmetric model of the stenosed segment, so that both global and local hemodynamics are captured without full three-dimensional simulation.

Load-bearing premise

The paper assumes that the periodic waviness imposed on the stenosis wall, with height calibrated from a single left circumflex coronary arterial cast, faithfully represents real lesion irregularity; if true plaque roughness differs, the reported FFR and iFR differences could shrink, grow, or reverse.

Editorial extensions

If this is right

  • A non-invasive FFR or iFR estimate computed on a smooth lumen will tend to overstate the functional capacity of an irregular lesion.
  • Identical percent stenosis does not imply identical functional severity when one lesion is irregular, so severity alone is an incomplete guide to intervention.
  • The rheological model changes the size of the irregularity effect but not its direction; quantitative thresholds therefore depend on model choice.
  • Because global boundary conditions come from the 1D tree and only the stenosed segment is resolved in 2D, irregularity-aware functional assessment remains computationally feasible for clinical use.
  • For intermediate stenoses (40–70%), where treatment decisions are hardest, irregularity shifts FFR and iFR values and can move a result across a decision threshold.

Reading between the lines

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

  • The paper does not quantify it, but if the central claim is right, plaque roughness becomes a candidate imaging biomarker: texture features extracted from the same CT scan could sharpen non-invasive FFR and iFR prediction at no extra clinical cost.
  • A direct testable extension would vary the roughness amplitude and wavelength around the calibration point; the sensitivity of FFR and iFR to these parameters would show whether the reported irregularity effect is robust or tied to the chosen waviness.
  • Because iFR requires no hyperemic agent, the same 1D–2D pipeline could be applied to resting whole-cycle indices; the irregularity-induced resistance could interact differently with wave-free-period assumptions than with hyperemic conditions.
  • If confirmed in patient-specific three-dimensional reconstructions, the result implies that smooth-lumen idealizations in non-invasive functional assessment should be corrected for roughness, especially in diffuse mild disease where irregular surfaces are common.
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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 / 5 minor

Summary. The paper presents a reduced-order CFD framework that couples a 1D model of the full arterial tree with a 2D axisymmetric model of a stenosed coronary artery, using patient-specific CT-based geometry described in the text. The authors compute FFR, iFR, and pressure drop for 40%, 50%, and 70% stenoses using Newtonian and non-Newtonian (power-law, Carreau-Yasuda, Casson) rheology models. The central reported finding is that irregularly stenosed arteries exhibit lower FFR and iFR values and higher pressure drops than smooth stenosed arteries at the same nominal severity. The paper also includes grid independence studies and validation against literature waveforms for the 1D and 2D solvers.

Significance. If the central irregular-versus-smooth contrast is robust, the finding that surface irregularity acts as an independent flow-resistance factor would be clinically relevant for non-invasive FFR/iFR estimation. The paper's strengths include an explicit 1D-to-2D boundary-condition pipeline, systematic comparison of four rheology models, grid independence checks, and validation against established numerical solutions. However, the significance is currently bounded by missing specification of the irregular lesion geometry and absent definitions of the clinical indices, which prevent reproduction and quantitative interpretation.

major comments (5)
  1. [Section 2.1] The analytic representation of the irregular stenosis is never specified. The paper states only that the irregularity height is 'calibrated' to a left circumflex coronary arterial cast and that the shape is assumed periodic, but it gives no wall-radius function, amplitude, wavelength, or number of undulations. Because the central irregular-versus-smooth contrast in Figures 8-10 depends entirely on this generated geometry, the authors must provide the exact formula and parameter values, and demonstrate that the minimal luminal area (and hence stenosis severity) is identical between the smooth and irregular cases.
  2. [Section 3] FFR and iFR are never defined. The manuscript does not state how these indices are computed from the 1D or 2D pressure/velocity fields, whether a hyperemic state is simulated for FFR, or which proximal and distal reference pressures are used. Without these definitions, the reported numerical values cannot be clinically interpreted or independently reproduced.
  3. [Section 2.2.5] The 2D validation is performed for a generic test case with diameter D = 1 m, viscosity μ = 1 Pa·s, and velocity U = 0.5 m/s. This demonstrates solver capability on idealized stenotic flows but does not validate the coronary-scale geometry, rheology, or the specific boundary-condition combination used in the clinical calculations. The authors should add a coronary-scale validation or explicitly qualify that the validation applies only to the underlying numerical scheme.
  4. [Table 1] Table 1 lists three single outlet pressure values (106.154, 104.296, and 93.303 mmHg) with no indication of whether these are mean, systolic, end-diastolic, or some time-averaged quantities. Since FFR is a ratio of distal to aortic pressure, the absolute FFR values reported in Figure 8 inherit the choice of these boundary conditions; the basis for these values and their relation to the 1D pressure waveforms must be clarified and justified.
  5. [Section 3] No comparison with measured FFR or iFR values is provided. The abstract claims a 'reliable, non-invasive diagnostic tool,' but without comparison to invasive or computed-tomography-derived FFR/iFR measurements from patients, the quantitative accuracy of the method is unverified. Add a validation against published clinical FFR/iFR data, or temper the clinical claim accordingly.
minor comments (5)
  1. [Section 2.1] There are two subsections labeled '2.1.4' (Grid independence study and Validation study), and the later section heading '2 2D Numerical details' should be renumbered as 2.2. The subsection numbering throughout the methodology should be made consistent.
  2. [Figure 5] The caption reads '1D boundary condition generated for different severity...', but the figure appears to show flow-rate waveforms. Make the caption consistent with the content, and clarify which variable is plotted.
  3. [Introduction] The abstract and introduction emphasize patient-specific multi-slice CT scans, but the methodology does not describe how CT images are segmented or converted into the 1D arterial tree and the 2D stenosis model. A brief description of the imaging-to-model pipeline is needed.
  4. [Section 2.1] The sentence 'The severity of stenosis of patient-specific cases are 40, 50 and 70 which are of intermediate grade stenosis' has grammatical errors and does not state whether severity is a diameter reduction or area reduction. Please define severity and correct the phrasing.
  5. [References] References [18] and [19] concern microfluidic particle sorting and appear unrelated to the stenosis validation context in which they are cited; please either integrate them into the text appropriately or remove them.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation found; the smooth-versus-irregular comparison is computed in the 2D model from stated boundary conditions, and the solver is validated against external literature.

full rationale

I walked the derivation chain and found no step that reduces to its own inputs. The 1D governing equations (Eqs. 1-2 and the tube law Eq. 3) are attributed to Sherwin et al. [3] and Mynard and Nithiarasu [4], and the LCG numerical method is attributed to [4,5,13]; refs. [5,13] are prior applications by the present authors, but the underlying method is externally established and the 1D solver is validated against Low et al. [15]. The 2D axisymmetric model is validated against Varghese et al. [16] and other external data. The boundary conditions for the 2D model (inlet flowrate and outlet pressure) are generated by the 1D arterial-tree simulation, not fitted to FFR or iFR targets; the smooth-versus-irregular comparison is then produced inside the 2D computation under identical 1D boundary conditions, so it is not identical to the model input. The irregularity amplitude is stated to be calibrated to an external left circumflex coronary arterial cast [11], with a periodic shape assumed; no shape equation, amplitude, or wavelength is reported, which is a reproducibility and geometric-validity limitation, but it is not circular because the FFR/iFR outputs are not baked into that geometry choice. The severity-level FFR trend may partly inherit the 1D outlet-pressure schedule shown in Table 1, but even if that limits physiological interpretation, it does not make the irregularity contrast circular. Self-citations [5,8,9,13,14] are contextual and not load-bearing; no uniqueness theorem is imported from the authors' prior work, and no fitted parameter is renamed as a prediction. Therefore no circular step meeting the evidentiary bar is identified.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The pipeline rests on standard 1D and 2D hemodynamic equations from the literature, plus several domain assumptions (Poiseuille friction, zero reflection, rigid axisymmetric wall, calibrated periodic irregularity). The main ad hoc input is the unreported irregularity geometry, which is a free parameter that directly drives the novel comparison. No new physical entities are introduced.

free parameters (2)
  • Surface irregularity height (amplitude) = Not reported (calibrated to one left circumflex arterial cast)
    Section 2.1 states the height is calibrated to the cast data and the shape is assumed periodic, but no numerical value or equation is given. This amplitude directly controls the severity of the irregularity and hence the reported FFR/iFR and pressure-drop differences.
  • Surface irregularity wavelength/periodicity = Not reported
    The periodic pattern is not specified, so the number and spacing of roughness elements is a free modeling choice that affects local pressure loss.
assumptions (7)
  • standard math 1D mass and momentum conservation with characteristic variables (Eqs. 1-5)
    Taken from Sherwin et al. [3] and Mynard-Nithiarasu [4]; used as the foundation of the 1D arterial tree model.
  • domain assumption Poiseuille steady laminar friction for the 1D friction term
    Section 2.1.1 states steady, laminar Poiseuille assumptions for friction, which neglects unsteady and entry effects in coronary flow.
  • domain assumption Linear elastic pressure-area relation with constant beta (Eq. 3)
    Wall compliance is modeled through a tube law with constant beta from the literature; it is not patient-specific.
  • domain assumption Zero reflection coefficient at the 1D outlet
    Section 2.1.3 applies a zero-reflection outlet, which is an idealized condition; real coronary microvascular beds reflect waves.
  • domain assumption 2D axisymmetric, rigid-wall, laminar incompressible flow
    Section 2.2 writes the 2D model without wall motion and assumes axisymmetry and laminar flow.
  • ad hoc to paper Periodic surface irregularity calibrated to a single cast
    The irregular lesion shape is assumed periodic with height calibrated to one arterial cast (Section 2.1); this ad hoc geometry is the key input for the central comparison.
  • domain assumption Non-Newtonian rheology coefficients from literature [12]
    Carreau-Yasuda, Casson and power-law coefficients are taken from Shibeshi and Collins [12] without listing values or validating them at coronary shear rates.

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Cite this review

Pith. "Pith review of Investigating the Impact of Arterial Irregularity On Clinical Parameters Using Reduced Order CFD Models In Stenosed Coronary Artery." pith.science (2026). https://pith.science/paper/KHCR5MBK

@misc{pith2026250513536,
  author       = {Pith},
  title        = {Pith review of: Investigating the Impact of Arterial Irregularity On Clinical Parameters Using Reduced Order CFD Models In Stenosed Coronary Artery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KHCR5MBK}},
  note         = {Machine review of arXiv:2505.13536}
}
read the original abstract

Coronary heart disease (CHD) remains a leading cause of mortality worldwide. This study introduces a novel approach that integrates patient-specific Multi-slice CT scans into CAD models, using a one-dimensional numerical framework to assess varying degrees of coronary artery stenosis. The computational analysis encompasses the entire arterial tree, with a particular focus on stenosed coronary arteries modeled analytically. Key parameters, such as area and velocity, are derived from one-dimensional characteristic equations based on forward and backward characteristic variables. A resistance model with zero reflection coefficient and realistic pressure waveform inputs is applied at the outflow and inflow, respectively. The global characteristics captured by the 1D model serve as boundary conditions for a 2D axisymmetric model that focuses on local characteristics. The numerical solvers are validated against existing literature, ensuring grid independence. Fractional Flow Reserve (FFR) and Instantaneous wave-free Ratio (iFR) are calculated using various non-Newtonian models across different stenosis severities. The study also investigates the impact of lesion irregularity in stenosed coronary arteries, finding that irregular arteries exhibit lower FFR and iFR values and higher pressure drops, indicating increased blood flow resistance. This method provides a reliable, non-invasive diagnostic tool for evaluating the functional severity of irregular coronary artery stenosis in clinical settings, effectively capturing both global and local hemodynamic characteristics.

Figures

Figures reproduced from arXiv: 2505.13536 by the authors.

Figure 1
Figure 1. Representative diagram of the computational domain. The computational domain for the 1D numerical simulation encompasses the full arterial tree having 61 segments, with the stenosed section (segment 4) specifically located in the left part of coronary tree, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 8
Figure 8. Comparison of FFR values for different smooth and irregular stenosed coronary arteries [PITH_FULL_IMAGE:figures/full_fig_p004_8.png] view at source ↗

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Reference graph

Works this paper leans on

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