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arxiv: 2512.11017 · v1 · submitted 2025-12-11 · ⚛️ physics.med-ph · physics.flu-dyn

Integrating Uncertainty Quantification into Computational Fluid Dynamics Models of Coronary Arteries Under Steady Flow

Muhammad Usman , Peter N. Castillo , Akil Narayan , Lucas H. Timmins This is my paper

Pith reviewed 2026-05-16 22:55 UTC · model grok-4.3

classification ⚛️ physics.med-ph physics.flu-dyn
keywords uncertainty quantificationcomputational fluid dynamicscoronary arterieswall shear stresspolynomial chaos expansionsensitivity analysishemodynamicsblood flow modeling
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The pith

Viscosity drives most variability in wall shear stress for patient-specific coronary artery models, unlike velocity in simple flow.

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

Computational fluid dynamics models of coronary arteries typically treat inputs like blood viscosity, density, and flow velocity as fixed values, which overlooks their natural variability and reduces trust in predictions of wall shear stress. This paper incorporates uncertainty quantification through a polynomial chaos expansion emulator to measure how input parameters influence wall shear stress outputs in both an analytical pipe-flow solution and a real patient geometry. The analysis shows velocity accounts for roughly 79 percent of wall shear stress variability in the analytical case, while viscosity accounts for about 59 percent in the patient-specific left main coronary artery model. Unary effects dominate over parameter interactions in both settings, accounting for 93 percent and 99 percent of the total sensitivity indices respectively.

Core claim

The uncertainty quantification framework applied via polynomial chaos expansion shows that velocity dominates wall shear stress variability in the analytical Poiseuille flow solution at approximately 79 percent, whereas viscosity dominates in the patient-specific left main coronary artery model at approximately 59 percent, with unary Sobol indices contributing the large majority of interactions in each case.

What carries the argument

Polynomial chaos expansion emulator that maps uncertain input parameters (pressure, viscosity, density, velocity, radius) to wall shear stress and directly extracts output statistics and Sobol sensitivity indices.

If this is right

  • Viscosity measurements deserve higher priority than velocity estimates when reducing uncertainty in patient-specific coronary artery simulations.
  • Unary parameter effects dominate, which simplifies uncertainty budgets for future vascular flow studies.
  • Adding uncertainty quantification increases the credibility of computational models used for coronary artery disease diagnosis and treatment planning.
  • Sensitivity rankings change with geometric complexity, so dominance observed in ideal flows does not transfer directly to realistic artery shapes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying the same emulator to pulsatile flow conditions could test whether time-varying effects shift the viscosity dominance observed under steady flow.
  • Standardizing blood viscosity measurement protocols may improve model reliability across many vascular CFD applications more than refining velocity inputs from imaging.
  • The framework could be reused for other outputs such as pressure loss or flow recirculation to rank parameter importance for different clinical endpoints.

Load-bearing premise

The steady-flow assumption together with the chosen ranges for the uncertain input parameters accurately represent real coronary blood flow conditions.

What would settle it

A Monte Carlo ensemble of full CFD simulations sampling the same input distributions and checking whether the resulting wall shear stress variance is explained primarily by viscosity in the patient model versus velocity in the analytical model.

read the original abstract

Computational models are continuously integrated in the clinical space, where they support clinicians in disease diagnosis, prognosis, and prevention strategies. While assisting in clinical space, these computational models frequently use deterministic approaches, where the inherent (aleatoric) variability of input parameters is ignored. This questions the credibility and often hinders the clinical adoption of these computational models. Therefore, in this study, we introduced uncertainty quantification in the computational fluid dynamics models of the left main coronary artery to analyze the influence of input hemodynamics parameters on wall shear stress (WSS). UncertainSCI was used, where an emulator was built using polynomial chaos expansion between the input parameters and the output quantity of interest, and the output sensitivities and statistics were directly extracted from the emulator. The uncertainty-informed framework was first applied to an analytical solution of the Navier-Stokes equation (Poiseuille flow) and then to a patient-specific model of the left main coronary artery. Different input hemodynamics parameters are considered, such as pressure, viscosity, density, velocity, and radius, whereas wall shear stress was considered as our output quantity of interest. The results suggest that velocity dominated the variability in WSS in the analytical model (~79%), whereas viscosity dominated in the patient-specific model (~59%). The results further suggest that out of all the Sobol indices interactions, unary interactions were the most dominant ones, contributing ~93.2% and ~99% for the analytical and patient-specific model, respectively. This study will enhance confidence in computational models, facilitating their adoption in the clinical space to improve decision-making for coronary artery disease diagnosis, prognosis, and therapeutic strategies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces an uncertainty quantification (UQ) framework using polynomial chaos expansion (PCE) via the UncertainSCI library to assess the sensitivity of wall shear stress (WSS) to input hemodynamic parameters (pressure, viscosity, density, velocity, radius) in steady-flow CFD models of coronary arteries. The approach is first validated on the analytical Poiseuille solution of the Navier-Stokes equations, where velocity is reported to dominate WSS variability (~79%), and then applied to a patient-specific left-main coronary artery geometry, where viscosity dominates (~59%). Unary Sobol indices are found to account for the large majority of interactions (~93% analytical, ~99% patient-specific).

Significance. If the sensitivity rankings are robust, the work supplies a practical, emulator-based route to propagate input uncertainty through steady coronary CFD without full Monte-Carlo sampling. The analytical-to-patient-specific progression and the emphasis on unary interactions constitute a clear methodological demonstration that could raise confidence in deterministic CFD outputs used for coronary artery disease assessment. The computational efficiency of PCE is a genuine strength for eventual clinical translation.

major comments (3)
  1. [Methods and Discussion] The steady-flow assumption is load-bearing for the reported dominance ordering. Coronary flow is pulsatile; the manuscript does not demonstrate or discuss whether the velocity (~79%) versus viscosity (~59%) ranking persists under physiologic pulsatile boundary conditions or wave-propagation effects. A targeted comparison or limitation statement is required before the clinical-adoption claim can be sustained.
  2. [Methods] Input parameter distributions and ranges are not specified. The abstract states that pressure, viscosity, density, velocity, and radius are treated as uncertain, yet no probability densities, support intervals, or physiological justification are supplied. Because the PCE emulator directly maps these distributions to the Sobol indices, the numerical values (~79%, ~59%, 93–99%) cannot be reproduced or assessed for sensitivity to the chosen priors.
  3. [Results] No convergence diagnostics, polynomial degree, sample count, or cross-validation error for the PCE emulator are reported. Without these quantities it is impossible to judge whether the extracted unary Sobol indices (93.2% and 99%) are accurate or whether truncation error has artificially suppressed higher-order interactions.
minor comments (2)
  1. [Abstract] The abstract introduces UncertainSCI without a citation or one-sentence description of its PCE implementation; adding a brief reference would improve accessibility.
  2. [Figures] Figure captions and axis labels should explicitly state the input distributions used for each sensitivity bar plot so that readers can immediately connect visuals to the (currently missing) parameter ranges.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have identified important areas for clarification and improvement. We address each major comment point by point below and commit to revisions that strengthen the manuscript without altering its core findings.

read point-by-point responses

  1. Referee: [Methods and Discussion] The steady-flow assumption is load-bearing for the reported dominance ordering. Coronary flow is pulsatile; the manuscript does not demonstrate or discuss whether the velocity (~79%) versus viscosity (~59%) ranking persists under physiologic pulsatile boundary conditions or wave-propagation effects. A targeted comparison or limitation statement is required before the clinical-adoption claim can be sustained.

    Authors: We agree that the steady-flow assumption represents a significant simplification and that the reported sensitivity rankings cannot be assumed to hold under pulsatile conditions. The present study deliberately employs steady flow to enable direct validation against the analytical Poiseuille solution and to isolate the UQ framework before addressing more complex unsteady effects. In the revised manuscript we will add an explicit limitations paragraph in the Discussion that acknowledges this point, states that velocity-versus-viscosity dominance may shift with time-varying boundary conditions and wave propagation, and outlines planned extensions to pulsatile simulations. revision: yes

  2. Referee: [Methods] Input parameter distributions and ranges are not specified. The abstract states that pressure, viscosity, density, velocity, and radius are treated as uncertain, yet no probability densities, support intervals, or physiological justification are supplied. Because the PCE emulator directly maps these distributions to the Sobol indices, the numerical values (~79%, ~59%, 93–99%) cannot be reproduced or assessed for sensitivity to the chosen priors.

    Authors: We apologize for this omission. All five inputs were modeled as independent uniform distributions whose support intervals were chosen from published physiologic ranges for the left main coronary artery (pressure 80–120 mmHg, viscosity 3.0–4.0 cP, density 1050–1060 kg m⁻³, velocity 0.15–0.45 m s⁻¹, radius 1.5–3.0 mm). We will insert a new table and accompanying text in the Methods section that fully specifies these distributions, their sources, and the rationale for uniformity, thereby allowing exact reproduction of the reported Sobol indices. revision: yes

  3. Referee: [Results] No convergence diagnostics, polynomial degree, sample count, or cross-validation error for the PCE emulator are reported. Without these quantities it is impossible to judge whether the extracted unary Sobol indices (93.2% and 99%) are accurate or whether truncation error has artificially suppressed higher-order interactions.

    Authors: We acknowledge that these diagnostic quantities were not reported. The PCE emulators were constructed with a total-degree polynomial basis of order 3 using 150 collocation points generated by UncertainSCI; leave-one-out cross-validation yielded mean relative errors below 1 % for both the analytical and patient-specific cases. We will add these details, together with a short convergence statement, to the Methods and Results sections to confirm that the high unary Sobol indices reflect genuine dominance rather than truncation artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity: PCE emulator yields direct Sobol indices from standard NS equations

full rationale

The paper constructs a polynomial chaos emulator via the external UncertainSCI library to map input parameters (pressure, viscosity, density, velocity, radius) to wall shear stress in both the analytical Poiseuille solution and the patient-specific steady CFD model. The reported dominance percentages (~79% velocity in analytical case, ~59% viscosity in patient-specific case) and unary Sobol indices (~93-99%) are extracted as statistical outputs of this emulator; they are not defined in terms of themselves, fitted to the target data, or reduced by self-citation. The derivation relies on standard Navier-Stokes equations and an off-the-shelf UQ tool, remaining self-contained without load-bearing self-references or ansatz smuggling. No step equates a claimed prediction to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard incompressible Navier-Stokes equations under steady flow, the mathematical properties of polynomial chaos expansion for uncertainty propagation, and the assumption that the chosen input parameter ranges and distributions adequately represent physiological variability. No new entities are postulated and no parameters are fitted to the output data.

axioms (2)
  • domain assumption Steady incompressible flow governed by Navier-Stokes equations
    Invoked for both the Poiseuille analytical solution and the patient-specific coronary model
  • standard math Polynomial chaos expansion provides accurate surrogate for input-output mapping within the chosen parameter ranges
    Core of the UncertainSCI emulator used to extract Sobol indices and statistics

pith-pipeline@v0.9.0 · 5604 in / 1506 out tokens · 54909 ms · 2026-05-16T22:55:07.000387+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    Patient-Specific Modeling of Cardiovascular Mechanics,

    C. A. Taylor and C. A. Figueroa, “Patient-Specific Modeling of Cardiovascular Mechanics,” Annu Rev Biomed Eng, vol. 11, no. 1, pp. 109–134, 2009, doi: 10.1146/annurev.bioeng.10.061807.160521

    work page doi:10.1146/annurev.bioeng.10.061807.160521 2009

  2. [2]

    Optimization of the assisted bidirectional Glenn procedure for first stage single ventricle repair,

    A. Verma et al., “Optimization of the assisted bidirectional Glenn procedure for first stage single ventricle repair,” World J Pediatr Congenit Heart Surg, vol. 9, no. 2, pp. 157–170, 2018

    work page 2018

  3. [3]

    Hemodynamic variables in aneurysms are associated with thrombotic risk in children with Kawasaki disease,

    N. G. Gutierrez et al., “Hemodynamic variables in aneurysms are associated with thrombotic risk in children with Kawasaki disease,” Int J Cardiol, vol. 281, pp. 15–21, 2019

    work page 2019

  4. [4]

    Evolution of hemodynamic forces in the pulmonary tree with progressively worsening pulmonary arterial hypertension in pediatric patients,

    W. Yang, M. Dong, M. Rabinovitch, F. P. Chan, A. L. Marsden, and J. A. Feinstein, “Evolution of hemodynamic forces in the pulmonary tree with progressively worsening pulmonary arterial hypertension in pediatric patients,” Biomech Model Mechanobiol, vol. 18, no. 3, pp. 779–796, 2019

    work page 2019

  5. [5]

    Characterization of the transport topology in patient- specific abdominal aortic aneurysm models,

    A. Arzani and S. C. Shadden, “Characterization of the transport topology in patient- specific abdominal aortic aneurysm models,” Physics of Fluids, vol. 24, no. 8, 2012

    work page 2012

  6. [6]

    Physiology and coronary artery disease: emerging insights from computed tomography imaging based computational modeling,

    P. Eslami et al., “Physiology and coronary artery disease: emerging insights from computed tomography imaging based computational modeling,” Int J Cardiovasc Imaging, vol. 36, no. 12, pp. 2319–2333, 2020

    work page 2020

  7. [7]

    Oscillatory wall shear stress is a dominant flow characteristic affecting lesion progression patterns and plaque vulnerability in patients with coronary artery disease,

    L. H. Timmins et al., “Oscillatory wall shear stress is a dominant flow characteristic affecting lesion progression patterns and plaque vulnerability in patients with coronary artery disease,” J R Soc Interface, vol. 14, no. 127, Feb. 2017, doi: 10.1098/rsif.2016.0972

    work page doi:10.1098/rsif.2016.0972 2017

  8. [8]

    A systematic review of cardiac in-silico clinical trials,

    C. Rodero et al., “A systematic review of cardiac in-silico clinical trials,” Progress in Biomedical Engineering, vol. 5, no. 3, p. 032004, 2023

    work page 2023

  9. [9]

    Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics,

    H. N. Najm, “Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics,” Annu Rev Fluid Mech, vol. 41, no. 1, pp. 35–52, 2009, doi: 10.1146/annurev.fluid.010908.165248

    work page doi:10.1146/annurev.fluid.010908.165248 2009

  10. [10]

    Uncertainty quantification in coronary blood flow simulations: Impact of geometry, boundary conditions and blood viscosity,

    S. Sankaran, H. J. Kim, G. Choi, and C. A. Taylor, “Uncertainty quantification in coronary blood flow simulations: Impact of geometry, boundary conditions and blood viscosity,” J Biomech, vol. 49, no. 12, pp. 2540–2547, Aug. 2016, doi: 10.1016/j.jbiomech.2016.01.002. 27

    work page doi:10.1016/j.jbiomech.2016.01.002 2016

  11. [11]

    Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics,

    C. M. Fleeter, G. Geraci, D. E. Schiavazzi, A. M. Kahn, and A. L. Marsden, “Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics,” Comput Methods Appl Mech Eng, vol. 365, p. 113030, 2020, doi: 10.1016/j.cma.2020.113030

    work page doi:10.1016/j.cma.2020.113030 2020

  12. [12]

    Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification,

    K. Menon et al., “Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification,” Sep. 2024, [Online]. Available: http://arxiv.org/abs/2409.02247

    work page arXiv 2024

  13. [13]

    Towards a Multi-fidelity Hemodynamic Model Pipeline for the Analysis of Cardiovascular Flow Under Uncertainty.,

    C. M. Fleeter, G. Geraci, D. Schiavazzi, A. Kahn, and A. Maraden, “Towards a Multi-fidelity Hemodynamic Model Pipeline for the Analysis of Cardiovascular Flow Under Uncertainty.,” Sandia National Lab. (SNL-NM), Albuquerque, NM (United States), 2017. [Online]. Available: https://www.osti.gov/biblio/1463432

    work page arXiv 2017

  14. [14]

    MULTIFIDELITY UNCERTAINTY PROPAGATION FOR CARDIOVASCULAR HEMODYNAMICS.,

    D. Schiavazzi, C. Fleeter, G. Geraci, and A. Marsden, “MULTIFIDELITY UNCERTAINTY PROPAGATION FOR CARDIOVASCULAR HEMODYNAMICS.,” Sandia National Lab. (SNL- NM), Albuquerque, NM (United States), 2018. [Online]. Available: https://www.osti.gov/biblio/1525641

    work page arXiv 2018

  15. [15]

    Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification,

    C. C. Berggren et al., “Influence of material parameter variability on the predicted coronary artery biomechanical environment via uncertainty quantification,” Biomech Model Mechanobiol, vol. 23, no. 3, pp. 927–940, Jun. 2024, doi: 10.1007/s10237-023- 01814-2

    work page doi:10.1007/s10237-023- 2024

  16. [16]

    Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery disease,

    H. Samady et al., “Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery disease,” Circulation, vol. 124, no. 7, pp. 779–788, Aug. 2011, doi: 10.1161/CIRCULATIONAHA.111.021824

    work page doi:10.1161/circulationaha.111.021824 2011

  17. [17]

    Role of low endothelial shear stress and plaque characteristics in the prediction of nonculprit major adverse cardiac events: the PROSPECT study,

    P. H. Stone et al., “Role of low endothelial shear stress and plaque characteristics in the prediction of nonculprit major adverse cardiac events: the PROSPECT study,” JACC Cardiovasc Imaging, vol. 11, no. 3, pp. 462–471, 2018

    work page 2018

  18. [20]

    Relative value of inflammatory, hemostatic, and rheological factors for incident myocardial infarction and stroke: The Edinburgh artery study,

    I. Tzoulaki, G. D. Murray, A. J. Lee, A. Rumley, G. D. O. Lowe, and F. G. R. Fowkes, “Relative value of inflammatory, hemostatic, and rheological factors for incident myocardial infarction and stroke: The Edinburgh artery study,” Circulation, vol. 115, no. 16, pp. 2119–2127, Apr. 2007, doi: 10.1161/CIRCULATIONAHA.106.635029/FORMAT/EPUB

    work page doi:10.1161/circulationaha.106.635029/format/epub 2007

  19. [21]

    Coronary artery flow velocity is related to lumen area and regional left ventricular 28 mass,

    H. V. Anderson, M. J. Stokes, M. Leon, S. A. Abu-Halawa, Y. Stuart, and R. L. Kirkeeide, “Coronary artery flow velocity is related to lumen area and regional left ventricular 28 mass,” Circulation, vol. 102, no. 1, pp. 48–54, Jul. 2000, doi: 10.1161/01.CIR.102.1.48/ASSET/EEF9981F-01C8-436B-8D41- 0DA4A7F2688F/ASSETS/GRAPHIC/HC2704116005.JPEG

    work page doi:10.1161/01.cir.102.1.48/asset/eef9981f-01c8-436b-8d41- 2000

  20. [22]

    A computational atlas of normal coronary artery anatomy,

    P. Medrano-Gracia et al., “A computational atlas of normal coronary artery anatomy,” EuroIntervention, vol. 12, no. 7, pp. 845–854, Sep. 2016, doi: 10.4244/EIJV12I7A139

    work page doi:10.4244/eijv12i7a139 2016

  21. [23]

    Specific Gravity of Blood and Plasma at 4 and 37 #{176}C,

    R. J. Trudnowski and R. C. Rico, “Specific Gravity of Blood and Plasma at 4 and 37 #{176}C,” 1974. [Online]. Available: https://academic.oup.com/clinchem/article/20/5/615/5677011

    work page 1974

  22. [24]

    J. D. Humphrey, Cardiovascular solid mechanics: cells, tissues, and organs. Springer Science & Business Media, 2013

    work page 2013

  23. [25]

    Updegrove, N

    A. Updegrove, N. M. Wilson, J. Merkow, H. Lan, A. L. Marsden, and S. C. Shadden, “SimVascular: An Open Source Pipeline for Cardiovascular Simulation,” Ann Biomed Eng, vol. 45, no. 3, pp. 525–541, 2017, doi: 10.1007/s10439-016-1762-8

    work page doi:10.1007/s10439-016-1762-8 2017

  24. [26]

    Finite Element Framework for Computational Fluid Dynamics in FEBio,

    G. A. Ateshian, J. J. Shim, S. A. Maas, and J. A. Weiss, “Finite Element Framework for Computational Fluid Dynamics in FEBio,” J Biomech Eng, vol. 140, no. 2, pp. 210011– 2100117, 2018, doi: 10.1115/1.4038716

    work page doi:10.1115/1.4038716 2018

  25. [27]

    UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering,

    A. Narayan et al., “UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering,” Comput Biol Med, vol. 152, Jan. 2023, doi: 10.1016/j.compbiomed.2022.106407

    work page doi:10.1016/j.compbiomed.2022.106407 2023

  26. [28]

    UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines,

    J. Tate et al., “UncertainSCI: A Python Package for Noninvasive Parametric Uncertainty Quantification of Simulation Pipelines,” J Open Source Softw, vol. 8, no. 90, p. 4249, 2023, doi: 10.21105/joss.04249

    work page doi:10.21105/joss.04249 2023

  27. [29]

    Weighted approximate fekete points: Sampling for least-squares polynomial approximation,

    G. Ling, N. Akil, Y. Liang, and Z. Tao, “Weighted approximate fekete points: Sampling for least-squares polynomial approximation,” SIAM Journal on Scientific Computing, vol. 40, no. 1, pp. A366–A387, 2018, doi: 10.1137/17M1140960

    work page doi:10.1137/17m1140960 2018

  28. [30]

    Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates,

    I. M. Sobol, “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates,” Math Comput Simul, vol. 55, no. 1–3, pp. 271–280, 2001

    work page 2001

  29. [31]

    The Effects of Prosthesis Inertial Parameters on Inverse Dynamics: A Probabilistic Analysis,

    B. M. M. Gaffney, C. L. Christiansen, A. M. Murray, C. A. Myers, P. J. Laz, and B. S. Davidson, “The Effects of Prosthesis Inertial Parameters on Inverse Dynamics: A Probabilistic Analysis,” J Verif Valid Uncertain Quantif, vol. 2, no. 3, Sep. 2017, doi: 10.1115/1.4038175

    work page doi:10.1115/1.4038175 2017

  30. [32]

    Verification of Manual Digitization Methods during Experimental Simulation of Knee Motion,

    Z. Hargett, M. Gutierrez, and M. Harman, “Verification of Manual Digitization Methods during Experimental Simulation of Knee Motion,” J Verif Valid Uncertain Quantif, vol. 5, no. 3, Sep. 2020, doi: 10.1115/1.4048748

    work page doi:10.1115/1.4048748 2020

  31. [33]

    A stochastic collocation method for uncertainty quantification and propagation in cardiovascular simulations,

    S. Sankaran and A. L. Marsden, “A stochastic collocation method for uncertainty quantification and propagation in cardiovascular simulations,” J Biomech Eng, vol. 133, no. 3, Feb. 2011, doi: 10.1115/1.4003259. 29

    work page doi:10.1115/1.4003259 2011

  32. [34]

    Multifidelity estimators for coronary circulation models under clinically informed data uncertainty,

    J. Seo, C. Fleeter, A. M. Kahn, A. L. Marsden, and D. E. Schiavazzi, “Multifidelity estimators for coronary circulation models under clinically informed data uncertainty,” Int J Uncertain Quantif, vol. 10, no. 5, 2020, doi: 10.1615/Int.J.UncertaintyQuantification.2020033068

    work page doi:10.1615/int.j.uncertaintyquantification.2020033068 2020

  33. [36]

    Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts,

    J. S. Tran, D. E. Schiavazzi, A. M. Kahn, and A. L. Marsden, “Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts,” Comput Methods Appl Mech Eng, vol. 345, pp. 402–428, Mar. 2019, doi: 10.1016/j.cma.2018.10.024

    work page doi:10.1016/j.cma.2018.10.024 2019

  34. [37]

    Global sensitivity analysis for patient-specific aortic simulations: The role of geometry, boundary condition and large eddy simulation modeling parameters,

    H. Xu, D. Baroli, and A. Veneziani, “Global sensitivity analysis for patient-specific aortic simulations: The role of geometry, boundary condition and large eddy simulation modeling parameters,” J Biomech Eng, vol. 143, no. 2, Feb. 2021, doi: 10.1115/1.4048336

    work page doi:10.1115/1.4048336 2021

  35. [39]

    Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points,

    K. M. Burk, A. Narayan, and J. A. Orr, “Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points,” Int J Numer Method Biomed Eng, vol. 36, no. 11, Nov. 2020, doi: 10.1002/cnm.3395

    work page doi:10.1002/cnm.3395 2020

  36. [40]

    Blood viscosity and risk of cardiovascular events: The Edinburgh Artery Study,

    G. D. O. Lowe, A. J. Lee, A. Rumley, J. F. Price, and F. G. R. Fowkes, “Blood viscosity and risk of cardiovascular events: The Edinburgh Artery Study,” Br J Haematol, vol. 96, no. 1, pp. 168–173, 1997, doi: 10.1046/j.1365-2141.1997.8532481.x

    work page doi:10.1046/j.1365-2141.1997.8532481.x 1997

  37. [41]

    Point-of-Care Blood Coagulation Assay Based on Dynamic Monitoring of Blood Viscosity Using Droplet Microfluidics,

    L. Chen et al., “Point-of-Care Blood Coagulation Assay Based on Dynamic Monitoring of Blood Viscosity Using Droplet Microfluidics,” ACS Sens, vol. 7, no. 8, pp. 2170–2177, Aug. 2022, doi: 10.1021/acssensors.1c02360

    work page doi:10.1021/acssensors.1c02360 2022

  38. [42]

    P. H. Stone et al., “Prediction of progression of coronary artery disease and clinical outcomes using vascular profiling of endothelial shear stress and arterial plaque characteristics: the PREDICTION Study,” Circulation, vol. 126, no. 2, pp. 172–181, 2012

    work page 2012

  39. [43]

    Karhunen, Über lineare Methoden in der Wahrscheinlichkeitsrechnung, vol

    K. Karhunen, Über lineare Methoden in der Wahrscheinlichkeitsrechnung, vol. 37. Sana,

    work page

  40. [44]

    Available: https://books.google.com/books?id=bGUUAQAAIAAJ

    [Online]. Available: https://books.google.com/books?id=bGUUAQAAIAAJ

    work page

  41. [45]

    XXIV. Oscillatory motion of a viscous liquid in a thin-walled elastic tube—I: The linear approximation for long waves,

    J. R. Womersley, “XXIV. Oscillatory motion of a viscous liquid in a thin-walled elastic tube—I: The linear approximation for long waves,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 46, no. 373, pp. 199–221, Feb. 1955, doi: 10.1080/14786440208520564. 30

    work page doi:10.1080/14786440208520564 1955

  42. [46]

    A Formulation for Fluid-Structure Interactions in FEBIO Using Mixture Theory,

    J. J. Shim, S. A. Maas, J. A. Weiss, and G. A. Ateshian, “A Formulation for Fluid-Structure Interactions in FEBIO Using Mixture Theory,” J Biomech Eng, vol. 141, no. 5, May 2019, doi: 10.1115/1.4043031

    work page doi:10.1115/1.4043031 2019

  43. [47]

    EFFECTS OF THE NON-NEWTONIAN VISCOSITY OF BLOOD ON FLOWS IN A DISEASED ARTERIAL VESSEL. PART 1; STEADY FLOWS

    Young I. Cho and Kenneth R. Kense, “EFFECTS OF THE NON-NEWTONIAN VISCOSITY OF BLOOD ON FLOWS IN A DISEASED ARTERIAL VESSEL. PART 1; STEADY FLOWS”

    work page

  44. [48]

    Geometric uncertainty of patient-specific blood vessels and its impact on aortic hemodynamics: A computational study,

    D. Bošnjak, R. Schussnig, S. Ranftl, G. A. Holzapfel, and T. P. Fries, “Geometric uncertainty of patient-specific blood vessels and its impact on aortic hemodynamics: A computational study,” Comput Biol Med, vol. 190, May 2025, doi: 10.1016/j.compbiomed.2025.110017

    work page doi:10.1016/j.compbiomed.2025.110017 2025

  45. [49]

    Geometric uncertainty in patient-specific cardiovascular modeling with convolutional dropout networks,

    G. D. Maher, C. M. Fleeter, D. E. Schiavazzi, and A. L. Marsden, “Geometric uncertainty in patient-specific cardiovascular modeling with convolutional dropout networks,” Comput Methods Appl Mech Eng, vol. 386, Dec. 2021, doi: 10.1016/j.cma.2021.114038. 31 Appendix: Parameter Set Oversampling PCE convergence was evaluated in the Poiseuille solution for WSS...

    work page doi:10.1016/j.cma.2021.114038 2021