Pith. sign in

REVIEW 2 major objections 6 minor 99 references

The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A 10 percent uncertainty in the heart muscle's squeezing pressure can spread simulated coronary flow and wall shear stress by 27 percent.

desk verdict Solid forward UQ on a deformable coronary model, but the headline 27% flow/TAWSS variability is driven by an assumed 10% intramyocardial pressure input, so the magnitude is conditional even if the ranking is likely right. read the letter →

arxiv 1908.07522 v2 pith:IEKLW34A submitted 2019-08-20 physics.med-ph physics.comp-phphysics.flu-dyn

Jongmin Seo , Daniele E. Schiavazzi , Andrew M. Kahn , Alison L. Marsden This is my paper · ORCID
classification physics.med-phphysics.comp-phphysics.flu-dyn
keywords coronarycirculationuncertaintyquantificationfluid-structureinteractionpatient-specificsimulationintramyocardialpressureKarhunen-Loèveexpansionmulti-waveletstochasticwallshearstress
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 tries to establish how much uncertainty in the input parameters of a patient-specific coronary simulation with deformable walls translates into uncertainty in clinically relevant outputs such as pressure, flow, wall shear stress, and wall deformation. It claims that uncertainty in the inlet pressure waveform passes through almost linearly, while uncertainty in the intramyocardial pressure derivative is the dominant driver of flow and wall shear stress variability, with a 10% input coefficient of variation producing up to 27% output variability. It also claims that wall stiffness uncertainty affects only wall deformation and that the morphometry exponent has little influence on any output. The practical consequence is that deterministic coronary simulations, especially of wall shear stress, should be reported with confidence intervals because one boundary-condition input alone can induce a spread of roughly one quarter in those values.

What carries the argument

The mechanism is a sub-modeled left coronary artery with Arbitrary-Lagrangian-Eulerian fluid-structure interaction, coupled at six outlets to lumped-parameter coronary boundary conditions that include the intramyocardial pressure and its time derivative. A pulsatile pressure is prescribed at the inlet, so flow is driven by the pressure difference between the inlet and the downstream intramyocardial pressure. Each uncertain input is represented by random variables: inlet pressure and the intramyocardial pressure derivative through Karhunen-Loève expansion of Gaussian processes, Young's modulus through a Gaussian distribution from tensile-test data, and the morphometry exponent through a uniform distribution. Uncertainty is propagated by Monte Carlo, quasi-Monte Carlo, stochastic collocation, and a multi-wavelet stochastic expansion that adaptively refines the stochastic domain. The load-bearing lever is the 10% systolic perturbation of the intramyocardial pressure derivative, because it directly modifies the pressure gradient that drives coronary flow and therefore produces the reported 27% variability in flow and wall shear stress.

What would settle it

An independent clinical estimate of the systolic time-derivative of intramyocardial pressure variability, propagated through the same left coronary model, would confirm or replace the central 27% figure; if the true coefficient of variation is, for example, 5% instead of 10%, the flow and wall shear stress coefficient of variation would be roughly half the reported value.

Watch

Extended reading notes

Core claim

The paper's central quantitative discovery is a separation of uncertainty transmission paths in a left coronary artery sub-model with deformable walls. A 7% coefficient of variation in the inlet pressure waveform, measured from repeated catheterization data in six patients, transmits almost unchanged, about 7%, to outlet pressure and wall deformation, and about 5% to flow rate and time-averaged wall shear stress. A 10% coefficient of variation assumed for the systolic time derivative of intramyocardial pressure produces up to 27% coefficient of variation in flow rate and wall shear stress, while leaving pressure and deformation variability below 3%. Young's modulus uncertainty, modeled as a Gaussian with 17% coefficient of variation from human coronary tensile-test data, affects only wall deformation, also at about 17%, leaving hemodynamics nearly unchanged. Morphometry exponent uncertainty in the range 2.4 to 2.8 has negligible effects. These results indicate which uncertain inputs must be measured more tightly before coronary simulations can report flow and wall shear stress with clinical confidence.

Load-bearing premise

The load-bearing premise is the assumed 10% coefficient of variation for the intramyocardial pressure time derivative during systole; this distribution was assumed rather than inferred from clinical data, and it drives the largest reported output variability.

Editorial extensions

If this is right

  • If these results transfer to other coronary anatomies, deterministic coronary simulations should be interpreted with confidence intervals: a 10% uncertainty in the systolic intramyocardial pressure derivative alone can spread time-averaged wall shear stress by up to 27% coefficient of variation.
  • Flow and time-averaged wall shear stress variability track each other, while pressure and wall deformation variability track each other, so one member of each pair can serve as a practical proxy for the other in uncertainty reporting.
  • Uncertainty in vessel wall stiffness has little bearing on hemodynamic outputs in this small-deformation coronary model, but it must be controlled when wall deformation itself is the quantity of interest.
  • The multi-wavelet stochastic expansion estimates means and standard deviations accurately with roughly 50 or fewer model evaluations, making uncertainty quantification tractable for deformable coronary sub-models.
  • Improving the measurement of intramyocardial pressure, rather than inlet pressure, is the bottleneck for accurate flow and wall shear stress predictions.

Reading between the lines

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

  • If the reported near-linear transmission of inlet pressure variability holds in stenosed vessels, outlet pressure variability could be approximated directly from inlet measurement variability without a full fluid-structure simulation, a shortcut that could be tested on synthetic stenotic geometries.
  • Because the intramyocardial pressure derivative was perturbed only during systole, the systolic-window definition is a hidden sensitivity; perturbing the derivative over the full cardiac cycle would test how much of the 27% figure depends on that modeling choice.
  • The near-decoupling of hemodynamics from wall mechanics suggests a rigid-wall model with identical pressure boundary conditions may reproduce the flow and wall shear stress variability at lower computational cost, which a direct rigid-wall comparison could verify.
  • The 27% spread in time-averaged wall shear stress implies that plaque-progression risk categories based on a single deterministic value may misclassify patients near thresholds, so reporting the full output distribution would be more clinically informative.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The manuscript performs forward uncertainty quantification for a patient-specific left coronary artery model with deformable walls, using an ALE fluid-structure interaction framework and lumped-parameter network outlet boundary conditions. Stochastic inputs are the inlet coronary pressure waveform (modeled from catheterization data via a Karhunen-Loève expansion), the intramyocardial pressure time derivative (assumed 10% peak-relative standard deviation), the morphometry exponent (uniform on 2.4 to 2.8), and the wall Young's modulus (Gaussian with literature-based moments). Uncertainty propagation is carried out with Monte Carlo, quasi-Monte Carlo, stochastic collocation, and multiwavelet stochastic expansion, first on analytic benchmarks and then on the coronary model using 1203 simulations. The main findings are that 7% input coefficient of variation in inlet pressure propagates to about 7% cv in outlet pressure and wall deformation and about 5% cv in flow and wall shear stress; 10% peak-relative variability in the intramyocardial pressure derivative produces up to 27% cv in flow rate and time-averaged wall shear stress; the morphometry exponent has negligible effect; and Young's modulus uncertainty affects wall deformation only, with about 17% cv. The authors conclude that the multiwavelet method is superior to quasi-Monte Carlo and stochastic collocation for this class of problems.

Significance. If the input distributions are accepted, the paper is a useful demonstration of uncertainty quantification in deformable-wall coronary simulations and provides a fair, sample-counted comparison of propagation methods. The strengths include the use of actual intra-coronary catheterization data for the inlet pressure, a boundary-layer mesh convergence study, explicit reporting of the 1203 simulation count, and systematic benchmarks against analytic and nonlinear test problems. The qualitative ranking, namely that intramyocardial pressure uncertainty dominates flow and wall shear stress variability while wall stiffness uncertainty affects mainly wall mechanics, is clinically plausible and worth reporting. However, the leading quantitative claim of 27% cv in flow and TAWSS is conditional on an assumed 10% peak-relative standard deviation for the intramyocardial pressure derivative, and the paper's own limitation statement concedes that the random input distributions were assumed rather than inferred from clinical data. The title's promise of 'clinically-derived parametric data uncertainty' is therefore not supported for the central quantitative result.

major comments (2)
  1. [Secs. 3.2, 4.4, and 5] The 10% peak-relative standard deviation assigned to the intramyocardial pressure derivative in Sec. 3.2 is a modeling assumption, not an estimate from clinical data. Section 5 explicitly states that 'the distribution of the random inputs were assumed in this study rather than inferred from available clinical data.' Because dPim/dt appears as a direct source term in the distal-pressure ODE, Eq. (4), the reported 27% cv in flow rate and time-averaged wall shear stress (Sec. 4.4) is approximately proportional to this assumed input amplitude. The authors should either estimate this input from clinical measurements, calibrate it against available data, or explicitly present the 27% as conditional and include a sensitivity sweep over the input amplitude. As written, the paper's leading quantitative result and the title's 'clinically-derived' claim are not supported for this input.
  2. [Sec. 2] There is an internal inconsistency in the wall thickness specification. The text states a uniform wall thickness h=0.08 mm, then says this is 'consistent with' a coronary wall thickness of 1.0±0.2 mm reported in two echocardiographic studies, and 'larger than' a typical wall thickness equal to 10% of the vessel radius. For a left main diameter of 4 mm, 10% of the radius is 0.2 mm, and the cited 1.0 mm value is 12.5 times larger than 0.08 mm. This inconsistency directly affects the wall deformation quantity of interest and the FSI results. Please correct the value or the citations, and assess how sensitive the wall-mechanics conclusions are to this parameter.
minor comments (6)
  1. [Sec. 3.2] The phrase '10% cv in the intramyocardial pressure' is misleading because a coefficient of variation is conventionally defined relative to a nonzero mean, whereas the mean of dPim/dt over a cardiac cycle is near zero; the quantity used is a peak-relative standard deviation and should be labeled as such throughout.
  2. [Secs. 3.4 and 4.6] The Young's modulus input is specified as σ[Es]=0.24 MPa in Sec. 3.4 but as Es∼N(1.48, 0.28^2) in Sec. 4.6; the reported 17% cv in wall deformation is consistent with neither value exactly (16.2% or 18.9%). Please reconcile the two specifications.
  3. [Sec. 4.1] The functions in Eq. (10) are the Sobol' functions, but the text describes the test as a 'ten dimensional sine response surface'; reword to avoid confusion with the sinusoidal benchmark in Eq. (8).
  4. [Sec. 4.2] The name 'Kraichnan-Orzag' is misspelled; it should be 'Kraichnan-Orszag'.
  5. [Sec. 5] The sentence 'The MW showed but showed the best performance on discontinuous response surfaces' contains a typographical repetition, and the abstract's broad claim that multiwavelet expansion is 'superior' to stochastic collocation should be qualified because stochastic collocation outperforms all methods on the smooth sine benchmark (Fig. 7).
  6. [Sec. 3.1] The selection of the correlation length lc=T/2 is stated after 'examining the covariances for the six patients,' but no quantitative comparison of candidate correlation lengths is shown; please provide the covariance fit or the KL eigenvalue decay to justify this choice.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: forward uncertainty propagation with independently benchmarked methods and no output-calibrated inputs; the assumed dPim/dt distribution is a data limitation, not a circular step.

full rationale

This is a forward uncertainty propagation study. Input distributions are constructed from intra-coronary catheterization data (Sec. 3.1: 5-7% cv in coronary pressure), literature values (Sec. 3.3 morphometry exponent, Sec. 3.4 Young's modulus), or an explicitly stated modeling assumption (Sec. 3.2: Pim,t sigma = 10% of its maximum absolute value during the cardiac cycle), and none of these inputs is calibrated against the reported quantities of interest. No equation in the paper defines an input in terms of an output, and the near-linear propagation of variability emphasized in Sec. 4.3 is explained from Poiseuille flow and thick-walled cylinder relations, not from fitting. The 7% inlet-pressure cv propagating to about 7% cv in pressure and deformation, and the 10% dPim/dt input producing up to 27% cv in flow and TAWSS, are sensitivity results rather than predictions obtained by re-inserting the target quantities. The method comparison is anchored to analytic benchmarks with known moments (Secs. 4.1-4.2), so the claim that multiwavelet stochastic expansion performs favorably does not rest solely on self-citation. Self-citations to prior MW work [74, 76, 89] and to the baseline Pim,t waveform [88] provide starting points or methodological settings, but the load-bearing accuracy and ranking claims are independently benchmarked against MC, QMC, SC, and analytic solutions. Section 5 explicitly concedes that 'the distribution of the random inputs were assumed in this study rather than inferred from available clinical data'; this is a limitation on clinical grounding and should be weighed as correctness or validity risk, but it is not circularity because the assumed input amplitude is not derived from the outputs. No step in the derivation chain reduces to its own inputs by construction, so the appropriate finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The forward uncertainty propagation is not circular: input distributions come from catheterization data, literature, or explicit assumptions, and output statistics are not fed back into the inputs. The main burden is the assumed Pim_t distribution and the structural wall modeling choices, not a fitted output mapping.

free parameters (4)
  • Intramyocardial pressure derivative uncertainty amplitude = 10% of maximum baseline dPim/dt
    Assumed, not measured; drives the largest reported output variability (27% cv in flow and TAWSS).
  • KL correlation length for coronary pressure process = 0.5 s (T/2)
    Selected after visual examination of patient covariances, not estimated by maximum likelihood; controls the number of effective KL modes.
  • Wall thickness h = 0.08 mm
    Uniform structural wall thickness chosen for the mesh; inconsistent with cited coronary wall thickness of 1.0±0.2 mm, so quantitative wall deformation results are sensitive to this choice.
  • Morphometry exponent range = U(2.4, 2.8)
    Bounded interval from literature, not from measured coronary resistance data; effect on outputs is small, so this choice is less consequential.
assumptions (7)
  • standard math Incompressible Navier-Stokes equations in ALE form govern blood flow
    Used as the fluid model in Section 2, Eq. (1).
  • domain assumption Blood is a Newtonian fluid
    Stated in Section 2; appropriate for large arteries but excludes shear-thinning effects.
  • domain assumption The arterial wall is isotropic, homogeneous, Saint Venant-Kirchhoff hyperelastic with uniform thickness
    Section 2; the paper acknowledges three-layer and nonlinear models are future work.
  • domain assumption The diastolic CT configuration is stress-free, with no pre-stress
    Explicitly assumed in Section 2; affects absolute deformation values.
  • domain assumption Coronary pressure variability follows a Gaussian process with exponential covariance, variance 7% of mean, correlation length 0.5 s
    Section 3.1; supported by catheterization histograms and eigenvalue decay, but the exponential kernel and correlation length are chosen.
  • domain assumption Intramyocardial pressure is approximated by left ventricular pressure and its derivative, with 10% variability in systole only
    Section 3.2; Pim cannot be measured directly, so this drives the headline sensitivity.
  • domain assumption All uncertain inputs are independent
    Section 5 limitation; correlations and interactions are neglected.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls." pith.science (2026). https://pith.science/paper/IEKLW34A

@misc{pith2026190807522,
  author       = {Pith},
  title        = {Pith review of: The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IEKLW34A}},
  note         = {Machine review of arXiv:1908.07522}
}
read the original abstract

Cardiovascular simulations are increasingly used for non-invasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due to input uncertainty is a key step toward further integration of cardiovascular simulations in the clinical workflow. In this study, we present uncertainty quantification in computational models of the coronary circulation to investigate the effect of uncertain parameters, including coronary pressure waveform, intramyocardial pressure, morphometry exponent, and the vascular wall Young's modulus. We employ a left coronary artery model with deformable vessel walls, simulated via an ALE framework for FSI, with a prescribed inlet pressure and open-loop lumped parameter network outlet boundary conditions. Stochastic modeling of the uncertain inputs is determined from intra-coronary catheterization data or gathered from the literature. Uncertainty propagation is performed using several approaches including Monte Carlo, Quasi MC, stochastic collocation, and multiwavelet stochastic expansion. Variabilities in QoI, including branch pressure, flow, wall shear stress, and wall deformation are assessed. We find that uncertainty in inlet pressures and intramyocardial pressures significantly affect all resulting QoIs, while uncertainty in elastic modulus only affects the mechanical response of the vascular wall. Variability in the morphometry exponent has little effect on coronary hemodynamics or wall mechanics. Finally, we compare convergence behaviors of statistics of QoIs using several uncertainty propagation methods. From the simulation results, we conclude that the multi-wavelet stochastic expansion shows superior accuracy and performance against Quasi Monte Carlo and stochastic collocation methods.

Figures

Figures reproduced from arXiv: 1908.07522 by the authors.

Figure 1
Figure 1. (a) Left coronary artery (LCA) sub-model and geometrically multi-scale patient-specific aorto-coronary [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. LCA computational mesh with deformable walls. The lumen mesh is colored with cyan and the wall mesh [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Clinical data from cardiac catheterization. (a) Seven measurements of pulsatile pressure waveforms in the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Post-processed intra-coronary pressure waveforms from six patients. Each pressure waveform is plotted in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: (a-c) Histograms of Patient 1 pressure data at four points in time. The red lines represent a Gaussian [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Stochastic modeling using the Karhunen-Lo`eve expansion. (a) Eight modes of scaled eigenfunctions from [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Model response and sampling distributions in forward uncertainty propagation. (a) The response surface of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Sampling methods and convergence rates for the discontinuous sine response surface from equation (9). [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Convergence rates for the ten dimensional sine response surface from equation (10). (a) Absolute errors [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Uncertainty propagation through the Kraichnan-Orzag problem. (a) the response surface of [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: 200 realizations of QoI for six branches of LCA model with the perturbed pulsatile inlet pressure. [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: (Top) CDF estimates of QoIs in LAD obtained from QMC and MW approach. (bottom) Mean and [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: Six realizations of the wall shear stress contours on the LCA model resulting from uncertainty in the [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: Realizations and statistics of the QoIs in two branches resulting from the perturbed time derivative of [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: Mean and standard deviations of LCA QoIs resulting from uncertainty in the morphometry law. The [PITH_FULL_IMAGE:figures/full_fig_p020_15.png]
Figure 16
Figure 16. Figure 16: Mean and standard deviations of LCA QoI resulting from uncertainty in the Young’s modulus. The error [PITH_FULL_IMAGE:figures/full_fig_p020_16.png]
Figure 17
Figure 17. Figure 17: Statistics of the QoIs in six branches resulting from all perturbed inputs. Ensemble averaged quantities [PITH_FULL_IMAGE:figures/full_fig_p021_17.png]
Figure 18
Figure 18. Figure 18: Convergence of mean quantities of interest (a-d) and standard deviations (e-h) resulting from perturbing [PITH_FULL_IMAGE:figures/full_fig_p022_18.png]
Figure 19
Figure 19. Figure 19: Convergence of mean quantities of interest (a-d) and standard deviations (e-h) resulting from perturbing [PITH_FULL_IMAGE:figures/full_fig_p023_19.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

99 extracted references · 80 canonical work pages

  1. [1]

    High Performance Computer Applications 6th International Conference , volume 595, 1 2016

    2016

  2. [2]

    Agarwal and N

    N. Agarwal and N. Aluru. A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties. Journal of Computational Physics , 228:7662–7668, 2009

    2009

  3. [3]

    Bangalore Ramachandra, A

    A. Bangalore Ramachandra, A. Kahn, and A. Marsden. Patient-specific simulations reveal significant differences in mechanical stimuli in venous and arterial coronary grafts. Journal of cardiovascular translational research, 9(4):279–290, 2016

    2016

  4. [4]

    Baumann, R

    S. Baumann, R. Wang, U. J. Schoepf, D. H. Steinberg, J. V. Spearman, R. R. Bayer, C. W. Hamm, and M. Renker. Coronary ct angiography-derived fractional flow reserve correlated with invasive fractional flow reserve measurements –initial experience with a novel physician-driven algorithm. European Radiology, 25(4):1201–1207, 2015

    2015

  5. [5]

    Baumler, V

    K. Baumler, V. Vedula, A. Sailer, J. Seo, P. Chiu, G. Mistlbauer, F. Chan, M. Fischbein, A. Marsden, and D. Fleischmann. Fluid–structure interaction simulations of patientspecific aortic dissection.Biomechanics and Modeling in Mechanobiology, pages 1–22, 2020

    2020

  6. [6]

    Bazilevs, V

    Y. Bazilevs, V. Calo, J. Cottrell, T. Hughes, A. Reali, and G. Scovazzi. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering , 197:173–201, 2007

    2007

  7. [7]

    Benjamin, S

    E. Benjamin, S. Virani, C. Callaway, A. Chamberlain, A. Chang, S. Cheng, S. Chiuve, M. Cushman, F. Delling, R. Deo, 23 et al. Heart disease and stroke statistics-2018 update: a report from the American Heart Association. Circulation, 137(12):e67, 2018

    2018

  8. [8]

    D. Bergel. The static elastic properties of the arterial wall. Journal of Physiology , 156:445–457, 1961

    1961

Show all 99 references
  1. [9]

    Biehler, M

    J. Biehler, M. Gee, and W. Wall. Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme. Biomechanics and Modeling in Mechanobiology , 14:485–513, 2015

    2015

  2. [10]

    Biehler and W

    J. Biehler and W. Wall. The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms. International Journal for Numerical Methods in Biomedical Engineering , 34(e2922), 2017

    2017

  3. [11]

    Blatman and B

    G. Blatman and B. Sudret. Adaptive sparse polynomial chaos expansion based on least angle regression. Journal of Computational Physics, 230(6):2345–2367, 2011

    2011

  4. [12]

    Bogren, R

    H. Bogren, R. Klipstein, D. Firmin, R. Mohiaddin, S. Underwood, R. Rees, and D. Longmore. Quantitation of ante- grade and retrograde blood flow in the human aorta by magnetic resonance velocity mapping. American Heart Journal, 117(6):1214–1222, 1989

    1989

  5. [13]

    Boileau, S

    E. Boileau, S. Pant, C. Roobottom, I. Sazonov, J. Deng, X. Xie, and P. Nithiarasu. Estimating the accuracy of a reduced-order model for the calculation of fractional flow reserve (FFR). International Journal for Numerical Methods in Biomedical Engineering, 34(1):e2908, 2018. e2...

    2018

  6. [14]

    Brault, L

    A. Brault, L. Dumas, and D. Lucor. Uncertainty quantification of inflow boundary condition and proximal arterial stiffness–coupled effect on pulse wave propagation in a vascular network. International Journal for Numerical Methods in Biomedical Engineering, 33(e2859), 2017

    2017

  7. [15]

    Changizi and C

    M. Changizi and C. Cherniak. Modeling the large-scale geometry of human coronary arteries. Canadian Journal of Physiology and Pharmacology, 78:603–611, 2000

    2000

  8. [16]

    Chen and A

    P. Chen and A. Quarteroni. A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods. Journal of Computational Physics , 298:176–193, 2015

    2015

  9. [17]

    P. Chen, A. Quarteroni, and G. Rozza. Simulation-based uncertainty quantification of human arterial network hemody- namics. International Journal for Numerical Methods in Biomedical Engineering , 29:698–721, 2013

    2013

  10. [18]

    Coogan, J

    J. Coogan, J. Humphrey, and C. Figueroa. Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation. Biomech. Model Mechanobi- ology, 12:79–93, 2013

    2013

  11. [19]

    Dodge Jr., B

    J. Dodge Jr., B. Brown, E. Bolson, and H. Dodge. Lumen diameter of normal human coronary arteries: influence of age, sex, anatomic variation, and left ventricular hypertrophy or dilation. Circulation, 86(1):232–246, 1992

    1992

  12. [20]

    P. S. Douglas, G. Pontone, M. A. Hlatky, M. R. Patel, B. L. Norgaard, R. A. Byrne, N. Curzen, I. Purcell, M. Gutberlet, G. Rioufol, U. Hink, H. W. Schuchlenz, G. Feuchtner, M. Gilard, D. Andreini, J. M. Jensen, M. Hadamitzky, K. Chiswell, D. Cyr, A. Wilk, F. Wang, C. Rogers, B...

    2015

  13. [21]

    Esmaily-Moghadam, Y

    M. Esmaily-Moghadam, Y. Bazilevs, and A. Marsden. A bi-partitioned iterative algorithm for solving linear systems arising from incompressible flow problems. Computer Methods in Applied Mechanics and Engineering , 286:40–62, 2015

    2015

  14. [22]

    Esmaily-Moghadam, T

    M. Esmaily-Moghadam, T. Hsia, and A. Marsden. A non-discrete method for computation of residence time in fluid mechanics simulations. Physics of Fluids , 25(11):110802, 2013

    2013

  15. [23]

    Esmaily Moghadam, I

    M. Esmaily Moghadam, I. Vignon-Clementel, R. Figliola, and A. Marsden. A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations. Journal of Computational Physics , 244:63–79, 2013

    2013

  16. [24]

    H. Faure. Good permutations for extreme discrepancy. Journal of Number Theory , 42(1):47–56, 1992

    1992

  17. [25]

    Figueroa, I

    C. Figueroa, I. Vignon-Clementel, K. Jansen, T. Hughes, and C. Taylor. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Computer Methods in Applied Mechanics and Engineering , 195(41- 43):5685–5706, 2006

    2006

  18. [26]

    Fleeter, G

    C. Fleeter, G. Geraci, D. Schiavazzi, A. Kahn, M. Eldred, and A. Marsden. Multilevel multifidelity approaches for cardiovascular flow under uncertainty. Technical Report SAND2018-2780O, Center for Computing Research Summer Proceedings, A.D. Baczewski and M.L. Parks, eds., Sandia...

    2017

  19. [27]

    Frauenfelder, M

    T. Frauenfelder, M. Lotfey, T. Boehm, and S. Wildermuth. Computational fluid dynamics: Hemodynamic changes in abdominal aortic aneurysm after stent-graft implantation. CardioVascular and Interventional Radiology , 29(4):613–623, Aug 2006

    2006

  20. [28]

    M. H. Friedman, C. B. Bargeron, O. J. Deters, G. M. Hutchins, and F. F. Mark. Correlation between wall shear and intimal thickness at a coronary artery branch. Atherosclerosis, 68(1):27–33, 1987

    1987

  21. [29]

    Geraci, M

    G. Geraci, M. Eldred, and G. Iaccarino. A multifidelity control variate approach for the multilevel Monte Carlo technique. Technical report, Stanford University, 2015

    2015

  22. [30]

    Ghanem and P

    R. Ghanem and P. Spanos. Stochastic finite elements: a spectral approach . Courier Corporation, 2003

    2003

  23. [31]

    C. M. Gibson, L. Diaz, K. Kandarpa, F. M. Sacks, R. C. Pasternak, T. Sandor, C. Feldman, and P. H. Stone. Relation of vessel wall shear stress to atherosclerosis progression in human coronary arteries. Arteriosclerosis and Thrombosis: A Journal of Vascular Biology , 13(2):310–...

    2019

  24. [32]

    Gijsen, A

    F. Gijsen, A. van der Giessen, A. van der Steen, and J. Wentzel. Shear stress and advanced atherosclerosis in human coronary arteries. Journal of Biomechanics , 46(2):240–247, 2013

    2013

  25. [33]

    Gow and C

    B. Gow and C. Hadfield. The elasticity of canine and human coronary arteries with reference to postmortem changes. Circulation Research, 45:588–594, 1979

    1979

  26. [34]

    Gradus-Pizlo, B

    I. Gradus-Pizlo, B. Bigelow, Y. Mahomed, S. Sawada, K. Rieger, and H. Feigenbaum. Left anterior descending coronary artery wall thickness measured by high-frequency transthoracic and epicardial echocardiography includes adventitia. The 24 American Journal of Cardiology , 9:27–32, 2003

    2003

  27. [35]

    Grande Gutierrez, O

    N. Grande Gutierrez, O. Shirinsky, N. Gagarina, G. Lyskina, R. Fukazawa, S. Ogawa, J. Burns, A. Marsden, and A. Kahn. Assessment of coronary artery aneurysms caused by Kawasaki disease using transluminal attenuation gradient analysis of computerized tomography angiograms. The ...

    2017

  28. [36]

    Gundert, A

    T. Gundert, A. Marsden, W. Yang, D. Marks, and J. J. LaDisa. Identification of hemodynamically optimal coronary stent designs based on vessel caliber. IEEE Transactions on Biomedical Engineering , 58(7):1992–2002, 2012

    1992

  29. [37]

    Habib, E

    S. Habib, E. Parham, M. M. C., S. Jin, D. S. S., M. Charles, T. L. H., Q. A. A., and G. D. P. Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery disease. Circula...

    2019

  30. [38]

    J. Halton. On the efficiency of certain quasi-random sequences of points in evaluating multidimensional integrals. Nu- merische Mathematik, 2(1):84–90, 1960

    1960

  31. [39]

    Heroux, R

    M. Heroux, R. Bartlett, V. Howle, R. Hoekstra, J. Hu, T. Kolda, R. Lehoucq, K. Long, R. Pawlowski, E. Phipps, A. Salinger, H. Thornquist, R. Tuminaro, J. Willenbring, A. Williams, and K. Stanley. An overview of the Trilinos project. ACM Transactions on Mathematical Software , ...

    2005

  32. [40]

    Hirai, S

    T. Hirai, S. Sasayama, T. Kawasaki, and S. Yagi. Stiffness of systemic arteries in patients with myocardial infarction. Circulation, 80:78–86, 1989

    1989

  33. [41]

    Holzapfel, G

    G. Holzapfel, G. Sommer, C. Gasser, and P. Regitnig. Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. American Journal of Physiology-Heart and Circulatory Physiology, 2...

    2005

  34. [42]

    M. C. Hsu and Y. Bazilev. Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulation. Finite Elements in Analysis and Design , 47(6):593–599, 2011

    2011

  35. [43]

    Hutchins, M

    G. Hutchins, M. Miner, and J. Boitnott. Vessel caliber and branch-angle of human coronary artery branch-points. Circulation Research, 38:572–576, 1976

    1976

  36. [44]

    Jaquet, L

    C. Jaquet, L. Najman, H. Talbot, L. Grady, M. Schaap, B. Spain, H. Kim, I. Vignon-Clementel, and C. Taylor. Generation of patient-specific cardiac vascular networks: a hybrid image-based and synthetic geometric model. IEEE Transactions on Biomedical Engineering, 66:946–955, 2017

    2017

  37. [45]

    Karimi, M

    A. Karimi, M. Navidbakhsh, A. Shojaei, and S. Faghihi. Measurement of the uniaxial mechanical properties of healthy and atherosclerotic human coronary arteries. Materials Science and Engineering , C33:2550–2554, 2013

    2013

  38. [46]

    H. Kim, I. Vignon-Clementel, C. Figueroa, J. LaDisa, K. Jansen, J. Feinstein, and C. Taylor. On coupling a lumped param- eter heart model and a three-dimensional finite element aorta model.Annals of Biomedical Engineering, 37(11):2153–2169, 2009

    2009

  39. [47]

    Kissas, Y

    G. Kissas, Y. Yang, E. Hwuang, W. Witschey, J. Detre, and P. Perdikaris. Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4d flow mri data using physics-informed neural networks. Computer Methods in Applied Mechanics and Eng...

    2020

  40. [48]

    B.-K. Koo, A. Erglis, J.-H. Doh, D. V. Daniels, S. Jegere, H.-S. Kim, A. Dunning, T. DeFrance, A. Lansky, J. Leipsic, and J. K. Min. Diagnosis of Ischemia-Causing Coronary Stenoses by Noninvasive Fractional Flow Reserve Computed From Coronary Computed Tomographic Angiograms: R...

    1989

  41. [49]

    Kraichnan

    R. Kraichnan. Direct-interaction approximation for a system of several interacting simple shear waves. Physics of Fluids , 6:1603–1609, 1963

    1963

  42. [50]

    Kural, M

    M. Kural, M. Cai, D. Tang, T. Gwyther, J. Zheng, and K. Billiar. Planar biaxial characterization of diseased human coronary and carotid arteries for computational modeling. Journal of Biomechanics , 45:790–798, 2012

    2012

  43. [51]

    Kurata, A

    A. Kurata, A. Coenen, M. M. Lubbers, K. Nieman, T. Kido, T. Kido, N. Yamashita, K. Watanabe, G. P. Krestin, and T. Mochizuki. The effect of blood pressure on non-invasive fractional flow reserve derived from coronary computed tomography angiography. European Radiology, 27(4):141...

    2017

  44. [52]

    H. Lan, A. Updegrove, N. Wilson, G. Maher, S. Shadden, and A. Marsden. A re-engineered software interface and workflow for the open-source SimVascular cardiovascular modeling package. Journal of Biomechanical Engineering , 140(024501), 2018

    2018

  45. [53]

    Le Maitre, M

    O. Le Maitre, M. Reagan, H. Najm, R. Ghanem, and O. Knio. A atochastic projection method for fluid flow II. random process. Journal of Computational Physics , 181:9–44, 2002

    2002

  46. [54]

    C. Long, A. Marsden, and Y. Bazilevs. Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Computional Mechanics, 54:921–932, 2014

    2014

  47. [55]

    O. L. Maitre and O. M. Knio. Spectral methods for uncertainty quantification. Springer, 2010

    2010

  48. [56]

    F. Mall. A study of the structural unit of the liver. American Journal of Anatomy , 5:227–308., 1905

    1905

  49. [57]

    A. Marsden. Optimization in cardiovascular modeling. Annual Review of Fluid Mechanics , 46:519–546, 2014

    2014

  50. [58]

    Marsden and M

    A. Marsden and M. Esmaily-Moghadam. Multiscale modeling of cardiovascular flows for clinical decision support. Applied Mechanics Reviews, 67:030804, 2015

    2015

  51. [59]

    Mayrovitz and J

    H. Mayrovitz and J. Roy. Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Heart and Circulatory Physiology, 245(6):1031–1038, 1983

    1983

  52. [60]

    Migliavacca, L

    F. Migliavacca, L. Petrini, M. Colombo, F. Auricchio, and R. Pietrabissa. Mechanical behavior of coronary stents inves- tigated through the finite element method. Journal of Biomechanics , 35(6):803–811, 2002

    2002

  53. [61]

    J. K. Min, J. Leipsic, M. J. Pencina, D. S. Berman, B.-K. Koo, C. van Mieghem, A. Erglis, F. Y. Lin, A. M. Dunning, P. Apruzzese, M. J. Budoff, J. H. Cole, F. A. Jaffer, M. B. Leon, J. Malpeso, G. B. J. Mancini, S.-J. Park, R. S. Schwartz, L. J. Shaw, and L. Mauri. Diagnostic Ac...

    2012

  54. [62]

    C. Murray. The physiological principle of minimum work. I. the vascular system and the cost of blood volume. Proceedings of the National Acadademy of Science , 12:207–214, 1926

    1926

  55. [63]

    Nichols, M

    W. Nichols, M. O’Rourke, and C. Vlachopoulos. McDonald’s Blood Flow in Arteries Theoretical, Experimental, and Clinical Principles. CRC Press, 6th edition, 2011

    2011

  56. [64]

    Orszag and L

    S. Orszag and L. Bissonnette. Dynamics properties of truncated Wiener-Hermite expansions. Physics of Fluids , 10(12):2603–2163, 1967

    1967

  57. [65]

    Patel, J

    D. Patel, J. Janicki, and T. Carew. Static anisotropic elastic properties of the aorta in living dogs. Circulation Research, XXV:765–779, 1969

    1969

  58. [66]

    Pearson, R

    A. Pearson, R. Guo, D. Orsinelli, P. Binkley, and T. Pasierski. Transesophageal echocardiographic assessment of the effects of age, gender, and hypertension on thoracic aortic wall size, thickness, and stiffness. 1994, 128:344–351, American Heart Journal

    1994

  59. [67]

    Perry, M

    R. Perry, M. Joseph, D. Chew, P. Aylward, and C. De Pasquale. Coronary artery wall thickness of the left anterior descending artery using high resolution transthoracic echocardiography – normal range of values. Echocardiography, pages 759–764, 2013

    2013

  60. [68]

    Peterson, R

    L. Peterson, R. Jensen, and J. Parnell. Mechanical properties of arteries in vivo. Circulation Research, VIII:622–639, 1960

    1960

  61. [69]

    Podessor, F

    B. Podessor, F. Neumann, M. Neumann, W. Schreiner, G. Wollnek, and R. Mallinger. Outer radius-wall thickness ratio, a postmortem quantitative histology in human coronary arteries. Acta Anatomica, 163:63–68, 1998

    1998

  62. [70]

    Sankaran, M

    S. Sankaran, M. Esmaily-Moghadam, A. Kahn, E. Tseng, J. Guccione, and A. Marsden. Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Annals of Biomedical Engineering , 40(10):2228–2242, 2012

    2012

  63. [71]

    Sankaran, H

    S. Sankaran, H. Kim, G. Choi, and C. Taylor. Uncertainty quantification in coronary blood flow simulations: impact of geometry, boundary conditions and blood viscosity. Journal of biomechanics , 49(12):2540–2547, 2016

    2016

  64. [72]

    Sankaran and A

    S. Sankaran and A. Marsden. The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow. Physics of Fluids , 22(121902), 2010

    2010

  65. [73]

    Sankaran and A

    S. Sankaran and A. Marsden. A stochastic collocation method for uncertainty quantification and propagation in cardio- vascular simulations. Journal of Biomechanical Engineering , 133(3):031001, 2011

    2011

  66. [74]

    Schiavazzi, G

    D. Schiavazzi, G. Arbia, C. Baker, A. Hlavacek, T. Hsia, A. Marsden, I. Vignon-Clementel, and the Modeling of Congenital Hearts Alliance (MOCHA) Investigators. Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation. International ...

    2016

  67. [75]

    Schiavazzi, A

    D. Schiavazzi, A. Baretta, G. Pennati, T. Hsia, and A. Marsden. Patient-specific parameter estimation in single-ventricle lumped circulation models under uncertainty. International journal for numerical methods in biomedical engineering , 33(3):e02799, 2017

    2017

  68. [76]

    Schiavazzi, A

    D. Schiavazzi, A. Doostan, and G. Iaccarino. Spase multiresolution regression for uncertainty propagation. International Journal for Uncertainty Quantification , 4(4):303–331, 2014

    2014

  69. [77]

    J. Seo, C. Fleeter, A. Kahn, A. Marsden, and D. Schiavazzi. Multi-fidelity Estimators for Coronary Artery Models Under Clinically-informed Data Uncertainty. International Journal for Uncertainty Quantification , In review, 2020

    2020

  70. [78]

    J. Seo, D. Schiavazzi, and A. Marsden. Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels. Computational Mechanics, 64:717–739, 2019

    2019

  71. [79]

    T. Sherman. On connecting large vessels to small: the meaning of Murray’s law. Journal of General Physiology, 78(4):431– 453, 1981

    1981

  72. [80]

    S. Smolyak. Quadrature and interpolation formulas for tensor products of certain classes of functions. In Doklady Akademii Nauk, volume 148, pages 1042–1045. Russian Academy of Sciences, 1963

    1963

  73. [81]

    I. Sobol. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. , 16:236–242, 1976

    1976

  74. [82]

    Taylor, T

    C. Taylor, T. Fonte, and J. Min. Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve. Journal of the American College of Cardiology , 61:2233–41, 2013

    2013

  75. [83]

    L. H. Timmins, D. S. Molony, P. Eshtehardi, M. C. McDaniel, J. N. Oshinski, D. P. Giddens, and H. Samady. Oscillatory wall shear stress is a dominant flow characteristic affecting lesion progression patterns and plaque vulnerability in patients with coronary artery disease. Jour...

    2020

  76. [84]

    L. H. Timmins, D. S. Molony, P. Eshtehardi, M. C. McDaniel, J. N. Oshinski, H. Samady, and D. P. Giddens. Focal association between wall shear stress and clinical coronary artery disease progression. Annals of Biomedical Engineering, 43(1):94–106, 2015

    2015

  77. [85]

    L. H. Timmins, J. Suo, P. Eshtehardi, D. S. Molony, M. C. McDaniel, J. N. Oshinski, D. P. Giddens, and H. Samady. Com- parison of angiographic and ivus derived coronary geometric reconstructions for evaluation of the association of hemody- namics with coronary artery disease p...

    2016

  78. [86]

    M. Tipping. Sparse Bayesian learning and the relevance vector machine. Journal of Machine Learning Research, 1:211–244, 2001

    2001

  79. [87]

    Towns, T

    J. Towns, T. Cockerill, M. Dahan, I. Foster, K. Gaither, A. Grimshaw, V. Hazlewood, S. Lathrop, D. Lifka, G. Peter- son, R. Roskies, J. Scott, and N. Wilkins-Diehr. XSEDE: Accelerating scientific discovery. Computing in Science and Engineering, 16(5):62–74, 2014

    2014

  80. [88]

    J. Tran, D. Schiavazzi, A. Bangalore Ramachandra, A. Kahn, and A. Marsden. Automated tuning for parameter identifi- cation and uncertainty quantification in multi-scale coronary simulations. Computers & Fluids , 142:128–138, 2017. 26

    2017

  81. [89]

    J. Tran, D. Schiavazzi, A. Kahn, and A. Marsden. Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts. Computer Methods in Applied Mechanics and Engineering , 345:402–428, 2019

    2019

  82. [90]

    Updegrove, N

    A. Updegrove, N. Wilson, J. Merkow, H. Lan, A. Marsden, and S. Shadden. SimVascular: an open source pipeline for cardiovascular simulation. Annals of Biomedical Engineering , 45(3):525–541, 2016

    2016

  83. [91]

    A. G. van der Giessen, H. C. Groen, P.-A. Doriot, P. J. de Feyter, A. F. van der Steen, F. N. van de Vosse, J. J. Wentzel, and F. J. Gijsen. The influence of boundary conditions on wall shear stress distribution in patients specific coronary trees. Journal of Biomechanics , 44(6...

    2011

  84. [92]

    Vedula, J

    V. Vedula, J. Lee, H. Xu, C. Kuo, T. Hsiai, and A. Marsden. A method to quantify mechanobiologic forces during zebrafish cardiac development using 4-D light sheet imaging and computational modeling. PLoS Computational Biology, 13(10):e1005828, 2017

    2017

  85. [93]

    Wan and G

    X. Wan and G. Karniadakis. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Journal of Computational Physics , 209:617–642, 2005

    2005

  86. [94]

    Williams and C

    C. Williams and C. Rasmussen. Gaussian processes for machine learning , volume 2. MIT press Cambridge, MA, 2006

    2006

  87. [95]

    Xiu and S

    D. Xiu and S. Sherwin. Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network. Journal of Computational Physics , 226:1385–1407, 2007

    2007

  88. [96]

    W. Yang, J. Feinstein, and A. Marsden. Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise. Computer methods in applied mechanics and engineering , 199(33-36):2135–2149, 2010

    2010

  89. [97]

    Zamir, P

    M. Zamir, P. Sinclair, and T. Wonnacott. Relation between diameter and flow in major branches of the arch of the aorta between diameter and flow in major branches of the arch of the aorta. Journal of Biomechanics, 25(11):1303–1310, 1992

    1992

  90. [98]

    Zhou and Y

    J. Zhou and Y. Fung. The degree of nonlinearity and anisotropy of blood vessel elasticity. Proceeedings of the National Academy of Science, 94:14255–14260, 1997

    1997

  91. [99]

    Y. Zhou, G. Kassab, and S. Molloi. On the design of the coronary arterial tree: a generalization of Murray’s law. Physics in Medicine & Biology , 44(12):2929, 1999. 27

    1999

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.