Research / Computational Methods / 02 / 02

Efficient Computational Modeling and Uncertainty Quantification

High-fidelity computational models provide detailed information on cardiovascular flow and mechanics but often require substantial computational resources. We develop physics-based reduced-order models that retain geometry-dependent hemodynamic characteristics at a lower computational cost. We combine these models with probabilistic methods to quantify variability in model predictions and identify influential physiological and mechanical parameters. This framework supports efficient parameter studies, uncertainty quantification, and sensitivity analysis in subject-specific cardiovascular simulations.

One high-fidelity solution opening out into thousands of fast ones — a 3D coronary pressure field, the same vessel as a centerline model, and a spread of resulting FFR values
High-fidelity information, carried into a reduced computational model, and spent on the large ensembles that uncertainty analysis needs.

Data-Calibrated Reduced-Order Modeling

We construct one-dimensional reduced-order models in which geometry-dependent pressure–flow relationships are calibrated from a small set of three-dimensional CFD simulations. The calibrated coefficients account for pressure losses associated with stenosis, curvature, branching, and other geometric features that are difficult to represent with empirical relations alone. The resulting model retains the principal pulsatile hemodynamic response of each vascular geometry while reducing the cost of repeated simulations.

Vascular geometry → a small set of 3D CFD runs at different flow rates → the calibrated pressure–flow relation → the 1D centerline model → pulsatile pressure and flow waveforms
A few three-dimensional solutions at different flow rates fix the pressure–flow relation for one geometry; the one-dimensional model then carries it through the cardiac cycle.

Efficient Pulsatile Hemodynamic Simulation

The calibrated reduced-order model enables efficient simulation of time-dependent pressure and flow in idealized and subject-specific vascular geometries. We evaluate the model through comparisons with full three-dimensional CFD simulations under multiple flow and anatomical conditions. This comparison allows the computational benefit of model reduction to be assessed together with the associated approximation error.

3D CFD pressure field, the 1D model's pressure distribution, and the two waveforms overlaid — with relative error and computation time beneath, annotated with the hardware each was run on
The reduced-order result set against the three-dimensional one it approximates, with the error and the cost of each reported alongside the conditions they were measured under.

Uncertainty Quantification of Fractional Flow Reserve

Physiological parameters and boundary conditions vary among individuals and across cardiac cycles, which introduces uncertainty into computational estimates of fractional flow reserve. We combine the calibrated coronary reduced-order model with physiologically informed lumped-parameter networks and polynomial chaos expansion. This framework propagates physiological input variability to the predicted FFR distribution at a computational cost that would be difficult to achieve with repeated three-dimensional simulations.

Physiological inputs grouped as systemic circulation, cardiac function, coronary resistance and myocardial compression → their probability distributions → the reduced-order ensemble → the resulting FFR distribution by stenosis severity
Variability in the physiological inputs is propagated through the reduced-order model, so the result is a distribution of FFR rather than a single value.

Global Sensitivity Analysis and Prediction Robustness

We use global sensitivity analysis to determine how individual physiological parameters contribute to variability in FFR. Under the investigated conditions, myocardial compression is the dominant contributor, followed by systemic and cardiac parameters that affect aortic pressure. The analysis also indicates that cycle-averaged FFR remains relatively robust within the investigated physiological parameter space, although its variability changes systematically with stenosis severity.

A parameter-importance bar chart naming only the influential parameters, above a plot of mean FFR against its standard deviation coloured by stenosis severity
Sensitivity analysis distinguishes parameters that govern the mean hemodynamic response from those that primarily affect prediction variability.

Model Verification and Scope

We assess reduced-order predictions against full three-dimensional CFD results before their use in large-scale parameter studies. Model performance is evaluated in terms of waveform agreement, spatial pressure distribution, relative error, computational cost, and robustness across anatomical and physiological conditions. The calibrated model is intended to complement, rather than replace, high-fidelity simulation when detailed three-dimensional flow structures are required.

Suited to the reduced-order modelRequires full three-dimensional CFD
Pulsatile pressure and flowLocal velocity structures
Parameter sweepsRecirculation and secondary flow
Uncertainty quantificationDetailed wall shear stress
Sensitivity analysisComplex local flow phenomena
Preliminary optimizationHigh-fidelity mechanistic analysis

Selected work

2020

Physics driven reduced order model for real time blood flow simulations

Computer Methods in Applied Mechanics and Engineering 364:112963

2016

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

Journal of Biomechanics 49(12):2540–2547

Computational Methods 2 topics in this area
Multiscale and Multiphysics ModelingEfficient Computational Modeling and Uncertainty Quantification