Multifidelity Estimators for Coronary Circulation Models Under Clinically Informed Data Uncertainty

Seo, Jongmin; Fleeter, Casey; Kahn, Andrew; Marsden, Alison L.; Schiavazzi, Daniele E.

doi:10.1615/int.j.uncertaintyquantification.2020033068

Cited by 16 publications

(17 citation statements)

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“…In the special case of zero initial conditions, this relationship simplified to the inequality in Equation ( 21 The same study is repeated in Figure 5b for starting from steady state initial conditions. Compared to zero initial conditions, the number of cardiac cycles required to each an asymptotic pressure with an error of ∞ ≤ 1 % are much lower: n ∞ ∈ [2,12]. Flow is converged within a maximum of 5 cardiac cycles.…”

Section: Initial Conditionsmentioning

confidence: 99%

“…Three-dimensional (3D) blood flow simulations are commonly coupled with zero-dimensional (0D) lumped parameter models, representing the downstream vasculature at the model's boundary [1,2,3,4]. These lumped parameter models are analogous to an electric circuit, with resistors and capacitors modeling the viscosity of the blood and the elasticity of the vessel wall, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…For pressure (left), the results confirm the linear relationship between the single model time constant τ T and the number of cardiac cycles n ∞ from Equation(21) (black line). For a range of model time constants τ T ∈ [0.3, 9.6] we find the range of cardiac cycles n ∞ ∈[2, 44]. The number of cardiac cycles to reach a periodic flow solution (right) is not correlated to the model time constant and is, in general, much lower than the number of cycles n ∞ to reach a periodic pressure.…”

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confidence: 96%

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On the periodicity of cardiovascular fluid dynamics simulations

Pfaller,

Pham,

Wilson

et al. 2021

Preprint

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Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no standardized method to determined whether a simulation has yet reached that periodic state. In this work, we propose use of the asymptotic error measure to quantify the difference between simulation results and their ideal periodic state using lumped-parameter modeling. We further show that initial conditions are crucial in reducing computational time and develop an automated framework to generate appropriate initial conditions from a one-dimensional model of blood flow. We demonstrate the performance of our initialization method using six patientspecific models from the Vascular Model Repository. In our examples, our initialization protocol achieves periodic convergence within one or two cardiac cycles, leading to a significant reduction in computational cost compared to standard methods. All computational tools used in this work are implemented in the open-source software platform SimVascular. Automatically generated initial conditions have the potential to significantly reduce computation time in cardiovascular fluid dynamics simulations.

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Section: Initial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 96%

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On the periodicity of cardiovascular fluid dynamics simulations

Pfaller,

Pham,

Wilson

et al. 2021

Preprint

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“…Iterative optimization, as well as parameter sweeps are required to explore a design space with multiple parameters or to identify a personalized treatment plan [1]. In uncertainty quantification (UQ) or sensitivity analysis, several thousand simulations are commonly required to quantify the confidence in the simulation's predictions based on uncertainties in the parameters [2,3]. Finally, fast feedback is essential for clinical decision-making.…”

Section: Introductionmentioning

confidence: 99%

“…LPN boundary conditions for 3D models are also used in parameter estimation problems with UQ [18,19,20]. A combination of 3D, 1D, and 0D models can be advantageous in multi-fidelity UQ approaches [2] and parameter estimation problems [3]. Standard approaches for UQ in cardiovascular modeling pose challenges due to a large number of uncertain inputs and the high computational cost of realistic 3D simulations.…”

Section: Introductionmentioning

confidence: 99%

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

Pfaller,

Pham,

Verma

et al. 2021

Preprint

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Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computer. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood flow and pressure with only a fraction of the cost. They can accelerate uncertainty quantification, optimization, and design parameterization studies. Previously, these models needed to be created laboriously by hand, and this limited assessment of their approximation accuracy to very few models in prior studies. This work proposes a fully automated and openly available framework to generate and simulate 0D and 1D models from 3D patient-specific geometries. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against full 3D solutions in a comprehensive comparison with N = 73 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1 % to 10 % for both 0D and 1D models, at the caps and inside the vessel branches. Though they have minimally higher approximation errors than 1D, we recommend using 0D models due to their robustness and computational efficiency. Automatically generated reduced-order models can significantly speed up model development and shift the computational load from high-performance to personal computers.

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

Seo

Schiavazzi

Kahn

et al. 2020

Numer Methods Biomed Eng

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Cardiovascular simulations are increasingly used for noninvasive 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 Arbitrary‐Lagrangian‐Eulerian framework for fluid‐structure interaction, 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 Monte Carlo sampling, stochastic collocation, and multi‐wavelet stochastic expansion. Variabilities in the quantities of interest, 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 used to distribute the total downstream vascular resistance to the single outlets, has little effect on coronary hemodynamics or wall mechanics. Finally, we compare convergence behaviors of statistics of QoIs using several uncertainty propagation methods on three model benchmark problems and the left coronary simulations. 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.

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Multifidelity Estimators for Coronary Circulation Models Under Clinically Informed Data Uncertainty

Cited by 16 publications

References 0 publications

On the periodicity of cardiovascular fluid dynamics simulations

On the periodicity of cardiovascular fluid dynamics simulations

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

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

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