Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model

Bertaglia, Giulia; Caleffi, Valerio; Pareschi, Lorenzo; Valiani, Alessandro

doi:10.1016/j.jcp.2020.110102

Cited by 21 publications

(31 citation statements)

References 36 publications

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“…The mathematical model here presented recalls the blood flow model presented and discussed in [11,12,14], to which the reader is referred for further details.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…A viscoelastic constitutive tube law, relating pressure to cross-sectional area, is defined through the SLSM and added in partial differential equation (PDE) form to the main system of governing equations, composed by the equations of conservation of mass and momentum, giving rise to the so-called augmented fluid-structure interaction (a-FSI) system [12,14]. The a-FSI blood flow model, with the mathematical system solved through an Asymptotic-Preserving (AP) IMEX Runge-Kutta scheme in time and a Finite Volume (FV) method in space, has already been validated in previous single-vessel studies, demonstrating its capability to correctly simulate flow rate and pressure trends in patient-specific simulations [12,14] and also assessing its sensitivity to uncertainties inherent the viscoelastic parameters involved [11].…”

Section: Introductionmentioning

confidence: 99%

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Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid-structure interaction system

Piccioli,

Bertaglia,

Valiani

et al. 2021

Preprint

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A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel wall. Particularly, it has been demonstrated that the addition of a viscous contribution to the mechanical characterization of vessels brings positive results when compared to in-vivo measurements. In this context, the implementation of boundary conditions able to keep memory of the viscoelastic contribution of vessel walls assumes an important role, especially when dealing with large circulatory systems. In this work, viscoelasticity is taken into account in entire networks via the Standard Linear Solid Model. The implementation of the viscoelastic contribution at boundaries, namely inlet, outlet and junction, is carried out considering the natively hyperbolic nature of the mathematical model. Specifically, a non-linear system is established based on the definition of the Riemann Problem at junctions, characterized by rarefaction waves separated by contact discontinuity waves, among which the mass and the total energy are conserved. Basic junction test cases are analyzed, such as a trivial 2vessels junction, for both a generic artery and a generic vein, and a simple 3-vessels junction, considering an aortic bifurcation scenario. The chosen IMEX-SSP2 Finite Volume scheme is demonstrated to be second-order accurate in the whole domain and well-balanced, even when including junctions. Two benchmark arterial networks are then implemented, differing in number of vessels and in viscoelastic parameters. Comparison of the results obtained in the two networks underlines the high sensitivity of the model to the chosen viscoelastic parameters. In these numerical tests, the network-wise conservation of the contribution provided by the viscoelastic characterization of vessel walls is assessed. Finally, numerical results of pressure waveforms in the common carotid artery and in the femoral artery of the second network simulated are compared with in-vivo data recorded from different healthy subjects.

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“…The mathematical model here presented recalls the blood flow model presented and discussed in [11,12,14], to which the reader is referred for further details.…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid-structure interaction system

Piccioli,

Bertaglia,

Valiani

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…and consequently, from (7), we obtain a proportionality relation between the fluxes and the spatial derivatives (Fick's law):…”

Section: Macroscopic Formulation and Diffusion Limitmentioning

confidence: 99%

“…At each internal stage of the IMEX scheme (26), we apply a Total-Variation-Diminishing (TVD) Finite Volume discretization to evaluate the numerical fluxes [7,8]. To achieve second order accuracy also in space, while avoiding the occurrence of spurious oscillations, a classical minmod slope limiter has been adopted.…”

Section: Asymptotic-preserving Imex Finite Volume Schemementioning

confidence: 99%

Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties

Bertaglia,

Liu,

Pareschi

et al. 2021

Preprint

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Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to produce realistic scenarios of the spread of infection. In this paper, we introduce a bi-fidelity approach to quantify uncertainty in spatially dependent epidemic models. The approach is based on evaluating a high-fidelity model on a small number of samples properly selected from a large number of evaluations of a low-fidelity model. In particular, we will consider the class of multiscale transport models recently introduced in [6,10] as the high-fidelity reference and use simple two-velocity discrete models for low-fidelity evaluations. Both models share the same diffusive behavior and are solved with ad-hoc asymptotic-preserving numerical discretizations. A series of numerical experiments confirm the validity of the approach.

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“…Fluid-Structure Interaction (FSI) problems arise in many scientific and engineering applications including, to name only a few, aircraft aeroelasticity 1,2,3 , parachute inflation dynamics 4,5,6 , hemodynamics 7,8,9 , and lithotripsy 10,11 . Besides the development of mathematical models, seamless integration of observation data with these models starts to play a significant role to improve the prediction and quantify uncertainty for FSI, for example, calibration of hemodynamic model parameters to match patient data 12,13,9 and structural damage detection using sensor data and a digital twin 14,15,16 . The integration can be formulated as a data-based calibration problem.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework

Cao¹,

Huang

2021

Preprint

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Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction systems characterized by large structural deformations. Numerical methods to solve these problems, including embedded/immersed boundary methods, are typically not differentiable and lack smoothness. We propose a framework that is built on unscented Kalman filter/inversion to efficiently calibrate and provide uncertainty estimations of such complicated models with noisy observation data. The approach is derivative-free and non-intrusive, and is of particular value for the forward model that is computationally expensive and provided as a black box which is impractical to differentiate.The framework is demonstrated and validated by successfully calibrating the model parameters of a piston problem and identifying the damage field of an airfoil under transonic buffeting.

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Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model

Cited by 21 publications

References 36 publications

Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid-structure interaction system

Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid-structure interaction system

Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties

Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework

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