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

Piccioli, Francesco; Bertaglia, Giulia; Valiani, Alessandro; Caleffi, Valerio

doi:10.1016/j.jcp.2022.111364

Cited by 20 publications

(22 citation statements)

References 77 publications

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“…The flow rate through the aortic valve, q AV ( t ), was computed at every time step and prescribed as the inflow to the aortic root. The coupling between the cardiac model and the arterial domain was accomplished using the following Riemann invariants associated with the genuinely non‐linear field at the proximal boundary of the physical domain, 18

{normalΓ}_{1} = u - 4 c, {normalΓ}_{2} = p - K (\sqrt{α} - 1),

where u ( x , t ) is the cross‐sectional averaged blood velocity, c ( x , t ) is the pulse wave velocity, p ( x , t ) is the cross‐sectional averaged blood pressure (BP), K ( x ) is the wall stiffness coefficient, and α = A ∕ A 0 is the dimensionless luminal cross‐sectional area, where A ( x , t ) and A 0 ( x ) are the time–varying dimensional and equilibrium luminal cross‐sectional areas, respectively 23 …”

Section: Methodsmentioning

confidence: 99%

The effect of cardiac properties on arterial pulse waves: An in‐silico study

Piccioli

Valiani

Alastruey

et al. 2022

Numer Methods Biomed Eng

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This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped‐parameter model of the left part of the heart was coupled to a one‐dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.

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{normalΓ}_{1} = u - 4 c, {normalΓ}_{2} = p - K (\sqrt{α} - 1),

Section: Methodsmentioning

confidence: 99%

The effect of cardiac properties on arterial pulse waves: An in‐silico study

Piccioli

Valiani

Alastruey

et al. 2022

Numer Methods Biomed Eng

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“…We remark here that, generally, one needs to choose m > 0 and n ∈ [−2, 0] in order to preserve desirable mathematical properties of the PDE system [42,34].…”

Section: Elastic Constitutive Lawmentioning

confidence: 99%

“…If we consider the SLS constitutive law (18) as closing equation for the governing system (1), we obtain an augmented fluid-structure interaction (FSI) system of the cardiovascular bio-fluid dynamics, which reads [6,8,34]:…”

Section: Asymptotic Limitsmentioning

confidence: 99%

“…The second eigenvector of the system is associated with a linearly degenerate (LD) characteristic field, while the first and the third define genuinely non-linear fields (leading to the formation of shocks or rarefaction waves) [34]. Concerning the Riemann Invariants of the system, those associated with the LD field result [6,34] Γ…”

Section: Asymptotic Limitsmentioning

confidence: 99%

“…Several studies have already shown that, in general, one-dimensional (1D) modeling coupled with lumped-parameter, zero-dimensional (0D) models, derived from full threedimensional (3D) models by means of simplifying assumptions about flow, structure, and their interaction, is sufficient to obtain realistic and accurate numerical results, particularly when the flow is predominantly unidirectional [46,33,44]. Moreover, in contrast to 3D simulations with prohibitively high computational costs, 1D models allow for the investigation of the hemodynamics of the entire main circulatory system [1,31,34].…”

Section: Introductionmentioning

confidence: 99%

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Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods

Bertaglia¹,

Pareschi²

2023

Preprint

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In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.

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First blood: An efficient, hybrid one‐ and zero‐dimensional, modular hemodynamic solver

Wéber

Gyürki

Paál

2023

Numer Methods Biomed Eng

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Low‐dimensional (1D or 0D) models can describe the whole human blood circulation, for example, 1D distributed parameter model for the arterial network and 0D concentrated models for the heart or other organs. This paper presents a combined 1D‐0D solver, called first_blood, that solves the governing equations of fluid dynamics to model low‐dimensional hemodynamic effects. An extended method of characteristics is applied here to solve the momentum, and mass conservation equations and the viscoelastic wall model equation, mimicking the material properties of arterial walls. The heart and the peripheral lumped models are solved with a general zero‐dimensional (0D) nonlinear solver. The model topology can be modular, that is, first_blood can solve any 1D‐0D hemodynamic model. To demonstrate the applicability of first_blood, the human arterial system, the heart and the peripherals are modelled using the solver. The simulation time of a heartbeat takes around 2 s, that is, first_blood requires only twice the real‐time for the simulation using an average PC, which highlights the computational efficiency. The source code is available on GitHub, that is, it is open source. The model parameters are based on the literature suggestions and on the validation of output data to obtain physiologically relevant results.

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

Cited by 20 publications

References 77 publications

The effect of cardiac properties on arterial pulse waves: An in‐silico study

The effect of cardiac properties on arterial pulse waves: An in‐silico study

Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods

First blood: An efficient, hybrid one‐ and zero‐dimensional, modular hemodynamic solver

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