Blood Flow

Figueroa, C. Alberto; Taylor, Charles A.; Marsden, Alison

doi:10.1002/9781119176817.ecm2068

Cited by 6 publications

(6 citation statements)

References 211 publications

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“…The blood is assumed to be incompressible. Starting from the mass and momentum conservations, the following classical 1-D equations in the cylindrical coordinate system can be derived for the current model under the assumption that the axial displacement is negligible; there is no flow through the lumen wall along the z direction; and velocity and pressure are uniform in the cross-section (Sherwin et al 2003;van de Vosse & Stergiopulos 2011;Figueroa, Taylor & Marsden 2017):…”

Section: Governing Equationsmentioning

confidence: 99%

“…It is worth noting that (2.3) is derived assuming small displacement (u r r) and the vessel wall to be incompressible, linear elastic, thin-walled and longitudinally tethered (Sherwin et al 2003). This set of equations (2.2) and (2.3) have been widely used in numerical studies of pulse wave propagation in arteries with tapering and variable wall properties (Sherwin et al 2003;Alastruey et al 2011;van de Vosse & Stergiopulos 2011;Figueroa et al 2017).…”

Section: Governing Equationsmentioning

confidence: 99%

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Analytic solution for pulse wave propagation in flexible tubes with application to a patient-specific arterial tree

Wu,

Zhu

2023

J. Fluid Mech.

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In this paper, we present an analytic solution for pulse wave propagation in a flexible arterial model with tapering, physiological boundary conditions and variable wall properties (wall elasticity and thickness). The change of wall properties follows a profile that is proportional to $r^\alpha$ , where $r$ represents the lumen radius and $\alpha$ is a material coefficient. The cross-sectionally averaged velocity and pressure are obtained by solving a hyperbolic system derived from the mass and momentum conservations, and they are expressed in Bessel functions of order $(4-\alpha )/(3-\alpha )$ and $1/(3-\alpha )$ , respectively. The solution is successfully validated by comparing it with numerical results from three-dimensional (3-D) fluid–structure interaction simulations. Subsequently, the solution is employed to study pulse wave propagation in an arterial model, revealing that the wall properties and the physiological outlet boundary conditions, such as the resistor–capacitor–resistor (RCR) model, play a crucial role in characterizing the input impedance and reflection coefficient. At low-frequency range, the input impedance is found to be insensitive to the wall properties and is primarily determined by the RCR parameters. At high-frequency range, the input impedance oscillates around the local characteristic impedance, and the oscillation amplitude varies non-monotonically with $\alpha$ . Expressions for the input impedance at both low-frequency and high-frequency limits are presented. This analytic solution is also successfully applied to model flow inside a patient-specific arterial tree, with the maximum relative errors in pressure and flow rate never exceeding $1.6\,\%$ and $9.0\,\%$ when compared with results from 3-D numerical simulations.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Analytic solution for pulse wave propagation in flexible tubes with application to a patient-specific arterial tree

Wu,

Zhu

2023

J. Fluid Mech.

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“…With the purpose of achieving higher speedups during the solution time, we consider the approximation of the convective term given in Eq. (24) speedups are, from N c = 10 to N c = 120 and using the same notation adopted in Table 2, 56(998), 36(620), 22(464), 10(313), 5(215). The POD tolerances are constant and take the values u = 4e-3 and p = 8e-5.…”

Section: Online Phase On the Artificial Geometrymentioning

confidence: 99%

“…This term broadly encompasses a variety of pathological cases ranging from heart disease to many other peripheral vascular diseases. Consequently, the numerical simulation of blood flow in the cardiovascular system has gained considerable attention during the last twenty years as a valuable quantitative tool for the study and diagnosis of such conditions [5,24].…”

Section: Introductionmentioning

confidence: 99%

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Pegolotti,

Pfaller,

Marsden

et al. 2020

Preprint

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We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g. straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by proper orthogonal decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

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Section: Introductionmentioning

confidence: 99%

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Pegolotti

Pfaller

Marsden

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier–Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton–Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

show abstract

Blood Flow

Cited by 6 publications

References 211 publications

Analytic solution for pulse wave propagation in flexible tubes with application to a patient-specific arterial tree

Analytic solution for pulse wave propagation in flexible tubes with application to a patient-specific arterial tree

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Model order reduction of flow based on a modular geometrical approximation of blood vessels

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