Computational modelling of 1D blood flow and its applications

Franke, V.; Peiró, Joaquim; Sherwin, Spencer J.; Parker, Kim H.; Ling, Wee; Fisk, Nicholas M.

doi:10.1051/proc:2002010

Cited by 5 publications

(7 citation statements)

References 10 publications

(11 reference statements)

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“…In reality, the external nose influences the approaching inspired flow. Preliminary studies on the variations in inflow conditions are reported in Franke et al (2005). In more comprehensive studies to be reported elsewhere (Taylor et al in preparation), the geometric contraction from nasal vestibule to nasal valve is shown to reduce the dependence of the flow in the cavity to that pertaining at the nares.…”

Section: Internal and External Anatomical Form And Nasal Airflowmentioning

confidence: 98%

“…Mesh convergence checks employed up to 29 million interior elements to fill a single half-cavity. The element count is far higher than hitherto used, but ensures very high spatial resolution of both WSS and its gradients; other convergence studies in steady laminar flow (Franke et al (2005), and to be reported elsewhere) show that lower resolutions (3-5 million elements in a carefully graded, hybrid mesh) are adequate to resolve pressure, velocity and overall shear stress.…”

Section: Nasal Airway Form and The Modelling Of Functionmentioning

confidence: 99%

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Nasal architecture: form and flow

Doorly

Taylor

Gambaruto

et al. 2008

Phil. Trans. R. Soc. A.

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Current approaches to model nasal airflow are reviewed in this study, and new findings presented. These new results make use of improvements to computational and experimental techniques and resources, which now allow key dynamical features to be investigated, and offer rational procedures to relate variations in anatomical form. Specifically, both replica and simplified airways of a single subject were investigated and compared with the replica airways of two other individuals with overtly differing geometries. Procedures to characterize and compare complex nasal airway geometry are first outlined. It is then shown that coupled computational and experimental studies, capable of obtaining highly resolved data, reveal internal flow structures in both intrinsically steady and unsteady situations. The results presented demonstrate that the intimate relation between nasal form and flow can be explored in greater detail than hitherto possible. By outlining means to compare complex airway geometries and demonstrating the effects of rational geometric simplification on the flow structure, this work offers a fresh approach to studies of how natural conduits guide and control flow. The concepts and tools address issues that are thus generic to flow studies in other physiological systems.

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Section: Internal and External Anatomical Form And Nasal Airflowmentioning

confidence: 98%

Section: Nasal Airway Form and The Modelling Of Functionmentioning

confidence: 99%

Nasal architecture: form and flow

Doorly

Taylor

Gambaruto

et al. 2008

Phil. Trans. R. Soc. A.

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“…The density and viscosity of the blood are treated as constants. With these assumptions, the mass and momentum conservation laws can be written as

\frac{∂A}{∂t} MathClass-bin+ \frac{\partial (uA)}{∂x} MathClass-rel= 0

\frac{∂u}{∂t} MathClass-bin+ u \frac{∂u}{∂x} MathClass-bin+ \frac{1}{ρ} \frac{∂p}{∂x} MathClass-rel= \frac{f}{ρ}

where A ( x , t ) is the cross‐sectional area of the vessel, u ( x , t ) is the average velocity of the fluid at a section, p ( x , t ) is the internal pressure at a cross section, ρ is the blood density

(ρ \approx 1060 {kg/m}^{3})

and f ( x , t ) is the friction force due to viscosity. The expression for f depends on the blood viscosity, μ = 0.0035 kg∕ms, and the friction force may be expressed as

f MathClass-rel= MathClass-bin- 8 πμ \frac{u}{A}

Alternatively, the governing equations may be expressed in a standard form as

\frac{\partial bold-italicU}{∂t} MathClass-bin+ \frac{\partial bold F}{∂x} MathClass-rel= bold-italicS

where

bold-italicU MathClass-rel= ([], \begin{matrix} falsefalsearray \\ arraycenter A \\ arraycenter u \end{matrix}) MathClass-punc, bold F MathClass-rel= ([], \begin{matrix} falsefalsearray \\ arraycenter uA \\ arraycenter \frac{u^{2}}{2} + \frac{p}{ρ} \end{matrix}) MathClass-punc, bold-italicS MathClass-rel= ([], \begin{matrix} falsefalsearray \\ arraycenter 0 \\ arraycenter ... \end{matrix})

…”

Section: Mathematical Problemmentioning

confidence: 99%

“…The density and viscosity of the blood are treated as constants. With these assumptions, the mass and momentum conservation laws can be written as [2,12,14,46,[48][49][50][51] @A…”

Section: Governing Equationsmentioning

confidence: 99%

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

Low

Loon

Sazonov

et al. 2012

Numer Methods Biomed Eng

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In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

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“…Since the width of the pressure wave produced by the heart is much greater than any vessel diameter, the one-dimensional assumption is valid for studying systemic circulation (Avolio, 1980;Alastruey et al, 2007;Steele et al, 2007;Mynard and Nithiarasu, 2008;Raines et al, 1974;Wan et al, 2002;Low et al, 2012;Stergiopulos et al, 1992;Chen et al, 2013;Blanco et al, 2012;Kufahl and Clark, 1985;Urquiza et al, 2006;Franke et al, 2002;Watanabe et al, 2013). Some of the recent publications in this area adopted Locally Conservative Galerkin (LCG) technique, which was developed in (Nithiarasu, 2004, Thomas et al, 2008 using an explicit Taylor-Galerkin method along with the characteristic variables.…”

Section: Introductionmentioning

confidence: 99%

Robust Finite Element Approaches to Systemic Circulation Using the Locally Conservative Galerkin (LCG) Method

Hasan¹,

Nithiarasu

2016

Proceedings of the Indian National Science Academy

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In this paper novel finite element algorithms for robustly solving flow equations of a systemic circulation are presented and compared. A novel, Locally Conservative Galerkin (LCG) method is developed by adopting semi-and fully-implicit time discretisations to address the behavior of blood flow in the human circulatory system. These techniques are efficient for nonlinear system of equations used in blood flow models and achieve rapid convergence. Several comparisons are made between the methods to demonstrate the validity and stability of the current numerical models to solve the blood flow characteristics in a human body.

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Computational modelling of 1D blood flow and its applications

Cited by 5 publications

References 10 publications

Nasal architecture: form and flow

Nasal architecture: form and flow

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

Robust Finite Element Approaches to Systemic Circulation Using the Locally Conservative Galerkin (LCG) Method

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