An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model

Clipp, Rachel B.; Steele, Brooke N.

doi:10.3934/mbe.2012.9.61

Cited by 6 publications

(8 citation statements)

References 34 publications

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“…This suggests that the overall compliance does not differ significantly between the pulmonary arterial and venous trees. Consequently, we use a constant compliance

\frac{E h}{r_{0}} = 195 normalm normalm normalH normalg false(\approx 26 normalk normalP normala false),

approximately the same value used by Clipp & Steele (2009, 2012), for both pulmonary arteries and veins. This value gives simulated pressure waveforms consistent with the physiological ranges of 8.8 ± 3.3–22 ± 4.2 mmHg (Greenfield & Douglas, 1963; Herve et al , 1989), 10–25 mmHg (Fung, 1996) and 8–25 mmHg (Hall, 2011) in the proximal pulmonary arteries.…”

Section: Methodsmentioning

confidence: 99%

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

Qureshi

Vaughan

Sainsbury

et al. 2014

Biomech Model Mechanobiol

108

135

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A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen and coworkers (Ottesen et al., 2003; Olufsen et al., 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii ≥ 50µm. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment of circulatory diseases within the lung.

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“…This suggests that the overall compliance does not differ significantly between the pulmonary arterial and venous trees. Consequently, we use a constant compliance

\frac{E h}{r_{0}} = 195 normalm normalm normalH normalg false(\approx 26 normalk normalP normala false),

Section: Methodsmentioning

confidence: 99%

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

Qureshi

Vaughan

Sainsbury

et al. 2014

Biomech Model Mechanobiol

108

135

View full text Add to dashboard Cite

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“…effects of the respiratory cycle). These are well known [6] and should be contained within the uncertainty bounds of the model. Figure 5.…”

Section: Importance Of Correcting For Model Mismatchmentioning

confidence: 99%

“…Several previous studies [3][4][5][6][7] have developed 1D fluiddynamics models predicting pulmonary blood flow and pressure. However, only a few [3,4] have aimed at devising subject-specific predictions by estimating model parameters.…”

Section: Introductionmentioning

confidence: 99%

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

Păun

Colebank

Olufsen

et al. 2020

J. R. Soc. Interface.

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This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

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“…Various types of outflow boundary conditions have been used in the previous works, including the constant resistance model (CR) [ 18 – 21 ], the tapering-vessel model [ 22 ], the Windkessel model (WK) [ 6 , 23 – 26 ], and the structured tree model (ST) [ 17 , 27 – 30 ]. In a number of specialized applications, a non-constant resistance model has been used to model the effect of cerebral autoregulation in the brain [ 31 ], and a structured tree model incorporating the effects of geometry, compliance, and respiration has been used to mimic the pulmonary vascular system [ 32 , 33 ]. It has also been reported that outflow boundary conditions can greatly affect the wave profile in the upstream arteries [ 11 , 28 ].…”

Section: Introductionmentioning

confidence: 99%

“…The impedance of a structured tree, which is the ratio of the Fourier coefficient of the blood pressure to that of the flow rate at the inlet of the structured tree, is obtained from the linearized system of the one-dimensional model of blood flow in the structured tree. With the ST model, detailed characteristics of the pulse wave such as the dicrotic wave are observed in the simulations [ 11 , 29 , 30 , 32 , 33 ]. Therefore, it is important to carry out a systematic comparison among these models.…”

Section: Introductionmentioning

confidence: 99%

Outflow Boundary Conditions for Blood Flow in Arterial Trees

Huang

Cai

2015

PLoS ONE

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In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models.

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An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model

Cited by 6 publications

References 34 publications

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

Outflow Boundary Conditions for Blood Flow in Arterial Trees

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