Computer simulation of arterial flow with applications to arterial and aortic stenoses

Stergiopulos, Nikolaos; Young, Donald F.; Rogge, Thomas

doi:10.1016/0021-9290(92)90060-e

Cited by 444 publications

(482 citation statements)

References 17 publications

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“…Several topological descriptions of the main arteries have been presented elsewhere, rendering useful information and consistent results with medical records and experimental data [2,38,43,48].…”

Section: Introductionmentioning

confidence: 79%

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

2013

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Abstract.A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries and 44 perforator arteries, with lumen radii ranging from 0.24 cm -axillary artery-to 0.018 cmperforator arteries. The modeling of blood flow in deformable vessels is governed by a well-known set of hyperbolic partial differential equations that accounts for mass and momentum conservation and a constitutive equation for the arterial wall. The variational formulation used to solve the problem and the related numerical approach are described. The model rendered consistent pressure and flow rate outputs when compared with patient records already published in the literature. In addition, an application to dimensionally-heterogeneous modeling is presented in which the developed arterial network is employed as an underlying model for a three-dimensional geometry of a branching point to be embedded in order to perform local analyses.Mathematics Subject Classification. 76Z05, 92C10, 92C30.

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Section: Introductionmentioning

confidence: 79%

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

2013

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“…The choice of the nodal set {Y (m) , α (m) } Q m=1 should be made such that an accurate integration rule can be con- (30) is an approximation to the exact coefficients defined by equation (29). Subsequently, equation (31) is an approximation of the exact gPC expansion (28).…”

Section: Stochastic Collocation Methodsmentioning

confidence: 99%

“…Time-domain analysis was investigated by Wang & Parker [33,34] who adopted a semi-analytical time-space domain approach to model the linearised wave motion in arteries. The method of characteristic has also previously been applied by Skalak [27], Stettler et al [30,31] and Stergiopulos et al [29]. More recently aeronautical-type numerical modelling techniques have been applied to the problem, (e.g.…”

Section: Reduced Modelling Of Arterial Networkmentioning

confidence: 99%

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Xiu

Sherwin

2007

Journal of Computational Physics

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Reduced models of human arterial networks are an efficient approach to analyse quantitative macroscopic features of human arterial flows. The justification for such models typically arise due to the significantly long wavelength associated with the system in comparison to the lengths of arteries in the networks. Although these types of models have been employed extensively and many issues associated with their implementations have been widely researched, the issue of data uncertainty has received comparatively little attention. Similar to many biological systems, a large amount of uncertainty exists in the value of the parameters associated with the models. Clearly reliable assessment of the system behaviour can not be made unless the effect of such data uncertainty is quantified.In this paper we present a study of parametric data uncertainty in reduced modelling of human arterial networks which is governed by a hyperbolic system. The uncertain parameters are modelled as random variables and the governing equations for the arterial network therefore become stochastic. This type stochastic hyperbolic systems have not been previously systematically studied due to the difficulties introduced by the uncertainty such as a potential change in the mathematical character of the system and imposing boundary conditions. We demonstrate how the application of a high-order stochastic collocation method based on the generalized polynomial chaos expansion, combined with a discontinuous Galerkin spectral/hp element discretisation in physical space, can successfully simulate this type of hyperbolic system subject to restrictions on the uncertainty interval. Building upon a numerical study of propagation of uncertainty and sensitivity in a simplified model with a single bifurcation, a systematical parameter sensitivity analysis is conducted on the wave dynamics in a multiple bifurcating human arterial network. Using the physical understanding of the dynamics of pulse waves in these types of networks we are able to provide an insight into the results of the stochastic simulations, thereby demonstrating the effects of uncertainty in physiologically accurate human arterial networks.

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“…For the outlet boundary condition, physiologically motivated three-element Windkessel boundary conditions are used widely 22,24 . This requires estimation of three quantities (two resistances: proximal -R p , and distal -R d , and one compliance -C) at each outlet from noninvasive data.…”

Section: Parameter Estimation For Model Personalizationmentioning

confidence: 99%

Non-Invasive Hemodynamic Assessment of Aortic Coarctation: Validation with In Vivo Measurements

et al. 2012

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We propose a CFD-based approach for the non-invasive hemodynamic assessment of pre-and post-operative coarctation of aorta (CoA) patients. Under our approach, the pressure gradient across the coarctation is determined from computational modeling based on physiological principles, medical imaging data, and routine non-invasive clinical measurements. The main constituents of our approach are a reduced-order model for computing blood flow in patientspecific aortic geometries, a parameter estimation procedure for determining patient-specific boundary conditions and vessel wall parameters from non-invasive measurements, and a comprehensive pressure-drop formulation coupled with the overall reduced-order model. The

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Computer simulation of arterial flow with applications to arterial and aortic stenoses

Cited by 444 publications

References 17 publications

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Non-Invasive Hemodynamic Assessment of Aortic Coarctation: Validation with In Vivo Measurements

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