A mathematical model of circulation in the presence of the bidirectional cavopulmonary anastomosis in children with a univentricular heart

Pennati, Giancarlo; Migliavacca, Francesco; Dubini, Gabriele; Pietrabissa, Riccardo; Leval, Marc R. de

doi:10.1016/s1350-4533(96)00071-9

Cited by 65 publications

(66 citation statements)

References 29 publications

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“…1, the interplay between local and systemic dynamics in determining the boundary conditions for a numerical simulation was well evident before mathematical multiscale models were developed. In fact, in [147] a 3D rigid simulation of the cavopulmonary anastomosis was assisted by a lumped parameter model. The latter was a lumped parameter network covering the entire circulation with the role of finding boundary data to be properly prescribed to the stand-alone restricted 3D model of the region of interest.…”

Section: An Annotated Review Of Selected Workmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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Section: An Annotated Review Of Selected Workmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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“…Namely, it was assumed that r R ¼ 0.7, r C ¼ 0.3 and t ¼ 0.00625 s for both lungs, on the basis of values adopted in previous LPM models of pulmonary vasculature [11][12][13] and clinical measurements [14].…”

Section: Multi-scale Modelsmentioning

confidence: 99%

Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning

et al. 2011

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Cavopulmonary connections are surgical procedures used to treat a variety of complex congenital cardiac defects. Virtual pre-operative planning based on in silico patient-specific modelling might become a powerful tool in the surgical decision-making process. For this purpose, three-dimensional models can be easily developed from medical imaging data to investigate individual haemodynamics. However, the definition of patient-specific boundary conditions is still a crucial issue. The present study describes an approach to evaluate the vascular impedance of the right and left lungs on the basis of pre-operative clinical data and numerical simulations. Computational fluid dynamics techniques are applied to a patient with a bidirectional cavopulmonary anastomosis, who later underwent a total cavopulmonary connection (TCPC). Multi-scale models describing the surgical region and the lungs are adopted, while the flow rates measured in the venae cavae are used at the model inlets. Pre-operative and post-operative conditions are investigated; namely, TCPC haemodynamics, which are predicted using patient-specific pre-operative boundary conditions, indicates that the pre-operative balanced lung resistances are not compatible with the TCPC measured flows, suggesting that the pulmonary vascular impedances changed individually after the surgery. These modifications might be the consequence of adaptation to the altered pulmonary blood flows.

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“…Specific instances of systems like the one in (3.5) can be found, e.g., in [11,13]. In the quoted references, lumped parameters systems featuring, respectively, 16 and 48 state variables for the description of the whole circulation have been proposed for a specific investigation of the coronary bed.…”

Section: 2mentioning

confidence: 99%

Analysis of a Geometrical Multiscale Model Based on the Coupling of ODE and PDE for Blood Flow Simulations

Quarteroni¹,

Veneziani²

2003

Multiscale Model. Simul.

173

142

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Abstract. In hemodynamics, local phenomena, such as the perturbation of flow pattern in a specific vascular region, are strictly related to the global features of the whole circulation (see, e.g., [L. Formaggia et al., Comput. Vis. Sci., 2 (1999), pp. 75-83]). In [A. Quarteroni, S. Ragni, and A. Veneziani, Comput. Vis. Sci., 4 (2001), pp. 111-124] we have proposed a heterogeneous model, where a local, accurate, three-dimensional description of blood flow by means of the NavierStokes equations in a specific artery is coupled with a systemic, zero-dimensional, lumped model of the remainder of circulation. This is a geometrical multiscale strategy, which couples an initialboundary value problem to be used in a specific vascular region with an initial-value problem in the rest of the circulatory system. It has been successfully adopted to predict the outcome of a surgical operation (see [K. Laganà et al., Biorheology, 39 (2002) Barcelona, Spain, 2000]). However, its interest goes beyond the context of blood flow simulations. In this paper we provide a well-posedness analysis of this multiscale model by proving a local-in-time existence result based on a fixed-point technique. Moreover, we investigate the role of matching conditions between the two submodels for the numerical simulation.Key words. geometrical multiscale models, blood flow simulations, fixed-point techniques AMS subject classifications. 35M20, 35Q30, 76D03, 65L05, 76Z05PII. S1540345902408482 1. Introduction. In computational fluid dynamics there might be the need for accurately simulating the flow in a subregion of a complex system that can be reasonably represented by a hydraulic network. One may think, for instance, of a system for water supply for which there is the interest of ascertaining the spatial variations of velocity and pressure only in a specific pipeline or in a reservoir. Another instance, which has motivated our investigation, is the blood circulatory system. Here the underlying (low cost) model is based on an analogy with electric circuits and can predict the time evolution of average physical quantities (flow rate and pressure) in the different compartments of the overall system (see, e.g., [15,27]). Yet, there is the interest of carrying out three-dimensional (3D) simulations on a sensible region (e.g., a coronary bypass, a carotid bifurcation, a stented artery, etc.). In these cases, the local investigation requires the specification of boundary conditions on the interface between the region of interest and the remainder of the network. In fact, the significance of numerical results is strictly related to the capability of the numerical device of properly accounting for the exchange of information with the global network. Actually, it is well known that, in the circulatory system, local behavior of blood flow in a specific region is strictly related to the systemic features of the circulation. For

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A mathematical model of circulation in the presence of the bidirectional cavopulmonary anastomosis in children with a univentricular heart

Cited by 65 publications

References 29 publications

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning

Analysis of a Geometrical Multiscale Model Based on the Coupling of ODE and PDE for Blood Flow Simulations

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