On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems

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.

show abstract

“…The same framework has been applied in [26] to an interface equation related to flow rates and total pressure.…”

Section: Further Developments and Commentsmentioning

confidence: 99%

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

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

169

157

View full text Add to dashboard Cite

show abstract

“…Coupling conditions at the interface are needed to enforce the conservation of mass flux (flow rate) and mean normal stress (traction) (Blanco et al . , a ; Formaggia et al . ; Malossi et al .…”

Section: Global‐to‐local Haemodynamics: 3d–1d Coupled Modelsmentioning

confidence: 99%

“…), this distinction can be considered negligible compared to the simpler mean normal stress formulation for typical cardiovascular flow regimes (Blanco et al . a ). Mass flux and traction are also particularly desirable coupling quantities since they are readily translatable into standard Dirichlet and Neumann boundary conditions on each subdomain.…”

Section: Global‐to‐local Haemodynamics: 3d–1d Coupled Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Roadmap for cardiovascular circulation model

Safaei

Bradley

Suresh

et al. 2016

The Journal of Physiology

Self Cite

View full text Add to dashboard Cite

Computational models of many aspects of the mammalian cardiovascular circulation have been developed. Indeed, along with orthopaedics, this area of physiology is one that has attracted much interest from engineers, presumably because the equations governing blood flow in the vascular system are well understood and can be solved with well-established numerical techniques. Unfortunately, there have been only a few attempts to create a comprehensive public domain resource for cardiovascular researchers. In this paper we propose a roadmap for developing an open source cardiovascular circulation model. The model should be registered to the musculo-skeletal system. The computational infrastructure for the cardiovascular model should provide for near real-time computation of blood flow and pressure in all parts of the body. The model should deal with vascular beds in all tissues, and the computational infrastructure for the model should provide links into CellML models of cell function and tissue function. In this work we review the literature associated with 1D blood flow modelling in the cardiovascular system, discuss model encoding standards, software and a model repository. We then describe the coordinate systems used to define the vascular geometry, derive the equations and discuss the implementation of these coupled equations in the open source computational software OpenCMISS. Finally, some preliminary results are presented and plans outlined for the next steps in the development of the model, the computational software and the graphical user interface for accessing the model.

show abstract

“…We address the uncoupled time-marching of the two subcompartments via explicit coupling schemes. Note that this approach clearly differs from [26,5], where partitioned iterative procedures acting on averaged/integrated interface quantities are proposed.…”

Section: Introductionmentioning

confidence: 99%

Explicit Coupling Schemes for a Fluid-Fluid Interaction Problem Arising in Hemodynamics

Fernández¹,

Gerbeau²,

Smaldone³

2014

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

In this work we propose a new approach to the loosely coupled time-marching of a fluid-fluid interaction problems involving the incompressible Navier-Stokes equations. The methods combine a specific explicit Robin-Robin treatment of the interface coupling with a weakly consistent interface pressure stabilization in time. A priori energy estimates guaranteeing stability of the splitting are obtained for a total pressure formulation of the coupled problem. The performance of the proposed schemes is illustrated on several numerical experiments related to simulation of aortic blood flow.Schémas de couplage explicites pour un problème d'interaction fluide-fluide en hémodynamique Résumé : Dans cet article, nous proposons une nouvelle approche pour le couplage faible de deux fluides incompressibles régis par les équations de Navier-Stokes. Ces méthodes combinent un traitement spécifique Robin-Robin explicite des conditions d'interface avec une stabilisation de la pression à l'interface faiblement consistante en temps. Une estimation d'énergie a priori garantissant la stabilité du dćouplage en temps est obtenue pour une formulation en pression totale du système couplé. Les propriétés des méthodes proposées sont illustrées dans des expériences numériques motivées par la simulation de la circulation du sang dans la aorte.Mots-clés : interaction fluide-fluide, fluide incompressible, discrétisation en temps, schéma de couplage faible, schéma Robin-Robin, méthode des éléments finis, méthode de Nitsche.

show abstract

On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems

Cited by 11 publications

References 24 publications

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

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

Roadmap for cardiovascular circulation model

Explicit Coupling Schemes for a Fluid-Fluid Interaction Problem Arising in Hemodynamics

Contact Info

Product

Resources

About