Publication

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Alfio Quarteroni, Luca Formaggia, Christian Vergara
2013
Journal Articles

Abstract

In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the 1D model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the 1D model and highlighting the best one in view of the physical consistency. (c) 2012 Elsevier Inc. All rights reserved.

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https://infoscience.epfl.ch/entities/publication/4f11d566-90bb-4c39-95b1-2b315d714211

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Alfio Quarteroni, Luca Formaggia, Christian Vergara
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/4f11d566-90bb-4c39-95b1-2b315d714211

About this result

Related concepts (16)

Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.

One-dimensional space

In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number. In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself.

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