Biomedical Engineering Reference
In-Depth Information
9
The role of the variational formulation in the
dimensionally-heterogeneous modelling of the
human cardiovascular system
Pablo J. Blanco, and Ra ul A. Feij oo
Abstract.
The modelling of the cardiovascular system entails dealing with different
phenomena pertaining to different time, constitutive and geometrical scales. Specif-
ically, the problem of integrating various geometrical scales can be understood from
a kinematical point of view, which means to integrate models with different kine-
matics, and in particular different dimensionality. In this context, all the variational
machinery can be employed to derive consistent variational formulations according
to the underlying kinematical hypotheses that rule over the corresponding models. In
this work we discuss the application of variational formulations to model the blood
flow in the cardiovascular system making use of heterogeneous representations. Two
examples of applications are used to show the capabilities and potentialities of the
present approach.
9.1 Introduction
The cardiovascular system (CVS) can be viewed as the integration of different parts,
at different geometric/time scales and different physiological mechanisms, into a
whole
with rather complex structural and functional behaviour. These different com-
ponents, scales and functionalities are inseparably coupled by virtue of the interac-
tions between local and global phenomena. In such context, the interplay of such
Pablo J. Blanco
LNCC - National Laboratory for Scientific Computing and INCT-MACC - National Institute of
Science and Technology in Medicine Assisted by Scientific Computing, Av. Get ulio Vargas 333,
Quitandinha, 25651-075, Petr opolis, RJ, Brazil
e-mail: pablo.j.blanco@gmail.com
Ra ul A. Feij oo ( )
LNCC - National Laboratory for Scientific Computing and INCT-MACC - National Institute of
Science and Technology in Medicine Assisted by Scientific Computing, Av. Get ulio Vargas 333,
Quitandinha, 25651-075, Petr opolis, RJ, Brazil
e-mail: feijooraul@gmail.com
