Biomedical Engineering Reference
In-Depth Information
ripheral/venous/pulmonary and cardiac circulations. In this work, valves are mod-
elled using an ideal model of a diode, not allowing for backflow to occur. This last
point was addressed in [31], in which phenomenological models of the cardiac valves
were proposed in order to model more accurately the opening and closing phases of
the valves accounting for certain pathological conditions like valve regurgitation and
stenosis. In the field of modelling blood flow in specific vessels, several works dealt
with the use of heterogeneous representations in order to couple local and global
hemodynamics phenomena. This has been mostly carried out using 3D and 1D (or
0D) models to couple blood flow in complex arterial geometries with either full or
partial models for the systemic dynamics [6, 8, 9, 18, 21, 28, 43, 60, 62].
In the context of the previous paragraphs, the model introduced here for the entire
cardiovascular system borrows the most important features of the different models
available in the literature, and their integration leads to a model with more descrip-
tive and predictive capabilities.
Evidently, the dynamics captured by the model depends on whether the model is
open or closed. This can be understood by looking at the constituent vascular entities
in each model, as described below.
•
Open-loop model of the CVS composed by:
-
a 1D model of the arterial network;
-
0D Windkessel models for the arterioles and capillaries;
-
3D models for specific vessels.
•
Closed-loop model of the CVS composed by:
- a 1D model of the arterial network;
- 0D Windkessel models for the arterioles and capillaries;
- 3D models for specific vessels;
- 0D models for venules, veins and cavas;
- 0D models for the four cardiac chambers;
- 0D models for the four cardiac valves.
Fig. 9.4 shows a schematic representation of the closed-loop CVS. Notice that the
venous circulation is coupled to the arterial network through three points: the upper
and lower body connections and the aortic root, closing the loop. The open-loop
model is obtained by removing the elements from the capillary level to the aortic
root. In the latter case boundary conditions are imposed at the Windkessel terminals
(constant pressure), and at the aortic root (a given flow rate).
The glossary of the terms used in Fig. 9.4 is given in Table 9.1. In this table
N
sa
denotes the total number of systemic arteries and
N
wlb
and
N
wub
are the number
of Windkessel models pertaining to the lower and upper parts of the body, respec-
tively, with
N
w
=
N
wlb
+
N
wub
the total number of Windkessel elements in the arterial
side.
