Case Studies of the Human Cardiovascular System - Computational Hemodynamics: Theory, Modelling and Applications - page 200

CCA inlet as well as the ICA and ECA outlets. In their settings, the flow division
ratio of the ICA to ICA was assumed to be 7:3, which they referred to as an average
physiological value under normal conditions (Ku and Giddens 1987). However,
similar to Steinman et al. (2000) they model the resistance effect downstream of the
arterial network by assuming specific flow division ratios. A more accurate setting
by Long et al. (2002) implemented the 55:45 ratio based on magnetic resonance
flow measurements, However, although this configuration is patient-specific, it is
fixed for a steady flow while the real flow division ratio is transient and dependent
on the flow rate profiles through the ICA and ECA. The study by Marshall et al.
(2004a) took into account this transient property and reported the ECA/ICA flow
division ratio of a healthy carotid artery with a time-averaged value of 0.39:1.
It is worth noting that the flow division ratio of ICA to ECA is not affected
by the stenosis alone, but also by the downstream resistance of the arterial bed. It
is important that models consider the downstream peripheral vascular impedance
when simulating the carotid arterial intravascular flow. This is achieved by develop-
ing a downstream peripheral vascular model to incorporate its flow resistance. The
downstream resistance model can be used for computational studies of idealistic ge-
ometries that relate to the carotid bifurcation, an artery with varying stenosis, or an
artery that has lumen reconstruction based on virtual stenting (Cebral et al. 2001).
Experimental measurements of the outlet boundary conditions for specific stenosed
artery cases may be unfeasible, which necessitates the use of a downstream periph-
eral vascular model.
The development of a CHD model that incorporates the downstream peripheral
impedance effect is used when the outlet flow conditions are not available. The
proposed modelling accuracy can be verified by numerical simulations based on a
healthy carotid bifurcation case study (Dong et al. 2013a). The haemodynamic dif-
ferences between the proposed and fixed flow division ratio can be addressed based
on an atherosclerotic carotid bifurcation. Finally, the influence of atherosclerosis on
the intravascular blood flow can be accessed and evaluated based on the extracted
local risk indicators.
In this example, two porous beds with different permeability configurations
were connected with the ICA and ECA branches each. Darcy's Law (Batchelor
1967) was used to establish the correlation between the pressure difference across
the porous bed ΔP , the volume flow rate Q , and the permeability k by the follow-
ing equation:

=− kA

∆ P

Q

(7.7)

η L

P

where L P is the length of the porous medium, A is the cross-sectional area to the
blood flow, and η is the blood flow viscosity. To maintain numerical stability, L p is
chosen as 10 times the diameter of the extension (Figure 7. 16 ).
The pressure difference ΔP between large arteries and capillaries reported from
Pries et al. (1995) is around 60 mmHg. The geometry details of the proposed porous
medium are shown in Table 7.2 .