Biomedical Engineering Reference
In-Depth Information
7.2.6
Comments on Modelling Issues
The reconstructed human cardiovascular system model from Chap. 3 and 4 was
used in this case study. Modelling the blood flow process raises some important
conditions that need to be determined, such as:
• is the flow
laminar or turbulent
,
•
steady or unsteady
,
• additional equations that are needed to account for blood flow behaviour being
Newtonian or non-Newtonian
,
• the type of
inlet/outlet
conditions for the arterial branches.
Laminar flows are normally characterised by a smooth motion where the fluid's
viscosity dominates allowing high molecular diffusion and dampening out any fluc-
tuations in the flow. This leads to adjacent layers of fluid sliding past each other
in an orderly fashion (like layers of lamina). However for an atherosclerotic ar-
tery, which has a complex geometry that is highly convoluted, flow separation and
recirculation can exist especially in the stenosed region where a rapid decrease
in the cross-sectional area of the artery is observed, and thereby enhancing flow
instabilities. Although flow separation and recirculation are typical characteristics
of turbulent flow, the presence of these characteristics does not necessarily assume
the flow is turbulent, since its existence can be found in laminar flows with geom-
etries that exhibit separation.
The dimensionless parameter, the Reynolds number (
Re
) is often used to deter-
mine the flow regime. For higher velocities the effects of turbulent disturbances
become significant with the presence of velocity fluctuations in the flow field while
for lower velocities the viscosity dominates to dampen out any fluctuations. The
critical flow rate and therefore the
Re
number at which the flow changes from a lam-
inar to a turbulent flow regime is difficult to succinctly define due to the complexity
of the artery which has led to some debate concerning the type of blood flow regime
to implement for numerical simulations. Table
7.1
summarises the model settings
for recent atherosclerotic carotid bifurcation simulation studies. Experimental stud-
ies by Chen et al. (2006), Fan et al. (2009) and Long et al. (2000) have suggested
that a laminar flow regime dominates. Simulation by Cheung et al. (2010), Botnar
et al. (2000), Lee et al. (2008), Birchall et al. (2006) configured a turbulent flow
model whereby at the stenosis, a disturbed laminar regime results.
In the context of CFD applications, existing uncertainties and difficulties remain
in the modelling of embedded transition flow. The laminar flow assumption taken
in the current CFD simulation is not strictly applicable in attempting to capture the
onset of transitional flow. On the other hand, most existing turbulence models that
have been developed primarily for fully turbulent flows cannot be directly applied
to capture transitional flow.
Flow in a healthy and non-stenosed artery is dominantly laminar while turbu-
lence is usually induced through the curvatures within the stenosed arterial geom-
etry (Ku et al. 1985b). A number of numerical studies have also been performed to
Search WWH ::
Custom Search