Biomedical Engineering Reference
In-Depth Information
Fig. 7.33
Plot of venae
cavae average flow
velocities versus time
fully resolve any transitional behaviour, the sophisticated LES and Direct Numeri-
cal Simulations models need to be used since they are based on the Navier-Stokes
equations. In this case study, a laminar flow model.
Figure
7.32
shows flow entering the right atrium chamber through the inferior-
and- superior vena cava (IVC and SVC), and exits through the tricuspid valve (TV).
For simplicity, the velocity boundary condition that was applied at the IVC and
SVC assumes a uniform spatial profile and has a direction that is normal to the
surface. A parabolic profile may not be the correct assumption given that the up-
stream flow may be highly skewed at high velocities. In addition, different degrees
of skewness exist for different velocities. To avoid these complications, a uniformly
spaced profile is used. For the TV outlet, a transient pressure profile with zero gradi-
ent in the spatial domain is implemented at a virtual outflow to ensure that the flow
will be constant. Given that the IVC and SVC in-flows vary throughout the cardiac
cycle (see Fig.
7.33
and Table
7.8
), the inlet boundaries require a-priori knowledge
of the IVC and SVC velocity time histories. Logically, this is obtained from physi-
cal experiments (Wexler et al. 1968). For this study, in-vivo measurements were
used to generate the time histories.
Flow in the right atrium chamber is simulated from the end-diastolic state to the
early-systole state, i.e., corresponding to the normalised time segment of 0.60-1.00
in one cardiac cycle (refer to Fig.
7.33
). To avoid start-up effects from unsteady
flows, the flow field was simulated over three periodic cycles where the final flow
field predictions were taken at the third cycle. Spatial discretisation of the advec-
tion terms in the Navier-Stokes equations was performed by using a high resolution
scheme, while the transient scheme used a second order backward Euler scheme
with a time step size of 0.002 s.
While the MRI scans were taken over a complete cardiac cycle of the heart
chamber, the scope of the numerical simulations was limited to examining the
flow in the right atrium during the diastole and systole phases. In particular, fo-
cusing on particular phases of the cardiac cycle allows the flow analysis to be
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