Biomedical Engineering Reference
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carried out in the simpler context of an internal flow in a rigid vessel. This is
due to the fact that modelling the entire cardiac cycle requires a fluid-structure
interaction (FSI) approach and the physical structure of the heart chamber is a
dynamic parameter, making complicated to simulate the entire cardiac cycle. The
rigid boundary wall assumption instead of elastic ones based on the FSI approach
allows the simulation to converge and hence produce a set of predicted results.
However this comes at the expense of real physiological cyclic movement of the
heart contracting and expanding. In reality, a contraction in the heart will reduce
the volume and any cross-sectional area where the blood flows through. Con-
sidering mass conservation, the contraction is expected to intensify the velocity
and vorticity fields. However, if we implement FSI for this simulation, the blood
pressure during atrial systole will stretch the vessel elastically causing the veloc-
ity and vorticity fields to attenuate.
7.5.3
Comparison of CFD and PC-MRI Vorticity Fields
Flow results by numerical simulation and phase contrast magnetic resonance im-
aging are presented in this section. Then, their velocity and vorticity fields are
compared in terms of flow pattern development. Figure
7.34
shows three snapshots
of the CFD flow visualisation in the right atrium solution domain corresponding
to the time instants of
t/T
= 0.66, 0.74 and 0.82 per time cycle of 1.0. These were
selected to match the MRI time frame indices
n
t
= 9, 11 and 13 out of a total of 25
frames. Collectively, they form the basis for comparison between the CFD simula-
tions and phase-contrast-MRI experiments.
The velocity vectors in the CFD plots are superimposed on the vorticity con-
tours. The velocity vectors are used to depict flow direction on the plane itself,
thereby implying a tangential projection. A normalized scale is used for the vector
length. For the vorticity contours, the clockwise/anti-clockwise direction of the ro-
tation is provided by using the y-axis as a reference axis, while the figure shows the
in-plane view of the selected slice. The normal to the slice is almost lying parallel to
the y-axis and the plane is chosen is based on the MRI plane.
Cardiac flow analysis that is based on histograms of vorticity field distributions
for both modes of flow generation can give a clear overview of their flow differ-
ences with some form of quantification (Wong et al. 2009a, b, 2010c).
7.5.4
Computational Haemodynamics Analysis of Heart
Chamber
Based on the distribution of CFD and phase-contrast-MRI vorticity fields,
the difference in their means and standard deviations are in the order of zero
(Difference in means: Δ
ω
≤ 2.02 s
−1
, and difference in standard deviations:
Δ
σ
≤ 4.07 s
−1
for a range of vorticity values at approximately − 25 to + 25 s
−1
). The
agreement in the CFD simulations and MRI experiments reinforces the evidence
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