Biomedical Engineering Reference
In-Depth Information
1960
). We assumed that cardiac output remained unchanged since the aortic steno-
sis was moderate and that it is unlikely that either the perfusion or the metabolic
demands of the subject were altered significantly. It follows that, in order to main-
tain cardiac output, contractility of the heart (i.e., the elastance) must increase. In
addition, changes in elastance affect filling of the heart, thus requiring an increase
in left atrial pressure to maintain the same end diastolic volume. The final left atrial
pressure was 14 mmHg and the maximum elastance was 1.52 mmHg/mL.
15.2.5 Early Arterial Remodeling
Early arterial vascular remodeling (i.e., within the first 10 days or so) was simu-
lated by modifying wall properties to reflect stiffening and thickening of the tho-
racic aorta proximal to the coarctation, the coronary vessels, and the neck vessels.
These changes were based on findings that the pulse wave velocity can increase by
as much as two-fold with aging and that many adaptive processes associated with
aging are similar to those associated with hypertension (Wolinsky,
1972
; Nichols
and O'Rourke,
2005
). Updated values of stiffness and thickness are illustrated in
Fig.
15.3
. Briefly, the stiffness of the aortic arch, coronary tree, and neck vessels
was increased by 100 %, 50 % and 50 %, respectively, while the thickness was
increased 15 %. We assumed that the cerebral vasculature did not experience any
changes in stiffness or thickness during this early period (Hayenga,
2010
). We also
did not prescribe any associated changes in vascular lumen largely because of the
lack of associated experimental data and the possible competing effects of changes
in distal resistances (e.g., cerebral autoregulation) and local shear-regulated vasodi-
latation. The prescribed changes in vascular stiffness and thickness affected cardiac
afterload, hence additional cardiac compensation was required to maintain cardiac
output after arterial remodeling. The final left atrial pressure was 16 mmHg and the
maximum elastance was 1.82 mmHg/mL. All other outlet boundary conditions (ar-
terial and coronary) remained the same for baseline, acute cardiac compensation,
and early arterial remodeling.
15.2.6 Data Analysis
Simulation data were analyzed using the open-source software Paraview (Kitware,
Inc. Clifton Park, NY). Pressure, flow, and cyclic wall strain were analyzed at five
different locations within the vasculature (see Fig.
15.4
): the proximal descending
aorta (P-Ao), left anterior descending (LAD) coronary artery, left common carotid
artery (LCCA), left middle cerebral artery (LMCA), and basilar artery (BA). Mean
circumferential wall strain was calculated based on changes in the cross sectional
area of the vessel over a cardiac cycle using the following Green-Lagrange type
expression
E
θθ
=
1
)/
2, where
A
t
is the cross sectional area at any given
time
t
and
A
D
is a reference diastolic value (note: using area effectively represents
radius squared as needed in the nonlinear measure of strain).
(A
t
/A
D
−
