Biomedical Engineering Reference
In-Depth Information
16.2.3.2 Boundary Conditions
From the CMR analysis, specifically the through-plane phase contrast images, time-
varying flow conditions across the cardiac cycle are known for all TCPC vessels of
interest. The standard practice of TCPC simulations with this IB solver is to impose
these flows (either as time-averaged or time-varying flat velocity profiles) at the
inlets and the prescribed flow split at the outlets of the computational domain. Sur-
gical modeling simulations present the additional challenge of physiologic changes
(perhaps both acute and chronic) in the rest of the circulatory system in response
to Fontan surgery. The work of Fogel et al. (
1996
) indicates that such changes have
an impact on the cardiac output and thus systemic venous flows; the impact on the
pulmonary vasculature and/or distribution has only be reported in a single patient
case (Pennati et al.,
2011
) demonstrating unanticipated variations. In other words,
simply imposing the measured flow conditions on the surgical model is unlikely to
sufficiently represent the post-operative state.
There are thus several strategies that have been employed to combat this chal-
lenge. First is the parametric variation of the outflow distributions imposed: if a
60 %
/
40 % RPA/LPA distribution was measured pre-operatively, the proposed op-
tions might also be evaluated at 40
/
60, 50
/
50, and 70
/
30 to simulate possible out-
flow distributions. The finite and physiologically bounded nature of this parameter
space facilitates these variations. The primary guide in making such determinations
is the presence and hypothesized evolution of PAVMs in the given patient. For ex-
ample, a presumed decrease in the number of malformations present would increase
the effective vascular resistance of the pulmonary beds, leading to a decrease in lo-
cal flow. Additionally, natural growth and development is likely to vary the relative
distribution of pulmonary flows over the life of the patient, so identifying solutions
that are robustly able to handle such variation is desirable.
Similarly, the inflow conditions can be selectively varied, both with respect to
bulk flow rates and relative vessel distributions. However, it is important to note
that the parameter space for the inlet values may not be as well constrained as the
outlets, both with respect to magnitude and distribution variations, particularly as
the number of inlet vessels increases (such as cases like in Fig.
16.2
). Furthermore,
the factors that mediate such changes, either at the level of the ventricular output or
the relative compliances of the systemic vascular bed, are not as easy to define or
predict, and no data yet exist in the literature to set a precedent.
Significant research and ongoing development efforts are focused on the use of
multi-dimensional models to create a comprehensive view of the cardiovascular cir-
cuit (Laganà et al.,
2005
; Migliavacca et al.,
2006
; Kim et al.,
2009
). That is, the
three-dimensional CFD domain is coupled with 0-dimensional lumped parameter
models to capture the global hemodynamics. This multi-dimensional approach may
address some of the limitations of prospective modeling efforts by providing a more
rigorous means of determining the post-operative boundary conditions, particularly
for the inlets. Of course, validation of such models will be critical and, as the work
of Pennati et al. (
2011
) demonstrates, lumped parameter models alone may not be
sufficient for capturing the range of possible patient-specific responses.
