ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

physiopathology and to create a representative hemodynamics model preoperatively to
explore several virtual surgical options or optimize them. In the last section, we then
discuss aspects such as sensitivity to input data and surgery planning predictability
enhanced by 3D-closed loop representation of the circulation coupling.
3. METHODS
3.1 Mathematical and numerical methods
In these patient-specific applications, 3D simulations can only be realistically carried
out in a few branches, while the rest of the circulation must be taken into account
through appropriate boundary conditions. A number of numerical methods can be used
to solve the 3D incompressible Navier-Stokes equations, here Newtonian. Most work
presented in this article has been done with an in-house finite element solver (see
references in [2]). Flow at the boundaries where the velocity profile is not prescribed, is
often complex, an interplay between patient-specific geometry and flow. Due to this or
to physiological flow rate time oscillations, flow reversal can occur at the coupling
boundaries, inducing numerical instabilities. Several remedies have been proposed and
compared ([3] and references herein): the stabilization approach proved to be the more
robust one. Coupling of the 3DNS with reduced models (0D or 1D) of the rest of the
circulation is a continuing matter of research (see the already cited papers for
references). In this work, the coupling has been done implicitly (with a monolithic
approach described in [2, 4]) or explicitly [5, 6]. The former is numerically more stable
while the latter more modular, especially for closed-loop models of the circulation.
Recently, we proposed an approach that combines these two qualities [7].
3.2 From patient data to boundary conditions specification
The 3D model is constructed from magnetic resonance imaging, giving the geometrical
information of the main vessels, which for the applications of this paper consist in the
superior (SVC) and inferior (IVC) venae cavae, the left and right pulmonary arteries
(PA) and their main branches, and possibly artificial grafts. Velocity or pressure must
be prescribed as boundary conditions to the 3DNS. However, for patient-specific multibranched
models, these are rarely quantities that are measured in the clinics for each
boundary. Thus a relationship between pressure and flow must be prescribed from a
reduced-order model that represents the circulation outside of this outlet, and which
parameters need to be chosen in coherence with available imaging, catheterization or
pressure cuff clinical data [1]. Phase-contrast magnetic resonance imaging gives
temporal flow information usually at the inlet of the domain and in a few other
locations, such as for the applications considered in this paper flow to the left and right
pulmonary artery. Resolution issues may restrict this information to an average flow
split between the two lungs. In addition, catheterization measurements may also be
acquired in several locations, giving direct or indirect average pressure values, such as
aorta, atria, SVC, IVC or the pulmonary arteries (PA). Their limited spatial resolution
prohibits imposing them directly as boundary conditions. Furthermore, for predictive
simulations (such as intervention planning and change of the geometry or physiological
state), pressure and flows at the boundaries are part of the solution. Tuning of the
parameters is then necessary so that the 3D simulation is reflective of measured data,
such as of the average flow rate measured in a few vessels and of blood cuff pressure or