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

3.3 Working hypothesis
The blood was considered as a Newtonian incompressible fluid, with a viscosity of 3 cP
and a density of 1060 Kg/m 3 . The computational fluid dynamics (CFD) simulations
were run with the software Fluent (Ansys Fluent, Fluent Inc, Lebanon, NH) using
rigid wall models, while lumped parameter network (LPN) equations were written and
solved with a C compiler.
3.4 CFD stand alone simulations
With the solely knowledge of the 3D geometry and the flow curves of the patient, CFD
simulations were performed in order to characterize the resistances offered by the local
anatomy of the pulmonary branches. The time-varying patient’s MPA flow, as
measured from MR data, was imposed at the inlet, while the measured RPA flow was
imposed at the right outlet. A constant atrial pressure of 1067 Pa was set at the left
outlet. Three cardiac cycles were simulated and results from the last cycle were used for
post-processing. Pressure drops (ΔP) measured on each branch were plotted against the
flow (Q) streaming in the branch, and a second degree polynomial relationship was
obtained for each side.
3.5 LPN simulations
A LPN was developed as in figure 2 to model the pulmonary circulation of each patient.
Patient’s time-varying MPA flow (QMPA) was imposed as inlet of the network, and the
values of the resistances in the network were tuned in order to obtain the same flow split
and flow curves of the patient [Spilker et al, 2010] at the outlets (QRPA and QLPA).
The ΔP/Q equations derived from the patient-specific CFD stand alone simulations
were used to represent the RPA and LPA non-linear resistances (RRPA and RLPA), while
the downstream resistances of the pulmonary tree were modelled with the linear
resistances RR1, RR2, RL1 and RL2. The capacities CR1 and CL1 represent the compliance
of the patient-specific geometries, whereas CR2 and CL2 simulate the distensibility of the
pulmonary vascular tree. The ratio between the inner and the outer resistances (RR1, RL1
and RR2, RL2 respectively) was set to 0.3, and the total PVR were assumed to range from
1 WU (mmHg/l/min) up to 10 WU because no pressure data were available from the
patients’ reports.
Fig. 2 – Lumped parameter network of the pulmonary circulation.
The relation between the total resistance and the total compliance on each branch was
defined according to allometric equations as in Pennati et al, 2011. Values of the