Translational Research: Multi-Scale Models of the Pulmonary Circulation in Health and Disease - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 263

associated with the parent P. As flow and pressure were calculated only in an
isolated arterial tree (without feedback from venous and/or capillary models)
boundary conditions had to be specified at each of the *32,000 terminal arteries.
Burrowes et al. [ 22 ] assumed a constant inlet pressure (2 kPa at the main pul-
monary artery) and outlet pressure (1.25 kPa at each terminal vessel) with a
gravitationally dependent gradient of external (pleural) pressure of 0.25 cmH 2 O
per cm of lung height [ 49 ]. Regional perfusion was therefore determined via a
combination of heterogeneous arterial resistance (via vascular branching and
dimensional asymmetry), the hydrostatic effect of gravity acting on the weight of
blood, and an induced (linear) gradient in pressure external to the blood vessels
(pleural pressure).
The simple rigid tube model presented by Burrowes et al. [ 22 ] was able to
predict that the asymmetry of the arterial tree could introduce a significant het-
erogeneity in pulmonary blood flow. The study was able to show for the first time
in a computational model, a marked heterogeneity in pulmonary perfusion
superimposed upon a gravitational gradient. This simple blood flow model was
quickly built upon to gain physiological insight into the mechanisms determining
the distribution of pulmonary perfusion [ 25 , 26 , 28 ]. Blood vessel elasticity was
incorporated, initially using a non-linear model for vessel elasticity [ 28 ] based on
experimental data for lung vessels [ 50 ], but with a functional form derived for the
elasticity of systemic vessels. Later [ 25 ], a simpler functional form for vessel
diameter (D) was adopted, based on the studies of Krenz and Dawson [ 51 ] who
showed that the elasticity of pulmonary vessels can be assumed to be approxi-
mately linear with transmural pressure (P tm ) and effectively independent of vessel
size and species,

D ¼ D 0 ð 1 þ aP tm Þ ; ð 3 Þ

where a = 0.02/mmHg is the elasticity of a vessel. Simulation studies in the new
model highlighted the significant influence that vascular structure could have on
pulmonary perfusion distribution [ 26 , 28 ], supporting experimental studies that
suggested that posture and gravitational factors have a relatively minor effect on
blood flow [ 15 , 52 ]. A species comparison in models of the human (biped) and
sheep (quadruped) showed that differences in branching asymmetry could explain
significant differences in perfusion distribution that had been observed between
animal and human studies [ 25 ]. However, these models neglected two important
gravitational influences on pulmonary perfusion distribution: the deformation of
lung tissue under gravity (the model assumed a uniform distribution of acinar
units), and the effect of alveolar inflation and air pressure on the microvasculature
(only isolated arterial trees were modeled and so acinar level boundary conditions
were necessarily assigned assumed pressure values).
The first limitation was addressed via concurrent development of an imaging
based model of pulmonary tissue elasticity and deformation. The same lung vol-
umes that had been segmented from imaging data and used as host volumes for
airway and blood vessel trees were used to construct curvilinear finite element