Translational Research: Multi-Scale Models of the Pulmonary Circulation in Health and Disease - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 267

diameter 8 lm[ 1 ]) meaning that each neutrophil typically has to deform in order to
pass through the pathway of capillaries from arteriole to venule [ 65 ]. Neutrophils
are less deformable than RBCs and effectively block capillary pathways for the
duration of the time they take to deform (which depends on the size of the neu-
trophil compared with the blood vessel it blocks, and the activation state of the
neutrophil). The sequestering of neutrophils in the lung is thought to play a vital
role in host defense, acting as the secondary line of defense by destroying any
unwanted foreign material that may have penetrated the system. Models of pul-
monary blood flow at the capillary level are generally designed to account for these
phenomena as best as possible without losing mathematical simplicity.
3.1 Modeling the Microcirculation: Fluid Flow
and Cellular Transit
There have been two general approaches taken to modeling flow through the
pulmonary capillaries: the tube flow approach (typical of systemic microcircula-
tion models) and the sheet flow approach. Figure 3 shows illustrations of a tube
flow model [ 30 ] and the sheet flow model [ 66 ]. There is clearly a difference in
geometrical complexity between the two. Each geometric model has its limitations
and its merits, summarized below.
Tube flow models (Fig. 3 ) explicitly represent each individual capillary seg-
ment within a portion of the microcirculation. Flow models are set up as in any
other flow problem—using equations of conservation of mass and momentum—
within a network of vessels. Given an initial assumed hematocrit distribution and
individual capillary resistance, the pressure and flow can be calculated within the
network, assuming elastic vessels. Then a rheological analysis is conducted, that
incorporates the non-Newtonian properties of the blood. In this procedure the
distribution of RBCs is calculated, using empirically derived models that account
for the Fahraeus and Fahraeus-Lindqvist effects as well as the phase separation
effect (the disproportionate distribution of RBCs and plasma at bifurcations).
Conservation of RBCs and plasma is enforced at each capillary junction and the
new hematocrit distribution is used to update the apparent viscosity of blood in
each capillary vessel. In the pulmonary circulation this type of model includes the
impact of both alveolar and intra-pleural pressures on the estimated diameter of
each capillary segment. This tube flow approach has been used successfully to
represent flow in both the systemic [ 67 - 69 ] and pulmonary microcirculation
[ 30 , 70 , 71 ]. The use of tube flow models provides predictions of flow and cellular
transit properties within each individual capillary. The discrete tubular nature of
these models also enables simulation of the impact of individual capillary
blockage, via neutrophils, on capillary blood flow [ 30 , 71 ]. While these types of
models are more realistic in structure than the sheet flow model and provide more
detailed flow and cellular transit information, current computational limitations