Translational Research: Multi-Scale Models of the Pulmonary Circulation in Health and Disease - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 268

Fig. 3 A comparison between different geometric models that describe the pulmonary capillary
beds. The sheet model of Fung et al. [ 66 ] assumes the capillary flow to occur between two elastic
sheets connected with 'posts' of connective tissue. The tube model explicitly represents each
individual capillary segment within a portion of the microcirculation. Tube models have been
incorporated into anatomic models of the alveolar structure, where capillary segments cover a
polyhedral representation of alveolar ducts (the anatomic model is reproduced from [ 30 ] with
kind permission from Springer Science and Business Media)

mean that only a small subset of capillary tissue can be modeled. This means that a
detailed tube flow model cannot be easily coupled with models of the pulmonary
macrocirculation ( Sect. 2.1 ), and flow or pressure boundary conditions must be
assumed in each subset of capillary tissue. A simpler model of the capillary bed is
required to couple macro- to micro-scale behaviors.
A much simpler approach to modeling the pulmonary microvasculature was
proposed by Fung and Sobin [ 60 ] in 1969, and developed considerably in sub-
sequent years [ 66 , 72 - 76 ]. This model is termed the 'sheet flow' model as it
approximates blood flow through the pulmonary capillaries covering several
alveoli as a sheet of fluid flowing around ''posts'' of connective tissue that are
bounded on either side by compliant endothelial tissue (Fig. 3 ). As such, the model
predicts averaged flow streamlines through each inter-alveolar septum. By ana-
lyzing the fluid mechanics of flow in this structure as well as comparison with
silicone models of the structure, simple equations describing blood flow in the
pulmonary capillaries were derived, where flow is proportional to the fourth power
of sheet height (which reflects capillary diameter). The model is able to provide
good general agreement with experimental data for flow and resistance across the
pulmonary capillary bed, and is able to provide a description of partial capillary
bed collapse when venous blood pressures are less than alveolar air pressures [ 73 ].
Again, when the sheet flow model is considered in isolation, pressure or flow
boundary conditions must be prescribed at capillary inlets, and coupling of macro-
and

micro-scale models must be achieved to minimize the need for these

conditions.