Translational Research: Multi-Scale Models of the Pulmonary Circulation in Health and Disease - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 257

and structural mechanisms [ 12 - 16 ], the model has been significant in showing how
physical laws can be combined elegantly and concisely to explain physiological
function. Since that era numerous mathematical models have emerged to provide
interpretation of experimental measurements of the pulmonary circulation, to
summarize hypotheses, and more recently to quantify the relative effects of gravity
and structure on pulmonary blood flow distribution [ 17 ].
Mathematical models of the pulmonary circulation have taken either a systems
(electrical analogue) approach or a biophysical approach (based on the fluid
dynamics properties of the system). Geometrically, these mathematical models
have developed from the 'lumped parameter' with each of the arterial, capillary
and venous systems lumped into single 'resistors' [ 18 ], through symmetric [ 19 ],
fractal [ 20 ], and regular asymmetric [ 21 ] branching structures, to the current
anatomically based volume-filling branching geometries [ 22 ] that represent the
state-of-the art for modeling the spatially-distributed geometry of the pulmonary
arterial and venous trees. Each of these model types fills a role in understanding
the function of the pulmonary circulation. Following the philosophy that a
mathematical model should only be as complex as to capture the essential func-
tions under investigation (i.e. 'more is not always better'), lumped parameter and
regular branching models play an important role in investigating the global
response to pathologies that are diffuse (i.e. are distributed relatively evenly
throughout the lung, e.g. [ 23 , 24 ]). However, as they cannot capture the complex
structure of the lung they cannot be used to investigate the relationship between
vascular branching structure and flow distribution, or to study pathologies that
present heterogeneously in the lung or within the population. To address this
limitation multi-scale models have recently emerged that couple scale-specific
structure and function in the macro- and micro-vessels with biophysical function in
other components of the pulmonary system that influence how the circulation
behaves [ 22 , 25 - 32 ]. This type of model has been used successfully to investigate
the effect of pulmonary embolism (via blood clots in the lungs) on regional and
total organ gas exchange and blood pressure; pulmonary embolism has a variable
impact between individuals and significant localized effects [ 32 - 34 ]. The evolu-
tion of these multi-scale models will be described in the following sections.
1.1 Unique Features of the Pulmonary Circulation
The pulmonary circulation is distinct from the systemic circulation in its structure
and function. Notably, the lung receives almost the entire cardiac output from the
right ventricle (RV). Because the height of the lung is on the order of only 30 cm,
this requires far lower RV pressure (typical systolic range of 15-30 mmHg) than
the LV pressure that is needed to drive blood to the systemic circulation (typical
systolic range of 100-140 mmHg). The pulmonary circulation is therefore
described as a 'low pressure' system, which is facilitated by its relatively low
resistance.