Biomedical Engineering Reference
In-Depth Information
In order to exchange gases the lung depends on a harmonious relationship
between ventilation and perfusion. The air and blood are guided by a complex
branching system [ 1 ], where they are exposed to variations of transmural and
transpulmonary pressures [ 2 ]. Thus, the ability of this organ to perform its essential
function is intimately related to both its mechanical behaviour and its geometry.
Moreover, there is a strong dependence of function and structure [ 3 ]. Therefore,
many pulmonary diseases either are caused by failures on the structure or directly
affect the structure (e.g. asthma, emphysema, atelectasis etc.).
A major challenge for the next generations of physiologists is to integrate the
large amount of biological information (in rapid growth) in consistent quantitative
models [ 4 ]. The models summarize briefly the information, and interacting with
experiments, show properties and remove contradictions, which are not evident by
simple description of its parts.
1.1
Mechanical Properties of Lung Parenchyma
The lung parenchyma is the tissue where the exchange of gases occurs. It is com-
posed of alveoli and alveolar ducts. Tensile testings of the lung parenchyma show
stress-strain curves with all characteristics of a soft tissue [ 5 - 7 ]. The extracellular
matrix of soft tissues is rich in collagen and elastin fibres. The concentration and
spatial organization of collagen and elastin fibres are the main factors which defines
the mechanical properties of each type of soft tissue [ 8 ]. At small deformations
elastin provides stiffness and stores most of the strain energy. The collagen fibres are
comparatively inextensible and usually wavy at rest. With increasing deformation
the collagen bundles are gradually stretched at the direction of deformation, what
strongly increases the tissue's stiffness. This composite behaviour is analogous to
the fibrous tissue of a nylon stocking, where elastin does the role of the rubber band
and collagen the nylon's.
1.2
Idealized Geometry of the Pulmonary Alveolus
Recent descriptions based on histological analysis have shown that the the alveolar
walls are shared between neighbour alveoli and form a structure similar to a
honeycomb [ 9 , 10 ]. Therefore, the airways in the lung parenchyma are series of
branching corridors with polygonal walls and their dead ends are called alveoli.
There are no “inner” and “outer” parts of the alveoli, instead there are septa which
divide either an alveolus from another or an alveolus from an alveolar duct.
Dale [ 11 ] proposed a geometric model in which the parenchyma takes the form
of a tessellation of second order regular polyhedra with 14 faces, see Fig. 1 .This
kind of polyhedron is also know as tetrakaidecahedran, truncated octahedron or
simply 14-hedron. It has the advantages of being regular, being convex, filling the
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