Webs, trees and branches - Complex Webs: Anticipating the Improbable - page 63

Figure 2.11. A silicone cast of a human lung. Note the balance between apparently local randomness and the
global organization within which it is contained.

any given generation. For example, after eight generations there are 2 8 256 tubes

with a broad distribution of tube lengths and diameters and this procedure continues
for another twelve generations. Consequently, the statistical distribution of sizes with
generation number becomes an important consideration in understanding how the lung
functions.
One's second impression stands in sharp contrast to the first and that is how well the
inter-generational and intra-generational variabilities of bronchial trees are organized.
The bronchial tree, despite its asymmetries, so evident in Figure 2.11 , clearly follows
some ordering principles. There is a pattern underlying the variability of sizes: lung
structure appears roughly similar from one generation of tubes to the next. This paradox-
ical combination of variability and order emerges from the fractal model of bronchial
architecture [ 92 ]. The details of this model we leave for subsequent discussion, but we
note here that this model suggests a mechanism for the organized variability inherent in
physiologic structure and function. The essential concept underlying this kind of “con-
strained randomness” is scaling. It is true that the general notion of scaling was well
established in biology through the work of Thompson and others; however, the kind of
scaling we have in mind here does not follow the classical argument given earlier. But
before we turn to these more modern ideas let us look at some other types of scaling.
The discussion of classical scaling up to this point is consistent with the data and
the analysis of Weibel and Gomez for ten generations of the bronchial tree. However, a
remarkable systematic deviation from the exponential scaling behavior is found for the
remaining ten generations as depicted in Figure 2.12 . Weibel and Gomez attributed this
deviation to a change in the flow mechanism in the bronchial tree from that of minimum
resistance to that of molecular diffusion. West et al .[ 92 ] observed that this change in
the average diameter can equally well be explained without recourse to such a change in
flow properties. We postpone this discussion until we have discussed the idea of fractals
in some detail. However, we can show that the data reveal a different kind of scaling.

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