Biomedical Engineering Reference
In-Depth Information
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Figure 1.5
Spiral distribution of primordia around the
cylindrical stem, after development on a plane, as observed
by Bravais in 1837. The neighboring primordia differ by
Fibonacci numbers: 1 along the solid lines, 3 along the
dashed lines. After [42].
be explained in a similar manner. A vortex interpretation of the 5-7 pair in SAM
growth was given in [52].
In a trial to explain the phyllotaxis pattern, Newell, Shipman, and Sun assume
that the auxin-produced growth is proportional, in a first approximation, to how
much average tensile stress the local elemental volume (which will contain many
cells) feels. This is best measured by the trace of the stress tensor at that location.
Fluctuations in auxin concentration influence the mechanical forces in the tunica
by creating uneven growth and are manifested by an additional strain contribution
in the stress-strain relationships. On the other hand, inhomogeneities in the stress
distribution are assumed to lead to changes in auxin concentration. The exact way
in which stresses influence biological tissue growth (weight-bearing bones and
fruit stems become stronger) is still an open challenge to biologists [53].
Gebhardt in 1911 found a similarity between bone formation and the chemistry of
colloids [54, 55]. He found that collagen fibrils are organized into distinct lamellae,
the molecular orientations being parallel in each lamella. Much later, in 1988, it was
pointed out by Giraud-Guille that together with normal (i.e., Gebhardt's) plywood
architecture, a twisted plywood distribution of collagen fibrils in human compact
bone osteons is observed, comparable with a liquid crystalline self-assembly [56].
Geometrical resemblance of long fibrils and long molecules leads to a similar
arrangement of these objects.
