Biomedical Engineering Reference
In-Depth Information
It would mean that bears have biological mechanisms to prevent disuse osteoporo-
sis. This may be accomplished by targeting genes and circulating hormones that
are differentially expressed in bears and humans during disuse [271].
1.5
Comments
Both the structure and function of a bone are complex characteristics that have not
been understood well by researchers in the fields of medical sciences and mechan-
ics. Since a bone could be treated as an organ, a tissue, or a hard tissue, different
methods of describing behaviour of the bone and its physiology could be used,
including mathematical topology, partial differential equations, elasticity, strength
of materials, mechanics of porous media, diffusion and electrophoretic theories,
chemistry, and optical and X-ray experimental methods. In such a description,
different models of a bone could be presented including those resembling living
and nonliving matter. In the present paper a number of the above methods of
describing a bone, are presented.
V. I. Arnold, in his address at the Conference on Teaching of Mathematics in
Palais de Decouverte in Paris, on 7 March 1997, said, ''Mathematics is a part of
physics. Physics as an experimental science is a part of natural science. Mathematics
is a part of physics where experiments are cheap.
...
The mathematical technique
of modeling consists of ignoring some experiments and providing a deductive
model in such a way as if it coincided with reality. The fact that this path, which
is obviously incorrect from the point of view of natural science, often leads to
useful results in physics is called 'the inconceivable effectiveness of mathematics
in natural sciences' (or 'the Wigner principle'). Here one can add a remark by
I. M. Gel'fand: there exists yet another phenomenon which is comparable in its
inconceivability with the inconceivable effectiveness of mathematics in physics
noted by Wigner - this is the equally inconceivable ineffectiveness of mathematics
in biology'' [272].
A mathematical structure is hidden in the world around us. A moderate opinion
by Andrzej Lasota expresses belief that mathematics is the very structure of the
world. ''Not a description of the structure, but structure itself. There is no doubt
that a mathematician can create strange objects and he may think that he has
strayed far from reality. But this is a resemblance of truth only. If his creation is
good mathematics, it will sooner or later prove to be a component of reality'' [273].
A number of examples where mathematics is efficient in biology can be found
in the literature. In particular, considerable progress has been made in recent
years in the understanding of the molecular and microstructural properties of
bone components, especially on molecular level, which is of general interest in
biology, physics, and medicine. Different approaches have resulted, owing to both
the difficulty and importance of the problem. As a recent example, Jakob Bohr
and Kasper Olsen suggested that the close packing forms the underlying principle
behind the structure of collagen. It is shown that the unique zero-twist structure
