Biomathematical Interpretation of Organismic Growth
F. COLLOT
Abstract
An example is given for the derivation of a general equation of growth assuming proportionality of growth to an energetic flow through the organism. It is
also shown how, on the basis of this assumption, malignant growth can be understood.
Concepts like shape, function, cellular differentiation, rate of complexity
etc. are usually thought of as scientific concepts; this, however, is incorrect
since only measurable concepts deserve the term "scientific". For this reason
it is necessary to give precise meaning to any of the terms used and to find a
mathematical or physical equivalence for them. The example to be outlined
will help us to understand the intellectual approach we recommend.
We start with the evident fact that growth of an organism needs a
certain amount of energy and that the intensity of growth is proportional
to the quantity of energy available at any given moment. Let us call "incident energy" (IE) the energy absorbed by an organism, such as that
provided by food, oxygen or carbon dioxide for plants, after having subtracted the energy stored in the form of glycogen, starch, lipids etc. Hence,
let dqj be the quantity of incident energy during the time dt and ~~j an
energetic flow that we call incident flow gJj. Let us call "reflected energy"
(RE) the energy which returns to the external world as work performed by
muscle activity, as heat produced, as chemical or electrical energy, etc., and
let gJr be the reflected flow. The energetic flow available for growth,
called gJ GO is:
gJa = gJi - gJr
(1)
dv
This flow gJa is proportional to the intensity of the growth cit ' v being
the volume of the organism at time t or the number of cells.
dv
--elt = gJj - gJr
(2)
To integrate this differential equation it is necessary to write gJi and gJ'
in terms of v. We can admit reasonably that the incident flow gJj is proportional to v:
gJj = a v + c
(3)
F. COLLOT
Abstract
An example is given for the derivation of a general equation of growth assuming proportionality of growth to an energetic flow through the organism. It is
also shown how, on the basis of this assumption, malignant growth can be understood.
Concepts like shape, function, cellular differentiation, rate of complexity
etc. are usually thought of as scientific concepts; this, however, is incorrect
since only measurable concepts deserve the term "scientific". For this reason
it is necessary to give precise meaning to any of the terms used and to find a
mathematical or physical equivalence for them. The example to be outlined
will help us to understand the intellectual approach we recommend.
We start with the evident fact that growth of an organism needs a
certain amount of energy and that the intensity of growth is proportional
to the quantity of energy available at any given moment. Let us call "incident energy" (IE) the energy absorbed by an organism, such as that
provided by food, oxygen or carbon dioxide for plants, after having subtracted the energy stored in the form of glycogen, starch, lipids etc. Hence,
let dqj be the quantity of incident energy during the time dt and ~~j an
energetic flow that we call incident flow gJj. Let us call "reflected energy"
(RE) the energy which returns to the external world as work performed by
muscle activity, as heat produced, as chemical or electrical energy, etc., and
let gJr be the reflected flow. The energetic flow available for growth,
called gJ GO is:
gJa = gJi - gJr
(1)
dv
This flow gJa is proportional to the intensity of the growth cit ' v being
the volume of the organism at time t or the number of cells.
dv
--elt = gJj - gJr
(2)
To integrate this differential equation it is necessary to write gJi and gJ'
in terms of v. We can admit reasonably that the incident flow gJj is proportional to v:
gJj = a v + c
(3)