How life maintains itself
Chaos and fractals in human physiology
Not only in evolution, but also in the functioning of organisms chaos plays a presumably great role. Chaos is used here not in the sense of ‘complete disorder’ but in the sense of unpredictable within specified limits.
In the recent discussions over whether or not human embryos should be destroyed we often speak about pre-embryos (the 2 to 8 celled stage) as if a complete human could be found there; in other words we proceed from the idea that everything has been determined in the DNA. You couldn’t build a complete human if every cell and every connection (nerve or artery) had been completely pre-programmed. In reality chance plays a great role. We can even suppose that chaos in the functioning of our body means that all is going well, but that tight regularity means not all is well...
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Fractal |
The conventional opinion is that the body is a machine built according to an orderly principle and working to perfect rhythms. If irregularities occur it means deviations, a sign of disease or old age. Inspired by non-biological disciplines scientists have had a closer look and discovered that tight regularity means precisely a sign of ageing or disease.
Irregular and unpredictable behaviour is an important characteristic of health. A slightly irregular fractal-like design can be found in many places in the construction of biological systems - precisely these irregularities give flexibility and the possibility of adjustment.
The concepts chaos and fractals belong to the discipline of non-linear dynamics: the search for systems which react to mutually independent factors. This theory gives us insights into the phenomenon of epidemics, into the kinetics of certain chemical reactions, changes in the weather, etc. Under certain circumstances systems which are determined only by few factors, behave chaotically, in other words: they become unpredictable.
The word chaos in this context does not mean the complete absence of any order, as we understand it in daily life. It means a certain degree of ‘randomness’, variability, unpredictability, and these can often be related to fractal systems.
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Above and below: ‘Fractals’ in the intestines: folds with every enlargement. |
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Fractal systems are often the result of chaotic non-linear dynamics. Whenever a chaotic process has created a form (e.g. the seacoast, the atmosphere, a geological fold in the Earth’s crust) we find fractals (coastlines, cloud formations, geological formations).
Yet the ideas about fractals developed at first as geometric forms, specifically arising when ‘playing’ with computer figures: precisely the same form appears, reduced in size and increased etc. With ever-increasing enlargement, idealised fractals exhibit precisely the same pattern; some neurones also exhibit this: branches of branches of branches. In the wall of the intestines this can also be seen: folds repeat themselves in the folds on the cells. If one records heartbeats graphically over different intervals, the same figure is to be seen, the small and large variations follow the same pattern.
The body is full of fractals; the best researched are those of the lungs. Already in 1962 researchers analysed the construction of the lungs and the diameters of the bronchi, and these are built according to the (mathematical) principle of fractals.
The heartbeat has a fractal-like rhythm, the coronary arteries have a fractal structure just like the fibres of the heart valves, the fibrous structure of the heart muscle’s fibres and the wiring of the Hiss-Purkinje system (the ‘nerve system of the heart’ which conducts impulses in the hearttissue).
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Portion of the lung - a typical fractal appearance. |
All these fractal systems have different functions: enlarging surface area in the intestines, the lungs and the blood vessels, distributing substances in the bronchi and gall ducts, distributing information through the neurones. Precisely because of their strong irregularity and ‘redundancy’ fractal systems are nearly invulnerable. Even after fairly severe injuries to the bundles of Hiss and Purkinje, the heart can keep on beating fairly normally..
Fractal structures in the body arise through the slow dynamics of the development (seen both embryonically and evolutionally). In these processes ‘deterministic chaos’ reigns. It also seems very functional that for example blood vessels, nerves and lung-branching - built this way according to a repetitive system - are based on the working of genes that only supply a type of basic principle, in which everything repeats itself.
When scientists at first applied chaos theory to physiological systems, they expected to find chaotic processes especially among the elderly and the ill, which seems logical. If for example you measure the resting heartbeat, it appears very regular, but if the heartbeats are analysed closely, there is no regularity at all. In young adults with a heart rate of 60 beats per minute this can vary with a difference of 20 within seconds, and over a whole day it can vary from 40 to 180 beats per minute!
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Fractals in the blood vessels. |
Initially this variability was explained by homeostasis: every reaction is a reaction on another variation and serves to ensure that the different values remain constant. It would then be probable that the ability to maintain homeostasis decreases with illness or age and therefore more fluctuation occurs.
If we examine the fluctuations in frequency closely over a number of hours, we notice an irregular form, which remains visible if the time scale is decreased. Nothing can be seen of a fixed regularity, it appears to be a chaotic system.
If we analyse diverse rhythms in terms of chaos theory it appears that a healthy heart is a chaotic system, but a sick heart often exhibits an increasing degree of regularity.
The (chaotic) heart beat is the result of activity of the nervous system: the sinoatrial node (the pacemaker)receives signals from the autonomic nervous system: the sympathetic and the parasympathetic, the first speeding it up and the second retarding it. The result is a continual tug of war on the pacemaker, and this results in a continual fluctuation of the frequency. With a transplanted heart these nerve bundles have been severed and the heartbeat is much more regular.
In the nervous system chaos is also a normal phenomenon; the systems which are responsible for hormone emissions for example, show chaotic activity curves.
A chaotic dynamic in heart beat, nervous system and other systems has definite functional advantages: such systems are influenced by many factors and can react to that directly, they are flexible and can adjust themselves to unpredictable changes. In illness there is often a loss in variation.
The biological clock is also never perfectly regular: if we always had to fall asleep and wake up at a fixed time, we wouldn’t be able to stay awake with a sick child...
In illness such as for example Parkinson’s, epilepsy and depression, the nervous system exhibits much more regularity than in healthy persons. The number of white blood cells varies irregularly in healthy persons, but in leukaemia it is very regular.
Our physiology could be one of the most attractive areas in which to study fractals and chaos.
Louise E. Pihlajamaa-Glimmerveen
On fractals: http://math.rice.edu/~lanius/frac/
Also see the article on The role of chance
and the article Antichaos and evolution
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Bibliography consulted:
Arnold van den Hooff: DE SCHOK DER BIOLOGIE Essays over the place for biology in our vision of the human being (SUN Nijmegen 1995)
Karl Sigmund GAMES OF LIFE Explorations in ecology evolution and behaviour (Penguin books 1995)
and several articles in Scientific American.
by
 drs. L.E. Pihlajamaa- Glimmerveen |
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