49.

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Page 146
2.2.9—
Example of Using the Phase Space Set to Differentiate Random and Deterministic Mechanisms:
The Beating of Heart Cells
When Glass et al. electrically stimulated chick heart cells in culture at a certain rate, the timing between the beats of the heart cells seemed to occur at random. Was the timing between the beats generated by a random mechanism or by a deterministic mechanism?
They measured the time f between each stimulation and the subsequent beat number n. They constructed the phase space set from this time sequence f (n). Each point in the phase space set had coordinates X= f (n) and Y= f (n+1).
If the timing between beats was generated by a random process based on chance, then the phase space set would fill this 2-dimensional phase space. The phase space set did not fill the 2-dimensional phase space. The phase space set was approximately 1-dimensional. This means that the timing between the beats can be described by a deterministic relationship. They derived the mathematical form of this relationship. It depended on the times of the previous beat and the previous stimulation. They showed that this relationship arises from the properties of the refractory period when the heart cell is recycling after a beat.
These experiments probe the biochemical and electrical processes that occur when a heart cell recycles after a beat. They are also a model of the whole heart. The stimulations correspond to the pulses from the sinoatrial node that initiates the heartbeat, and the cells correspond to the ventricle, the main pump of the heart. Thus the equations that describe this experiment may also shed light on the causes of irregular heart rhythms. Present methods control such problems by using large electrical currents to force the heart out of its irregularities. If such irregular heart rhythms are deterministic, they might be controlled by much smaller electrical currents applied at appropriate times computed from the deterministic relationship.

 
[Cover] [Abbreviated Contents] [Contents] [Index]


Fractals and Chaos Simplified for the Life Sciences
Fractals and Chaos Simplified for the Life Sciences
ISBN: 0195120248
EAN: 2147483647
Year: 2005
Pages: 261

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