3.2 Electrophysiology of the Heart

|

75

Section E: The cardiac muscle cells of the main chambers are now excited via the

Purkinje-fibres, which can be seen as the S-wave in the ECG.

Section F: Once all the cardiac muscle cells of the main chambers have been excited,

the main chambers contract, which increases the pressure there, the valves open

and the blood is forced out of the chambers into the aorta or the pulmonary artery.

At the same time, the atria are also filled with blood during this expulsion phase.

As an ST segment it is found in the ECG between the S wave and the T wave.

Section G: Since in the meantime all heart cells have been excited, the conduction of

impulses between the atria and the main chambers is normally only possible via

the His bundle and the AV node, and the cells also need a certain time (refractory

period) until they can be excited again by an action potential; the excitation from

the main chambers can no longer spread back into the atria. The relaxation phase

or diastole now begins, recognisable as a T-wave in the ECG.

Section H: Finally, all cells of the main chamber return to their resting state by repol-

arising. Now a new cardiac cycle can begin again by stimulating an action poten-

tial from the sinus node.

3.2.4 Modelling the Excitation System

As already explained in subsection 3.2.1, a simple system of three coupled oscillat-

ors can be used to model cardiac excitation, which generates the rhythm of the sinus

node, the AV node and the His bundle with the Purkinje-fibres. In this system, the

sinus node oscillator has the highest natural frequency and controls the other oscil-

lators (AV node and HP complex) from the outside (see Figure 3.13). The coupling is

particularly strong from the sinus node to the AV node and from the AV node to the His

bundle with the Purkinje fibres. Other couplings are also present, but much weaker,

so they do not need to be considered in the modelling.

Oscillating Nerve Cells Potentials in the Heart

In modelling the nerve cells with three oscillators for SA node, AV node and His bundle

with the Purkinje-fibres, one can in principle start from the investigation carried out

by Hodgkin and Huxley on the giant axon of the squid [28]. Although the equations

they set up correctly describe the potentials produced, they are very complicated.

Fitzhugh [15] succeeded in simplifying them considerably without substantially dis-

torting the representation of the correct potential. Independently, Nagumo [53] also

succeeded in doing so, which eventually led to the common FitzHugh-Nagumo-model:

_v = v −¹

3 ^{v3 −w + Iext}

τ ^_w = v −a −bw .

(3.24)

Here v is the membrane potential, w and τ are auxiliary variables, and Iext is an ex-

ternal current. Fitzhugh also calls this model the Bonhoeffer-Van-der-Pol oscillator,