We shall now set about estimating the various parameters of the model and the rangs of travel of the thresholds in the SAN and AVN. A clue to the value of Tr is provided by the fact that during heavy exercise maximum heart rates of around 200 beats per minute are recorded [costill, et al, 1973]. If we assume that this maximum is limited by the refractory period we have the estimate
Tr = 0.3s (4.1)
Eqn. 4.1 gives only an upper bound to Tr. considerably higher frequencies are indeed observed in the e.c.g. during ventricular fibrillation, but it seems likely that they reflect the chaotic, zigzag pattern of wave travel in that arrhythmia rather than the maximum firing rate of individual cells.
To prevent interference of successive output pulses under conditions of maximum firing we must [assuming that TO is constant at all frequencies]have TO < Tr. we shall here ddopt the value
TO = 0.2s (4.2)
The value of TO does not contradict the observation that cardiac action potentials last for about 0.3s: it may be interpreted as that portion of the action potential during which significant current is injected from an active cell over the membrane of its neighbor, in the correct polarity to stimulate it.
Tm now follows from specifying the maximum period to be allowed, short of cardiac arrest. There is little to go on here, other than the fact that heart rates of the order of 35 beats per minute are sometimes observed in highly trained endurance athletes at rest. Applying a factor of safety, we assign 26 beats per minute as the lowest frequency of the model, corresponding to the convenient figure
Tm = 2s (4.3)
The above considerations are summarized on Fig. 4.6. Which also shows various threshold level. The levels marked SMR refer to the ‘standard man at rest’ and have been taken as the conventional values of 0.86s [70 beats per minute] for SAN and 1.2s [50 beats per minute] for AVN. The designation I refers to ‘intrinsic’ conditions, that is, silence in both nerves. According to Green [1972] the intrinsic heart rate is 150 beats per minute, which corresponds to the SAN [I] period of 0.4s.
The remaining levels have has to be filled in by trial and error, aided by some extrapolations and linearisations, hence they are offered with trepidation. The first assumption is that parasympathetic stimulation acting alone brings both SAN and AVN to the 2.3s period just before cardiac arrest [CA]. Designation THIS LEVEL OF STIMULATION BY fp=1p.u. and assuming linearity between fp and the period, the points SAN,AVN [CA] and SAN[I] are now joined on the period control characteristic of Fig. 4.7. locating SAN[SMR] on this line [at 0.86s] and placing AVN [SMR] DIRECTLY ABOVE IT [AT 1.23S], the AVN control line can be drawn. It intersects the fp=0 axis at AVN [I],which corresponds to 0.85s [71 beats per minute].