12.3.3 Excitation by a current with any shape
It is possible to determine the equation for the local potential V and to calculate its value at any given
point in time with any given shape of current.
An equation can also be determined for the development of the threshold.
These equations required a solid understanding of mathematics and come under the field of specialist
electrophysiology. This is why we believe there is no purpose in expanding these equations as part of this
work.
However, it can be noted that using these equations, which give the variation of V and , it is possible to
study the excitation process with any given shape of current and for any given duration.
If the durations of current applied were longer, the threshold would increase and excitation would only
occur if V became equal to S. In these cases, the intensity-duration relationship must be reconsidered
as the rheobase does not keep the value 𝐼𝑜; instead, it increases to a value 𝐼 1 > 𝐼𝑜 determined by the
excitation and accommodation constants. The actual rheobase 𝐼𝑜 is linked to the observed rheobase I1 by
the relationship:
1 l0/1-e
-t/e
is the
chronaxy
(
tch
) when
1 2l0
therefore
2l0 l0/1 - e
tch/k
2l0 (1 - e
tch/k
l0
2 (1 - e
tch/k
1
2 - 2e
tch/k
1
2e
tch/k
1
e
tch/k
1/2
e
1/tchk
1/2
e
tch/k
2
1n2 tch/k
therefore
t
ch
(1n2k
This means that the chronaxy =
.
12.3.4 Chronaxy - excitation constant
relationship
As the chronaxy is a value that characterises tissue excitability,
it is worth determining the relationship which links it to the
other factor that characterises excitation: k.
The chronaxy is the useful time corresponding to a stimulation
current which has an intensity double that of the rheobase, i.e.
2 Io. It is therefore very easy to find the relationship between
the chronaxy and the excitation constant based on the formula
giving the intensity-duration relationship.
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