1 2 . e l e c t r O t H e r a P y t H e O ry
107
EN
WIRELESS PROFESSIONAL
The excitation process is therefore determined by two time constants:
𝑘
the excitation constant
𝜆
the accommodation constant
These are independent from each other. This means that, to a large extent,
𝜆
can be modified by
experiment separately to
𝑘
, by changing the ionic concentration of Calcium (Ca). These two constants
have values that are very different to each other, but
𝜆
is always much larger (100 to 200 times) than
𝑘
. In
the case of human motor neurons, approximate values of 300 μs can be retained for
𝑘
and 50 ms for
𝜆
.
This means that
𝑘
must be lower than
𝜆
for the excitation process to occur. The local potential (V) can
therefore increase more quickly than the threshold
S
and catch up with it. If
k
were greater than
𝜆
, the
threshold would increase more quickly than the local potential, which would never catch up with the
threshold.
12.3.2 Study of the excitation process using a constant current
For the sake of simplicity, at this stage we will only study the excitation process produced by a constant
current. The same study can be carried out using exponential, sinusoidal, linear, progressive, or any other
type of current, as the results are similar.
For example, let us use the values:
𝑘
= 1 ms.
𝜆
= 50 ms.
The issue in the excitation process is whether V will catch up with S or will S have time to escape.
The local potential V starts at Vo and increases exponentially according to the relationship to a final value
depending on the intensity of the current.
ØV = V-Vo = V m ax (1-e
-t/k
)
The threshold
𝑆
starts from
𝑆𝑜
and increases according to a more complicated curve, which can only be
shown in part, and up to a value depending on the final stable value of
𝑉
, if excitation has not occurred in
the meantime.
In Figure 2a, the intensity of the current is set at a value (we will take as 1), which, without
accommodation, would allow
𝑉
to reach
𝑆𝑜
and to trigger excitation.
In fact
𝑉
reaches the value
𝑆𝑜
but in the meantime the threshold increased, therefore
𝑉
=
𝑆𝑜
<
𝑆
and excitation cannot occur.
To allow
𝑉
to reach the value
𝑆
, the current must be 8% more intense.
This is shown in Figure 2b, where the threshold has just been reached in 4 ms (indicated by the arrow),
that is the principal useful time.