The McGill Physiology Virtual Lab

Compound Action Potential

Strength-Duration curve

The objective of this part of the lab is to study the interdependence between stimulus strength and stimulus duration in activating the nerve, and to construct a Strength-Duration Curve.




We have seen how the shape, amplitude and duration of the CAP change as the stimulus strength increases, because progressively stronger stimulation activates more and more individual nerve fibres, whose individual action potentials summate to yield a CAP.  Thus when the stimulus is stronger, a larger number of fibres reach threshold.

However, the threshold for activation of a fibre depends not only on stimulus strength, but also on the duration of the stimulus.
Depolarization of an excitable membrane requires flow of electrical charge across the membrane. Because of the dominant electrical capacitance of the membrane, the relevant parameter for effective membrane depolarization is the total amount of charge transferred across the membrane.
For a short duration stimulus generating a steady trans-membrane current, the charge (Q) transferred is proportional to the product of current I and time T:

Q = I x T

Hence if the amount of charge required to activate the fiber is Qt, and the stimulus duration is D, the current It required to achieve activation will be:

It = Qt / D

This suggests that a graph of threshold stimulus strength versus stimulus duration should show a decline to near zero as stimulus duration is increased. In other words, the stimulus strength required to reach threshold should decrease during more prolonged stimulation. Note that we can use voltage (V) and current (I) interchangeably as the measure of stimulus strength.

The Strength-Duration Curve for a typical neural membrane is similar, but differs in that the curve clearly flattens out with long stimulus durations, reaching an asymptote called the RHEOBASE. When the stimulus strength is below the rheobase, stimulation is ineffective even when stimulus duration is very long.

The discrepancy between the observed shape of the Strength-Duration curve and that predicted by the equation above, is due to the fact that the predicted relationship is true for an ideal capacitor, with no leakage resistance.  During prolonged stimulation (large values of t), the equation fails to predict the charge transfer across the nerve membrane because under these conditions the actual charge transfer is less than predicted, owing to leakage due to the appreciable electrical resistance of the membrane. Because of the interplay between resistive and capacitive effects in the membrane, charge transfer (and membrane potential) actually rises exponentially to a plateau during prolonged stimulation, instead of increasing linearly with time.  Thus if the stimulus is too small, the membrane potential never reaches threshold.

When examining the Strength-Duration relationship in a nerve trunk, containing thousands of nerve fibres, one must be careful to consider which of these many fibres the threshold in question pertains to. The threshold stimulus voltage for the CAP as a whole is actually the threshold for the fastest, most excitable fibres in the nerve. As it is difficult to accurately determine this threshold, the procedure outlined below uses as a reference signal a CAP whose peak amplitude is about one fifth of Maximal. Thus this threshold is clearly the threshold for another less excitable group of fibres.


To begin, the stimulus duration is set to 1.0 ms using the knob on the stimulator.

STEP A:  The stimulus voltage is increased slowly until a CAP appears.  In this example, we have adjusted the voltage until the CAP amplitude fills two intervals of the horizontal grid on the screen.  This CAP amplitude will be used as a reference for the rest of the experiment. (Another reference line can also be chosen, provided it is kept throughout the exercise)

We read the stimulus voltage from the stimulator, and the corresponding stimulus duration (in this first case 1 ms) and enter this pair of values into a table. Thus this stimulus duration and voltage have brought to threshold a small group of excitable fibres in the nerve, although they are not the most excitable.

STEP B:  Now we slowly decrease stimulus duration until the CAP disappears.  (We stop when the display shows a flat line where the CAP used to be). 

Then we repeat STEP A; that is, increase the stimulus voltage until the CAP reaches the reference amplitude noted above. (In this case filling two intervals of the grid).   We read the new stimulus voltage and stimulus duration from the stimulator and enter the pair of values into the table.
This procedure is repeated until we have 10 different pairs of values.  Using our data, the strength-duration curve is plotted:
0.64 1.0
0.8 0.42
1.0 0.25
1.2 0.18
1.42 0.134
1.62 0.105
2.0 0.082
2.4 0.063
2.82 0.05
3.45 0.038

Besides the Rheobase, the Strength-Duration Curve also provides another piece of information, the Chronaxie.  The Chronaxie is a duration measurement, corresponding to twice the Rheobase. 

From the graph above, the Rheobase is approximately 0.64 volts, and the Chronaxie is about 0.16 ms.


Questions and answers

Q:  What is the significance of the Rheobase?
A: Usually around the 1 ms mark on the strength-duration curve, the curve flattens out at the Rheobase, the point where a progressive increase in pulse duration is no longer associated with a progressive decrease in voltage.  In other words, for longer stimulus durations, the minimal voltage required to bring the nerve to threshold will be the Rheobase.
Q:  What is the significance of the Chronaxie?
A:  Given that two nerves have the same Rheobase, the Chronaxie (the stimulus duration corresponding to twice the rheobase) can give an indication of their relative excitabilities.  In the strength-duration curve to the right, nerve B is the more excitable.
Q:  How would the strength-duration curve for a set of slow fibres (not very excitable) compare to the strength-duration curve for a set of quick fibres (very excitable)?
A:  The curve for the slower fibres would be shifted to the right, indicating that for a given stimulus strength, a longer stimulus duration would be needed to bring the slower fibres to threshold.

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