The relation of Rushton's ‘liminal length’ for excitation to the resting and active conductances of excitable cells

The minimum (or liminal) length of an excitable cable that must lie above the inward current threshold in order to initiate propagation is derived using a simple polynomial representation of the ionic current-voltage relation.2. This model is then used to obtain an approximate equation for the liminal length that may easily be applied to excitable cells using experimental measurements of the ionic current.3. The equations are used to show that the liminal length in cardiac Purkinje fibres is expected to be much smaller than in squid nerve. The values calculated are similar to those obtained by Fozzard & Schoenberg (1972) from strength-duration curves.4. It is shown that the strength-duration curve for non-uniform excitation is virtually independent of the resting membrane resistance. The strength-duration time constant may not, therefore, be related to the membrane time constant.