Many of the mathematical models for cell membranes that have been investigated so far deal with non-myelinated nerve fibres of cold blooded animals or myelinated nerve fibres; this diploma thesis examines a slightly adapted Hodgkin-Huxley (HH) model, which shall model a non-myelinated nerve fibre of warm blooded animals. This model is compared with other membrane models found in literature. The original HH model was developed in 1952 for the unmyelinated giant axon of the squid. By changing the maximal ionic conductances gion, the ion channels are adapted so that gNa almost equals that of the model which was developed by Chiu, Ritchie, Rogart, Stagg, and Sweeney (CRRSS) for mammalian myelinated nerve fibres. Changing the ionic conductances is necessary to avoid the heat block, a phenomenon that prohibits spike propagation at high temperatures.
In this thesis, the local models, where current flow along the axon is prevented, as well as different propagation models are examined and compared with each other. Adapted HH models with different factors for the ionic conductances are analyzed, and models for myelinated nerve fibres with different insulating properties are investigated.
Comparison shows that the total number of ions that cross the cell membrane through the ionic channels in the HH model during an action potential is smaller than that in any other model. The total number of sodium ions that cross the membrane at some distance from the stimulated region in the CRRSS model is, for example, three times the number of sodium ions that pass the corresponding membrane area in the HH model.
The injected stimulating threshold current in the HH model is also smaller than those in the other models. The conduction velocity of an action potential along the unmyelinated HH fibre is higher than that according to any other examined membrane model, and can be increased by modeling myelinated nerve fibres. In a 1 mym thick axon, the conduction speed can be heightened to 16 m/s. As regards the shape of the action potentials, the spike in the adapted HH model is unusually short, which can be observed in the local model as well as in the propagation models.
The spike is quite different to those in the CRRSS and the SRB model, which were created for modeling the membrane of a mammalian myelinated nerve fibre and a human myelinated nerve fibre, respectively. This indicates that the adapted HH model is not adequate for modeling the membrane of warm blooded animals.
One possible reason might be that the value of Q10 in the HH model is not constant but changes with temperature. Another reason might be that the HH model does not take account of different types of sodium channels.