Some uncertainty aspects in models for neural engineering

Neural engineering is a rather young, rapidly evolving field in science, interfacing the living neuronal system and technical equipment. This study has its background in neuroprosthetics, particularly in Deep Brain Stimulation which works on neurons in the Subthalamic Nucleus (STN). In order to study the significance of alterations in geometrical parameters on the characteristics of the action potential (AP), i.e. on the neuronal impulse, the FitzHugh Nagumo equations are solved for an idealized homogeneous axon model, based on the finite element method. Minimal and maximal values for radius and length of the STN axon are taken from literature. Applying a stochastic model, we quantify the uncertainty in the AP´s characteristics due to geometrical alterations. For fixed membrane excitation, the relation of the AP width versus radius and length of the axon is observed.