I am interested in dendrites with active spines and their ability to process and propagate signals along the length of the dendrite, and ultimately signal propagation throughout the entire dendritic tree to the soma. Dendritic spines provide a surface area for synaptic contact from the axons of other neurons. The physical properties of spines, e.g. size, shape and membrane characteristics, can change according to the quantity and pattern of activity received in that spine head. This constant adaptation is believed to be an important factor in learning and memory and logical computations within the dendritic tree. Models for spiny dendritic tissue have been shown to admit saltatory travelling wave solutions since the current in one spine may induce an action potential in neighbouring spines. The successful propagation of these solutions is dependent on spine spacings, spine stem resistance and any noise in the system. I am interested in developing a model to include the back propagation of action potentials which has been observed in experimental work and is believed to be an important process in the learning of the neuron and so the changing nature of the spines. I would also like to explore the effects of dendritic tree morphology on the propagation of signals from distal to proximal dendrites. This is an important consideration since real neurons have very different dendritic trees e.g. Purkinje cell morphology is very different to that if the Pyramidal cell. Noise is a very important aspect in any realistic model since the environment in which the neuron sits is inherently noisy due to the activity in nearby axons and dendrites. I hope to explore the effects of noise on any model which I develop over the course of my Ph.D.