Mathematical physiological modeling of the relation between local field potentials and spikes recorded inside the subthalamic nucleus

During the last decade, the subthalamic nucleus (STN) has drawn the attention of clinicians and researchers becoming the main target for high-frequency deep brain stimulation of the basal ganglia in patients suffering from movement disorders such as dystonia or Parkinson´s disease. Currently, a great effort is made both in Medicine and Neurosciences for understanding and modeling in details how the STN cells work. The aim of this work is the development of a phenomenological model of an STN neuron that receives the local field potentials as its input and outputs a spike train. The model is physiologically inspired by the temporal summation observed in neurons. After estimating the model´s numerical parameters and stochastic properties by fitting the available intranuclear data, we show that the model can predict with reasonable accuracy single spikes as well as the presence of bursts by following closely the recorded spiking rhythm.