Journal of Neuroscience Methods 174 (2008) 281–291 Contents lists available at ScienceDirect Journal of Neuroscience Methods journal homepage: www.elsevier.com/locate/jneumeth Estimation of neuronal firing rates with the three-state biological point process model Emanuel E. Zelniker a,∗ , Andrew P. Bradley b , Joanna E. Castner c , Helen J. Chenery c , David A. Copland c , Peter A. Silburn d a Department of Computer Science, Queen Mary, University of London, London E1 4NS, United Kingdom b School of Information Technology and Electrical Engineering, The University of Queensland, Queensland 4072, Australia c Division of Speech Pathology, The University of Queensland, Queensland 4072, Australia d School of Medicinie, The University of Queensland, Queensland 4072, Australia article info Article history: Received 6 February 2007 Received in revised form 6 May 2008 Accepted 9 May 2008 Keywords: Poisson process Deep-brain stimulation Micro-electrode recordings Thresholding functional Neuronal firing rates Parameter estimation abstract In the subcortex of the human brain, neuronal firing events are stochastic and the inter-arrival times of action potentials (APs) are highly irregular. It has been shown that stimulation of the subthalamic nucleus (STN), a small subcortical structure located within the basal ganglia, can help ameliorate the motor symptoms associated with Parkinson’s disease (PD). However, success of image guided stereotactic surgery is reliant upon the refinement of the anatomic target (in this case the STN) based on micro- electrode recordings (MERs) of background activity and firing rate. In practice MERs must be analysed on-line and in real-time. Currently, the most common method of performing on-line MER analysis is a manual thresholding procedure. However, this is subjective in nature and often complicated by the presence of variable amounts of background noise. Therefore, in this paper, we present an automated adaptive thresholding technique, based on a modified ‘top-hat’ operator, which detects APs exceeding the local background activity. We then go on to model these inter-arrival times using a coupled Poisson process that provides improved estimates of both inter-burst and intra-burst neuronal firing activity in the STN. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved. 1. Introduction In the subcortex of the human brain, neuronal firing events are stochastic in nature and so the inter-arrival times of action potentials (APs) are highly irregular. While this phenomenon can sometimes be adequately described using Poisson models Heeger (2000), it is often confounded by the combination of the highly irregular neuronal firing events and the fact that in vivo measure- ments are often contaminated by high levels of background noise. This poses a great challenge to automated or semi-automated anal- ysis of neural activity measured in vivo. It has been demonstrated that stimulation of the subthalamic nucleus (STN), a small subcortical structure located within the basal ganglia, can help to improve the motor symptoms of Parkinson’s Disease (Hutchison et al., 1998; Sterio et al., 2002; Chen et al., 2006). However, in order to stimulate the STN one must first locate the tar- get and then accurately position a stimulus electrode in this area. ∗ Corresponding author. Tel.: +44 207 882 5230. E-mail addresses: zelniker@dcs.qmul.ac.uk (E.E. Zelniker), bradley@itee.uq.edu.au (A.P. Bradley). Currently, this is done by utilizing a stereotactic frame that guides the micro-electrode to a target in the frontal subcortex (usually the STN or globus pallidus interna, GPi). The precise location of the tar- get is initially found using a combination of computed tomography (CT) and magnetic resonance imaging (MRI). Data is then recorded from the micro-electrode as it progresses towards the target. Fea- tures extracted from the micro-electrode recordings (MERs), such as background activity and neuronal firing rate, are then used for precise identification of the borders of the STN (Israel and Burchiel, 2004). Micro-electrode recordings are commonly used in functionally awake neurosurgical procedures, such as Deep-Brain Stimulation (DBS), as they provide a method of verifying the location of tar- get structures via their observed neurophysiological properties (Hutchison et al., 1998; Sterio et al., 2002; Quiroga et al., 2004). The high-impedance micrometer tip of the micro-electrode probe allows for functional investigation of small populations of neurons within the STN. Alternatively, Local Field Potentials (LFPs) have also been used to confirm target location either during or post surgery (Engel et al., 2005; Chen et al., 2006). Local Field Potentials are mea- sured between the individual pairs of electrodes that are positioned towards the terminus of the stimulus lead, adjacent electrodes 0165-0270/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2008.05.026