Simulating extracellular signatures of action potentials using single compartment neurons and geometrical filtering
Résumé
Simulating extracellular recordings of single/multiple neurons or of complete populations is an important and challenging task both for understanding the nature of extracellular field potentials (LFP) at different scales and for validating signal processing tools (e.g. despiking/ spike sorting). State of the art models [1], based on neuron models having multiple active or passive compartments, show that the extracellular signatures of both synaptic sources and membrane sources during action potentials depend on the geometry of the neurons and on the position of the measuring electrode with respect to this geometry. The simulation methodology, based on the NEURON environment [2] and the LFPy python package [3], could require a high computational burden for large neuronal populations [4].
We propose a new method to simulate the extracellular images of action potentials. Our method takes into account the geometry of the neuron and the position of the electrode, but only requires to model the dynamics of a single compartment. Different shapes are next obtained using a filter based on the geometrical properties of the recording setup, with an overall much smaller computational burden.
More precisely, we start from the classical assertion that at every time instant t, the potential recorded by the electrode is a weighted sum of the membrane currents of all compartments, the weights depending on the medium conductivity (assumed constant) and the geometry (relative position of the compartments and the electrode). The basic idea of our method is to model the membrane current sources active during the action potential as a moving dipole, oriented parallel to the axon and moving with a certain speed along it. In this case, one can show that this weighted sum is equivalent to a convolution between a geometry-conductivity based filter and the membrane currents of a single active compartment. Our model of extracellular spikes is thus generated by a single-compartment Hodgkin-Huxley neuron, convolved with a filter, analytically computed using the shape of the considered neuron.
We have tested our model by comparing it with the NEURON/LFPy simulation of a neuron having the same structure (same shape and number of active compartments), in our case a simple ball-stick model (see figure). The resulting extracellular spikes showed a very good correlation between the two models (mean value above 0.9). Moreover, their shapes were also close to experimental extracellular recordings reporting different spike shapes, depending on the type of neuron (inhibitory/excitatory) and on the position of the electrode with respect to the soma or to the axon [5].
[1] Einevoll, G.T. et al (2013) Modelling and analysis of local field potentials for studying the function of cortical circuits. Nat. Rev. Neuroscience, 14(11), 770.
[2] Hines, M.L., & Carnevale, N.T. (1997). The NEURON simulation environment. Neural Comput., 9(6), 1179-1209.
[3] Lindén, H. et al (2014) LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Frontiers in neuroinformatics, 7, 41.
[4] Camunas-Mesa, L.A., & Quian-Quiroga R. (2013) A detailed and Fast Model of Extracellular Recordings. Neural Comp., 25(5), 1191-1212.
[5] Robbins, A.A. et al (2013) Short duration waveforms recorded extracellularly from freely moving rats are representative of axonal activity. Frontiers in neural circuits, 7, 181.