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Fast simulation of extracellular action potential signatures based on a morphological filtering approximation

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Abstract

Simulating extracellular recordings of neuronal populations is an important and challenging task both for understanding the nature and relationships between extracellular field potentials at different scales, and for the validation of methodological tools for signal analysis such as spike detection and sorting algorithms. Detailed neuronal multicompartmental models with active or passive compartments are commonly used in this objective. Although using such realistic NEURON models could lead to realistic extracellular potentials, it may require a high computational burden making the simulation of large populations difficult without a workstation. We propose in this paper a novel method to simulate extracellular potentials of firing neurons, taking into account the NEURON geometry and the relative positions of the electrodes. The simulator takes the form of a linear geometry based filter that models the shape of an action potential by taking into account its generation in the cell body / axon hillock and its propagation along the axon. The validity of the approach for different NEURON morphologies is assessed. We demonstrate that our method is able to reproduce realistic extracellular action potentials in a given range of axon/dendrites surface ratio, with a time-efficient computational burden.

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Notes

  1. This simplifying assumption lacks in reproducing the intrinsic dendritic filtering shown in e.g., Lindén et al. (2010), as it will be discussed further in the Results section.

  2. In other words, the dipolar moment at time t will be defined as j(t) = Ca(rk+ 1 −rk)Ik(t).

  3. The same reasoning could be applied for (rk + 1 −rk) in Eq. 5 and Ca coefficient.

  4. It is well known that a single compartment NEURON can not generate any extracellular potential because the Kirchhoff’s current law is not respected – the net transmembrane current must necessarily be equal to zero. The simplest NEURON model able to generate an LFP signature is then a two-compartment model where the membrane current enter the NEURON at one compartment and leaves at the other compartment.

  5. A similar figure comparing performances of 1μ m and 2μ m diameter axons can be found in the Supplementary Material.

  6. These values correspond in fact to τk equal to 21, respectively 12 samples, at a sampling frequency of 106Hz. These values are the median speeds over the optimal speed values for all configurations having a given axon diameter (for example, 0.45 is the medians of optimal v for all BS models with an axon of 2μ m diameter).

  7. Note that this would allow to create signals for training or evaluating spike sorting algorithms (Lewicki 1998; Rey et al. 2015). Recall that these algorithms are based on distinct features of the EAPs (amplitude, width... etc), which our simulator is able to reproduce for varying positions. Note that supplementary variability could be in principle obtained by varying also the parameters of the HH model.

  8. Only the part due to the EAP, no synaptic currents were taken into account, see Aussel et al. (2019) for preliminary results on the relative contributions of both synaptic and EAP currents to the extracellular potential.

  9. When a single HH compartment is simulated for all 5000 neurons.

  10. Other detailed simulation techniques such as Thorbergsson et al. (2012) and Dura-Bernal et al. (2019) are also based on NEURON, having thus more or less the same advantages (in terms of precision) and caveats (computing time).

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  1. CNRS, CRAN, Université de Lorraine, F-54000, Nancy, France

    Harry Tran, Radu Ranta, Steven Le Cam & Valérie Louis-Dorr

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  1. Harry Tran
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Tran, H., Ranta, R., Le Cam, S. et al. Fast simulation of extracellular action potential signatures based on a morphological filtering approximation. J Comput Neurosci 48, 27–46 (2020). https://doi.org/10.1007/s10827-019-00735-3

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