Error Analysis and Quantification in Neuron Simulations

Abstract

Abstract. The Blue Brain Project (BBP) uses the NEURON simulator to model the electrical activity of large networks of morphologically detailed neurons. Each individual neuron is typically described by a model that couples the actions of localized membrane mechanisms with an electrical system described by the cable equation on a topology derived from the neuron's dendritic tree. NEURON discretizes the electrical problem in space with finite differences. The system is then solved in time with an implicit Euler or Crank-Nicolson scheme, using Strang splitting to decouple the evolution of the mechanisms from the membrane potential. A typical spatial discretization of a single neuron will have hundreds of elements, and the resulting linear system for the implicit solver is almost tridiagonal.In this paper, we present a detailed analysis of the different sources of error arising from the biological and mathematical models underlying NEURON simulations. We provide a detailed account of the mathematical model, identify and evaluate the sources of uncertainty in the biological and numerical models and quantify the errors resulting from the model discretization and from the choice of the integrator. Post-processing based techniques are applied to assess the numerical error in the solution. Of particular interest is the analysis of the discontinuities arising from the pointwise synaptic processes that constitute part of the model, including the effects of voltage-proportional synaptic conductance.We validate our analysis through a series of numerical experiments on a branched dendrite model incorporating Hodgkin-Huxley distributed ion channels with simple alpha-synapes and biologically realistic AMPA/NMDA activated synapses. This model exhibits the action-potential behaviour with fast dynamics characteristic of a typical simulation of a network of neurons.

An Optimizing Multi-platform Source-to-source Compiler Framework for the NEURON MODeling Language

“…Linear and independent ODEs have been typically replaced by an analytic solution that treats the coefficients as constant over a time step. NMODL increases the runtime performance by performing algebraic simplification and optionally replacing computationally expensive exponential calculations with the (1, 1) Pade approximant [5], consistent with the overall second order correct simulation accuracy (as suggested in [6], and implemented in [1]).…”

An optimizing multi-platform source-to-source compiler framework for the NEURON MODeling Language

“…Linear and independent ODEs have been typically replaced by an analytic solution that treats the coefficients as constant over a time step. NMODL increases the runtime performance by performing algebraic simplification and optionally replacing computationally expensive exponential calculations with the (1, 1) Pade approximant [44], consistent with the overall second order correct simulation accuracy (as suggested in [45], and implemented in [26]).…”