A Sparse Reformulation of the Green’s Function Formalism Allows Efficient Simulations of Morphological Neuron Models

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green’s function (GF) formalism can be rewritten to scale as with the number of inputs lo...

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Bibliographic Details
Published in:Neural computation 2015-12, Vol.27 (12), p.2587-2622
Main Authors: Wybo, Willem A. M., Boccalini, Daniele, Torben-Nielsen, Benjamin, Gewaltig, Marc-Oliver
Format: Article
Language:English
Subjects:
Algorithms
Axons - physiology
Computer Simulation
Dendrites - physiology
Letters
Linear Models
Models, Neurological
Nerve Fibers, Myelinated - physiology
Neurons
Nonlinear Dynamics
Partial differential equations
Proof theory
Simulation
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Summary:We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green’s function (GF) formalism can be rewritten to scale as with the number of inputs locations, contrary to the previously reported scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.
ISSN:0899-7667
1530-888X
DOI:10.1162/NECO_a_00788