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A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations.

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M - Front Neuroinform (2015)

Bottom Line: This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions.To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers.Finally, we discuss limitations of the novel technology.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Science, Bergische Universit├Ąt Wuppertal Wuppertal, Germany.

ABSTRACT
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

No MeSH data available.


Related in: MedlinePlus

Iterative neuronal updates. Communication of spikes and gap-junction related data is carried out in steps of dmin (long gray lines), which denote the minimum synaptic transmission delay in the network. Within each communication interval neurons update their dynamics in steps of h (shorter light gray lines); here dmin = 4 h at time . Turquoise curves show the approximation of the membrane potential, which is used by the connected neuron to compute the solution in the current interval. (A) First iteration with constant approximation for the membrane potential of the connected neuron. At the end, a new approximation of the just computed membrane potential is passed to the connected neurons. (B) Further iteration with the approximation of the membrane potential from last iteration. This part is the actual iteration process which can be done multiple times. (C) After the final iteration a constant extrapolation for the next time step is communicated.
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Figure 5: Iterative neuronal updates. Communication of spikes and gap-junction related data is carried out in steps of dmin (long gray lines), which denote the minimum synaptic transmission delay in the network. Within each communication interval neurons update their dynamics in steps of h (shorter light gray lines); here dmin = 4 h at time . Turquoise curves show the approximation of the membrane potential, which is used by the connected neuron to compute the solution in the current interval. (A) First iteration with constant approximation for the membrane potential of the connected neuron. At the end, a new approximation of the just computed membrane potential is passed to the connected neurons. (B) Further iteration with the approximation of the membrane potential from last iteration. This part is the actual iteration process which can be done multiple times. (C) After the final iteration a constant extrapolation for the next time step is communicated.

Mentions: The discrimination between the preliminary updates and the final update is necessary, since during a preliminary update the neuron will not issue any spiking events, as shown in Algorithm 2. The incoming spiking events in each iteration are hence the same. On the other hand, only within a preliminary update a neuron will send secondary events conveying the interpolation of its membrane potential to its peers. The final, non-preliminary update conveys the extrapolation of the membrane potential to the other neurons, which will be used in the first iteration of the next time step. Figure 5 shows the realization of the iterative update process for two neurons with special focus on the communication of the interpolation coefficients. The first computation of the time step is calculated with a constant extrapolation of the membrane potential of the connected neurons. In every further iteration of the same time interval the interpolation generated with the last iteration is used. Accordingly the interpolation of the current membrane potential is computed during preliminary iterations, while for the final iteration a constant extrapolation is send to the scheduler. Thereby the interpolation coefficients are computed as described in Section 2.1.2 and saved in an array. The same applies for the receiving side (Algorithm 3), where the coefficients from the incoming connections are accumulated as described in Section 2.1.2.


A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations.

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M - Front Neuroinform (2015)

Iterative neuronal updates. Communication of spikes and gap-junction related data is carried out in steps of dmin (long gray lines), which denote the minimum synaptic transmission delay in the network. Within each communication interval neurons update their dynamics in steps of h (shorter light gray lines); here dmin = 4 h at time . Turquoise curves show the approximation of the membrane potential, which is used by the connected neuron to compute the solution in the current interval. (A) First iteration with constant approximation for the membrane potential of the connected neuron. At the end, a new approximation of the just computed membrane potential is passed to the connected neurons. (B) Further iteration with the approximation of the membrane potential from last iteration. This part is the actual iteration process which can be done multiple times. (C) After the final iteration a constant extrapolation for the next time step is communicated.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4563270&req=5

Figure 5: Iterative neuronal updates. Communication of spikes and gap-junction related data is carried out in steps of dmin (long gray lines), which denote the minimum synaptic transmission delay in the network. Within each communication interval neurons update their dynamics in steps of h (shorter light gray lines); here dmin = 4 h at time . Turquoise curves show the approximation of the membrane potential, which is used by the connected neuron to compute the solution in the current interval. (A) First iteration with constant approximation for the membrane potential of the connected neuron. At the end, a new approximation of the just computed membrane potential is passed to the connected neurons. (B) Further iteration with the approximation of the membrane potential from last iteration. This part is the actual iteration process which can be done multiple times. (C) After the final iteration a constant extrapolation for the next time step is communicated.
Mentions: The discrimination between the preliminary updates and the final update is necessary, since during a preliminary update the neuron will not issue any spiking events, as shown in Algorithm 2. The incoming spiking events in each iteration are hence the same. On the other hand, only within a preliminary update a neuron will send secondary events conveying the interpolation of its membrane potential to its peers. The final, non-preliminary update conveys the extrapolation of the membrane potential to the other neurons, which will be used in the first iteration of the next time step. Figure 5 shows the realization of the iterative update process for two neurons with special focus on the communication of the interpolation coefficients. The first computation of the time step is calculated with a constant extrapolation of the membrane potential of the connected neurons. In every further iteration of the same time interval the interpolation generated with the last iteration is used. Accordingly the interpolation of the current membrane potential is computed during preliminary iterations, while for the final iteration a constant extrapolation is send to the scheduler. Thereby the interpolation coefficients are computed as described in Section 2.1.2 and saved in an array. The same applies for the receiving side (Algorithm 3), where the coefficients from the incoming connections are accumulated as described in Section 2.1.2.

Bottom Line: This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions.To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers.Finally, we discuss limitations of the novel technology.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Science, Bergische Universit├Ąt Wuppertal Wuppertal, Germany.

ABSTRACT
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

No MeSH data available.


Related in: MedlinePlus