Fig 1.
Schematic of the dynamical processes that occur within and between neural populations.
Gray circles are quantities associated with interactions between populations (i.e., a and b), while white circles are quantities associated with a population (i.e., a or b). Spike-rate fields ϕab arriving at neurons of type a from ones of type b are modulated by the synaptic dynamics, and undergo dendritic dynamics to produce postsynaptic subpotentials Vab. These contributions are linearly summed in the dendritic tree, eventually resulting in charging currents at the soma that give rise to the soma potential Va, after allowing for capacitive effects and leakage. Action potentials generated at the axonal hillock are averaged over a population of neurons. Then, when the mean soma voltage exceeds a threshold, the mean firing rate Qa of the population is obtained via a nonlinear response function. Finally, the pulses propagate away across the axonal tree and the dendrites of the receiving population c as the set of average spike-rate fields ϕca. Note that self-connections with b = a or c = a are included.
Table 1.
NFT quantities and associated SI units.
Fig 2.
The response to a delta-function input, via Lab as defined in Eq (5), for decay rate parameter αab = 45 s−1 and rise rate parameter βab = 185 s−1. This function peaks at t = ln(β/α)/(β − α) for α ≠ β.
Table 2.
Symbols, configuration parameters and units.
Table 3.
Auxiliary functions available in the module +nf.
Fig 3.
Simplified diagram of NFTsim’s call graph.
The execution of a simulation is controlled by the class Solver. Initial conditions are given in terms of firing rates Qb which are then propagated to other populations via Propagator. Synaptic connections are handled via Coupling. The incoming activity to postsynaptic Population undergoes dendritic dynamics via Dendrite. The sum of individual contributions Vab and the resulting firing response are handled by FiringResponse. The class Timeseries is used to represent external inputs Qx from a stimulus Population. Lastly, the class Outlet stores the variables that are written to the output file.
Fig 4.
NFTsim classes associated with biophysical processes.
This diagram illustrates the relationship of the classes in the library and the biophysical transformations they represent. Input variables are on the left, while output variables are on the right. Gray boxes are classes associated with interactions between populations, while white boxes are classes associated with internal mechanisms of a population.
Fig 5.
Schematic of the discretized spatial domain.
The model has two populations: Population 1 and Population 2. Geometrically, each population is represented by a grid of 12 nodes, which are labeled with integers. The grid is rectangular with dimensions 4 × 3 nodes. The number of nodes of the longest side is specified by Longside nodes. The physical size, Lx, of each population is different. Thus, each node in Population 1 has a linear size of Δx1, and of Δx2 in Population 2. Each spatial point (e.g., r1, r9, r11) is at the center of a grid cell. The subscript denotes the node index on this grid. Also, rn denotes the actual position in the largest population; in the smallest population rn denotes a rescaled physical dimension. Lastly, the borders of the grid are depicted with dashed lines to denote periodic boundary conditions (PBCs), which represent structures with planar geometry and toroidal topology.
Fig 6.
Schematic of the grid used by the class Stencil.
This class retrieves the four nearest neighbors (labeled n, s, e, w) of a central point c. These five points define the pattern known as a five-point stencil. The cells in light blue are the ghost cells required to implement periodic boundary conditions. The prime, double-prime and triple prime indices represent copies of the corresponding indices in the vertical, horizontal and diagonal directions, respectively.
Fig 7.
Neural activity of the model described in e-erps.conf.
The cortical population is driven by two square pulses. The first pulse is positive, while the second pulse is negative. For illustrative purposes, in each panel the mean spatial value of ϕee(x, y, t) has been subtracted, so the color reflects deviations from the mean at that specific time. Each panel shows a surface plot of s−1 propagating radially outwards from the stimulation sites, and an inset with a planar view of the same quantity, at different times: (a) 42 ms; (b) 52 ms; (c) 62 ms; (d) 77 ms; (e) 86 ms; (f) 104 ms.
Fig 8.
Timeseries of neural activity of the model described in e-erps.conf.
The cortical population is driven by two temporal square pulses applied at the center of the grid as shown in Fig 7. Here, we illustrate the timeseries of ϕee from a few nodes close to the vicinity of (gray lines) and at the stimulation sites. The vertical dashed lines mark the onset time of the positive (red dashed) and negative (blue dashed) stimulation inputs, respectively. (a) the axonal field at the site receiving the positive stimulus is highlighted in red while the time evolution of the same axonal field at neighbouring locations is shown as gray lines. (b) the axonal field at the site receiving the negative input is highlighted in blue.
Fig 9.
Schematic of four representative neural field models.
The quantities ϕab are the fields propagating to population a from population b. Dashed lines represent inhibitory connections. (a) Corticothalamic model including excitatory (e), mid-range (m), inhibitory (i), reticular (r), specific relay (s) and external non-specific (n) populations. (b) Corticothalamic model including excitatory (e), inhibitory (i), reticular (r), specific relay (s), and external (n) populations. (c) Cortical model comprising excitatory (e) and inhibitory (i) cortical populations plus an external input field from a subcortical population (s). (d) Purely excitatory (e) cortical model with input from a subcortical population (s).
Fig 10.
Comparison of analytic and numeric EEG power spectra in the corticothalamic system.
The dynamics of the EIRS model were simulated using the wake parameters from [6] for their Figure 2. The linear analytic spectrum (black dashed solid) is compared against the spectra computed from simulations (solid line).
Table 4.
NFTsim simulation and output size parameters, and runtime and memory usage symbols.
Table 5.
Benchmarks for different grid sizes using NFTsim v.0.1.5.