iqr: A Tool for the Construction of Multi-level Simulations of Brain and Behaviour

Abstract

The brain is the most complex system we know of. Despite the wealth of data available in neuroscience, our understanding of this system is still very limited. Here we argue that an essential component in our arsenal of methods to advance our understanding of the brain is the construction of artificial brain-like systems. In this way we can encompass the multi-level organisation of the brain and its role in the context of the complete embodied real-world and real-time perceiving and behaving system. Hence, on the one hand, we must be able to develop and validate theories of brains as closing the loop between perception and action, and on the other hand as interacting with the real world. Evidence is growing that one of the sources of the computational power of neuronal systems lies in the massive and specific connectivity, rather than the complexity of single elements. To meet these challenges—multiple levels of organisation, sophisticated connectivity, and the interaction of neuronal models with the real-world—we have developed a multi-level neuronal simulation environment, iqr. This framework deals with these requirements by directly transforming them into the core elements of the simulation environment itself. iqr provides a means to design complex neuronal models graphically, and to visualise and analyse their properties on-line. In iqr connectivity is defined in a flexible, yet compact way, and simulations run at a high speed, which allows the control of real-world devices—robots in the broader sense—in real-time. The architecture of iqr is modular, providing the possibility to write new neuron, and synapse types, and custom interfaces to other hardware systems. The code of iqr is publicly accessible under the GNU General Public License (GPL). iqr has been in use since 1996 and has been the core tool for a large number of studies ranging from detailed models of neuronal systems like the cerebral cortex, and the cerebellum, to robot based models of perception, cognition and action to large-scale real-world systems. In addition, iqr has been widely used over many years to introduce students to neuronal simulation and neuromorphic control. In this paper we outline the conceptual and methodological background of iqr and its design philosophy. Thereafter we present iqr’s main features and computational properties. Finally, we describe a number of projects using iqr, singling out how iqr is used for building a “synthetic insect”.

Appendix: Predefined Neuron Types in iqr

Linear Threshold Neuron

Graded potential neurons are modelled using linear threshold cells. The membrane potential of a linear threshold cell i at time t + 1, v _i (t + 1), is given by

$$ \begin{array}{lll} \label{eq:linth-vm} v_i(t+1) &=& {VmPrs}{}_i v_i(t)\\ &&+ {ExcGain}{}_i \sum_{j=1}^{m} w_{ij} a_j(t-\delta_{ij})\\ &&- {InhGain}{}_i \sum_{k=1}^{n} w_{ik} a_k(t-\delta_{ik}) \end{array} $$

(7)

where VmPrs _i  ∈ {0,1} is the persistence of the membrane potential, ExcGain _i and InhGain _i are the gains of the excitatory and inhibitory inputs respectively, m is the number of excitatory inputs, n is the number of inhibitory inputs, w _ij and w _ik are the strengths of the synaptic connections between cells i and j and i and k respectively, a _j and a _k are the output activities of cells j and k respectively, and δ _ij  ≥ 0 and δ _ik  ≥ 0 are the delays of the projection from cell j to i and k to i respectively (Table 2).

Table 2 Overview over the parameters of the standard iqr neuron types

The output activity of cell i at time t + 1, a _i (t + 1), is given by

$$ \begin{array}{lll} \label{eq:linth-act} & &{\kern-6pt}a_i(t+1)\notag\\&& = \left\{\! \begin{array}{ll} v_i(t\!+\!1) & \mbox{with probability } \!{Prob}{}\! \mbox{ for } v_i(t\!+\!1) \!\geq \! \!{ThSet}{}\\ 0 & \mbox{otherwise} \end{array} \right.\\ \end{array} $$

(8)

where ThSet is the membrane potential threshold, and Prob is the probability of activity.

Integrate & Fire Neuron

Spiking cells are modelled with an integrate-and-fire cell model. The membrane potential is calculated using Eq. 7. The output activity of an integrate-and-fire cell at time t + 1, a _i (t + 1) is given by

$$ \begin{array}{lll} \label{eq:i&f-act} &&{\kern-6pt}a_i(t+1)\\&&{\kern3pt}=\!\left\{\! \begin{array}{ll} {SpikeAmpl}{} & \mbox{with probability } \!{Prob}{}\! \mbox{ for } v_i(t\!+\!1)\\& \geq {ThSet}{}\\ 0 & \mbox{otherwise} \end{array} \right.\\ \end{array} $$

(9)

where SpikeAmpl is the height of the output spikes, ThSet is the membrane potential threshold, and Prob is the spike probability.

After cell i produces a spike, the membrane potential is hyperpolarized such that

$$ \label{eq:i&f-reset} v_i^{'}(t+1) = v_i(t+1) - {VmReset}{} $$

(10)

where $v_i^{'}(t+1)$ is the membrane potential after hyperpolarization and VmReset is the amplitude of the hyperpolarization.

Sigmoid Neuron

The iqr sigmoid cell type is based on the perceptron cell model often used in neural networks. The membrane potential of a sigmoid cell i at time t + 1, v _i (t + 1), is given by Eq. 7. The output activity, a _i (t + 1) is given by

$$ \begin{array}{lll} \label{eq:sigmoid-act} a_i(t+1) &=& 0.5*(1 + \tanh(2*{Slope}{}\\&&*(v_i(t+1)-{ThSet}))) \end{array} $$

(11)

where Slope is the slope and ThSet is the midpoint of the sigmoid function respectively.

Random Spike Neuron

A random spike cell releases a spike per timestep with a user-defined spike probability. The time series of the output spikes forms a Poisson process. Unlike the other cell types, it receives no input and has no membrane potential. The output of a random spike cell i at time t + 1, a _i (t + 1), is given by

$$ \label{eq:randspk-act} a_i(t+1)=\left\{ \begin{array}{ll} {SpikeAmpl}{} & \mbox{with probability } {Prob}{}\\ 0 & \mbox{otherwise} \end{array} \right. $$

(12)