Brain structure

The brain is the core of the nervous system in most of the species of the Animal Kingdom: vertebrates and invertebrates. Octopuses, for instance, are remarkable because of their complex brains which lead to intelligent behavioural patterns. It is well known, for example, that octopuses are able to open closed jars.

Dogfish shark brain, “The soul of man”, P. Carus, 1905.

Among insects, bees stand out among the species with the largest mini-brain: a total of 900,000 neurons whose intricate interconnections allow these insects to remember the location of the flower fields and the path required to reach them, and to transmit this information to the rest of the hive by means of the “bee dance” studied by the ethologist and Medicine Nobel Prize Karl von Frisch in the middle of last century.

Honeybee (Apis mellifera) collecting nectar. Bees are considered the “Rolls Royce” of the neuroscience of insects due to the size and organization of their mini-brain.

In terms of complexity (but not relative size), the human brain evolved over the past 2 million years to become the finest in the world. With a total of ten billion neurons (as many as stars in a typical galaxy) and ten thousand connections (synapses) per neuron, the human brain can be described as the most complex physical system of the known Universe. Trying to unravel, or at least put some light on how these complex systems are capable of carrying out the tasks for which they have been designed by evolution: pattern recognition, memory, behavioral planning, intelligence and even consciousness, is the focus of current neuroscience.

Cellular Automata Model

A model that captures the essential structure of the brain must contain a large number of units, called “nodes”, which are interconnected by links representing synapses as shown in the figure below:

Each node or neuron can be simulated with three states:

(i) neuron at rest, one which is capable of being excited by the neighbours in the network structure to which it’s connected.

(ii) active neuron, one which is emitting electro-chemical impulses through its dendrites.

(iii) refractory neuron, one which has recently stopped firing and must undergo a period of time before returning to idle.

Resting neurons can be excited with a certain probability by active neurons in the previous time step.

So defined, our model shows similarities with the SIRS model (Susceptible-Infected-Recovered-Susceptible) Mathematical Epidemiology, where resting neurons play the role of individuals susceptible to disease, active neurons are infected individuals and refractory correspond with recovered.

It is quite common in Applied Mathematics that the same model developed with very different goals naturally emerge in another completely different field of research.

So, this is a cellular automaton model: A mathematical model in which a set of units called automata evolve according to a predetermined set of rules creating highly complex patterns, some of which can be found in Nature, and that were studied by S. Wolfram, creator of Mathematica program (see A New Kind of Science Online, S. Wolfram, http://www.wolframscience. com/nksonline/toc.html )

A marine snail whose shell structure shows a pattern similar to that generated by Rule 30 of Wolfram. Photo: Richard Ling richard@research.canon.com.au, 2005.

Experience in BOINC projects for epidemic (Respiratory Syncytial Virus) allows us to build up a model to study the propagation of signals in a simulated brain. The mini-brain study will have a million neurons which puts it in the range of advanced brains among insects.

Project Aims

Although our model of simulated mini-brain neurons has the same number of neurons as the one of a bee, we do not intend, of course, to explains the entire repertoire of behaviours of a real bee. Our goal, more modest, is to explain the collective activity typical of the neural network.

It is known that brain oscillations, quasi-periodic behaviour in rhythmic brain electrical activities, are present from insects to humans. In the case of bees, locusts, or the fruit fly, oscillations in connection with the encoding of odour have been found .

In the case of human beings, the purpose of these oscillations appears to have been shaped by evolution. Theta waves appear to be associated with memory, attention and even consciousness.

These oscillations allow insects to discriminate between very similar odours.

An oscillation of 10 Hz. Local potential represents the activity of a large number of neurons.

What are we computing?

This project will explore the parameter space of the model to determine those regions that could correspond to the synchronous activity of the brain and explain its role in odour discrimination tasks (in insects) or memory and attention (in humans).

For each Work Unit the model provides a network of 1,000,000 generated neurons with a specific degree of connectivity k. It uses two types of neurons:

inhibitory neurons
These neurons, when active, have the effect of inhibiting the excitation of a resting neuron that could be activated by a neighbouring excitatory neuron.

excitatory neurons
These neurons, when active, are able to trigger (excite) their resting neighbours.

The model assigns to each type of neuron one of the above three possible states (resting, activated or refractory) and chooses a range of interconnection values between neurons, and then it checks if these values provide a synchrony in neuronal activity and therefore if the suggested model is feasible or not.