Our model of brain activity is unusual in being explicity based on the brain's physiology. This is unusual because it is generally assumed that the legendary complexity of the brain precludes any realistic simulations -- even with supercomputers. However, we have found that, by averaging over fine structural details, we can construct a model of EEG that makes use of only a few parameters, for example the average strengths of connections between neurons, the average decay constants for neural responses, and the average speed of transmission between neurons. These simplifications are considerable, but nevertheless manage to retain the essential character of typical neurons and of extended collections of neurons like the cortex.
With the above assumptions, together with a driving signal of simple white noise, it is possible to reproduce typical EEG spectra. This is demonstrated elsewhere.
The applet below attempts to model cortical event related potentials (ERPs). The assumed brain model is identical to that used to model EEG spectra -- the difference lies only in the form of the driving signal. The stimulus used here is a spatio-temporal Gaussian: its time of arrival at the talamus and its centre (after projection to the cortex) can be ajusted, as can its width in time and space.
There is a practical application for this: by adjusting the model parameters so that the model and measured ERPs match (something we can do automatically) we are inferring the values of the parameters, and thereby quantifying the brain's physiological state. Currently the only option, where mental disorders are concerned, is to observe the behaviour of the patient. However now we can record a simple ERPs and fit the data to our model, and the derived physiological parameters can then be used as an objective measures to assist in diagnosis.
The dendritic parameters are all rate constants (1/time constant). When an impulse arrives at a neuron it creates a localized perturbation in the neuron's voltage, which then spreads through the dendritic tree, ultimately affecting the voltage at the cell `body' - the region where new impulses are generated. The parameters alpha and beta describe the typical rate fall and rise of these perturbations in neuron potentials. Since they have a (temporal) smoothing effect, they behave like lowpass filters. For simplicity we force alpha and beta to have a fixed ratio, and the thalamic rate constants (eta1 and eta2) to mirror the cortical values. (When iota appears in addition to eta, then iota refers to rate constants in the reticular nucleus.) The parameter gamma is distinct from the other rate constants: it is the ratio of cortical transmission speed and the range of cortical axons, and as such contributes directly to spatial damping, and indirectly to the power spectrum.
The gain parameters are amplifications. The ratio in output firing rate to input firing rate is a function of (a) the number of synapses, (b) the size of the perturbation produced at each synapse, and (c) the excitability of the neuron. The last of these is closely related to how close the neuron's average voltage is to its firing threshold. There are several gains because there are several systems of neurotransmitters and there are several distinct brain regions being modelled.
The delay parameter is due to the finite times involved in transmission of signals between the cortex and thalamus.
The normalization parameter is function of the overall size of the driving signal and various sources of gains and attenuation. It has no effect on the spectral shape.
The stim parameters describe the timing and location of the stimulus with respect to the measured point. The stimulus also has a temporal and spatial width, which can be specfied also.
The XYZ parameters are derived from other parameters. They represent, in a summary form, the cortical (X), corticothalamic (Y) and intrathalamic (Z) gains.
Chris Rennie