Evolutionary brain model The "triune theory of the brain" McLean, P. (2003) is one of several models used to theorize the organizational structure of the brain. The most ancient neural structure of the brain is the brain stem or "lizard brain". The second phase is limbic or paleo-mammalian brain and performs the four functions needed for animal survival – fighting, feeding, fleeing, and fornicating. The third phase is the neocortex or the neo-mammalian brain. The higher cognitive functions which distinguish humans from other animals are primarily in the cortex. The reptilian brain controls muscles, balance, and autonomic functions, such as breathing and heartbeat. This part of the brain is active, even in deep sleep. The
limbic system includes the
hypothalamus, hippocampus, and amygdala. The neocortex includes the cortex and the cerebrum. It corresponds to the brain of primates and, specifically, the human species. Each of the three brains is connected by nerves to the other two, but each seems to operate as its own brain system with distinct capacities. (See illustration in
Triune brain.)
PDP / connectionist model The connectionist model evolved out of Parallel Distributed Processing framework that formulates a metatheory from which specific models can be generated for specific applications. PDP approach (Rumelhart, J. L., McClelland, J. L., and PDP Research Group (1986)). In the structural brain connectivity type, the connectivity is a sparse and directed graph. The functional brain connectivity has bidirectional graphs. The effective brain connectivity is bidirectional with interactive cause and effect relationships. Another representation of the connectivity is by matrix representation (See Sporns, O. (2007)). Neural Simulation Language (NSL) has been developed to provide a simulation system for large-scale general neural networks. It provides an environment to develop an object-oriented approach to brain modeling. NSL supports neural models having as basic data structure neural layers with similar properties and similar connection patterns. Models developed using NSL are documented in Brain Operation Database (BODB) as hierarchically organized modules that can be decomposed into lower levels.
Artificial neural networks As mentioned in Section 2.4, development of artificial neural network (ANN), or neural network as it is now called, started as simulation of biological neuron network and ended up using artificial neurons. Major development work has gone into industrial applications with learning process. Complex problems were addressed by simplifying the assumptions. Algorithms were developed to achieve a neurological related performance, such as learning from experience. Since the background and overview have been covered in the other internal references, the discussion here is limited to the types of models. The models are at the system or network level. The four main features of an ANN are topology, data flow, types of input values, and forms of activation (Meireles, M. R. G. (2003), Munakata, T. (1998)). Topology can be multilayered, single-layered, or recurrent. Data flow can be recurrent with feedback or non-recurrent with feedforward model. The inputs are binary, bipolar, or continuous. The activation is linear, step, or sigmoid. Multilayer Perceptron (MLP) is the most popular of all the types, which is generally trained with back-propagation of error algorithm. Each neuron output is connected to every neuron in subsequent layers connected in cascade and with no connections between neurons in the same layer. Figure 4 shows a basic MLP topology (Meireles, M. R. G. (2003)) that most are familiar with. We can equate the routers at the nodes in telecommunication network to neurons in MLP technology and the links to synapses.
Computational neuron models Computational neuroscience is an interdisciplinary field that combines engineering, biology, control systems, brain functions, physical sciences, and computer science. It has fundamental development models done at the lower levels of ions, neurons, and synapses, as well as information propagation between neurons. These models have established the enabling technology for higher-level models to be developed. They are based on chemical and electrical activities in the neurons for which electrical equivalent circuits are generated. A simple model for the neuron with predominantly potassium ions inside the cell and sodium ions outside establishes an electric potential on the membrane under equilibrium, i.e., no external activity, condition. This is called the resting membrane potential, which can be determined by Nernst Equation (Nernst, W. (1888)). An equivalent electrical circuit for a patch of membrane, for example an axon or dendrite, is shown in Figure 5. EK and ENa are the potentials associated with the potassium and sodium channels respectively and RK and RNa are the resistances associated with them. C is the capacitance of the membrane and I is the source current, which could be the test source or the signal source (action potential). The
resting potential for potassium-sodium channels in a neuron is about -65 millivolts. The membrane model is for a small section of the cell membrane; for larger sections it can be extended by adding similar sections, called compartments, with the parameter values being the same or different. The compartments are cascaded by a resistance, called axial resistance. Figure 6 shows a compartmental model of a neuron that is developed over the membrane model. Dendrites are the postsynaptic receptors receiving inputs from other neurons; and the axon with one or more axon terminals transmits neurotransmitters to other neurons. The second building block is the Hodgkin-Huxley (HH) model of the action potential. When the membrane potential from the dendrites exceeds the resting membrane potential, a pulse is generated by the neuron cell and propagated along the axon. This pulse is called the action potential and HH model is a set of equations that is made to fit the experimental data by the design of the model and the choice of the parameter values. Models for more complex neurons containing other types of ions can be derived by adding to the equivalent circuit additional battery and resistance pairs for each ionic channel. The ionic channel could be passive or active as they could be gated by voltage or be ligands. The extended HH model has been developed to handle the active channel situation. Although there are neurons that are physiologically connected to each other, information is transmitted at most of the synapses by chemical process across a cleft. Synapses are also computationally modeled. The next level of complexity is that of stream of action potentials, which are generated, whose pattern contains the coding information of the signal being transmitted. There are basically two types of action potentials, or spikes as they are called, that are generated. One is "integrate-and-fire" (the one we have so far addressed) and the other which is rate based. The latter is a stream whose rate varies. The signal going across the synapses could be modeled either as a deterministic or a stochastic process based on the application (See Section 3.7). Another anatomical complication is when a population of neurons, such as a column of neurons in visionary system, needs to be handled. This is done by considering the collective behavior of the group (Kotter, R., Nielson, P., Dyhrfjeld-Johnson, J., Sommer, F. T., & Northoff, G. (2002)).
Spiking neuron models The action potential or the spike does not itself carry any information. It is the stream of spikes, called spike train, that carry the information in its number and pattern of spikes and timing of spikes. The postsynaptic potential can be either positive, the excitatory synapse or negative, inhibitory synapse. In modeling, the postsynaptic potentials received by the dendrites in the postsynaptic neuron are integrated and when the integrated potential exceeds the resting potential, the neuron fires an action potential along its axon. This model is the Integrate-and-Fire (IF) model that was mentioned in Section 2.3. Closely related to IF model is a model called Spike Response Model (SRM) (Gerstner, W. (1995)).
Nervous system development models No generalized modeling concepts exist for modeling the development of anatomical physiology and morphology similar to the one of behavior of neuronal network, which is based on HH model. Shankle, W. R., Hara, J., Fallon, J. H., and Landing, B. H. (2002) describe the application of neuroanatomical data of the developing human cerebral cortex to computational models. Sterratt, D., Graham, B., Gillies, A., & Willshaw, D. (2011) deal with the optimization of the computerized models of the visual cortex.
Modeling tools With the enormous number of models that have been created, tools have been developed for dissemination of the information, as well as platforms to develop models. Several generalized tools, such as GENESIS, NEURON, XPP, and NEOSIM are available and are discussed by Hucka, M. (2002). ==See also==