Stahl674 bmp

198 WALTER R. STAHL

not all necessary numerical constants are available in vivo to validate such very intricate models, which must therefore be considered as semi-quantitative partial simulators, govemed by a variety of physical and numerical invariants.

VIII. Neurophysiological Models

This class of models includes simulations of neurons, electrical be-havior of the brain, biochemical basis of memory, conditioned reflexes, and integrated brain functions other than thinking algorithms as such. It has not as yet been possible to create synthetic biochemical neurons and the cited models are clearly only partial ones, representing special aspects of nervous system function. The pertinent similarity criteria may vary from dimensionless variables madę up of electrical membranę parameters to purely phenomenological “performance scores” for an eyeball or arm tracking control system model.

A. Models of Neurons and Nerve Fibers

Mathematical representation and modeling of neurons and nerve fibers has been discussed in a long series of reports by Cole (1962). The well-known Hodgkin-Huxley eąuations goveming propagation of the nerve impulse and electrical membranę phenomena can be characterized as being a very adeąuate numerical model of the nerve fiber. The similarity invariants include a number of dimensional constants and some dimensionless ratios reąuired for solution of these eąuations. The form of the eąuations also implies relational criteria, as is true of all repre-sentations of physical action by differential eąuations. Rall (1962) has described a model of the neuron dendritic tree based on the same generał principles.

There have been many attempts to represent by mathematical means the electrical signal development in the brain; some of these are specif-ically concemed with models. Adey (1964) offers an integrated electrical model of mechanisms in the hippocampus, whereas Freeman (1964) proposed eąuations for a feedback model of individual neurons that leads to the observed types of over-all electrical activity in parts of the mam-malian cortex. The molecular biochemical basis of brains, and particu-larly memory function, is considered in a symposium volume edited by F. O. Schmitt (1962). This includes reports on “molecular memory models” and many other kinds of simulations.