Part 4

16. Hodgkin, A. L., and Huxley, A. F., “The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo,” J. Physiol. =116=:497-506 (1952)

17. Hodgkin, A. L., and Huxley, A. F., “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve,” J. Physiol. =117=:500-544 (1952)

18. Lewis, E. R., “An Electronic Analog of the Neuron Based on the Dynamics of Potassium and Sodium Ion Fluxes,” “Neural Theory and Modeling,” R. F. Reiss, ed., Palo Alto, California:Stanford University Press, 1964

19. Eccles, J. C., Physiology of Synapses, Berlin:Springer-Verlag, 1963

20. Grundfest, H., “Excitation Triggers in Post-Junctional Cells,” “Physiological Triggers,” T. H. Bullock, ed., Washington, D.C.:American Physiological Society, 1955

21. Rall, W., “Membrane Potential Transients and Membrane Time Constants of Motoneurons,” Exp. Neurol. =2=:503-532 (1960)

22. Araki, T., and Otani, T., “The Response of Single Motoneurones to Direct Stimulation,” J. Neurophysiol. =18=:472-485 (1955)

23. Moore, G. P., Perkel, D. H., and Segundo, J. P., “Stability Patterns in Interneuronal Pacemaker Regulation,” Proceedings of the San Diego Symposium for Biomedical Engineering, San Diego, California, 1963

24. Eccles, J. C., The Neurophysiological Basis of Mind, Oxford:Clarendon Press, 1952

Fields and Waves in Excitable Cellular Structures

R. M. STEWART

Space General Corporation El Monte, California

“Study of living processes by the physiological method only proceeded laboriously behind the study of non-living systems. Knowledge about respiration, for instance, began to become well organized as the study of combustion proceeded, since this is an analogous operation....”

J. Z. Young (24)

INTRODUCTION

The study of electrical fields in densely-packed cellular media is prompted primarily by a desire to understand more fully the details of brain mechanism and its relation to behavior. Our work has specifically been directed toward an attempt to model such structures and mechanisms, using relatively simple inorganic materials.

The prototype for such experiments is the “Lillie iron-wire nerve model.” Over a hundred years ago, it had been observed that visible waves were produced on the surface of a piece of iron submerged in nitric acid when and where the iron is touched by a piece of zinc. After a short period of apparent fatigue, the wire recovers and can again support a wave when stimulated. Major support for the idea that such impulses are in fact directly related to peripheral nerve impulses came from Lillie around 1920. Along an entirely different line, various persons have noted the morphological and dynamic similarity of dendrites in brain and those which sometimes grow by electrodeposition of metals from solution. Gordon Pask (17), especially, has pointed to this similarity and has discussed in a general way the concomitant possibility of a physical model for the persistent memory trace.

For review articles see: Lillie (13), Franck (6).

By combining and extending such concepts and techniques, we hope to produce a macroscopic model of “gray matter,” the structural matrix of which will consist of a dense, homogeneously-mixed, conglomerate of small pellets, capable of supporting internal waves of excitation, of changing electrical behavior through internal fine-structure growth, and of forming temporal associations in response to peripheral shocks.

A few experimenters have subsequently pursued the iron-wire nerve-impulse analogy further, hoping thereby to illuminate the mechanisms of nerve excitation, impulse transmission and recovery, but interest has generally been quite low. It has remained fairly undisturbed in the text books and lecture demonstrations of medical students, as a picturesque aid to their formal education. On the outer fringes of biology, still less interest has been displayed; the philosophical vitalists would surely be revolted by the idea of such models of mind and memory, and at the other end of the scale, contemporary computer engineers generally assume that a nerve cell operates much too slowly to be of any value. This lack of interest is certainly due, in part, to success in developing techniques of monitoring individual nerve fibers directly to the point that it is just about as easy to work with large nerve fibers (and even peripheral and spinal junctions) as it is to work with iron wires. Under such circumstances, the model has only limited value, perhaps just to the extent that it emphasizes the role of factors other than specific molecular structure and local chemical reactions in the dynamics of nerve action.

When we leave the questions of impulse transmission on long fibers and peripheral junctions, however, and attempt to discuss the brain, there can be hardly any doubt that the development of a meaningful physical model technique would be of great value. Brain tissue is soft and sensitive, the cellular structures are small, tangled, and incredibly numerous. Therefore (Young (24)), “ ... physiologists hope that after having learned a lot about nerve-impulses in the nerves they will be able to go on to study how these impulses interact when they reach the brain. , we must not assume that we shall understand the brain only in the terms we have learned to use for the nerves. The function of nerves is to carry impulses—like telegraph wires. The functions of brains is something else.” But, confronted with such awesome experimental difficulties, with no comprehensive mathematical theory in sight, we are largely limited otherwise to verbal discourses, rationales and theorizing, a hopelessly clumsy tool for the development of an adequate understanding of brain function. A little over ten years ago Sperry (19) said, “Present day science is quite at a loss even to begin to describe the neural events involved in the simplest form of mental activity.” This situation has not changed much today. The development, study, and understanding of complex high-density cellular structures which incorporate characteristics of both the Lillie and Pask models may, it is hoped, alleviate this situation. There would also be fairly obvious technological applications for such techniques if highly developed and which, more than any other consideration, has prompted support for this work.

Experiments to date have been devised which demonstrate the following basic physical functional characteristics:

(1) Control of bulk resistivity of electrolytes containing closely-packed, poorly-conducting pellets (2) Circulation of regenerative waves on closed loops (3) Strong coupling between isolated excitable sites (4) Logically-complete wave interactions, including facilitation and annihilation (5) Dendrite growth by electrodeposition in “closed” excitable systems (6) Subthreshold distributed field effects, especially in locally-refractory regions.

In addition, our attention has necessarily been directed to various problems of general experimental technique and choice of materials, especially as related to stability, fast recovery and long life. However, in order to understand the possible significance of, and motivation for such experiments, some related modern concepts of neurophysiology, histology and psychology will be reviewed very briefly. These concepts are, respectively:

(1) Cellular structure in the central nervous system (2) Short-term or “ephemeral” memory (3) The synapse (4) Inhibition (5) Long-term memory traces or engram (6) Spatially-diffuse temporal association and learning.

SOME CONTEMPORARY CONCEPTS

Since we are attempting to duplicate processes other than chemical, per se, we will forego any reference to the extensive literature of neurochemistry. It should not be surprising though if, at the neglect of the fundamental biological processes of growth, reproduction and metabolism, it proves possible to imitate some learning mechanisms with grossly less complex molecular structures. There is also much talk of chemical versus electrical theories and mechanisms in neurophysiology. The distinction, when it can be made, seems to hinge on the question of the scale of size of significant interactions. Thus, “chemical” interactions presumably take place at molecular distances, possibly as a result of or subsequent to a certain amount of thermal diffusion. “Electrical” interactions, on the other hand, are generally understood to imply longer range or larger scale macroscopic fields.

1. Cellular Structure