Physical oriented models of Nerve Nets -
hypothetic models and examples

Gerd Heinz

Subsequent models are physical reality in terms of the possibility, to verify them with physical models, with Hodgkin/Huxley-based, dynamical simulators, with PSI-Tools or with other dynamic network simulators.
Without the thumb experiment, models could not been verified in biological experiments until now.

Thumb Experiment

Result of the thumb experiment with two EEG-channels
An introductionary experiment by the author, measured by Electro-Encephalography. Stimulation of thumb by ring electrodes and recording of two nerves (n.radiali and n. medianus) shows the forthcoming of impulses in dependence of the location of the thumb. (Use a guard ring between thumb and sensor electrodes to avoid artefacts. Averaging ten times minimum). When you move the thumb position, the delay-difference between the sensor electrodes moves. The wave frontier passes more or less diagonally the sensor electrodes. When we suppose, that elsewhere (medulla spinalis, ganglion spinalis...) lay neurones in the circuit in a real distance (s), we can calculate the properties of this interference circuit with real velocities. But be care: the velocity of myelinised nerves is not usefull to calculate s. Interference circuits can be very fast - but only at transmission wires (v, w)! This simple interference circuit already demonstrates a mirrored projection (red to red, blue to blue). Thanks to Torsten Griepentrog, Landesklinik Teupitz for his help.

Three Elementary Functions of Neurons
Bursts as Neural Data Adress
Neighboorhoud Inhibition

Circuit drawing with equations

At different places in the neural net we find pulses grouped to bursts (d). At the other hand, we know, that nerves connect tree-like (b) in different ways. Acknowledged, that ("The velocity along the axon varies directly with its diameter, from less than one meter per second in thin axons, which are usually short, to more than 150 meters per second in thick axons...") nerves with the smallest diameter have the smallest velocities, it will be necessary, to create a substitute circuit (a) for that connection ("...The only significant delay within the nervous system is synaptic delay?..."). Circuit (a) produces on a single input pulse x(t) a burst with a delay mask M, if it has a low bias (OR-type). Also it can produce nothing with a high bias (AND-type). This neurone selects only a definitive pulse group, called burst. Is it possible, to find two nerve cells with the masks dependency M + M* = T, so the first neurone produces a burst, which only can receive the second neurone. The second neurone in (c) transforms the burst return to a single impulse.
We can note different things:
1) Neurons can communicate, if they have complementary masks (M + M* = T).
2) Nature have found a simple principle to address different data streams on a single axon. I suggest, to call this principle "neural data addressing".
3) With the same effect nature can use a principle to avoid neighbourhood excitement. Only neurones speak together, that have complementary masks. I propose, to call this method "neighbourhood inhibition".

Three elementary functions of neurons are known until now (see postscript documents):

First simulations (oct. 20th 1994, simulator Neuronet, FHTW Berlin, Heinz, Puschmann and Schoel) can be found at the publications chapter, postscript-file 'Projections and Coding in Pulspropagating Networks - Virtual Experiments' pages 18 and 23.

Measurment of Distances by Echo, Worldmodel

Simplified brain of a bat
Hypothetical interference model to measure any distance by echos. A generator neuron N emittes an excitement, exciting on two paths: one part is transformed into sound by the voice, the other part (red) walks slowly with speed v2 radial around the noise sensor (ear) D. In the moment the echo arrives D, an excitement expands with higher speed v1 circular from D. Then the location of an interference correlates with the distance of the echo-reflecting object. We get an interference map of the outside along the radial fibres.

Localisation of Noise

Jeffress idea according to Konishi 1993

Lloyd A. Jeffress model for noise localisation 1948 - historical the first, intermediale, projective interference circuit. Note, that the generating input map excites mirrored the detector foield - the neural network. A more right-hand noise location interferes to a more left-hand neural excitement and visa versa.

Mirrored Projections in the Spinal Cord
'Homunculus' as Hyperbolic Projection

Attention! Please avoid to infect your brain. The following, simplified model seems not to be confirm with surgeons experience nor with neuroanatomic results! It is not possible, to publish or to discuss this model in the academic press.
Against this model speeks: different, seeming right documented break down mechanisms of partial spinal cord accidents; a nerval crossing near the brain stem and the experience of neurosurgery.
The model is confirmed by: the presence of neurons in the spinal cord; a pulsewise information processing; reflexes and mirrored and topographic projections. The model creates Penfields Homunculus. Furthermore it produces field-like excitement maps in the brain in general, if we suppose the spinal cord carries more then two axons.
It is possible, that the model plays an important rule in the individual genesis.

Medulla spinalis and gyrus p.-centralis with homunculus

Simplified model of the medulla spinalis, created by the author. It is interesting, that such simple model can create Penfields 'Homunculus'. Without crossover, it produces a mirrored and height- specific projection. With PSI-Tools it can be possible, to map things more detailed, if detailed informations about delays are available.

Balancing the Skeleton

Virtual, simplified, interferential skelett stability circuit

We try to couple 30 bone-elements to create a tower high as a man, where the connection between each two elements is freely moveable. If you find an electronic controller that is able to hold this tower stable, avoid to read the rest!
If it is not possible to find such a control circuit, in accordance to the thumb-experiment we can use some parallel fibres, carrying a wave front from top to bottom. The local algorithm to get global control is: each element has to move its direction orthogonal to the wavefront, supposed the wavefront comes with any periodically 'clock'.

Chiasma Optikum and Cortical World Model

Wave interference maps in the Chiasma Optikum

We try to change the view between two different objects on our table. Because the relative position of the objects within the eye is not changed, the image must appear at the same place in visual cortex. But: we have to remark the view changes at different positions in our world model of the table too! To get such movement of maps see the 'Moving'-simulation in the picture part. The necessary delay-variation can be created from the control potential of the eye muscles.
Beside: Also the mirrored projections of the optical system appears 'interferential'. The wavelenght of impulses in the visual cortex reaches 0,1 millimeter. No wonder.

Access No. since dec. 12, 1996

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