Preamble 2024:
Simulation of sensory qualities of the skin
Here we want to investigate the question of why low excitation with a low firing rate leads to the most precise localization of a dominant individual stimulus, while strong field excitation with a high firing rate of the individual nerve leads to the practical extinction of the possibility of locating a dominant individual stimulus.
We could imagine the skin as the generator field and the detector field in the cortex.
Based on representations in neuroanatomy textbooks (Trepel, Duus, Eccles, etc.), somatotopic areas are considered to be innervated by three nerves.
From the perspective of interference networks, we are dealing with a "specific" system for which the equation k = d+1 applies (k channel number, d dimension, see "Dimension and channel number" [NI93], Chapter 7, p.148 (german).
Shingles gives us a practical impression of the sensory qualities of skin sensors. They range from hypersensitivity of the smallest areas to pain, which also causes chaotic muscle contractions and cramps in muscles directly under the skin. In detail, we find:
At the same time, we find a decrease in the sensory resolution of a source location (e.g. needle prick) in the order from top to bottom. One could assume that the idle frequency of the nervous sensors increases greatly due to the disease.
In order to clarify whether these phenomena are triggered by different receptors and stimulus conduction systems - this question seems to be answered in the affirmative by classical medicine - or whether we are dealing with a uniform sensory system whose properties only vary due to the pulse rate emitted by the sensors, this simulation of a three-channel, projective system in which only the pulse interval varies (and thus the pulse rate) was created in 1998.
Final note: the simulation parameters used here were not originally designed for the simulation of dermatomes. For the skin, the standardized unit system used for simulation should be varied by a factor of one hundred. For example, the unit of length could be assumed to be "100 mm" instead of "1 mm" and other units corrected accordingly.
With t = s/v and f = 1/t, one could therefore assume for a similar reference system* of identical speed v and with s* = 100 s also t* = 100 t and f* = 1/(100 t).
In order to maintain the historical reference, the historical first simulation results of this type from 1998 are shown here.
Gerd Heinz
In a three-channel somatotopic arrangement, it is to be investigated whether the repetition frequency of impulses, which can arise e.g. from increased pulse frequency in the generator field, but also from reduced refractoriness of axons or from conjugated phantom excitation, has an influence on the quality of the pulse interference image in the detector field.
We choose a very simple experimental setup, consisting of three connecting pathways (axons) between two neuronal fields (generator and detector field), whereby, for the sake of simplicity, it is assumed that a nerve network transmits the impulses within the fields (generator and detector) at a constant and predeterminable propagation speed.
If the time interval between the pulses is reduced, then below a certain limit cross-interferences of any pulse i with its predecessor (i-1) or successor (i+1) or further predecessors (i-n) or successors (i+n) occure in the image field of the detector. More and more cross-interferences then appears, and the self-interferences (pulses i with i) as the carrier of information can then hardly be identified. In an information technology sense, the association between generator and detector sources thus disappears, since more and more neurons are excited in the entire detector field.
If we imply that a detector field will have a higher energy turnover due to high cross interference than a field with neurons whose threshold is not reached, one could assume that increased cross-interference leads to a significantly increased energy turnover - perhaps even to a lack of oxygen and general supply.
As it is suspected that this effect could be related to pain or could represent it, we want to take a closer look at the situation in the simulation. We observe the resulting image qualities. The pulse frequency of the neurons in the generator field, which are arranged in the shape of a G for the simulation, is varied. All other parameters remain untouched.
The generator is an arrangement of pulsating points in the shape of a G. The transmitting axons originate at points 0, 1, 2. In the generator field of size (e.g. 1x1 mm) there is a constant conduction speed (e.g. 300 mm/s). Pulses have a duration of 0.2 ms. The generator and detector fields have (for the sake of simplicity) a homogeneous conduction speed, waves spread then out spherically.
The coordinates of the electrode locations in the generator and detector fields remain unchanged. Only the pulse interval is systematically varied from 7.5 to 1.5 milliseconds corresponding to 133 Hz < f < 1000 Hz (150 samples up to 20 samples at 20 kS/s).
The black pixels pulse one after the other. The generator speed is (normalized) 300, in the detector the pulses run at the normalized speed of 200. This slightly reduces the detector image. The generator and detector fields are normalized to 1x1. (If the time is measured in seconds and the space in millimeters, the conduction speed is in mm/sec).
In all simulations we assume an identical and constant runtime of the signals on the lines between the generator and detector fields. It does not matter how long this is in absolute terms (e.g. in the case of myelination). In the simulation it is assumed to be zero, it does not influence the result.
Each pulse consists of the sequence of values of the samples
PULSE SEQUENCE = 0.3000 1.0000 1.0000 1.0000 0.3000
In this case it has a flat roof and is about 0.2 ms long.
The generator produces a three-channel data stream of the following form. The time functions of the axons are 0: blue, 1: green, 2: red; the time axis is directed to the right:
If these three channels feed a detector field at locations (0, 1, 2), the result is an excitation of the type:
In our example, the values are multiplied (AND-type) at each interference location to be calculated; this is possible if no negative values occur in the time functions.
As a result, different image qualities are created in the detector field for the different pulse intervals selected (7.5 ms to 1 ms). All time functions are synthesized with 20 kSps.
If, for example, [mm] is selected as the unit of length, the unit of speed is [mm/s], and the time is fixed in seconds. In our case, the felt speed in the detector field is 200 mm/s = 0.2 m/s. The image size then corresponds to 1 mm x 1 mm.
1) 7.5 ms ~ 133 Hz 
2) 6.0 ms ~ 166 Hz 
3) 5.0 ms ~ 200 Hz 
4) 4.0 ms ~ 250 Hz 
5) 2.5 ms ~ 400 Hz 
6) 1.5 ms ~ 666 Hz 
7) 1.0ms ~ 1000Hz 
Simulation Parameters: Three-channel transmission, image field 1x1 millimeter, pulse width 0.2 ms. Conductive speeds: generator field 0.3 m/s, detector field 0.2 m/s
Up to an pulse interval of 7.5 ms (case 1), we do not observe any cross-interferences in the detector image field. From 6 ms (case 2), the first cross-interferences appeare in the upper part of the image. The higher the fire rate and the smaller the pulse interval, the stronger the cross-interferences become. At a distance of 2.5 ms (case 5), the projection of the "G" can no longer be recognised. It is then no longer possible to verify the exact location of any touch.
Automatic color calibration was used in the images in order to be able to observe qualitative characteristics. The effective values of the interference integrals increase absolutely with each additional cross interference (invisible in the images), so the average excitation in the detector field increases even more than can be seen in the images.
Since every excitation of a neuron consumes energy, the energy requirement in the detector field increases enormously with increasing firing rate.
(Addendum 2024 for shingles: Here we are probably dealing exclusively with an increase in the quiet (idle) firing rate of the neurons of the excitation field, which leads to cross-interference overflow in the detector field without excitation.)
1. Drugs that increase the threshold value of the detector neurons are almost useless, as they cannot change the situation much;
2. Drugs that reduce conduction speeds in the generator or detector field may alleviate cross interference, but may also lead to distorted images if they have different effects on the generator and detector fields (hallucinations, movement or zooming effect);
3. Drugs that reduce the firing frequency of neurons in the generator field or that of the transmitting axons (increasing the average refractory period) are effective;
4. Methods that increase the number of transmitting axons lead to greater overdetermination and thus to less cross interference; these are effective.
5. Reducing the number of channels means an increase in cross interference and thus in pain, while the firing of the field remains the same.
6. If channels are removed from a high-channel image, an overfiring effect also occurs in the detector field.
7. Depending on the threshold model, this small firing rate variation results in up to 10,000 times higher energy turnover in the detector field - in cortex massive undersupply is to be expected.
8. The effect can also be triggered by:
- pulse fire flowing into a single axon from outside
- phantom excitation in the generator-field (shingles)
- increased (!) conduction speed in the fields, e.g. also due to glia influence
Created Sept.17, 1998
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