E-homeostasis - analysis for a new method of rebuilding the function of the nervous system using an external negative feedback loop

What is this website not?
Not applicable to the currently used pharmacological agent.
It is not a description of the currently existing medical device.
It is not a publication on the subject of the currently known treatment method.
In that case, what is it?
It is an analysis for a method of restoring lost information flow between areas of the human body that are in selected functional relationships.
Under certain conditions, new treatments for multiple sclerosis (MS) and other diseases where rebuilding of the nervous system is required may be implemented. The proposed method is based on the temporary use of an extracorporeal branch replacing the damaged tissue that previously correctly transmitted stimuli. After the homeostatic restoration of physiological functions, this outer bypass is removed. An algorithm for such a process is presented here.
The said solution does not concern such cases, in which the transfer of information is carried only in the volume of the environment with the omission of the linear network.
After a short analysis it is worth to familiarise with the created functional model, which is the biggest part of the publication.

Jerzy Pikala

Hard questions

Central nervous system cells maintain their functional capacity thanks to appropriate homeostatic processes.
They do not have regenerative abilities after being damaged by neurodegenerative factors.
Perhaps natural homeostatic processing at the level of the central nervous system and its dependent objects is deliberately limited in this regard?
When treating diseases such as multiple sclerosis, are we only left with behavioral action?
What negative or positive effects might there be from externally manipulating the appropriate homeostatic relationships?
Could this create a generative system that increases the progression of the current disease or will cause the initiation of a new disease entity?
Could this create a stabilizing system that will stop disease progression or will cause her cure?
The a priori model presented below is not able to answer such questions. It is possible only when analyzing the a posteriori results of implementing a new medical method.
There is something to fight for. We are considering curing diseases that have never been cured so far.

E-homeostasis in a nutshell - from the analysis to the application

The behaviour of the appropriate levels of the numerous dynamic parameters in the nature provides the negative feedback. It is a stabilizing system, in contrast to the generator, which represents the positive feedback. We will use the simplified examples. A person sits next to a bonfire in a frosty environment. It is possible to approaching to (or moving away from) the only source of heat.
In the case of negative feedback, the person stabilizes the body temperature. When the body overheats, it moves away from the heat source; when it is cold, it approaches the source of heat.
In the case of positive feedback, when the body overheats, the person approaches the source of heat and is burnt; in the case of a cold feeling, the person moves away from the source of heat and freezes.
When parameters are not continuous but discrete variables and do not adopt extreme values (e.g. temperatures possible to adjust in the physiological range), we are often helped by the behaviour event with the omission of the feedback. There is no campfire, but we are exposed to the action of the sunlight or cold wind.
When our bodies overheat, we seek shadow.
Often, behavioral events are used in parallel with other treatment methods. They can then increase the effectiveness of these methods.
For example, it can be the operation of such devices as diathermies.

In case of the disease in the nervous system, our abilities to adjust to the more favourable conditions through the external intervention are strongly limited. The big amount of information forwarded by the neuron network causes that the description of their flow is an exceptionally difficult task. Very often we are dealing with the lack of communication between the correctly operating interpreter and the activation area (we will call it the activator) to which the stimuli do not reach through the network.
The interpreter creates a relationship between a set of information about irregularities in the physiological process and a set of control instructions that restore the correctness of this process.
The activator creates a function (in this publication, for simplicity - unary), whose appropriate set of values ​​guarantees stabilization in the pathologically endangered area. The arguments for this function must be appropriately dependent (they form a set of expected values) on the instructions of the interpreter in order to guarantee the correctness of such action.
It is worth to familiarise with the proposition of solving this problem presented further.

The modeled physiological process consists of many successive stabilizing processes.
This is due to the fact that external and internal factors exert a continuous influence on a specific area of the organism.
For each forced (from outside) stabilization process, one or more cycles of adaptation to new conditions are necessary.
Their number depends on the accuracy of estimating the range of acceptable expected values of the selected physiological parameter, which provides the stabilization.

As the main system representing the fragment of the biological neural network between the interpreter and the activator we will use the modelled replacement neuron - similarly to the replacement circuit known from electrotechnology.
We will try to fill the lacks in its processing through the use of a parallel external e-neuron.
The e-neuron will be the exact copy of the main neuron, however, the values on its inputs will differ due to the errors made during their calculation. This will be explained in a while when the so-called interpretation processing function will be defined for the needs of the presentation.
The external branch of the e-homeostasis will constitute as a bridge bypassing the one of the homeostasis loops compromised by a disease.

After clicking the Application button, you will be directed to considerations regarding one of the hypothetical possibilities of using the proposed solution.
It is a proposal for a new method of rebuilding the nervous system in the treatment of multiple sclerosis and other diseases.

However, it is worth to familiarise earlier with the important realizations in the functional model the description of which is presented below.
They concern the meeting of the conditions during the recovery of data from the interpreter and the ability to convert them into the form appropriate for the activator.

Replacement neuron

The modelled replacement neuron, presented on the picture below, has the ability to learn.
In the cycle of durning its learning, atomic unit is the k-this era symbolically presented as e_k.
The value of the response at the output of the neuron ou(e_k) is equal to the sum of the products of the values of weights set by the interpreter for the current era we_i(e_k) and the corresponding initial values (constants in the current stabilization process) at the inputs in_i(e₀).
The value on the neuron exit created during the era is comparable with the so-called expected value ev, which in the examined model remains selected for each learning cycle from the closed compartment between sv and hv i.e. from 0.9 up to 1.1.

The error made by the neuron in response to the set input values constitutes the difference between the expected value and the value on exit: ey(e_k)=ev−ou(e_k).
On its basis are calculated the adjustments for specific weights: aw_i=ey(e_k)∗lr∗in_i(e₀). The so-called learning rate lr is a constant value and in the further examinations it is equal to 0.9.
The values of the new weights for the subsequent era will amount to: we_i(e_k+1)=we_i(e_k)+aw_i.
The neuron teaching process progresses to the moment when the value on its exit will be equal (only theoretically - in our model the allowed difference module is not bigger than 0.01) to the expected value, which is then forwarded to the activator as the argument for activation function. At the same time the current cycle that is the macroscopic unit in time of the whole stabilisation process is ended.

Powering the e-neuron inputs

It is known that the general operations of the interpreters are possible to observe. For example, the impulses generated by the brain have been already discovered by Hans Berger in 1929.
We only see the resultants of vectors of voltage changes and it is very difficult to separate (at the exceptionally limited possibilities today - after almost one hundred years) the accurate waveforms of the specific interpreter. In addition, they are very often supressed by the surrounding tissues.

In the examined model, for ease, it has been adopted that the measured values are determined with the appropriate suppression functions separate for each input of the main neuron: dv_i=fd_i(we_i(e_k)∗in_i(e₀)).
The supressed signals are then individually amplificathened and such activities describe the gain functions approximately inverse for the suppression functions corresponding to them: fr_i()≅fd_i()⁻¹. Their composite provide the practically calculated values of the signals generated by the interpreter.
The composite of both functions give the interpretation processing functions: fr_i(fd_i())=ft_i(we_i(e_k)∗in_i(e₀)). The recovered approximate values on the interpreter exits are presented on the picture in the red fields. They are used to power inputs the external e-neuron.
Their relative errors (generated randomly for each stabilisation process) different for each input are contained in this publication between −50% and +50%.

Estimating the expected value

The activation function behaves like the electronic comparator, which is very important for the ability to use the e-homeostasis.
The correct reaction on the output of the model activator occurs when the argument value of the activation function is within the closed compartment (activation window) with a width of w.
Its border values are declared at random for each stabilisation process.
When the expected value belongs to this range, then the sufficient condition for achieving the stabilisation is met.
The existence of at least one of at common value from the activation window and the compartment in the scope from sv to hv is in this case a necessary condition.

We will create an important parameter (marked by us with the m symbol) calculated as the upper feature from the division of the sv−hv difference by the w value and increased by 1, that is: m=1+⌈(sv−hv)/w⌉.
It determines the sufficient amount of trials of estimating the expected value for the success of the stabilisation process.
For example, for sv=0.9 and hv=1.1 and w=0.03, m=8.
This means that for this case it will suffice to perform maximum 8 teaching cycles in order to achieve the stabilisation of the process.
At the happyest estimate of the expected value, one learning cycle is sufficient. With the most unlucky estimation, the necessary number of learning cycles is equal to m.

Achieving stabilization

Stabilization is a temporary condition.
Variable external and internal factors have a continuous impact on the stabilized area. The physiological parameters again reach values that need correction.
The corresponding receptors define the new value expected for Era 0 starting the next stabilization process.

The external loop of e-homeostasis is removed after the main neuron has taken control of the process.
When the main neuron does not take over the physiological functions, the e-loop remains in the system until such activities are restored.

To progress to the next part press the Era 0 button located under the picture.