Passive Spread Current (continued)

[somasimple]

Are you computing it using AP height at the node, the A value, and the length constant of the internode?

from the abstract;

Average internodal conduction time for normal ventral root fibres of internodal length between 0·75 and 1·45 mm is 19·7 ± 4·6 (S.D.) μsec at 37° C. Internodal conduction time appeared to show a minimum for fibres of internodal length 1·0 mm.

 

[somasimple]

Here is a graph that shows the problems with myelinated fibers.

 

[Dale]

Energy/momentum and the graph I provide (where you agreed) implies a solution of continuity (discontinuity) in the electric signal.

So as I understand what you are saying, your only objection to the cable theory is that it introduces some "discontinuity" in the signal which somehow violates the conservation of energy or conservation of momentum? Is this correct or did I misunderstand your objection?

Strictly speaking electromagnetic signals propagate at a finite speed and carry momentum, but all of circuit theory is based on the "small circuit" assumption. This is essentially the assumption that the size of the circuit is much smaller than one wavelength of the frequencies that will be used. Under that assumption the electrical signal can propagate instantaneously, or in other words for small enough circuits or low enough frequencies the speed of light is treated as infinite. Here we are talking about frequencies of a few kHz or less and distances of a few mm, so the assumption is very reasonable.

Your rejection of that assumption strikes me as rather silly. By insisting on treating the speed of light as finite in the neuron you will not improve the accuracy of anything since you will be correcting an effect that is ridiculously far below the experimental noise.

 

[somasimple]

A electric traveling wave must have one and only one time value per distance value because time is varying and wave moves (velocity>0).
A electric traveling wave must have one and only one electric value per time value because time is varying and wave moves (velocity>0).

May I rephrase these confusing assertions like this:
If a single electric traveling wave is initiated along a path (wire), there is one and only one wave that travels.

So as I understand what you are saying, your only objection to the cable theory is that it introduces some "discontinuity" in the signal which somehow violates the conservation of energy or conservation of momentum? Is this correct or did I misunderstand your objection?

Much more. If an AP is initiated along a myelinated axon then the cable theory expects one and only one AP at the time. The facts say the contrary. If there is only two then you have an energy problem.
If there is a continuity as expected in a wire you must able to draw all the transitions between a node and the next. If there is a discontuinity then the cable is cut or this is not a cable.

Under that assumption the electrical signal can propagate instantaneously, or in other words for small enough circuits or low enough frequencies the speed of light is treated as infinite. Here we are talking about frequencies of a few kHz or less and distances of a few mm, so the assumption is very reasonable.

It seems silly to violate the laws of Physics at any scale because it may provoke reasonably mistakes and false conclusions.
A computer works at the nano second scale and respects physics...

Your rejection of that assumption strikes me as rather silly. By insisting on treating the speed of light as finite in the neuron you will not improve the accuracy of anything since you will be correcting an effect that is ridiculously far below the experimental noise.

It seems irrational to contest recorded facts. Have you some references (other than theoretic) that contest the ones I brought?

 

[somasimple]

Your rejection of that assumption strikes me as rather silly. By insisting on treating the speed of light as finite in the neuron you will not improve the accuracy of anything since you will be correcting an effect that is ridiculously far below the experimental noise.

Insisting on this point increases the energetic problem and kills the cable theory because you increase the overlapping. The cable theory needs (in some way) a delay you seems to reject.
Your rejection of that assumption strikes me as rather silly.

 

[somasimple]

I'm preparing a movie that shows the discontinuity.
The movie will be based upon the strict facts.

 

[somasimple]

The "event" that you define to travel in the internode would correspond roughly to a fixed "phase" of the AP. Because the AP is changing shape and decaying in the internode, and also because a passive cable has no traveling wave solutions, the "phase" of an AP in the internode in cable theory can only be indirectly defined.

Strictly speaking electromagnetic signals propagate at a finite speed and carry momentum, but all of circuit theory is based on the "small circuit" assumption. This is essentially the assumption that the size of the circuit is much smaller than one wavelength of the frequencies that will be used. Under that assumption the electrical signal can propagate instantaneously, or in other words for small enough circuits or low enough frequencies the speed of light is treated as infinite. Here we are talking about frequencies of a few kHz or less and distances of a few mm, so the assumption is very reasonable.

NO! Violation of light speed, infinite energy => IMPOSSIBLE.
Unfortunately I have some other "electrical" objections because a passive component is bidirectional.

 

[Dale]

It seems silly to violate the laws of Physics at any scale because it may provoke reasonably mistakes and false conclusions.

If that is your position then the remainder of the discussion is pointless. You are rejecting all of circuit theory and therefore HH and cable theory as well since both use circuit theory. If you don't understand the difference between violating the laws of physics and taking a reasonable approximation to an appropriate limiting case, then you will need to do a full general relativistic and quantum mechanical treatment of the subject.
Good luck with that.

A computer works at the nano second scale and respects physics.

Actually, no, according to you a computer violates the laws of physics. Your computer, telephone, light bulbs, and every other electronic gadget you have was designed using the circuit theory that you reject, including the small circuit approximation that you claim violates the laws of physics rather than being a reasonable limiting case.

Your irrational bias clouds your outlook so much that you cannot even see the evidence that circuit theory works, evidence which is right in front of you as you read these words on a computer screen.

 

[somasimple]

Because the AP is changing shape and decaying in the internode

You reject the facts and your theory, Dalespam! That is a pity!
How can you observe such a decay or phase shift within an event that has a null duration?

Actually, no, according to you a computer violates the laws of physics. Your computer, telephone, light bulbs, and every other electronic gadget you have was designed using the circuit theory that you reject, including the small circuit approximation that you claim violates the laws of physics rather than being a reasonable limiting case.

A so little argument. I'm working with a simulator that help to create computer and used all around the world in electronics...

http://www.spectrum-soft.com/index.shtm
http://www.spectrum-soft.com/demo/schemati.shtm

Here is the cables
http://www.spectrum-soft.com/demo/ibis.shtm
http://www.spectrum-soft.com/demo/ltra.shtm

And as I said, I have a little experience in DSP.
http://www.algoless.com/courantscarre.pdf (Sorry it is in French).

 

[atyy]

[*]An electric signal is temporal. Then you must have one and only one electric value per time value.

This statement should be corrected to "Then you must have one and only one electric value per time value at any particular spatial position".

Does an axon myelinated or not follow strictly these laws?

How can you observe such a decay or phase shift within an event that has a null duration?

Unfortunately I have some other "electrical" objections because a passive component is bidirectional.

Do Huxley and Stämpfli model and discuss these points? If they do, what are their solutions? Are their solutions in accord with the laws of physics? Are their solutions reasonable? What would you suggest as improvements to their solutions? (I will probably not have the time to discuss with you within the next month or two, but if you have time to describe your answers, I would be interested in reading them.)

 

[somasimple]

Do Huxley and Stämpfli model and discuss these points? If they do, what are their solutions? Are their solutions in accord with the laws of physics? Are their solutions reasonable?

I'll dig these points but not aware, actually, of such a discussion.

 

[Dale]

I'm working with a simulator that help to create computer and used all around the world in electronics...

http://www.spectrum-soft.com/index.shtm
http://www.spectrum-soft.com/demo/schemati.shtm

Do you even realize that the software you are using is entirely based on circuit theory and the small circuit assumption that you so emphatically and unreasonably reject? Your use of it seems rather self-contradictory since you believe the following about circuit theory:

NO! Violation of light speed, infinite energy => IMPOSSIBLE.

Based on your statements here and in other threads your ultimate goal should probably be a full quantum-mechanical treatment of the action potential. If done well, such work would undoubtedly be published since it would be interesting. But nobody would use it because it wouldn't be any more accurate than the standard theory and it would take several orders of magnitude more computational power. All anyone would do is cite your work as a further justification for why the HH and cable theory models are sufficient.

In any case until you accept circuit theory there is no reason to discuss HH or cable theory, since circuit theory is fundamental to both. If you wish to have a discussion on circuit theory then you should probably start a thread in the EE forum.

 

[atyy]

The first excellent query raised by somasimple in this thread is: what is an appropriate model in which to understand Huxley and Stämpfli's records of the fast but finite AP propagation speed in the internode of a myelinated axon?

Huxley and Stämpfli themselves describe nodes as "active" and internodes as "passive". A naive application of linear passive cable theory gives an infinite speed of propagation for the minimal disturbance, and does not allow traveling wave solutions from which a signal velocity may be easily defined. This does not necessarily mean that a signal velocity cannot be defined, only that we may have to be careful about it. We should, however, ask whether Huxley and Stämpfli and cable theory use "passive" in the same sense. The HS model of myelinated axons appears to be a modification of the HH model for unmyelinated axons, and may therefore be relevant. In fact, a similar question about the meaning of "active" and "passive" can be asked about unmyelinated axons, as somasimple previously indicated.

The quotes in blue are somasimple's queries from an earlier thread: https://www.physicsforums.com/showthread.php?t=254044.

The Action Potential propagation involves a passive event called: Passive Spread or Electrotonic conduction.
Here is some references:
[NB: I have edited the quote by numbering the references - atyy]
R1 http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mcb.figgrp.6138
R2 http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=.0zyfzkapx787Lxyk2TNcPpbCOnVmwIAZMxK6R2
R3 http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mcb.figgrp.6145
R4 http://butler.cc.tut.fi/~malmivuo/bem/bembook/03/03.htm
It is defined a Constant Length that enables this passive event.

I brought these examples because they are the rare that have temporal values.
http://hawk.med.uottawa.ca/public/re...pagationAP.pdf
http://www.ncbi.nlm.nih.gov/books/bv...cb.figgrp.6145
This one says that the AP (of 2 ms duration) travels/runs at 1 mm/ms. So it must be a thin fiber since it runs at 1m/s. The space constant of such a fiber is around 0.1/0.2 mm but the "length" of the AP is 2mm. Centered on the peak value of the AP, the space constant is too short to activate any next patch of membrane.

I consider the queries excellent because R1 and R2 use the term "passive" in describing AP propagation, but as stated in post #29 of this thread:

So in fact, the linear passive cable equation is NOT the standard model for AP propagation in unmyelinated axons and somasimple is absolutely correct on that point!

Furthermore, R4, a discussion of linear passive cable theory for neurons, is a chapter entitled "subthreshold membrane phenomena", and therefore explicitly excludes APs. The reason AP length can be greater than the passive space constant is that the HH model includes passive and active elements, with no purely passive patch in the unmyelinated axon. R2 indicates this schematically with active Na⁺ channels distributed continuously along the entire axon length.

Now, if the HH model for unmyelinated axons contains both passive and active elements, then it presumably faces the same problem that the minimal disturbance propagates in a passive circuit with infinite velocity. Yet the HH model derives, in conjunction with the active elements, a traveling wave equation with well-defined finite signal propagation velocity. This may be relevant to understanding the HS model, since it is a modification of the HH model. R4 links to the following chapter which discusses the integration of passive and active elements in the HH model:
http://butler.cc.tut.fi/~malmivuo/bem/bembook/04/04.htm

A second excellent query raised by somasimple in this thread concerns the birectionality of the passive elements, whereas AP travel is unidirectional. R3 suggests that this may again be resolved by considering the integration of passive and active elements:
http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mcb.figgrp.6145

Finally, I note that somasimple's queries are not arcane, but pertain to multiple sclerosis, a disease of myelination.

 

[somasimple]

Do you even realize that the software you are using is entirely based on circuit theory and the small circuit assumption that you so emphatically and unreasonably reject? Your use of it seems rather self-contradictory since you believe the following about circuit theory:

I do not understand why you insist that way?
The software obeys to Physics and must not violate any basic rules:
A unique electric value per time value: It comes from the di/dt or dv/dt that must be finite. In other cases, you need a infinite energy. I'm sure a neuron has not.
A cable has a delay that is proportional with distance <=> The delay exists at any scale. If the distance is short, the delay is also short but is it negligible? The software does not neglect any delay because it is able to simulate circuits that work at very high frequencies (> 10 GHz). Delays become critical at such frequencies. In brief, it respectfully follows the fate of Physics: an object can't have two places at the same time and can't move from A to B (even a µm) instantly. It comes from the dl/dt that must be finite.
I think you may ask the software's authors: Do the simulations respect Physics?

Based on your statements here and in other threads your ultimate goal should probably be a full quantum-mechanical treatment of the action potential. If done well, such work would undoubtedly be published since it would be interesting.

I do not need Quantum Physics. Just basic laws of Physics. Some truth is located just in front of your nose.

Problem:
A cable has two ends that are connected to nodes. Because it is passive and because the cable is connected then you must have a continuity in the electric values within the cable.
You may simply divide your piece of cable in subunits. It will mimic the records(?)
Give me some values? (That is the third time I ask).
the model presented here is false. Since nodes aren't connected to external milieu, no current flows at nodes and no ground is indicated (the schema was perhaps simplified)
http://butler.cc.tut.fi/~malmivuo/bem/bembook/21/21.htm

Finally, I note that somasimple's queries are not arcane, but pertain to multiple sclerosis, a disease of myelination.

The paper data was collected with normal and desheated axons.
Edit:
http://www.ncbi.nlm.nih.gov/pubmed/...nel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum
This paper gives some light when myelin is still present.

 

[Dale]

I do not need Quantum Physics. Just basic laws of Physics.

Yes you do, otherwise you would be illogical or inconsistent. Circuit theory is a reasonable approximation of classical physics as applied to small circuits, but classical physics is a reasonable approximation of quantum mechanics as applied to macroscopic objects. Since you believe that such approximations are wrong "at any scale because it may provoke reasonably mistakes and false conclusions" then you must logically avoid them. It is irrational to accept one reasonable approximation and reject another reasonable approximation.

Give me some values? (That is the third time I ask).

Let's resolve the more fundamental difference about the validity of circuit theory first before we get into a detailed dispute of values for capacitances and resistances. It doesn't even make sense to argue about parameters to a model if we can't agree on the validity of the model itself.

 

[somasimple]

Your "silly", "illogical" and "irrational" arguments become annoying, DaleSpam.
You use them when you are unable to provide a scientific argument or reference.
Read Tasaki or the last paper I provided for clues.

 

[Moonbear]

This topic was already locked once, and we mean for it to STAY that way! Don't start it again.