4 ms·

This exact theory is also used to model the electrical behavior of neurons in the brain, with some slight differences (no inductances, non-linear resistances),

This exact theory is also used to model the electrical behavior of neurons in the brain, with some slight differences (no inductances, non-linear resistances), under the name "cable theory" https://en.wikipedia.org/wiki/Cable_theory https://en.wikipedia.org/wiki/Cable_theory I remember one professor mentioning the origin of this theory in undersea cable modeling at some point.

brunohaid 2y ago
Tried skimming the page but couldn't find the answer: do we know if the neural connection impedance is perfectly matched? It looks quite organic in shape, with teardrop connections and so on, but curious how nature did that job?
- phreeza 2y ago
  It is not always perfectly matched, because the mismatches can actually have a "computational" purpose, but e.g. the typical branching pattern of dendrites is pretty close to being matched . There is a chapter on this in the Dayan and Abbot textbook.
  - brunohaid 2y ago
    <3 awesome - this one https://boulderschool.yale.edu/sites/default/files/files/DayanAbbott.pdf https://boulderschool.yale.edu/sites/default/files/files/Day... ?
    - phreeza 2y ago
      Yes exactly. Chapter 6.3, though it is actually less detailed than I remembered.
      - brunohaid 2y ago
        Much appreciated! Maybe the impedance added some colorful garnish to your memory... :-)
        mattkrause 2y ago
        If this is your thing, you might also want to check out Christof Koch's Biophysics of Computation. Cable theory is introduced in one of the first few chapters.
- mannykannot 2y ago
  That's an interesting question. One follow-up question I would have is whether impedance matching is a relevant concept here, given that the model has no inductance (I'm guessing that's because the flow of charge is in the form of ions moving radially through the membrane. If neurons were more like transmission lines, would we be susceptible to interference from distant lightning?) I also skimmed the page and saw that equation 20 is not a wave equation (as the article says, it is a diffusion equation.) Again, I am not sufficiently knowledgeable to say whether that renders the question of impedance matching moot. Update: I see from the sibling thread and its excellent reference that the refractory period, where the sodium and potassium ions are being pumped back to their starting positions, suppresses reflection.
  - brunohaid 2y ago
    Sibling thread?
    - mannykannot 2y ago
      Sorry if that's not clear - I was referring to phreeza's reply to your question and the link you had posted below it, which is as far as the discussion had gone at that time. The refractory period, and its role in suppressing reflections, is mentioned in the reference you provided a link to.
      - brunohaid 2y ago
        Got it - haven't read it yet but, also thanks to your pointer, very much looking forward to!
      - deleted 2y ago
        [deleted]
amelius 2y ago
This looks different, as there is a completely resistive path from source to destination, which is not the case for transmission lines (as that would mean an instantaneous response which isn't possible due to the speed of light limit).
- phreeza 2y ago
  I think it's just a matter of scale, technically there is an inductance but the distances are so small and frequencies so low that they never really matter.
  - amelius 2y ago
    Yes, but then it is not a transmission line.
- CamperBob2 2y ago
  They're modeling delay with capacitance to 'ground', it seems. So there's capacitive reactance.
  - amelius 2y ago
    But that's not a complete model, as the output will start changing the moment the input changes. And a short burst will not appear so on the output.
    - phreeza 2y ago
      It will change instantaneously, but with a magnitude that decays exponentially with distance from the place the current is injected. The way signal propagation works is that you have "active" currents to ground that react to voltage changes in a nonlinear way. These lead to wave-like behavior in the transmission line, though it is quite nonlinear and harder to model than a straight up inductor.

brunohaid 2y ago

Tried skimming the page but couldn't find the answer: do we know if the neural connection impedance is perfectly matched? It looks quite organic in shape, with teardrop connections and so on, but curious how nature did that job?

phreeza 2y ago
It is not always perfectly matched, because the mismatches can actually have a "computational" purpose, but e.g. the typical branching pattern of dendrites is pretty close to being matched . There is a chapter on this in the Dayan and Abbot textbook.
- brunohaid 2y ago
  <3 awesome - this one https://boulderschool.yale.edu/sites/default/files/files/DayanAbbott.pdf https://boulderschool.yale.edu/sites/default/files/files/Day... ?
  - phreeza 2y ago
    Yes exactly. Chapter 6.3, though it is actually less detailed than I remembered.
    - brunohaid 2y ago
      Much appreciated! Maybe the impedance added some colorful garnish to your memory... :-)
      - mattkrause 2y ago
        If this is your thing, you might also want to check out Christof Koch's Biophysics of Computation. Cable theory is introduced in one of the first few chapters.
mannykannot 2y ago
That's an interesting question. One follow-up question I would have is whether impedance matching is a relevant concept here, given that the model has no inductance (I'm guessing that's because the flow of charge is in the form of ions moving radially through the membrane. If neurons were more like transmission lines, would we be susceptible to interference from distant lightning?) I also skimmed the page and saw that equation 20 is not a wave equation (as the article says, it is a diffusion equation.) Again, I am not sufficiently knowledgeable to say whether that renders the question of impedance matching moot. Update: I see from the sibling thread and its excellent reference that the refractory period, where the sodium and potassium ions are being pumped back to their starting positions, suppresses reflection.
- brunohaid 2y ago
  Sibling thread?
  - mannykannot 2y ago
    Sorry if that's not clear - I was referring to phreeza's reply to your question and the link you had posted below it, which is as far as the discussion had gone at that time. The refractory period, and its role in suppressing reflections, is mentioned in the reference you provided a link to.
    - brunohaid 2y ago
      Got it - haven't read it yet but, also thanks to your pointer, very much looking forward to!
    - deleted 2y ago
      [deleted]

amelius 2y ago

This looks different, as there is a completely resistive path from source to destination, which is not the case for transmission lines (as that would mean an instantaneous response which isn't possible due to the speed of light limit).

phreeza 2y ago
I think it's just a matter of scale, technically there is an inductance but the distances are so small and frequencies so low that they never really matter.
- amelius 2y ago
  Yes, but then it is not a transmission line.
CamperBob2 2y ago
They're modeling delay with capacitance to 'ground', it seems. So there's capacitive reactance.
- amelius 2y ago
  But that's not a complete model, as the output will start changing the moment the input changes. And a short burst will not appear so on the output.
  - phreeza 2y ago
    It will change instantaneously, but with a magnitude that decays exponentially with distance from the place the current is injected. The way signal propagation works is that you have "active" currents to ground that react to voltage changes in a nonlinear way. These lead to wave-like behavior in the transmission line, though it is quite nonlinear and harder to model than a straight up inductor.