does the diameter of the mylined affect the fh mod?

[melissamou]

hi, i inserted the fh.mod in my nodes, and i want to analysis the conduction speed of the action potential, according to some paper, the relation between conduction speed and the diameter of the fiber is linear. but when i increase the diameter of the fiber to more than 15um, i found the speed is slower than expected, however it is agree with expected speed when the diameter is lower than 15.

i don't know why it isn't liner? are there anything affect the diameter? by the way, i used extracellular stimulation, and the electric potential is from the result of comsol. i use vector,play(&e_extracellular(x), tvec) to add those potential to the center of each segment.

does the Ra affect this?
i use forall Ra=100 for different diamtere of the fiber?

so how to define the Ra, i saw one example defined it as follows

Code: Select all

local fac
	// ohm/cm must be converted to ohm-cm by multiplying by
	// cross sectional area
	fac = PI*diam^2/4 * 1e-8
	forall {
		Ra = 1.26e8 * fac
	}

now i have tried to define Ra like that, but when diameter is bigger, Ra is bigger the conduction speed is even lower, that's pity

[ted]

What is fh.mod? Anybody can call a file anything, regardless of its contents.


Determination of how fiber diameter affects conduction velocity is subject to many confounds*. Here are just a few of them.

1. Model design confounds. The proportionality between fiber diameter and conduction velocity was observed in real myelinated axons. When wet-lab experimentalists established this linear relationship, what did they mean by "fiber diameter"? just the diameter of the axon, or the combined diameter of the axon plus its myelin sheath? In real myelinated fibers, is thickness of the myelin sheath correlated with fiber diameter? Are length and diameter of nodes of Ranvier correlated with fiber diameter? How does internode length correlate with fiber diameter in real myelinated fibers? Do you think that any such correlations might affect your simulation results? If your models do not preserve the correlations among fiber properties that occur in nature, you are introducing confounds into your model.

2. Stimulus intensity confounds. Fiber diameter also affects the stimulus intensity required to elicit a spike. Stimulus intensity can affect apparent spike latency. A prolonged stimulus that is barely suprathreshold allows depolarizing current to spread far down the axon, causing gna inactivation and gk activation that can slow conduction through the affected part of the axon. A strong stimulus that lasts too long can force multiple nodes that are near the stimulating electrode to fire nearly simultaneously, resulting in artifactually short conduction latencies. You want a stimulus that is very brief (so charge can't spread very far) and large enough to reliably elicit a spike. Experimentalists typically choose 0.1 ms duration and adjust intensity to be 2 x threshold. If you're using fixed stimulus duration and intensity, you're introducing a confound by your choice of stimulus.

3. Stimulus localization confounds. Extracellular stimulation is not the best way to stimulate a fiber for conduction velocity measurements, because it deposits charge along a much larger length of the axon than if you used an intracellular stimulus. This causes changes in membrane potential that affect axonal excitability and conduction velocity. That's why experimentalists try to use bipolar stimulating electrodes with a short distance between the poles, and try to get the electrode as close as possible to a node of Ranvier. With a computational model, it's best to just use intracellular stimulation with a current source (IClamp) located in the axon at a node of Ranvier. If you are using an extracellular stimulus, especially a monopolar electrode, you are introducing yet another confound.

4. End-effect confounds. The best way to determine conduction velocity is to observe membrane potential at two different locations, separated by a known distance, and measure the times at which the spike crosses some value. Both recording sites should be far from the stimulus site (so spike initiation, which slows local conduction velocity, doesn't affect results) and also far from the distal termination of the axon (where sealed end effect can accelerate local velocity).

"How 'far from the ends' is far enough?"
Create a space plot of v over a path that extends along the entire length of the axon.
Turn on Keep Lines.
Use the Movie Run tool to launch a simulation.
(NEURON Main Menu / Tools / Movie Run brings up the tool; click on its Init & Run button to start a simulation that refreshes the space plot at every fadvance).
"Far enough from the ends" is the part of the axon where spike peak amplitude is unaffected by distance from either end.

5. Data analysis confounds. Time of peak is hard to measure precisely because the spike peak is relatively broad. It is better to find the point in the depolarizing phase when the spike is at half maximum amplitude (halfway between resting potential and the depolarized peak). In a simulation with fixed time steps, there is an unavoidable error of +- dt/2. NEURON's default integration method has only first order accuracy, so nothing is gained by trying to determine the "exact" time at which v reaches half max. If you set
secondorder = 1
membrane potential will have second order accuracy, and linear interpolation will give a second order correct value for the time at which half max is reached.

[melissamou]

Thanks very much for the detailed explaination.
I have follow your advice and use the Iclamp as stimulation. i am sure the diameter and other geoetry is right but still the result is not exactly linear, the slope is smaller when the diameter is bigger. i found in FH channel(Frankenhaeuser - Huxley channels for Xenopus) or hh.mod(Hodgkin-Huxley channel), the code has nothing to do with diameter. i think the total sodium conductance total potassium conductance, et al, are related to diameter. how does neuron deal with this?

[ted]

i am sure the diameter and other geoetry is right but still the result is not exactly linear, the slope is smaller when the diameter is bigger.

One factor I omitted from my previous post: spatial discretization can affect simulation results. Diameter and effective membrane capacitance affect the appropriate value for nseg. How are you deciding what value to use for nseg in your models? If you change diameter, you may also have to change nseg of internodes. If you are using the d_lambda rule, you'll have to calculate lambda_100 yourself, using the "effective specific membrane capacitance" of myelinated internodes; the code built into NEURON for calculating lambda_100 uses the specific membrane capacitance cm, but the "effective specific membrane capacitance" is much smaller--equals cm*cmyel/(cm+cmyel), where cmyel is the specific capacitance of the myelin itself.

There are many experimental and computational modeling articles on the anatomical and biophysical properties of myelinated axons, and the relationship between fiber diameter and conduction velocity. Have you read any of Stephen Waxman's papers, especially
Brill MH, Waxman SG, Moore JW, Joyner RW (1977)
Conduction velocity and spike configuration in myelinated fibres: computed dependence on internode distance.
J Neurol Neurosurg Psychiatry 40:769-74
or
Moore JW, Joyner RW, Brill MH, Waxman SD, Najar-Joa M (1978)
Simulations of conduction in uniform myelinated fibers. Relative sensitivity to changes in nodal and internodal parameters.
Biophys J 21:147-60
which have models in ModelDB?
Or have you read anything in his books
Physiology & Pathobiology of Axons
The Axon: Structure, Function and Pathophysiology

i think the total sodium conductance total potassium conductance, et al, are related to diameter. how does neuron deal with this?

You may have noticed that
(1) gnabar_hh, gkbar_hh, and gl_hh are in units of conductance/area
(2) sections have length and diameter
(3) segments are cyilndrical
Guess what NEURON does with this information . . .