Normal ripples, abnormal ripples, and fast ripples in a hippocampal model (Fink et al. 2015)

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"...We use a computational model of hippocampus to investigate possible network mechanisms underpinning normal ripples, pathological ripples, and fast ripples. Our results unify several prior findings regarding HFO mechanisms, and also make several new predictions regarding abnormal HFOs. We show that HFOs are generic, emergent phenomena whose characteristics reflect a wide range of connectivity and network input. Although produced by different mechanisms, both normal and abnormal HFOs generate similar ripple frequencies, underscoring that peak frequency is unable to distinguish the two. Abnormal ripples are generic phenomena that arise when input to pyramidal cells overcomes network inhibition, resulting in high-frequency, uncoordinated firing. In addition, fast ripples transiently and sporadically arise from the precise conditions that produce abnormal ripples. Lastly, we show that such abnormal conditions do not require any specific network structure to produce coherent HFOs, as even completely asynchronous activity is capable of producing abnormal ripples and fast ripples in this manner. These results provide a generic, network-based explanation for the link between pathological ripples and fast ripples, and a unifying description for the entire spectrum from normal ripples to pathological fast ripples."
1 . Fink CG, Gliske S, Catoni N, Stacey WC (2015) Network Mechanisms Generating Abnormal and Normal Hippocampal High-Frequency Oscillations: A Computational Analysis. eNeuro [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s): Hippocampus CA1 pyramidal GLU cell; Hippocampus CA1 basket cell;
Channel(s): I Na,t; I A; I K; I h;
Gap Junctions: Gap junctions;
Receptor(s): GabaA; NMDA; Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Oscillations; Epilepsy;
Implementer(s): Fink, Christian G. [cgfink at]; Gliske, Stephen [sgliske at]; Stacey, William [wstacey at];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; GabaA; NMDA; Glutamate; I Na,t; I A; I K; I h;
// $Id: calcrxc_a.hoc,v 1.4 2010/05/10 18:43:19 ted Exp ted $
/* Calculates the transfer resistances between 
extracellular stimulating|recording electrode(s) and a 
model neuron.  Relies on the principle of reciprocity, 
which assumes that the intervening bath and tissue can 
be treated as linear.  Suppose a stimulus current of 
amplitude Is, applied to a particular configuration of 
extracellular electrode(s), produces a potential Vext(x,y,z) 
at location (x,y,z).  Then the transfer resistance between 
the electrode(s) and (x,y,z) is 
  rx(x,y,z) = Vext(x,y,z)/Is
According to the principle of reciprocity, a transmembrane 
current Im(x,y,z) generated by membrane at (x,y,z) will 
produce a potential Vel that can be recorded at the 
extracellular electrode(s) and is given by
  Vel = rx(x,y,z) Im(x,y,z)

How to simulate extracellular stimulation

Insert the extracellular and xtra mechanisms in all sections that are 
subject to the extracellular field.
Compute the transfer resistance rx for every section that contains 
xtra, as illustrated below.
Construct a stimulus waveform template and copy it to a Vector.  
For each internal node along the axon, use this Vector to drive 
is_xtra(x).  The xtra mechanism uses the rx values to convert the 
stimulus current waveform into the proper amplitude and sign of the 
local extracellular field.

If rho, b, or c is changed, new_elec() must be invoked 
to make the changes take effect.

Monopolar electrode in an infinite medium

A conductive sphere of radius r0 is suspended in an infinite 
volume of solution that has resistivity rho [ohm cm].  Ignoring 
electrochemical effects at the electrode|solution interface, 
what is the resistance between the surface of the sphere and 
an infinitely distant ground electrode?

The surface area of a sphere with radius r is 4 PI r^2.
The resistance of a shell with thickness dr is 
  rho dr / 4 PI r^2
and the resistance is therefore
  INTEGRAL rho dr / 4 PI r^2
   = - rho / 4 PI r |     = rho / 4 PI r0
So to a first approximation, a monopolar stimulating electrode 
that delivers current I produces a field in which potential V 
is given by 
  V = I rho / 4 PI r
where r is the distance from the center of the electrode.

The principle of superposition may be applied to deal with an 
arbitrary number of monopolar electrodes, or even surface 
electrodes with different shapes and areas, which are located 
at arbitrary positions, and deliver arbitrary stimulus currents.
However, there are some noteworthy special cases.

Special case:  bipolar stimulation of an axon

Imagine a pair of stimulating electrodes that lie along 
a line parallel to an axon, like so:

=====================   ---
       o     o          ---
       |  b  |
       1     2

where b is the separation between the electrodes 
and c is the perpendicular distance from them to the axon.

For the sake of this example, assume that the electrodes 
straddle the midpoint of the axon.

The extracellular potential at location x produced by electrode 
1 is
  V1 = I rho / 4 PI r1
where r1 is the distance from electrode 1 to x.  This distance is
  r1 = sqrt( ((x-0.5)*L) + 0.5*b)^2 + c^2 )

Likewise the potential at x produced by electrode 2 is
  V2 = -I rho / 4 PI r2
where r2 is the distance from electrode 2 to x, i.e.
  r2 = sqrt( ((x-0.5)*L) - 0.5*b)^2 + c^2 )

The net extracellular potential at x is V1 + V2, i.e.
  Vnet = (I rho / 4 PI)*((1/r1) - (1/r2))
so the transfer resistance that converts the stimulus current I to 
an extracellular potential Vnet is simply
  rx = (rho / 4 PI)*((1/r1) - (1/r2))

Special case:  uniform field between two parallel plates

A uniform field has the same intensity and orientation at all 
points in space, and the extracellular potential at any point
is a linear function of displacement in the direction of the 
orientation of the field.

If an entire neuron lies in such a field, then without loss of 
generality we may assert that the extracellular potential is 0 
for all points that lie on some plane that is perpendicular to 
the field.  For this "zero potential surface" it is convenient 
to choose the plane that passes through a particular location 
in the cell, such as the 0 end of the soma.


// set up the transfer resistances

// what is the approximate resistivity of tissue anyway?
//rho = 35.4  // ohm cm, squid axon cytoplasm
	    // for squid axon, change this to seawater's value
rho = 351    // for living mammalian cells, change to brain tissue or Ringer's value  351 from brain resistivity paper

b = 400  // um between electrodes
c = 100  // um between electrodes and axon

proc setrx() {
  forall {
    if (ismembrane("xtra")) {
// avoid nodes at 0 and 1 ends, so as not to override values at internal nodes
      for (x,0) {
        r1 = sqrt( ((x-0.5)*L + 0.5*b)^2 + c^2 )
        r2 = sqrt( ((x-0.5)*L - 0.5*b)^2 + c^2 )
        // 0.01 converts rho's cm to um and ohm to megohm
        axon.rx_xtra(x) = (rho / 4 / PI)*((1/r1) - (1/r2))*0.01
// print r1, r2

// assume monopolar stimulation and recording
// electrode coordinates:
// for this test, default location is 50 microns horizontal from the cell's 0,0,0

// BILL:  for my model, I have the pyr cells in the yz plane (+/- 205) centered at x=0. The baskets are 10 um deep at x=10
// thus, electrode at x=-50 or -100 or -500 would be best.  These need to be called outside this function in setelec(-50, 0 ,0)
XE = -50  // um
YE = 0
ZE = 0

proc setrx() {  // now expects xyc coords as arguments
  forall {
    if (ismembrane("xtra")) {
// avoid nodes at 0 and 1 ends, so as not to override values at internal nodes
      for (x,0) {
//        r = sqrt((x_xtra(x) - xe)^2 + (y_xtra(x) - ye)^2 + (z_xtra(x) - ze)^2)
        r = sqrt((x_xtra(x) - $1)^2 + (y_xtra(x) - $2)^2 + (z_xtra(x) - $3)^2)
        // 0.01 converts rho's cm to um and ohm to megohm
        rx_xtra(x) = (rho / 4 / PI)*(1/r)*0.01
	//print secname(), "  \t", rx_xtra(x)

proc setelec() {
	xe = $1
	ye = $2
	ze = $3
	setrx(xe, ye, ze)

create sElec  // bogus section to show extracell stim/rec electrode location
objref pElec  // bogus PointProcess just to show stim location
objref gElec  // will be a Shape that shows extracellular electrode location

gElec = new Shape(0)  // create it but don't map it to the screen yet
// gElec.size(-245.413,275.413,-250,270)
gElec.view(-245.413, -250, 520.827, 520, 629, 104, 201.6, 201.28)

proc drawelec() {
	sElec {
		// make it 1 um long
		pt3dadd($1-0.5, $2, $3, 1)
		pt3dadd($1+0.5, $2, $3, 1)
		pElec = new IClamp(0.5)
	gElec.point_mark(pElec, 2)  // make it red

proc setelec() {
	xe = $1
	ye = $2
	ze = $3
	setrx(xe, ye, ze)
	//drawelec(xe, ye, ze)

// setrx(50, 0, 0)  // put stim electrode at (x, y, z)

setelec(XE, YE, ZE)  // put stim electrode at (x, y, z)

// print "Use setelec(x, y, z) to change location of extracellular recording electrode"

xpanel("Extracellular Electrode Location", 0)
  xlabel("xyz coords in um")
  xvalue("x", "XE", 1, "setelec(XE,YE,ZE)", 0, 1)
  xvalue("y", "YE", 1, "setelec(XE,YE,ZE)", 0, 1)
  xvalue("z", "ZE", 1, "setelec(XE,YE,ZE)", 0, 1)


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