Submyelin Potassium accumulation in Subthalamic neuron (STN) axons (Bellinger et al. 2008)

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Accession:121253
"To better understand the direct effects of DBS (Deep brain stimulation) on central neurons, a computational model of a myelinated axon has been constructed which includes the effects of K+ accumulation within the peri-axonal space. Using best estimates of anatomic and electrogenic model parameters for in vivo STN axons, the model predicts a functional block along the axon due to K+ accumulation in the submyelin space. ... These results suggest that therapeutic DBS of the STN likely results in a functional block for many STN axons, although a subset of STN axons may also be activated at the stimulating frequency. "
Reference:
1 . Bellinger SC, Miyazawa G, Steinmetz PN (2008) Submyelin potassium accumulation may functionally block subsets of local axons during deep brain stimulation: a modeling study. J Neural Eng 5:263-74 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Axon;
Brain Region(s)/Organism:
Cell Type(s): Subthalamus nucleus projection neuron;
Channel(s): I Na,p; I K; I Sodium; I_Ks; Na/K pump;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Axonal Action Potentials; Action Potentials; Deep brain stimulation; Sodium pump; Depolarization block;
Implementer(s): Bellinger, Steven [Steve.Bellinger at asu.edu];
Search NeuronDB for information about:  I Na,p; I K; I Sodium; I_Ks; Na/K pump;
COMMENT
Longitudinal diffusion of potassium
(equivalent modified euler with standard method and
equivalent to diagonalized linear solver with CVODE )
ENDCOMMENT

NEURON {
	SUFFIX kdifl
	USEION k READ ik WRITE ko
	RANGE ko, Dk, sp, rseg
}

UNITS {
  	(molar) = (1/liter)
  	(mM) = (millimolar)
	(um) = (micron)
	(mA) = (milliamp)
	FARADAY = (faraday) (coulomb)
	PI = (pi) (1)
}

PARAMETER {
	Dk = 1.85 (um2/ms)
	sp = 0.01 (um)
	rseg = 1.7 (um)
	extracellularVolumePerLength (um2)
	crossSectionalArea (um2)

}

ASSIGNED { ik (mA/cm2) }

STATE { ko (mM) }

INITIAL {
	extracellularVolumePerLength = PI * ( (rseg+sp)^2 - rseg^2 )
	crossSectionalArea = extracellularVolumePerLength
	
}

BREAKPOINT { SOLVE conc METHOD sparse }

KINETIC conc {
	COMPARTMENT extracellularVolumePerLength {ko}
	LONGITUDINAL_DIFFUSION Dk*crossSectionalArea {ko}
	~ ko << (ik/(FARADAY)*2*PI*rseg*(1e4))
}

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