Neuron Modeling for Neuroprosthetic Applications

F. Rattay

TU-BioMed

Vienna University of Technology

Wiedner Haupstr. 8-10/114, A-1040 Vienna, Austria

frank.rattay@tuwien.ac.at

 

Abstract

Text Box: BOX 1: Lumped Circuit Model of a Neuron The membrane voltage Vn of the n-th compartment obeys where C is the membrane capacity and R/2 the internal resistance between the center and the border of the compartment. Ion membrane current has to be calculated from a separate model. Injected current ¹ 0 may simulate synaptic inputs. The dots stand for terms that have to be added in cases of more than two neighbor elements. The term represents the influence from the external potential and is called the activating function. For details see [4-6]. Neuron modeling and computer simulation are powerful tools for the functional design of neuroprosthetic devices. Individual electrical and geometrical characteristics of neural substructures as well as ion current fluctuations can have surprising effects and should be studied in detail.

 

1.       Introduction

Modern electrical stimulation techniques as used e.g. in cochlear and retina implants or for the suppression of pain or spasms in spinal cord stimulation as well as ongoing developments in brain computer interfaces are not exclusively operating by stimulating long axons anymore [1-3]. To understand possible stimulation effects and on the other hand the electric fields generated by neural activities demands for the introduction of new tools. Computer simulation is one of them.

 

2.       Methods

Even a simple model of a neuron should consist of different subunits as the electrical properties of neural membranes are quite different in dendrite, soma, axon hillock, node, internode and unmyelinated terminal (Fig. 1). A subunit sometimes has to be divided into several compartments small enough so that the voltages at the inside (Vi,n) and at the outside (Ve,n) of the n-th compartment can be represented by a mean value, i.e. from the numerical point of view the length of a cylindrical compartment with diameter d is restricted by its space constant l (a compartment length <l/4 is recommended) with , where ri denotes intracellular resistivity and gm membrane conductance per square unit area [4].

3.       Results

Text Box: Fig. 5. Human auditory nerve response evoked by a stimulating impulse from a cochlear implant. (A) Straitened bipolar cochlear neuron in synaptic contact with a hair cell (top) and the position of a cochlear neuron relative to a spherical electrode. Extracellular resistivity re=0.3 kΩ.cm and calculation of potential from a 1 mA point source results in 1 V at r=0.24 mm, which is electrode radius. The values of the activating function f (insert A) are proportional to the slopes of the neural response curves at stimulus onset in B and C. The largest f value of the second peripheral node, P2, predicts the place of spike initiation in B. All slopes of membrane voltage in the central nodes are positive and strengthen the stimulus current to 1.2 mA causes additional spike initiation at central node C2 (C). The activating function value of P0 is also positive, but the much stronger negative activity in P1 compensates the excitation process quickly (insert C shows the part of the membrane voltage of the P0 compartment during the stimulus pulse as marked by arrows, magnification 5x). (D) –800 µA per 100 µs pulse initiates a spike at P1 which is in accordance with the activating function concept. (E) The smaller intensity of f at P4 allows spike initiation at –1200 µA. The P4 spike develops after the P1, but nevertheless the P4 spike activates the central axon. Note the different arrival times at the measuring electrode C5.

Spike initiation regions depend on polarity and stimulus strength. Thereby small variations in the pulse amplitude may cause essential different arrival times at the axon terminal. This is demonstrated with a bipolar neuron close to a stimulating electrode of a cochlear implant in Fig. 1: The simulated measuring electrode at central node C5 detects the arriving spike 0.6ms earlier in case B than in C. The medium surrounding the neural tissue was assumed to be homogeneous for this simulation but the result does not remarkably differ from a finite element evaluation [7].

Crossing the soma region causes a remarkable delay in a peripherally initiated spike (Fig. 1B) which is about of double length in man compared to cat. This phenomenon was explored by computer simulation and is based on the large capacity of the unmyelinated soma region which is unique in man. The simulated results are in good correlation with double peaks observed by neural response telemetry measurements in some cochlear implant patients [9].

Text Box: Fig. 2. Simulation of cochlear nerve response with a stochastic membrane model, where ion current fluctuations are proportional to the number of sodium channels in every compartment [8]. Situation as in Fig. 1. Note the larger jitter for weak stimulation, and the shift from peripheral spike initiation to the central axon for increase of stimulus amplitude which result in a bimodal firing pattern at 900 µA. Such responses are based on large populations of spiking neurons. Simulation of stochastic effects in a group of neurons can be done by introduction of a noisy ion current component in every compartment (Fig.2).

 

4.       Summary and Conclusions

Often the dendrite and soma region is involved in electrical nerve stimulation. In these cases the electrical and geometrical properties should be included in simulation work. The applied electric field cause different responses according to its orientation, strength and frequency characteristics and as a consequence of the neural cell compartments. In previous work we have analyzed the basic mechanisms and some curious effects which neural implant designers should be aware [4-8].

 

 

References

[1]  J.P. Rauschecker and R.V. Shannon. Sending sound to the brain. Science, Vol. 295, pp. 1025-1029, 2002.

[2]  S. Resatz and F. Rattay. Stimulating neural networks with microelectrodes: a modeling study for the retina implant. This volume.

[3]  W. Craelius, The bionic man: restoring mobility. Science, Vol. 295, pp. 1018-1021, 2002.

[4]  F. Rattay. The basic mechanism for the electrical stimulation of the nervous system. Neuroscience, Vol. 89, pp. 335-346, 1999.

[5]  F. Rattay. Electrical Nerve Stimulation: Theory, Experiments and Applications, Springer, Wien - New York, 1990.

[6]  F. Rattay, R.J. Greenberg and S. Resatz to appear in Neuron Modeling in Handbook of Neuroprosthetic Methods, Ed. P. LoPresti, CRC Press

[7]  F. Rattay, R.N. Leao and H. Felix. A model of the electrically excited human cochlear neuron. II. Influence of the three-dimensional cochlear structure on neural excitability, Hear. Res. Vol. 153, pp. 64-79, 2001.

[8]  F. Rattay, P. Lutter and H. Felix. A model of the electrically excited human cochlear neuron. I. Contribution of neural substructures to the generation and propagation of spikes, Hear. Res. Vol. 153, pp. 43-63, 2001.

[9]  N. Dillier, W.K. Lai, M. Wyttenbach, H. Jakits, T. Spillman, T. Linder and U. Frisch. First experiences with neural response telemetry (NRT). Report ENT Department University Hospital Zürich. 1997.