Model Summary as of January 25, 2003

Purpose

The goal of this model is to accuratelly model neuron activation from stimulating electrodes in a nerve trunk.  The initial results described here are qualitative and meant to illustrate the methods.  Numerical results are not yet meaningful.

Method

We start with a stained cross-section of a nerve, such as this one.  The original picture is greyscale, but has been recolored to indicate the different types of tissue present: axoplasm (green), myelin (red), endonurium (blue), and cell membrane (purple).  Note that the cell membrane in this picture is artificially large.  Geometric meshing methods do not deal well with vastly different spatial scales.   In this case, the axon diameter is on the order of microns, while the cell membrane is a few nanometers.  However, the cell membrane is a very high resistance layer and has a crucial effect on the model results.  To compensate, we have created an artificially thick cell membrane (about 1 tetvol thick on average) with a proportionately reduced conductivity.

Next we import this recolored slide into SCIRun.  Conductivities are assigned appropriate values and a tetvol mesh is built around the lattice geometry.  Even though this particular slide is 2D, the scirun mesh is 3D but very thin.  This particular mesh is a small portion of the original slide, used for demonstration purposes.

Now stimulating electrodes are placed in the mesh.  Constant currents of 1 and -1 (arbitrary units) are injected through each electrode, respectively.  The solution to the forward field problem is visualized using streamlines and the current density vector field.  In this picture, the streamlines show current flow through the volume based on seed points in a sphere surrounding one of the electrodes.  This method of seeding streamlines seems to make more intuitive sense to electrophysiologists, and produces results that are more consistent with with 2D streamlines shown in textbooks.  The streamline color indicates voltage according to the color bar at left.  Current density is visualized using the vector field.  In this case, both the size and color of the vector arrows indicate field magnitude (small, blue arrows = low density; large, red arrows = high density).  We see that current density is highest in the endoneurium surrounding the axons, but lower through the axons.  This is expected due to the low conductivity of myelin and the cell membrane.

As mentioned, our primary goal is to determine axon activation.  As a first attempt at this we examined the voltage gradient within the cell membrane.  If the gradient is above a user-defined threshold then the nerve is sufficiently depolarized at that point to initiate an action potential.  With this method, sites of initiation in the cell membrane are shown in red; areas that have not depolarized are shown in blue.

Next Steps

This is a purely resistive model and does not include the important capacitive properties of the cell membrane.  Further, this model is 2D and action potential initiation is better detected in 3D.  We are currently investigating methods to include capacitance, and to extend the 2D model to 3D, including nodes of Ranvier.