This project is designed by Dr. Karlo Malaga, Assistant Professor of Biomedical Engineering at Bucknell University.

Background

Volume Conductor is defined as a region of volume with specific conductivity, permittivity, and source current. Our goal is to solve for the potential and electric field everywhere within the volume. Since the brain has many regions with different electrical properties, we can break it down to many compartments and find the potential and electric field of each compartment. 

Finite element modeling is a numerical technique for solving partial differential equations that describe real-world physical phenomena. Finite element method is useful because it enables engineers to reduce the number of physical prototypes and experiments to reduce costs and optimize components in the design phase to develop improved products faster. 

Overview

Using COMSOL, I first created a simple volume conductor model of an electrode implanted in the center of the brain and then added a sphere representing scar tissue to the model. Then, I created a more complex volume conductor model of an electrode implanted in the center of the brain. For each model generated, I analyzed the potential distribution around the electrode using Finite-element method to monitor the generated DBS signal. 

DESIGN & ANALYSIS

1. Simple Model

Assumption: 

- ideal point electrode

- spherical brain

Coarse mesh

Extremely fine mesh

In COMSOL, the computational time for coarser mesh is 1s while the computational time for extremely fine mesh is 26s. Therefore, as the mesh density increases, it takes more time to compute the electric potential. However, as the finer mesh generates more results than the coarser mesh, higher-mesh-density plot is more accurate. Although the extremely fine mesh generates a denser plot (more points), the dominating pattern of the electric potential distribution around the electrode appear to be the same in two mesh cases.

2. Simple Model with Scar Tissue

The COMSOL’s electric potential suggest that with a scar, there is more electric potential around the electrode. The COMSOL result does not agree with my expectation that electric potential decreases in the presence of the scar because of the scar’s resistivity. I think that the scar should make the electric potential decrease because the scar has higher resistivity than the brain, thus hindering the stimulated current from traveling to further regions in the brain. 

3. Complex Model

4. Ground Boundary Condition

We want to have a small model that is easy enough to solve but also want to maintain the accuracy of the model so that electric potential can still be function of distance. The boundary, when too near the brain, will disrupt the function. Yet when the ground is too far away, the model will be very difficult and timely to solve. Considering these constraints, we want to choose a boundary that is moderate for both conditions so putting the ground at the surface of the sphere is a valid assumption. In order to test if the designated distance away from the electrode can be chosen as a reference boundary, we can make another model that has a radius larger than the radius we want for our ground boundary. Let’s say that the radius of the interested model is R and of the latter model is 2R. Then, in the latter model, we measure the voltage at R and check if it is 0. If the voltage is indeed 0, we can use R to be the radius of the ground boundary.

5. Ideal Electrode?

The three characteristics of an ideal electrode are that  (1) it is infinitely small, (2) it has zero input impedance, and (3) there is no shank. Because of these characteristics, it is difficult to create an ideal electrode because the two traits - small size and small impedance - are opposite. As the size of the electrode goes down, the impedance increases. Therefore, we have to optimize the electrode to make sure that it is small enough but also in an appropriate impedance range.