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Finite Elements

Linear vs. Quadratic

Finite element methods traditionally use linear basis functions to interpolate within an element. With this method, the results obtained are never more accurate than to within the size of an element and often the accuracy is even less. When solving the forward EEG problem, the electric potential is forced to be linear and the electric field is constant in an element when linear basis functions are used. This results in significant error near the source of the field and the head boundaries where the electric field changes the most.

We have implemented a finite element method that uses quadratic basis functions to obtain more accurate electric potentials throughout the torso when solving the forward ECG problem. When quadratic elements are used, the electric potential is more defined giving a more accurate result than can be determined by using only linear elements.

Linear

Quadratic

The quadratic basis functions have also been used to obtain more accurate electric potentials on the brain's cerebral cortex when solving the forward EEG problem. When quadratic elements are used, the electric potential on the cerebral cortex is more focused giving a more accurate result than can be determined by using only linear elements.

• Publications -- Finite Elements
• Image Gallery -- Finite Elements

Principal Researchers:

• Dr. David Weinstein
• Rob VanUitert
• Dr. Mike Kirby