How Finite Element Analysis Revolutionized a 100-Year Old Equation

K. Carlson [1], J. Arle [1], J. L. Shils [2], L. Mei [1],
[1] Beth Israel Deaconess Medical Center/Harvard Medical School, Boston, MA, USA
[2] Rush Medical Center, Chicago, IL, USA
Published in 2016

In 1901 Weiss proposed an equation predicting activation of nerve fibers by electrical stimulation, used in neuroscience and neuromodulation, which applies electric fields to modify nerve behavior in neurological disorders. Weiss’ equation is relative to geometry, electrode array, tissue conductivities, and waveform since it uses electrode amplitude. We replicated a leading calibrated nerve model in COMSOL Multiphysics® software and with it, examined the predicted electric potential gradient seen by the axon. This made it possible to convert the subjective Weiss equation predicting nerve thresholds to an absolute equation. We use the new method in our analyses of neuromodulation, e.g. of the spinal cord for chronic pain and vagus nerve for treatment of epilepsy.