  Background: Finite element method (FEM) simulations of the electric field
magnitude (EF) are commonly used to estimate the affected tissue surrounding
the active contact of deep brain stimulation (DBS) leads. Previous studies have
found that DBS starts to noticeably activate axons at approximately 0.2 V/mm,
corresponding to activation of 3.4 $\mu$m axons in simulations of individual
axon triggering. Most axons in the brain are considerably smaller however, and
the effect of the electric field is thus expected to be stronger with
increasing EF as more and more axons become activated.
  Objective: To estimate the fraction of activated axons as a function of
electric field magnitude.
  Methods: The EF thresholds required for axon stimulation of myelinated axon
diameters between 1 and 5 $\mu$m were obtained from a combined cable and
Hodgkin-Huxley model in a FEM-simulated electric field from a Medtronic 3389
lead. These thresholds were compared with the average axon diameter
distribution from literature from several structures in the human brain to
obtain an estimate of the fraction of axons activated at EF levels between 0.1
and 1.8 V/mm.
  Results: The effect of DBS is estimated to be 41$\cdot$EF - 7.4 % starting at
a threshold level EFt0 = 0.18 V/mm.
  Conclusion: The fraction of activated axons from DBS in a voxel is estimated
to increase linearly with EF above the threshold level of 0.18 V/mm. This means
linear regression between EF above 0.18 V/mm and clinical outcome is a suitable
statistical method when doing improvement maps for DBS.
