Abstract
Objective. 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−1, corresponding to activation of 3.4 μm 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. The objective of this study is to estimate the fraction of activated axons as a function of electric field magnitude. Approach. The EF thresholds required for axon stimulation of myelinated axon diameters between 1 and 5 μm 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−1. Main results. The effect of DBS is estimated to be 47·EF—8.8% starting at a threshold level EF t0 = 0.19 V mm−1. Significance. The fraction of activated axons from DBS in a voxel is estimated to increase linearly with EF above the threshold level of 0.19 V mm−1. This means linear regression between EF above 0.19 V mm−1 and clinical outcome is a suitable statistical method when doing improvement maps for DBS.
Highlights
Deep brain stimulation (DBS) is a well-established technique for symptomatic relief in movement disorders such as Parkinson’s disease, essential tremor, and cervical dystonia [1,2,3]
By comparing results from experimental studies [10, 11] with finite element method (FEM) simulations of the electric field around the DBS lead, it has been found that DBS starts to noticeably trigger axons at an electric field magnitude of about 0.2 V mm−1 at a pulse width of 60 μs and a pulse frequency of 130 Hz [12, 13]
The simulated external electric potential field, Ve, and electric field magnitude, EF = ∣ Ve ∣ (V mm−1) was exported along lines corresponding to axons with a tangential horizontal orientation to the middle of the active DBS contact in steps of 0.1 mm from 0.1 mm outside the edge of the contact at a radius, r = 0.735 mm to r = 6.735 mm measured from the center of the lead (figures 1(a)–(b), (d))
Summary
Deep brain stimulation (DBS) is a well-established technique for symptomatic relief in movement disorders such as Parkinson’s disease, essential tremor, and cervical dystonia [1,2,3]. By comparing results from experimental studies [10, 11] with finite element method (FEM) simulations of the electric field around the DBS lead, it has been found that DBS starts to noticeably trigger axons at an electric field magnitude of about 0.2 V mm−1 at a pulse width of 60 μs and a pulse frequency of 130 Hz [12, 13]. With a combination of FEM and individual axon simulations using a combined cable and Hodgkin-Huxley model, this threshold has been calculated to correspond to activation of axons with an outer diameter including the myelin sheath of 3.4 μm [12]. Very few axons in the human brain are this large with outer axon
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