Tissue and electrode capacitance reduce neural activation volumes during deep brain stimulation - PubMed (original) (raw)

Tissue and electrode capacitance reduce neural activation volumes during deep brain stimulation

Christopher R Butson et al. Clin Neurophysiol. 2005 Oct.

Abstract

Objective: The growing clinical acceptance of neurostimulation technology has highlighted the need to accurately predict neural activation as a function of stimulation parameters and electrode design. In this study we evaluate the effects of the tissue and electrode capacitance on the volume of tissue activated (VTA) during deep brain stimulation (DBS).

Methods: We use a Fourier finite element method (Fourier FEM) to calculate the potential distribution in the tissue medium as a function of time and space simultaneously for a range of stimulus waveforms. The extracellular voltages are then applied to detailed multi-compartment cable models of myelinated axons to determine neural activation. Neural activation volumes are calculated as a function of the stimulation parameters and magnitude of the capacitive components of the electrode-tissue interface.

Results: Inclusion of either electrode or tissue capacitance reduces the VTA compared to electrostatic simulations in a manner dependent on the capacitance magnitude and the stimulation parameters (amplitude and pulse width). Electrostatic simulations with typical DBS parameter settings (-3 V or -3 mA, 90 micros, 130 Hz) overestimate the VTA by approximately 20% for voltage- or current-controlled stimulation. In addition, strength-duration time constants decrease and more closely match clinical measurements when explicitly accounting for the effects of voltage-controlled stimulation.

Conclusions: Attempts to quantify the VTA from clinical neurostimulation devices should account for the effects of electrode and tissue capacitance.

Significance: DBS has rapidly emerged as an effective treatment for movement disorders; however, little is known about the VTA during therapeutic stimulation. In addition, the influence of tissue and electrode capacitance has been largely ignored in previous models of neural stimulation. The results and methodology of this study provide the foundation for the quantitative analysis of the VTA during clinical neurostimulation.

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Figures

Fig. 1

Fig. 1

Fourier FEM method. (A) The stimulus waveform was created in the time domain and (B) subsequently converted to the frequency domain (magnitude and phase shown) using a discrete Fourier transform. The voltage waveform within the volume during (C) current-controlled stimulation and (D) voltage-controlled stimulation was calculated from the Fourier FEM solver. The differences between the original and Fourier FEM waveforms were dependent on pulse width and capacitance values.

Fig. 2

Fig. 2

Cable model axons and finite element model. (A) 5.7 μm diameter myelinated cable model axon for calculation of stimulation thresholds (see McIntyre et al., 2002 for details). Each model axon included 21 nodes of Ranvier with 0.5 mm internodal spacing. Each internodal section of the model consisted of two paranodal myelin attachment segments (MYSA), two paranodal main segments (FLUT), and six internodal segments (STIN). The nodal membrane dynamics included fast (_N_af) and persistent (_N_ap) sodium, slow potassium (_K_s), and linear leakage (_L_k) conductances in parallel with the nodal capacitance (_C_n). The internodal segments were represented by a double cable structure of linear conductances with an explicit representation of the myelin sheath (Gm in parallel with Cm) and the internodal axolemma (Gi in parallel with Ci). (B) Axisymmetric FEM model of the electrode and surrounding medium (mesh outline in background). The electrode shaft (left side of picture) was an electrical insulator; the contact (black area of shaft) was a voltage or current source. Tissue medium had a conductivity of 0.3 S/m and dielectric constant from 1×104 to 1×106 F/m, while the electrode capacitance ranged from 1.66 to 6.65 μF. A 17× 7 array of axons was oriented perpendicular to the electrode (black circles, normal to the page) at distances from 1 to 4 mm lateral to the axis of the electrode in 0.5 mm increments, and from −4 to +4 mm vertically relative to the center of the electrode in 0.5 mm increments. Axons labeled with a ‘C’ were used for chronaxie calculation. The voltage solution (background shading according to scale at bottom) within the tissue medium was interpolated onto the cable model axons to determine action potential threshold.

Fig. 3

Fig. 3

VTA resulting from current-controlled monopolar stimulation. (A) Results are organized by dielectric values (rows) and pulse width (columns). Within each combination of dielectric and pulse width values are a pair of graphs. The graph on the left shows the time-dependent voltage waveform as calculated by the Fourier FEM solver at one representative point in the volume. The graph on the right is a spatial filled contour plot of the extent of the VTA as determined by threshold amplitude values, which correspond to the scale at right. (B) The volume in cubic millimeter by which the electrostatic model overstates the VTA compared to each dielectric value. Results are displayed as a function of stimulation current, where current values are consistent within each pulse width for the graphs in (A) and (B) as indicated by the column heading labels in (A). (C) Percent by which electrostatic model overstates VTA as a function of pulse width for current-controlled stimulation. Results are shown for different dielectric values with corresponding system time constants. Parts (B) and (C) share the legend.

Fig. 4

Fig. 4

VTA resulting from voltage-controlled monopolar stimulation. (A) Results are organized by capacitance values (rows) and pulse width (columns). Within each combination of capacitance and pulse width values are a pair of graphs. The graph on the left shows the time-dependent voltage waveform as calculated by the Fourier FEM solver at one representative point in the volume. The graph on the right is a spatial filled contour plot of the extent of the VTA as determined by threshold voltage values, which correspond to the scale at right. (B) The amount in cubic millimeter by which the electrostatic model overstates the VTA compared to each capacitance value. Results are shown as a function of stimulation voltage, where voltage values are consistent within each pulse width for the graphs in (A) and (B) as indicated by the column heading labels in (A). C) Percent by which electrostatic model overstates VTA as a function of pulse width for voltage-controlled stimulation. Results are shown for different capacitance values with corresponding system time constants. Parts (B) and (C) share the legend.

Fig. 5

Fig. 5

Dependence of chronaxie values on model and waveform. (A) Threshold voltages were determined for axons located 3 mm lateral from the electrode axis at 130 Hz, 60–450 μs pulse widths. Four different models were evaluated; a representative circuit diagram and sample waveform is shown for each. (B) Strength–duration curves for the four cases in part A with associated _T_ch values. Results for cases 1 through 3 reflect monopolar stimulation while Case 4 reflects bipolar stimulation. (C) Strength–duration curves for therapeutic effects and side effects of clinical monopolar DBS settings (±standard deviation) from Rizzone et al. (2001).

Fig. 6

Fig. 6

Equivalent circuit diagrams of neural stimulation field model. (A) Model 1: neural stimulation system including voltage or current source, electrode capacitance, tissue resistance and tissue capacitance. Model 2: Under current-controlled stimulation the electrode capacitance can be ignored. Model 3: Under voltage-controlled stimulation with DBS electrodes the tissue capacitance can be ignored. Model 4: Electrostatic approximation which includes only tissue resistance. (B) Interaction between electrode and tissue capacitance may occur during voltage-controlled stimulation when their values are comparable. Three cases are shown, each of which details the response of the full circuit model from part (A) under voltage-controlled stimulation for varying _C_electrode/_C_tissue ratios. Case 1: For the DBS electrode the interactions between electrode and tissue capacitance causes an error of about 1% in _V_tissue, _τ_=1.3 ms. Case 2: For a _C_electrode/_C_tissue ratio of 10, _V_tissue is reduced by 10%, _τ_=163 μs. Case 3: A _C_electrode/_C_tissue ratio of 1 causes a 50% reduction in _V_tissue and reduces τ to 28.7 μs.

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