Acute to long-term characteristics of impedance recordings during neurostimulation in humans

Abstract

Objective.This study aims to characterize the time course of impedance, a crucial electrophysiological property of brain tissue, in the human thalamus (THL), amygdala-hippocampus, and posterior hippocampus over an extended period.Approach.Impedance was periodically sampled every 5-15 min over several months in five subjects with drug-resistant epilepsy using an investigational neuromodulation device. Initially, we employed descriptive piecewise and continuous mathematical models to characterize the impedance response for approximately three weeks post-electrode implantation. We then explored the temporal dynamics of impedance during periods when electrical stimulation was temporarily halted, observing a monotonic increase (rebound) in impedance before it stabilized at a higher value. Lastly, we assessed the stability of amplitude and phase over the 24 h impedance cycle throughout the multi-month recording.Main results.Immediately post-implantation, the impedance decreased, reaching a minimum value in all brain regions within approximately two days, and then increased monotonically over about 14 d to a stable value. The models accounted for the variance in short-term impedance changes. Notably, the minimum impedance of the THL in the most epileptogenic hemisphere was significantly lower than in other regions. During the gaps in electrical stimulation, the impedance rebound decreased over time and stabilized around 200 days post-implant, likely indicative of the foreign body response and fibrous tissue encapsulation around the electrodes. The amplitude and phase of the 24 h impedance oscillation remained stable throughout the multi-month recording, with circadian variation in impedance dominating the long-term measures.Significance.Our findings illustrate the complex temporal dynamics of impedance in implanted electrodes and the impact of electrical stimulation. We discuss these dynamics in the context of the known biological foreign body response of the brain to implanted electrodes. The data suggest that the temporal dynamics of impedance are dependent on the anatomical location and tissue epileptogenicity. These insights may offer additional guidance for the delivery of therapeutic stimulation at various time points post-implantation for neuromodulation therapy.

Keywords: biological impedance; circadian cycle; epilepsy; implant effect; intracranial monitoring; neuromodulation.

Figure 1.

Impedance measurement. (A) The investigational Medtronics RC+S^™ is a rechargeable device that enables 16 electrode contact electrical stimulation and programmable 4 LFP sensing channels from bipolar electrode contact pairs. (B) Lateral x-ray after implantation of the bilateral ANT (3387-leads) and bilateral AMG-HPC (3391-lead) targets. The lead extensions are tunneled down the neck to the sub-clavicular device pocket. The 3391-lead has four contacts (surface area = 11.97 mm2) spanning 24.5 mm. The contacts are 3.0 mm long and separated by 4.0 mm. The 3387-lead has four contacts (contact surface area = 5.985 mm2) spanning 10.5 mm. The individual contacts are 1.5 mm long and separated by 1.5 mm. (C) Schematic diagrams of the microenvironment of the electrode and brain tissue (a) and the corresponding model using saline/microbead composites (b) for benchtop experiment. The 2-point measurement employs the same electrodes contacts (E1 & E2) for both electrical stimulation and voltage sensing. The 4-point impedance measurement uses different electrodes for stimulation (E1 & E4) and sensing (E2 & E3). The 4-point measurements eliminate the interface electrode-electrolyte polarization, related to electrical stimulation, from the voltage measurements. (D) The RC+S^™ calculates 2-point impedance using Ohm’s law, Z = V/I, where I is the injected current (0.4 mA, 80 μs pulse width) and V is the voltage response measured at 70 μsec. The voltage recording using 2-point measurement shows the voltage response to the impulse current (0.4 mA, 80 μs pulse width) with charging of the electrode-electrolyte double layer capacitor, which reaches an asymptotic voltage within ~50 μs. (E) Impedance measured using sinusoidal currents in saline/microbead composites (1 – 5000 Hz). The 2-point measurements are dominated at low frequency (< 500 Hz) by the frequency dependent capacitive double-layer related to the electrolyte polarization at the electrode-electrolyte interface. The 4-point impedance measurement, utilizing different electrodes for current injection and voltage response sensing, yields a purely resistive impedance with no frequency dependence (10 – 5000 Hz). The RC+S^™ impedance measurement (blue dashed line) can be seen to correlate with ~1000 Hz sinusoidal current input.

Figure 2.

Fitting the model to the impedance change in the first three weeks post-implant (S1, S2, S3 and S5). (A) The measured effective impedance values (Z) were fitted with a piecewise function consisting of a parabolic and an exponential function, Equation (1). The light purple dots show the sampled impedance measures. The orange curve indicates the fitted parabolic function, while the brown curve the fitted exponential function. $t_1$ is the time when the fitted function is at the minimum $c_1,t_0$ the boundary between the functions and $t_{\alpha }$ the time when the impedance is supposed to be at stable state (see Methods and Appendix). We define the time to reach stability as the time elapsed from $t_1$ to $t_{\alpha }$, i.e., $t_{\alpha }-t_1.c_2$. is the asymptotic level of the fitted exponential. Note that half-life $t_{1/2}$ is relative to the boundary $t_0$. (B) Boxplots of R² (goodness-of-fit, GOF) of the model fits of all individual channels shown in (C) (sample size $N$ of THL: $\left[N_{\text{left}}=16,N_{\text{right}}=16\right]$, AMG-HPC: [6, 8] and post-HPC: [10, 7]). (C) The raw impedance measures and the fitted models at each individual channel (see Supplementary Table 3 for the locations of the electrodes). The blue dots indicate the raw impedance, the red curves the fitted piecewise model and the cyan curves the fitted double exponential model. Arrows indicate apparent deficiency of the double exponential model. Note that subject S4 was excluded because no impedance measurement was performed in the first 9 days after device implantation and electrode EL_15 of S5 was disconnected after the implant. Abbreviation: exp., exponential.

Figure 3.

Characterization of acute to subacute impedance change post-implant (S1, S2, S3 and S5). Boxplots of (A) time of minimum impedance $\left(t_1\right)$ of the fitted models for all the available electrodes from the three areas at left/right hemisphere (sample size N of THL: $\left[N_{\text{left}}=16,N_{\text{right}}=15\right.]$, AMG-HPC: [6, 8] and post-HPC: [9, 7]), (B) half-life ([16, 15], [5, 8], [9, 7]), (C) time from the minimum impedance to reach stability ([16, 15], [5, 8], [7, 7]) and (D) the minimum ($c_1$, [16, 14], [6, 8], [10, 6]) and asymptotic ($c_2$, [16, 14], [6, 7], [10, 7]) impedance levels are shown. The solid-colored boxes are for $c_1$ and the no-filled ones $c_2$ in (D). For all boxplots, the blue boxes were from channels of the three anatomic areas at the left hemisphere and the orange ones at the right hemisphere. Note that S4 was not included in this analysis (see Methods and Figure 1) and that the sample size $N$ involved in significant test excluded outliers (see Supplementary Table 3 for total sample size). Significance test: two-sample t-test assuming unequal variances, * p < 0.01, ** p < 0.001; Abbreviation: THL, thalamus; AMG-HPC, amygdala-hippocampus; post-HPC, posterior hippocampus; Min., Minimum; imp., impedance.

Figure 4.

Characterization of impedance change during the gaps of therapeutic stimulation from subjects S1 – S4. (A) An example of impedance changes in vivo and in saline. The 2-point impedance was measured every two minutes from the electrodes EL_01 and EL_02 of a Summit RC+S^™ device immersed in a body of physiological saline. The red solid and dashed lines represent the measured impedance from these two electrodes (between 145 and 150 Ω, right axis). The vertical solid green line indicates the termination of a stimulation (frequency: 2 Hz, amplitude: 3.5 mA, pulse-width: 200 μsec) delivered for > 5 hours, which was resumed after 8 hours (indicated by the purple vertical solid line). As a comparison, the blue solid and dashed lines represent the impedance values of the two electrodes targeting the left THL of subject S3, aligned with those measured in the saline at stimulation offset (t = 0). The parameters of the stimulation delivered in S3 were the same as those for the saline experiment, except that the therapeutic stimulation resumed after ~9 hours (the dashed purple vertical line). We can see significant rebound of impedance (with maximum around 1000 to 1060 Ω) in this specific gap (~70 days post-implant). No such rebound can be seen in the impedance measures in the saline. (B) Impedance changes relative to the impedance values prior to the gaps (sample size of gaps 30, 5, 27, 29; see Methods for details). The upper row shows the impedance changes measured from the stimulation electrodes targeted in left/right THL of the four subjects. The lower row the impedance changes from the non-stimulation electrodes/channels in the THL. Each dot indicates the relative impedance change of median values in a gap. The dashed lines indicate the mean impedance rebound values estimated by the GEE model as a function of time, where the shaded areas indicate the 95% CI around the mean. A tuple of parenthesized three values of frequency (Hz), amplitude (mA) and pulse-width (μsec) display the stimulation states immediately before the gaps. For instance, a tuple of (2, 3.5, 200) indicates 2 Hz current pulse with 3.5 mA and 200 μsec pulse-width. (C) Boxplots of half-life measures from the stimulation electrodes. The blue plots show the half-life measures of the fitted exponential functions for the impedance change in the first 3 weeks (21 days) after the implant and the orange plots the half-life measures of the fitted exponential for the impedance in the gaps (sample size N of left: [first 21 days = 7, gaps = 108], N of right: [7, 86]). Note that all measures are from the stimulation electrodes targeted in THL and that subject S5 was not included in the analysis (see Methods). Abbreviations: THL, thalamus; stim., stimulation, chan., channels; CI, confidence interval.

Figure 5.

Long-term amplitude and phase of circadian cycles of impedance at THL, AMG-HPC and post-HPC. (A) Amplitude and (B) phase of circadian cycle of left/right hemisphere. Boxplots represent the distribution of the estimates (see Supplementary Table 4 for the number of samples) in a 100-day interval for each subject. Note that scales vary between panels for amplitude and are consistent for phase. S5 was excluded and no signals from left AMG-HPC structure of S2 (see Methods). Abbreviations: SD, standard deviation; THL, thalamus; AMG-HPC, amygdala-hippocampus; post-HPC, posterior hippocampus.