Stimulation Efficiency With Decaying Exponential Waveforms in a Wirelessly Powered Switched-Capacitor Discharge Stimulation System

Abstract

The purpose of this study was to test the feasibility of using a switched-capacitor discharge stimulation (SCDS) system for electrical stimulation, and, subsequently, determine the overall energy saved compared to a conventional stimulator. We have constructed a computational model by pairing an image-based volume conductor model of the cat head with cable models of corticospinal tract (CST) axons and quantified the theoretical stimulation efficiency of rectangular and decaying exponential waveforms, produced by conventional and SCDS systems, respectively. Subsequently, the model predictions were tested in vivo by activating axons in the posterior internal capsule and recording evoked electromyography (EMG) in the contralateral upper arm muscles. Compared to rectangular waveforms, decaying exponential waveforms with time constants >500 μs were predicted to require 2%-4% less stimulus energy to activate directly models of CST axons and 0.4%-2% less stimulus energy to evoke EMG activity in vivo. Using the calculated wireless input energy of the stimulation system and the measured stimulus energies required to evoke EMG activity, we predict that an SCDS implantable pulse generator (IPG) will require 40% less input energy than a conventional IPG to activate target neural elements. A wireless SCDS IPG that is more energy efficient than a conventional IPG will reduce the size of an implant, require that less wireless energy be transmitted through the skin, and extend the lifetime of the battery in the external power transmitter.

Fig. 1

Key power delivery/management blocks and stimulus waveforms of wireless stimulation systems. A power transmitter (Tx) drives a primary coil, L₁, at the carrier frequency, f_C, generating an ac voltage, V_COIL, across a secondary coil, L₂. (a) A conventional wireless system with voltage-controlled stimulation (VCS) or current-controlled stimulation (CCS). A rectifier and a regulator convert V_COIL to dc output voltage, V_DD, to supply a stimulator, which typically generates rectangular voltage or current stimuli. (b) The proposed wireless system with switched-capacitor discharge stimulation (SCDS). The SCDS system efficiently charges a storage capacitor bank, C_N and C_P, directly from the inductive link and transfers charge from the capacitors to tissue, generating decaying exponential stimuli.

Fig. 2

A magnetic resonance image of the cat head segmented into three regions. (a) A T1-weighted (T1w) magnetic resonance (MR) image was used to construct three volumes: a brain (yellow), a skull that surrounds the brain (red), and a region of lumped soft tissues (blue). Binary masks of the segmented volumes were overlaid on the T1w MR image and viewed in (b) coronal, (c) sagittal and (d) axial planes. The positive x axis points to the right of the head; the positive y direction in the superior direction (i.e., toward the top of the head); and, the positive z direction in the anterior direction (i.e., toward the mouth).

Fig. 3

Electrical stimulation of corticospinal tract (CST) axons in a model of the cat head. (a) Isopotential contours surrounding the active electrode in monopolar anodic configuration. (b) Applied rectangular and decaying exponential waveforms were voltage-regulated, asymmetric, and constructed so that the integral of the waveform with respect to time was zero. Waveforms consisted of a short 300 µs cathodic phase followed by a long 700 µs anodic phase and were delivered at 244 Hz. Note: normalized waveforms are shown in this graph. (c) The spatiotemporal distribution of extracellular potentials formed from parts a and b, based on (3), was used to stimulate CST axons in the model. The image shows the extracellular potentials applied to the CST axons at the onset of the stimulus pulse. Inset: a coronal view.

Fig. 4

Block diagram of the in vivo experimental setup with the SCDS system. The wirelessly-powered SCDS system and its recording setup enable simultaneous brain stimulation to the posterior IC and EMG recording from the upper arm muscles, respectively. The power Tx module, including the 2 MHz inductive link with primary (∅₁ = 2 cm) and secondary (∅₂ = 1 cm) coils and 1.2 cm coil spacing, was enclosed in a 15 (L) × 8 (W) × 5 (H) cm³ box. The SCDS prototype PCB occupied 3.4 × 2.9 cm² and housed the SCDS chip (5 × 2.4 mm²), 4 pairs of off-chip storage capacitors (1.6 × 0.8 mm² each, 5–10% tolerance, X5R/X7R, capacitance of 1 µF, 1 µF, 3.3 µF, and 4.7 µF), and a few off-chip components for testing.

Fig. 5

Efficiencies of rectangular and decaying exponential stimulus waveforms from computational models. Normalized (a) stimulus energy, (b) injected charge, and (c) peak stimulus voltage required to activate 50% of the population of model axons. Each result is the median value from 300 samples normalized by the value for the rectangular stimulus. (d) Normalized stimulus energy for decaying exponential waveforms with τ = 500 µs to activate 25%, 50%, 75%, and 100% of the population of model axons.

Fig. 6

In vivo stimulation efficiency of the SCDS system compared to the conventional VCS system. (a) The integral of rectified EMG voltage (IRE) vs. peak stimulus voltage and (b) IRE vs. stimulus energy graphs from in vivo experiments (n = 4).

Fig. 7

Comparison of stimulation efficiencies between SCDS and VCS systems. Peak voltage amplitude, stimulus energy, and injected charge of SCDS-based decaying exponential stimuli (storage capacitance of 2 µF or 10 µF) required to activate the half maximal IRE, normalized by those of VCS-based rectangular voltage stimuli (mean ± standard error, n = 4), based on (5).