Evaluation of novel stimulus waveforms for deep brain stimulation

Abstract

Deep brain stimulation (DBS) is an established therapy for the treatment of a wide range of neurological disorders. Historically, DBS and other neurostimulation technologies have relied on rectangular stimulation waveforms to impose their effects on the nervous system. Recent work has suggested that non-rectangular waveforms may have advantages over the traditional rectangular pulse. Therefore, we used detailed computer models to compare a range of charge-balanced biphasic waveforms with rectangular, exponential, triangular, Gaussian and sinusoidal stimulus pulse shapes. We explored the neural activation energy of these waveforms for both intracellular and extracellular current-controlled stimulation conditions. In the context of extracellular stimulation, we compared their effects on both axonal fibers of passage and projection neurons. Finally, we evaluated the impact of delivering the waveforms through a clinical DBS electrode, as opposed to a theoretical point source. Our results suggest that DBS with a 1 ms centered-triangular pulse can decrease energy consumption by 64% when compared with the standard 100 µs rectangular pulse (energy cost of 48 and 133 nJ, respectively, to stimulate 50% of a distributed population of axons) and can decrease energy consumption by 10% when compared with the most energy efficient rectangular pulse (1.25 ms duration). In turn, there may be measureable energy savings when using appropriately designed non-rectangular pulses in clinical DBS applications, thereby warranting further experimental investigation.

Figure 1

Stimulus waveforms. (a) Rectangular cathodic waveform with labeled phases. The cathodic stimulus pulse is followed by a zero current interphase interval of 0.1 ms, and then by an anodic recharge phase of 5 ms. (b) Cathodic stimulus pulse of the waveforms investigated. The non-rectangular pulses were defined such that their pulse width matched the corresponding rectangular pulse width at 50 % their peak amplitude. (c) Transmembrane voltage response of an axon node to a threshold stimulus using each waveform.

Figure 2

Extracellular membrane voltage during -1 mA stimulation with a (a) point-source electrode and (b) human DBS electrode. Seed points for neuron placement relative to the electrode were randomly distributed 2 mm along the x-axis, and 1 mm along y (perpendicular to the page) and z-axes. Current amplitude thresholds for action potential initiation with a (c) point-source electrode and (d) human DBS electrode. Stimulation with 100 μs duration rectangular waveforms. Neuron color represents the threshold for activation. Black markers indicate node of action potential initiation.

Figure 3

Comparison of charge and energy required to intracellularly activate a single myelinated axon. Current was injected into the central node of Ranvier via a simulated current clamp using 8 different waveforms (inset). Upper left: Strength-duration curve. Upper Right: Charge required for activation. Lower left: Energy required for activation. Lower right: Energy versus charge thresholds. Gaussian and centered triangular waveforms demonstrate minimal energy thresholds, and have significant overlap.

Figure 4

Peak current, charge and energy required to activate 25 of 50 neurons, averaged across 50 populations, using an extracellular point-source electrode. Error bars represent the standard error.

Figure 5

Peak current, charge and energy required to activate 25 of 50 neurons, averaged across 50 populations, using a DBS electrode. Error bars represent the standard error.

Figure 6

Energy recruitment curves. Stimulus energy required to activate 2 μm diameter fibers of passage with 1.25-ms rectangular, 1-ms centered-triangular and 1-ms Gaussian waveforms. In the inset, activation of 5.7 μm diameter fibers of passage demonstrated a global decrease in the energy required for recruitment relative to the 2.0 μm diameter fibers while still exhibiting a lower relative energy threshold with triangular and Gaussian waveforms. Error bars represent the standard error.

Figure 7

“Safe” activation with energy-optimal waveforms. DBS electrode used to stimulate a single fiber of passage. Waveform pulse width and amplitudes were adjusted to minimize energy injection. Left: Energy optimal stimulation with no limitation on charge injection. Right: Energy optimal stimulation with a charge injection limit of 1.38 μC. Rectangular (solid black), centered-triangular (dark gray, dashed) and Gaussian (light gray) waveforms had similar values, and have significant overlap.

Figure 8

Effects of tissue capacitance on waveform shape and energy threshold. (a) Waveforms (100 μs pulse width) were passed through a low-pass RC circuit (time constant of 3 or 30 μs). (b) Energy required to activate 50% of a population of fibers with a DBS electrode in a capacitive tissue medium.