Intramembrane Cavitation as a Predictive Bio-Piezoelectric Mechanism for Ultrasonic Brain Stimulation

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Intramembrane Cavitation as a Predictive Bio-Piezoelectric Mechanism for Ultrasonic Brain Stimulation

Michael Plaksin, Shy Shoham, and Eitan Kimmel

Phys. Rev. X 4, 011004 – Published 21 January 2014

Abstract

Low-intensity ultrasonic waves can remotely and nondestructively excite central nervous system (CNS) neurons. While diverse applications for this effect are already emerging, the biophysical transduction mechanism underlying this excitation remains unclear. Recently, we suggested that ultrasound-induced intramembrane cavitation within the bilayer membrane could underlie the biomechanics of a range of observed acoustic bioeffects. In this paper, we show that, in CNS neurons, ultrasound-induced cavitation of these nanometric bilayer sonophores can induce a complex mechanoelectrical interplay leading to excitation, primarily through the effect of currents induced by membrane capacitance changes. Our model explains the basic features of CNS acoustostimulation and predicts how the experimentally observed efficacy of mouse motor cortical ultrasonic stimulation depends on stimulation parameters. These results support the hypothesis that neuronal intramembrane piezoelectricity underlies ultrasound-induced neurostimulation, and suggest that other interactions between the nervous system and pressure waves or perturbations could be explained by this new mode of biological piezoelectric transduction.

Received 1 August 2013

DOI:https://doi.org/10.1103/PhysRevX.4.011004

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Michael Plaksin, Shy Shoham^*, and Eitan Kimmel^†

Faculty of Biomedical Engineering and Russell Berrie Nanotechnology Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel

^*Corresponding author. sshoham@bm.technion.ac.il
^†Corresponding author. eitan@bm.technion.ac.il

Popular Summary

A noninvasive method that can assess region-specific brain functions and modify and control aberrant brain activities would be a dream come true for neuroscience and neuromedicine. That is why the recently observed ability of low-intensity, focused ultrasound waves to stimulate neurons in different areas of the brain, including the area controlling visual function, has caused a great deal of excitement. Until now, however, this phenomenon was as mysterious as it is exciting: The relevant scientific literature on it is empirical and the explanations speculative. Both qualitative and quantitative understanding that can guide future investigations is missing. In this paper, we present a new, concrete “neuronal bilayer sonophore” model that attempts to address this gap in understanding.

We have recently proposed a biomechanical membrane model that predicts the emergence of pulsating nanobubbles, induced by ultrasound, inside bilayer membranes of stimulated biological cells and, in particular, neurons. The current neuronal bilayer sonophore model takes the earlier model further with another conceptually new step: coupling the membrane mechanics, through a membrane-structure-dependent capacitance, to the generation of membrane action potentials, that is, neuronal firing. Using the fundamental Hodgkin-Huxley model for the emergence of such action potentials, we show that the pulsating membrane leaflets generate oscillations in the membrane potential that lead to a slow potential buildup across the membrane—until the buildup is discharged as an action potential. This new understanding explains, quantitatively, to a reasonably good degree, the slow effect of ultrasonic stimulation and provides a good fit to very recent in vivo measurements of muscle responses in mouse motor cortex to ultrasound stimulation.

These new concepts should facilitate the development of focused ultrasound stimulation—currently the only method that allows for controlled noninvasive stimulation of excitable tissues with millimeter spatial resolution essentially anywhere in the brain—and have various applications in the diagnosis and treatment of brain disorders.

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Vol. 4, Iss. 1 — January - March 2014

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Figure 1
Neuronal bilayer sonophore model. (a) Biomechanical and bioelectrical structure of NBLS model of small membrane patch in a CNS pyramidal neuron. A round patch of the bilayer leaflets (radius $a$ , initial gap $Δ$ ) dynamically deforms into a dome shape with a maximal deflection $Z$ , radius of curvature $R (Z)$ and tension $T$ . The membrane equivalent circuit has a potential ( $V_{m}$ ), time-varying capacitance ( $C_{m}$ ), and Hodgkin-Huxley type ionic conductances ( $g_{m}$ ) and sources [ $v (g_{m})$ ]. (b, c) Mechano-electrical dynamics of first three cycles of the model membrane exposed to US (pressure amplitude 500 kPa and frequency 0.5 MHz): (b) Local deflection at each radial coordinate [ $z (r)$ ]. (c) Acoustic pressure (kPa), tension ( $mN / m$ ), combined attraction/repulsion force per area between the leaflets (sum of molecular and electrostatic forces $P_{M} + P_{e c}$ , kPa), membrane capacitance ( $μ F / {cm}^{2}$ ), and capacitive displacement current $\frac{d C_{m}}{d t} V_{m} (A / {cm}^{2})$ .
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Figure 2
The effect of continuous US stimuli (frequency 0.35 MHz, intensity $320 mW / {cm}^{2}$ ) on membrane potential & charge (top panels), and on sodium and potassium channels kinetics (bottom). (a) For stimulus duration of 30 ms, a single AP is generated immediately after the stimulus ends. Inset shows membrane potential oscillations. (b) For a stimulus duration of 40 ms, four APs are generated during the stimulus. Insets: magnified view of open probabilities for the M gate ( ${Na}^{+}$ channel kinetics) and the N and P gates ( $K^{+}$ channels).
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Figure 3
Relationship between US stimulus parameters and APs generation in NBLS model. (a) Threshold intensity versus frequency required to generate a single AP (duration: 30 ms). (b,c) Threshold intensity and energy per unit membrane area versus stimulus duration required to generate a single AP (frequency: 0.35 MHz). (d) The number of APs induced by US stimuli as a function of US intensity and stimulus duration (frequency: 0.35 Mhz). (e) Spike rate versus intensity for US frequencies (in MHz) of 0.25 (red squares), 0.4 (black squares), 0.5 (blue squares), 0.6 (gray squares), 0.8 (purple squares) and 1.0 (brown squares). (f) Latency before the appearance of the first AP during the US stimulation versus US intensity. Symbols and colors as in $(e)$
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Figure 4
Comparison of NBLS model predictions and in-vivo brain stimulation measurements [18]. (a) Success rates for eliciting motor responses versus US intensity at different frequencies (continuous stimulation for 40000 cycles). NBLS predictions (top panel) and the experimental results from Ref. [18] (bottom panel) are shown for US frequencies in the range 250 to 600 kHz (an additional 1 MHz simulation is also shown). Note that stimulus duration changes with the frequency (representative values shown). (b) Model-based predictions of success rate as a function of US pressure amplitude and stimulus duration (pressure amplitudes were normalized by maximal value used, 725 kPa; frequency: 0.5 MHz). For comparison, in-vivo measurements in two different mice [18] are shown in the upper part for the same US stimulation parameters. (c) Success rate as a function of duty cycle for simulation of NBLS model with pulsed-mode US (frequency: 0.5 MHz, Pulse repetition frequency: 1.5 kHz, stimulus duration: 80 ms, intensity: $10 W / {cm}^{2}$ spatial peak pulse average). Two experimental data points from Ref. [18] are shown for duty cycle values 30% and 100% (stars, other US parameters were similar to the simulated values). Error bars represent the standard error of the mean.
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