Article Figures & Data
Figures
- Figure 1.
Cortical and thalamic NICE models. A, Geometrical and biophysical representation structure of the NICE models: top view (left) of the US-induced dome-shaped BLS intermembrane cavities (light gray) in the plasma membrane bare zones (dark grey), bounded by cholesterol-rich protein islands (red areas). The equivalent electrical circuit of this biophysical complex structure (right) includes a potential (Vm), time-varying capacitance (Cm), and Hodgkin–Huxley type ionic conductances (gi) and sources (Vi). Each neuron type channels' composition is summarized in the neocortical and thalamic tables. B, Electrical dynamics during first three cycles of the model membrane exposed to US (f=0.69 MHz, 3.3 W/cm2): acoustic pressure (kPa), membrane capacitance (μF/cm2), and membrane potential (mV). C, A simplified network of RS, FS, and LTS cortical neurons. The filled black circles and open triangles are GABAA and AMPA- type synapses, respectively. The excitatory connections to the two FS and LTS inhibitory neurons are depressing and facilitating, respectively. The synaptic strength is represented by changes of the lines' thickness (logarithmically scaled) and ITh-RS and ITh-FS are the thalamic inputs.
- Figure 2.
Effect of continuous and pulsed US stimuli on the different cortical NICE-neurons (f=0.69 MHz). A, B, Effect of US stimulus (3.3 W/cm2, indicated by bars) on membrane potential and charge (top), sodium and potassium channels kinetics (middle), and on LTS neuron T-type calcium channels kinetics (bottom). Fifty millisecond continuous stimulus, effectively stimulates all neuron types (A), whereas a 300-ms-long pulsed stimulus (pulse repetition frequency (PRF) 100 Hz and duty-cycle 5%) causes only the LTS neuron to tonically fire a volley of APs (B). This selective LTS excitation is mediated through the elevation of the T-type calcium channels' S-gates open probability during the US off times (right), which elevates these channels' conductance and consequently amplifies the charge accumulation process that occurs during US's-on periods. C–E, Threshold intensity versus duration required to generate a single AP using constant duty-cycle (PRF, 100 Hz). The excitation thresholds for the RS and FS neurons at 5% duty-cycle are >3.5 orders of magnitude higher than for the LTS neuron (E), decreasing rapidly to ∼2× at 50% duty-cycle (C).
- Figure 3.
Detailed US response of LTS neurons (f=0.69 MHz). A, The contribution of each channel type to the accumulated membrane charge during 10 ms of CW versus a short-pulsed US stimulus (5% duty-cycle, PRF=100Hz): leak channels have the biggest contribution during the US-on period, whereas the T-type calcium channels dominate the US-off period. B, Leak and calcium channels' dynamical response to the first few US cycles (1.3 W/cm2); the hyperpolarized phase drives negative leak currents that insert positive charge into the cell, while rapidly suppressing the calcium conductance due to the changes in S- and U-type gates open probability p(t), through dynamical perturbations of the steady state probability (p∞), and the gates' time constants (τ). C, T-type calcium versus sodium channels' dynamical responses during sparse stimulation (5% duty-cycle, 1.3 W/cm2); the comparison highlights the dramatic changes during the US breaks in the calcium currents, open probability p(t) and the steady-state open probability (p∞) of the S- and U-type gates, whereas the Na+ gates are mostly dormant prior to action potential initiation (arrow). D, The pulsed US excitation thresholds of native RS and FS neurons versus following the chimeric addition of T-type calcium channels (RS+ and FS+).
- Figure 4.
Phase plane diagram of single-neuron responses to varying US stimulation duty-cycle and intensity versus experimental cortical neuromodulation parameters. The phase diagram boundaries denote threshold intensities for US-mediated responses (frequency 0.69 MHz, duration 500 ms) from excitatory RS neurons (green dashed lines indicating 10 Hz and 1 kHz PRFs) and inhibitory LTS interneurons (red dashed lines, changes only slightly for different PRFs, not shown). These boundaries separate the phase diagram into regions where either the inhibitory LTS neurons are activated alone (red, “suppression zone”) or the RS and the LTS neurons are jointly activated leading to net network stimulation (green, “activation zone”). The superposed bars indicate the experimental parameter ranges used in seven published cortical ultrasonic neuromodulation studies, color-coded according to the mediated responses: Ref. 1 (King et al., 2013; bars with diagonal lines), Ref. 2 (Yoo et al., 2011a), Ref. 3 (Kim et al., 2015), Ref. 4 (Kim et al., 2012), Ref. 5 (Kim et al., 2014), Ref. 6 (King et al., 2014), and Ref. 7 (Tufail et al., 2011). The excitation parameters reported for King et al. (2013) were those that caused stimulation success rates significantly higher than their noise floor (∼20%), with low-frequency CW intensities corrected for the expected formation of standing waves (Plaksin et al., 2014).
- Figure 5.
Simplified cortical NICE-network responses to different US waveforms and intensities. The US stimuli (US frequency and duration: 0.69 MHz and 1 s) are indicated by black bars (A–C). A, For a stimulus duty-cycle of 5% and 0.1 W/cm2 intensity (PRF, 100 Hz) no significant response to US is observed. B, Increasing the intensity to 3.3 W/cm2 causes FS and RS activity suppression due to strong LTS activation (∼40 Hz). C, Increasing the duty-cycle to 50% (PRF, 10 Hz) leads to high frequency activation of the RS and FS neurons, unsuppressed by the weaker LTS firing (only at the beginning of each US pulse). D, Phase plane diagram for the network responses to US with varying duty-cycle and intensity (PRF, 100 Hz). Marks a–c indicate the conditions of the respective simulations (matching the experimental observations of Yoo et al. (2011a) and marks d, e, indicate parameters from Kim et al. (2015) where the experimental responses were no longer suppressive. The vertical green bar represent human primary somatosensory cortex stimulation parameters used to evoke tactile sensations (Lee et al., 2015); f marks the only case where no response was observed. The green and red arrows and the inset depict the effect of increased thalamic input on the activation and suppression thresholds.
- Figure 6.
The response of thalamic NICE-TC and NICE-RE models to low duty-cycle US stimulation waveforms. The US stimuli (US intensity: 5.2 W/cm2; US frequency: 0.69 MHz; PRF, 100 Hz) are indicated by black bars (A–C). A, B, For a 1.5 s, 5% duty-cycle US stimulus, the TC cell fires a tonic 100 Hz volley of APs, whereas the RE cell fires only one volley and stops. Bottom, The currents' profiles of the segments marked in the top, where IU is the sum of Ih,
, and ILeak currents (see complete channel composition in the Theoretical framework section). C, Increasing the duty-cycle to 6% and 7% brings the RE neurons to fire periodical volleys and a constant volley of APs after two braked volleys, respectively. D, The relation between the TC and RE neurons' spike rates and the US stimulation duty-cycle, calculated for the last 0.5 s period of the 1.5-s-long US stimulation. - Figure 7.
Effect on cortical NICE-neuron models from different mammalian species (Pospischil et al., 2008) of continuous and 5% duty-cycle pulsed US stimuli (US intensity: 3.3 W/cm2; US frequency: 0.69 MHz; PRF, 100 Hz, indicated by bars). US stimulus effects on membrane potential, charge and channels kinetics for cortical neurons of two different mammals (RS and FS, ferret visual cortex; LTS, cat association cortex). The panel organization and responses were similar to those described in Figure 2 and are explained by the very same underlying mechanisms. For continuous stimuli (A; 100 ms duration) there isn't a major difference between the responses of the different neuron types, except for a delay in the LTS neuron firing due to low leaky channels' conductances that cause slower charge accumulation. For pulsed stimuli (B; 1500 ms duration), only the LTS neuron responded.
- Figure 8.
Effect of partial sonophore membrane area coverage during continuous and 5% duty-cycle pulsed US stimuli (US intensity: 3.3 W/cm2; US frequency: 0.69 MHz; PRF, 100 Hz, indicated by bars) on cortical RS (A) and LTS-NICE (B) neuron models, respectively. Partial coverage (here 75%) reduces the membrane potential oscillations down to a narrower range (>−150mV). Although the potential oscillations were more limited, the neurons' response to continuous and pulsed stimulation is still evident. Membrane capacitance was calculated as a weighted mean of the resting and dynamic capacitances:
, where fs is the active area fraction. - Figure 9.
Effect of purely sinusoidal capacitive drive on cortical RS and LTS-neuron models in continuous (A) and 5% duty-cycle (B) stimulation modes (
, CAmp
≈0.8 μF/cm2, f=0.69 MHz; PRF, 100 Hz, indicated by bars).
is the resting membrane capacitance. Although the sinusoidal and the intramembrane cavitation theory-based capacitance variations are fundamentally different, the basic qualitative neural responses remain the same. The CAmp was determined when 80% decline in the membrane capacitance (Fig. 1B; f=0.69 MHz and intensity 3.3 W/cm2) was taken into account.
Tables
Parameter Symbol Unit Value Source Biomechanical Parameters 1 Thickness of the leaflet nm 2 Plaksin et al., 2014 2 Initial gap between the two leaflets (uncharged) 1.4 3 Initial gap between the two leaflets (when charged) 1.26 (RS) Calculated from equilibrium state using Plaksin et al., 2014, their Eq. 2 4 1.26 (FS) 5 1.3 (LTS) 6 1.28 (TC) 7 1.21 (RE) 8 Attraction/repulsion pressure coefficient Pa 105 Plaksin et al., 2014 9 Exponent in the repulsion term x — 5 10 Exponent in the attraction term y — 3.3 11 Dynamic viscosity of the leaflets Pa·s 0.035 12 Dynamic viscosity of the surrounding medium 0.7·10−3 13 Diffusion coefficient of air in the surrounding medium m2·s−1 3·10−9 14 Density of the surrounding medium
kg·m−3 1028 15 Speed of sound in the surrounding medium
m·s−1 1515 16 Initial air molar concentration in the surrounding medium (O2+N2)
mol·m−3 0.62 17 Henry’s constant for dissolved air in the surrounding medium
Pa·m3·mol−1 1.63·105 18 Static pressure in the surrounding medium
Pa 105 19 Radius of the leaflets' boundary a nm 32 20 Width of the boundary layer between the surrounding medium and the leaflets
0.5 21 Areal modulus of the bilayer membrane
N·m−1 0.24 22 Relative permittivity of the intramembrane cavity
— 1 23 Membrane baseline capacitance per unit area
µF·cm−2 1 24 Surrounding medium temperature Tem K 309.15 Pospischil et al., 2008; Destexhe et al., 1998a Biophysical parameters 25 Maximal conductance of Na+ channels
mS·cm−2 56 (RS) Pospischil et al., 2008 50 (RS; Fig. 7) 26 58 (FS) 50 (FS; Fig. 7) 27 50 (LTS) 28 90 (TC) Destexhe et al., 1998a 29 200 (RE) 30 Maximal conductance of delayed-rectifier K+ channels
6 (RS) Pospischil et al., 2008 5 (RS; Fig. 7) 31 3.9 (FS) 10 (FS; Fig. 7) 32 4 (LTS) 5 (LTS; Fig. 7) 33 10 (TC) Destexhe et al., 1998a 34 20 (RE) 35 Maximal conductance of slow non-inactivating K+ channels
0.075 (RS) Pospischil et al., 2008 0.07 (RS; Fig. 7) 36 0.0787 (FS) 0 (FS; Fig. 7) 37 0.028 (LTS) 0.03 (LTS; Fig. 7) 38 Maximal conductance of low-threshold Ca2+ channels
0.4 (LTS) 39 2 (TC) Destexhe et al., 1998a 40 Maximal conductance of low- threshold Ca2+ channels
3 (RE) 41 Maximal conductance of leak potassium currents
0.0138 (TC) 42 Maximal conductance of hyperpolarization-activated mixed cationic current
0.0175 (TC) 43 Maximal conductance of non-voltage-dependent, nonspecific ions channels
0.0205 (RS) Pospischil et al., 2008 0.1 (RS; Fig. 7) 44 0.038 (FS) 0.15 (FS; Fig. 7) 45 0.019 (LTS) 0.01 (LTS; Fig. 7) 46 0.01 (TC) Destexhe et al., 1998a 47 0.05 (RE) 48 Nernst potential of Na+
mV 50 Pospischil et al., 2008 49 Nernst potential of K+
−90 50 Nernst potential of Ca2+ (LTS neuron)
120 51 Reversal potential of a hyperpolarization-activated mixed cationic current
−40 Destexhe et al., 1996a 52 Nernst potential of non-voltage-dependent, nonspecific ion channels
−70.3 (RS) Pospischil et al., 2008 −70 (RS; Fig. 7) 53 −70.4 (FS) −70 (FS; Fig. 7) 54 −50 (LTS) −85 (LTS; Fig. 7) 55 −70 (TC) Destexhe et al., 1998a 56 −90 (RE) 57 Spike threshold adjustment parameter
−56.2 (RS) Pospischil et al., 2008 −55 (RS; Fig. 7) 58 −57.9 (FS) −55 (FS; Fig. 7) 59 −50 (LTS) −55 (LTS; Fig. 7) 60 −52 (TC) Destexhe et al., 1998b 61 −67 (RE) Destexhe et al., 1996b 62 Decay time constant for adaptation at slow non-inactivating K+ channels
ms 608 (RS) Pospischil et al., 2008 1000 (RS; Fig. 7) 63 502 (FS) 1000 (FS; Fig. 7) 64 4000 (LTS) 1000 (LTS; Fig. 7) 65 The resting potential of the cell membrane
mV −71.9 (RS) Calculated from Pospischil et al., 2008 −70.4 (RS; Fig. 7) 66 −71.4 (FS) −70 (FS; Fig. 7) 67 −54 (LTS) −84.6 (LTS – Fig. 7) 68 −63.4 (TC) Calculated from Destexhe et al., 1998a 69 −89.5 (RE) 70 The effective depth beneath the membrane area for calcium concentration calculations (for TC and RE neurons)
nm 100 Destexhe et al., 1998a and Destexhe et al., 1996a 71 An extracellular Ca2+ concentration (for TC and RE neurons)
mm 2 72 Decay time constants of Ca2+ (for TC and RE neurons)
ms 5 73
current Ca2+ regulation factor
mm −4· ms−1 2.5·107 74
current Ca2+ regulation factor
ms−1 4·10−4 75
current Ca2+ regulation factor
0.1 76
current Ca2+ regulation factor
0.001 77 FS to RS neuron thalamic input current ratio RTH — 1.4 Hayut et al., 2011 78 Thalamic DC current input to the RS neuron
nA 0.17 Based on Destexhe and Paré.,1999 79 AMPA synaptic currents reversal potential
mV 0 Destexhe et al., 1996a 80 GABAA synaptic currents reversal potential
-85 81 Total maximal synaptic conductance used for RS to RS connection
μS 0.002 Calculated from Vierling-Claassen et al., 2010 82 Total maximal synaptic conductance used for RS to FS connection
0.04 83 Total maximal synaptic conductance used for RS to LTS connection
0.09 84 Total maximal synaptic conductance used for FS to RS connection
0.015 85 Total maximal synaptic conductance used for FS to FS connection
0.135 86 Total maximal synaptic conductance used for FS to LTS connection
0.86 87 Total maximal synaptic conductance used for LTS to RS connection
0.135 88 Total maximal synaptic conductance used for LTS to FS connection
0.02 89 AMPA rise time constant
ms 0.1 Vierling-Claassen et al., 2010 90 AMPA decay time constant
3 91 GABAA rise time constant from FS neuron
0.5 92 GABAA decay time constant from FS neuron
8 93 GABAA rise time constant from LTS neuron
0.5 94 GABAA decay time constant from LTS neuron
50 95 Short-term synaptic plasticity facilitation factor
(from RS to LTS)f — 0.2 96 Short-term synaptic plasticity facilitation factor time constant
(from RS to LTS)
ms 200 97 Short-term synaptic plasticity facilitation factor
(from RS to FS)f — 0.5 98 Short-term synaptic plasticity facilitation factor time constant
(from RS to FS)
ms 94 99 Short-term synaptic plasticity short-time depression factor
(from RS to FS)
— 0.46 100 Short-term synaptic plasticity short-time depression factor time constant
(from RS to FS)
ms 380 101 Short-term synaptic plasticity long-time depression factor
(from RS to FS)
— 0.975 102 Short-term synaptic plasticity long-time depression factor time constant
(from RS to FS)
ms 9200 103 Neuronal cell membrane area A μm2 11.88·103 (RS) Pospischil et al., 2008 104 10.17·103 (FS) 105 25·103 (LTS) 106 29·103 (TC) Destexhe et al., 1998a 107 14·103 (RE) The synaptic strengths were calculated from Vierling-Claassen et al. (2010), multiplying their individual synaptic strengths by the average number of converging connections from each type (Vierling-Claassen et al., 2010, their Table 3) and by the ratio of membrane areas between the NICE-neuron model and the respective model in their study. The latter normalization is consistent with an assumption that the total number of putative synapses on the dendrites and soma are proportional to a neuron's size (Gibbins et al., 1998).
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