NICE

NICE Model — Neuronal Intramembrane Cavitation Excitation

Overview

The NICE model (Krasovitski et al. 2011, extended by Plaksin et al. 2014/2016) was the first computational framework to formalize the intramembrane cavitation hypothesis into a quantitative biophysical model capable of predicting neuronal responses to ultrasound. It couples a bubble dynamics model (describing the oscillatory mechanics of the bilayer sonophore) with a modified Hodgkin-Huxley electrical model (describing membrane excitability), producing a unified electromechanical system driven directly by acoustic pressure input.

1. Bubble Dynamics: The Bilayer Sonophore

The core mechanical sub-model describes the radial oscillation of a single intramembrane gas pocket of radius R(t) under acoustic forcing. The governing equation is a modified Rayleigh-Plesset equation adapted for the bilayer geometry:

\[\rho_l \left( R\ddot{R} + \frac{3}{2}\dot{R}^2 \right) = P_{gas}(R) - P_0 - P_{ac}(t) - \frac{2\sigma(R)}{R} - \frac{4\mu_l \dot{R}}{R} - \frac{4\kappa_s \dot{R}}{R^2}\]

Where:

• \(\rho_l\) = liquid density of the surrounding medium
• \(R(t)\) = instantaneous sonophore radius
• \(P_{gas}(R)\) = intramembrane gas pressure (assumed ideal gas)
• \(P_0\) = ambient static pressure
• \(P_{ac}(t) = P_A \sin(2\pi f t)\) = oscillating acoustic pressure
• \(\sigma(R)\) = nonlinear surface tension of the bilayer leaflets (strain-dependent)
• \(\mu_l\) = fluid viscosity
• \(\kappa_s\) = membrane surface dilatational viscosity

The bilayer surface tension \(\sigma(R)\) is modeled as a nonlinear function of membrane strain, capturing the elastic stiffening of the lipid bilayer at large deformations:

\[\sigma(R) = \begin{cases} 0 & R \leq R_0 \\ K_A \frac{R^2 - R_0^2}{2R_0^2} & R > R_0 \end{cases}\]

Where \(K_A \approx 0.24\) N/m is the area expansion modulus of the bilayer and \(R_0 = 32\) nm is the resting sonophore radius.

2. Electrical Coupling: Modified Hodgkin-Huxley

The mechanical oscillation of the sonophore modulates the electrical properties of the membrane. The key coupling variable is the leaflet charge density \(Q_m\) (charge per unit area of the membrane), which replaces the standard membrane voltage \(V_m\) as the primary electrical state variable. The two are related through the time-varying membrane capacitance:

\[C_m(t) = \frac{\varepsilon_0 \varepsilon_r}{d(t)}\]

Where d(t) is the instantaneous membrane thickness, which decreases as the sonophore expands (conservation of bilayer volume). As C_m increases during expansion, the membrane voltage changes even at constant charge — this is the capacitive depolarization mechanism at the heart of NICE:

\[V_m(t) = \frac{Q_m}{C_m(t)}\]

The total membrane current balance equation becomes:

\[\frac{dQ_m}{dt} = -\sum_k I_k(V_m, \text{gating variables}) + I_{stim}\]

Where the ionic currents I_k follow standard HH kinetics (NaV, KV, leak), evaluated at the instantaneous V_m derived from \(Q_m / C_m(t)\). The key modification relative to standard HH is that C_m is no longer constant — it oscillates with the sonophore dynamics, injecting an effective capacitive current even in the absence of any direct ionic conductance change.

The effective capacitive current generated by membrane oscillation is:

\[I_{cap} = \frac{dQ_m}{dt}\bigg|_{C_m} = C_m(t)\frac{dV_m}{dt} + V_m \frac{dC_m}{dt}\]

The second term \(V_m \, dC_m/dt\) is the novel NICE term — absent in standard HH — that drives depolarization during sonophore expansion phases.

3. Neuronal Models Used

Plaksin et al. (2014) implemented NICE using the cortical regular spiking (RS) neuron model, with HH-style kinetics parametrized for mammalian cortex. Plaksin et al. (2016) extended this to a two-compartment model including:

• Regular Spiking (RS) pyramidal neuron
• Fast Spiking (FS) inhibitory interneuron
• Low-Threshold Spiking (LTS) interneuron

Each cell type carries different maximal conductances (\(\bar{g}_{Na}\), \(\bar{g}_{Kd}\), \(\bar{g}_M\), c\(\bar{g}_{Ca}\), \(\bar{g}_{AHP}\)) following the Pospischil et al. (2008) parametrization, and different resting membrane capacitances C_m0, which directly determine their sensitivity to the NICE capacitive term.

4. Key Predictions

• Excitation threshold: minimum acoustic pressure P_A required to generate APs decreases with decreasing carrier frequency (approaching sonophore resonance) and increasing duty cycle
• Cell-type selectivity: RS neurons have lower C_{m0} than FS neurons, making them more sensitive to capacitive driving — predicting selective excitation of pyramidal cells at moderate intensities
• Frequency window: optimal stimulation at ~0.5–1 MHz for the canonical R₀ = 32 nm sonophore
• Inhibitory interneuron recruitment: at higher intensities, FS interneurons are recruited, potentially explaining observed inhibitory network effects

5. Computational Cost and the Multi-Scale Problem

The NICE model operates across vastly different timescales simultaneously:

Numerically integrating the full coupled system across all these timescales simultaneously requires timesteps on the order of nanoseconds to resolve acoustic oscillations, while simulating physiologically relevant durations of hundreds of milliseconds. This makes direct NICE simulation computationally prohibitive for anything beyond a single point neuron over very short durations — a fundamental limitation that motivated the development of SONIC.

6. Strengths and Limitations

Strengths

• First principled mechanistic model linking acoustic pressure directly to membrane electrical dynamics
• Fully grounded in established biophysics: Rayleigh-Plesset bubble dynamics + HH formalism
• Naturally reproduces threshold behavior, frequency dependence, and cell-type selectivity
• No empirical fitting to neuronal ultrasound data — predictions emerge from physical parameters

Limitations

• Computationally intractable for realistic neuron morphologies or network simulations due to multi-scale timescale problem
• Bilayer sonophore never experimentally confirmed: R₀ = 32 nm is assumed, not measured
• Point neuron geometry: the original NICE model treats the entire neuron as a single isopotential compartment, ignoring dendritic integration and spatial heterogeneity
• No MS channel coupling: membrane tension generated by sonophore oscillation is not fed into mechanosensitive channel gating equations
• No thermal module: purely mechanical; temperature effects on channel kinetics are absent
• Homogeneous membrane assumption: ignores lipid composition heterogeneity, cytoskeletal constraints, and protein crowding that would modulate local sonophore dynamics