Membrane Charge Oscillations During Ultrasonic Neuromodulation by Intramembrane Cavitation

Abstract

To investigate the importance of membrane charge oscillations and redistribution in multicompartmental ultrasonic neuromodulation (UNMOD) intramembrane cavitation models. Methods: The Neuronal Intramembrane Cavitation Excitation (NICE) model and multi-Scale Optimized model of Neuronal Intramembrane Cavitation (SONIC) of UNMOD are compared for a nanoscale multicompartmental and point neuron approximation of the bilayer sonophore and surrounding proteins. The temporal dynamics of charge oscillations and their effect on the resulting voltage oscillations are investigated by fourier series analysis. Results: Comparison of excitation thresholds and neuronal response between nanoscale multi-compartmental and point models, implemented in the SONIC and NICE framework, demonstrates that the explicit modeling of fast spatial charge redistribution is critical for an accurate multi-compartmental UNMOD-model. Furthermore, the importance of modeling partial protein coverage is quantified by the excitability thresholds. Subsequently, we establish by fourier analysis that these charge oscillations are slowly changing in time. Conclusion: Fast charge redistribution significantly alters neuronal excitability in a multi-compartmental nanoscale UNMOD-model. Also the mutual exclusivity between protein and sonophore coverage should be taken into account, when simulating the dependency of neuronal excitability on coverage fractions. Charge oscillations are periodic and their fourier components change on a slow timescale. Furthermore, the resulting voltage oscillations decrease in energy with overtone number, implying that an extension of the existing multiscale model (SONIC) to multi-compartmental neurons is possible by taking into account a limited number of fourier components. Significance: First steps are taken towards a morphologically realistic and computationally efficient UNMOD-model, improving our understanding of the underlying ultrasonic neuromodulation mechanisms.

SECONIC: Towards multi-compartmental models for ultrasonic brain stimulation by intramembrane cavitation *

“…I ax is the axial current flowing into the considered compartment and S c is the compartmental cross-sectional membrane area. As in previous studies of computational UNMOD by intramembrane cavitation [29,30,38,39,46], a regular spiking cortical Pospischil-neuron model is used [47]. The membrane conductances and Nernst-potentials of the sodium, delayed-rectifier potassium, slowly non-inactivating potassium and non-specific leak currents are given by (g Na , g K , g M , g l ) = (56, 6, 0.075, 0.0205 The membrane capacitance of the sonophore C BLS depends on the maximal apex deflection Z (see figure 1):…”

“…Fortunately, it was demonstrated in our previous study, that the fourier components of the membrane charge oscillations are changing on a slow timescale and that most of the signal energy is contained within the lowest fourier overtones [46]. These results imply that an extension of the multi-scale optimized SONIC-model is possible, by replacing the membrane charge as a slow state variable with its most important fourier components.…”

“…The methodology of the NICE, SONIC and SECONIC models is illustrated schematically in figure 1. The values of the general model constants, definition of variables and functions and the membrane current dynamics, are the same as in our previous study on the importance of membrane charge oscillations in ultrasonic neuromodulation [46]. First, we briefly summarize the PSK-model for ultrasonic neuromodulation by intramembrane cavitation, in section 2.1.…”

“…However, in morphologically-realistic multicompartmental neurons, strong axial currents are caused by the large potential oscillations, predicted by the PSK-model [41]. These axial currents then result in fast oscillations of the membrane charge, breaking the multi-scale assumption and resulting in inaccurate integration of the multi-compartmental SONIC neuron model in terms of neuronal response and excitation threshold [46].…”

“…Third, a computationally efficient multi-compartmental algorithm SECONIC (Spatially Extended Charge Oscillating model of Neuronal Intramembrane Cavitation) is proposed and validated in the nanoscale bilayer sonophore UNMOD model. Here, as in [46], the nanoscale twocompartmental model of the bilayer sonophore and surrounding protein islands is chosen as a test-case for the design of a computationally efficient and accurate multi-compartmental UNMOD model, as the exact solution is known by the single-compartment model due to equipotentiality [46]. Finally, computational efficiency is compared between the different PSKmodels (NICE, SONIC, SECONIC) through measuring the simulation time for different ultrasonic pressures and sonophore coverage fractions.…”