Is Particle Strain an Underlying Mechanism of Ultrasound Neuromodulation?
Abstract
Ultrasonic neuromodulation represents a promising non-invasive approach for therapeutic applications, offering precise spatial targeting without the risks associated with invasive procedures. However, the complex multi-dimensional parameter space and limited understanding of underlying ultrasound-neuron interaction mechanisms create major hurdles for clinical translation. This study addresses these limitations through the development of strain-based computational models for ultrasound-neuron coupling. Strain is the primary mechanism of interaction between ultrasonic waves and tissue, and refers here to both the oscillating and steady deformation of neurons. The primary objective is to establish a comprehensive computational framework for quantifying ultrasonic effects caused by strain mechanisms, enabling a systematic analysis of diverse ultrasonic protocols and neural targets. The secondary objective involves implementing this framework for morphologically realistic neuronal models and determining the computational feasibility of multi-scale optimisation approaches. We implemented multi-compartmental neuronal models, focusing on an unmyelinated C-fibre model as a benchmark for understanding ultrasound-induced membrane dynamics. We then developed a strain-based modelling framework incorporating membrane deflection mechanisms and accounting for ultrasound-induced changes in membrane properties across varying conditions of pressure and frequency. Furthermore, analytical expressions were derived through mathematical expansion techniques for the membrane capacitance, membrane resistance, and axial resistance, enabling systematic exploration of parameter dependencies including pressure amplitude, frequency, and axon geometry. The framework incorporates electrical coefficients derived from cable theory and Hodgkin-Huxley formulations, allowing for a comprehensive evaluation of ultrasonic effects on gating kinetics. Extensive parameter space exploration across physiologically relevant ranges was conducted to evaluate computational requirements with particular focus on the feasibility of multi-scale optimisation with look-up tables. Multi-scale optimisation is necessary due to the numerical stiffness caused by the microsecond ultrasonic period, which improves computational efficiency and numerical accuracy. This computational framework establishes the foundation for systematic optimisation of ultrasonic protocols across diverse neurological applications through a mechanism-specific computational approach. The strain-based framework enables progression towards morphologically-realistic neural models, incorporating detailed channel properties and anatomical reconstructions to create comprehensive ultrasound-sensitive single-neuron models.