Tissue scale electrophysiological-mechanical continuum modelling for white matter transcranial ultrasound neuromodulation - Felix, C (2022)
Neurological disorders are a substantial health and economic burden worldwide. Low-intensity transcranial ultrasound stimulation (TUS) is now considered as one of the most promising treatments for neurological disorders due to its high spatial resolution compared to other non-invasive neuromodulation methods. While for many decades now, ultrasound has been known to be able to influence or modulate neuronal activities in the brain, its underlying mechanisms are still poorly understood. Maybe not fully unrelated, while nerve impulses have traditionally been considered to be a purely electrical phenomenon, a growing body of evidence is now pointing towards additional thermodynamic changes occurring alongside the action potential. Numerous models have been proposed to study this electromechanical coupling phenomenon. Among these, the flexoelectric theory is postulating that a temporal variation of strain gradient in the membrane leads to current creation. Whether or not this hypothesis is fully accurate microscopically in the context of TUS, it offers a phenomenological framework that could be used at the organ scale to quantify electrical induction in the presence of minute mechanical vibrations. However, the flexoelectric theory relies on formulations directly built on the microstructural description of the underlying dielectric polarisation. In membranes, this constrains the flexoelectricity modelling to simple membrane morphologies and prevents the simulation of flexoelectricity in large scale assemblies of multiple biological cells. To this end, this work proposes a homogenised bulk flexoelectric model focussing on the continuum level formulations of bundles of flexoelectric cylinders. This model was calibrated against a microscale formulation to ensure multiscale compatibility, but it can be directly used at the macroscale for the description of strain-gradient induced electromechanical coupling without the need to account for the microstructural polarisation. A 1D proof of concept is first proposed, followed by 2D and 3D formulations of the homogenised bulk flexoelectric model. The homogenised model is used for brain white matter tracts in the context of TUS, where ultrasound induced electrical activity arising within the tracts is simulated in a human head model in 2D and a monkey head model in 3D. In the latter case, a direct comparison against experimental models is proposed. In particular, this study proposes a way to predict the loss of brain region correlation during TUS. To conclude, the framework proposed here has the potential to fully capture multiphysics phenomena such as in TUS. The results from this study provide a theoretical building block to identify the desirable ultrasound parameters for clinical and/or experimental applications that can be used for the successful treatment of neurological disorders.