Unifying transcranial focused ultrasound and transcranial magnetic stimulation effects with calcium-dependent synaptic plasticity theory
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Low-intensity transcranial focused ultrasound stimulation (TFUS) is an emerging technology that shares features of both established invasive (e.g. deep brain stimulation; DBS) and noninvasive (e.g. transcranial magnetic stimulation; TMS) neurostimulation modalities. Like DBS, TFUS can target non-superficial brain structures with millimetre-level precision. Like TMS (and unlike DBS), the most important physiological effect of TFUS from a clinical perspective is its ability to induce neuroplastic changes (long term potentiation/depression; LTP/LTD) from relatively short stimulation sessions. Thus follows the intriguing possibility that, although TFUS and TMS have very different primary mechanisms of action (mechanoreceptive vs. electromagnetic), they might nevertheless share a common secondary mechanism of action (plasticity induction by temporally patterned stimulation). A quantitative mathematical theory of this secondary mechanistic pathway could therefore have important explanatory and predictive value in both modalities. Two major challenges to the development of such a theory, however, are i) experimental results showing contradictory plasticity effects between TFUS and TMS for nominally similar stimulation parameters, and ii) ineliminable waveform pattern differences (i.e. pulses vs. smooth sinusoids) even for highly aligned protocol designs such as continuous theta burst (cTB). Here we show that a mathematical model of calcium-dependent synaptic plasticity in corticothalamic circuits, already developed extensively for TMS, can indeed provide such a unified description of stimulation effects across these two modalities. Numerical simulations using this model for a range of TFUS and TMS protocols show plasticity effects consistent with empirical measurements of stimulation-induced cortical excitability modulation. In particular, our model addresses both of the above challenges, by i) reconciling apparently contradictory results across modalities for the same stimulation parameters, and ii) introducing a simple algebraic approach, which we term the ‘equivalent energy principle’, to defining corresponding (theta-burst) TMS and TFUS waveforms. The ability of the model to account for differing effects across multiple stimulation modalities provides further support for the underlying general theory describing calcium-based regulation of stimulation plasticity effects – which spans multiple scales of system organization from ion channel kinetics to neural population activity. Our work also provides a foundation for future bidirectional transfer of new experimental observations and insights between experimental and theoretical TFUS and TMS research, including strategies for model-based protocol optimization and discovery of novel plasticity-inducing TFUS and TMS paradigms.
Author Summary
Why do (low-intensity) transcranial focused ultrasound stimulation (TFUS) and transcranial magnetic stimulation (TMS) – respectively the most extensively studied and most clinically effective noninvasive neuromodulation technologies – produce lasting changes in brain activity after just minutes of stimulation, and why do they sometimes produce opposite effects? As decades of experimental, theoretical, and computational neurophysiology have taught us, this is most likely because the plasticity-inducing effects of TFUS and TMS they operate through a single common mechanism: the modulation of intracellular calcium concentrations, which drives long-term strengthening (LTP) or weakening (LTD) of those connections depending on how much calcium accumulates and for how long. Here we show that by treating TFUS and TMS as two different physical routes to the same biological substrate (calcium-dependent modulation of synaptic plasticity), their shared and divergent effects can be jointly explained by one common theory and corresponding mathematical model, with strong construct validity and broad explanatory reach. A key insight is our introduction of a simplifying ansatz – an “equivalent energy principle”, whereby the energy delivered to the brain is assumed to be identical for continuous theta-burst (cTB)-TFUS and cTB-TMS protocols with the same gross temporal structure. This allows us to show that apparently contradictory plasticity effects can be simply and parsimoniously explained by the stimulation waveform shape differences alone, without a single modified or free model parameter. For example, doubling cTB duration causes a switch from an LTP-like to an LTD-like effect for TMS but not for TFUS. Our framework offers a principled way of leveraging established TMS knowledge to guide TFUS parameter choices, and potentially vice versa in the future – providing a valuable bidirectional bridge between these two highly promising clinical neurotechnologies. It also suggests that other emerging neurostimulaton modalities such as transcranial electrical or photic techniques might be similarly interpretable through this theoretical lens.
