Numerical modelling of plasticity induced by transcranial magnetic stimulation

Abstract

We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short (<∼ 10 ms) and long (>∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual's electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes.

Calcium dependent plasticity applied to repetitive transcranial magnetic stimulation with a neural field model

“…Robinson et al 1997Robinson et al , 2005Wilson et al 2012;, as applied to excitatory and inhibitory populations within the cortex, then show how CaDP can be incorporated in this scheme with metaplasticity Robinson 2013, 2014). We then describe how the model can be linearized and applied also with STDP (Wilson et al 2014) which we optimize to give a realistic window function showing regimes of depression and potentiation, in agreement with other literature but using a different method.…”

“…9, and the standard parameters for this (taken from references Robinson 2014 except for the synaptic coupling terms which have been selected to match the gains used in Wilson et al 2014) are included in Table 1. The model and parameter set, without a delay term τ ab , cannot produce a strong alpha (≈10 Hz) peak in the spectrum of the firing-rate, but is consistent with the typical 'eyes open' approach taken in experimental rTMS in order to remove the complicating effects of an alpha rhythm.…”

“…The subtraction of the mean signal (denoted by the angle brackets) implies that the time average of φ x (t) over the protocol is zero (Wilson et al 2014), meaning φ x = δφ x . A further question concerns the effect of stimulation on the neurons.…”

“…We can then consider x(t) to repeat in a time-scale T , this is reasonable if T is much smaller than the timescale over which weights change. We note that for iTBS, T will be typically 10 s (2 s ON followed by 8 s OFF), whereas the mean weights may vary over a scale of order one minute or longer Wilson et al 2014;Ridding and Rothwell 2007) so such a description is reasonable.…”

“…Initially, an STDP approach was implemented to describe plasticity in a neural field scheme (Robinson 2011;. Wilson et al applied this to cTBS and iTBS with a two population linear model (Wilson et al 2014). However, the CaDP approach has recently been implemented but in a one population neural field model with a restricted range of protocols Robinson 2013, 2014).…”