Alpha rhythm subharmonics underlie responsiveness to theta burst stimulation via calcium metaplasticity

Reviewer #1 (Public review):

Summary:

The authors show that the lower frequency (~5Hz) stimulation of the intermittent theta-burst stimulation (iTBS) via repetitive transcranial magnetic stimulation (rTMS) serves as a more effective stimulation paradigm than the high-frequency protocols (HF-rTMS, ~10Hz) with enhancing plasticity effects via long-term potentiation (LTP) and depression (LTD) mechanisms. They show that the 5 Hz patterned pulse structure of the iTBS is an exact subharmonic of the 10 Hz high-frequency rTMS, creating a connection between the two paradigms and acting upon the same underlying synchrony mechanism of the dominant alpha-rhythm of the corticothalamic circuit.

First, the authors create a corticothalamic neural population model consisting of 4 populations: cortical excitatory pyramidal and inhibitory interneuron, and thalamic excitatory relay and inhibitory reticular populations. Second, the authors include a calcium-dependent plasticity model, in which calcium-related NMDAR-dependent synaptic changes are implemented using a BCM metaplasticity rule. The rTMS-induced fluctuations in intracellular calcium concentrations determine the synaptic plasticity effects.

Strengths:

The model (corticothalamic neural population with calcium-dependent plasticity, with TBS input for rTMS) is thoroughly built and analyzed.

The conclusions seem sound and justified. The authors justifiably link stimulation parameters (especially the alpha subharmonics iTBS frequency) with fluctuations in calcium concentration and their effects on LTP and LTD in relevant parts of the corticothalamic circuit populations leading to a dampening of corticothalamic loop gains and enhancement of intrathalamic gains with an overall circuit-wide feedforward inhibition (= inhibitory activity is enhanced via excitatory inputs onto inhibitory neurons) and a resulting suppression of the activity power. In other words: alpha-resonant iTBS protocols achieve broadband power suppression via selective modulation of corticothalamic FFI.

(1) The model is well-described, with the model equations in the main text and the parameters in well-formatted tables.

(2) The relationship between iTBS timing and the phase of rhythms is well explained conceptually.

(3) Metaplasticity and feedforward inhibition regulation as a driver for the efficacy of iTBS are well explored in the paper.

(4) Efficacy of TBS, being based on mimicry of endogenous theta patterns, seems well supported by this simulation.

(5) Recovery between periods of calcium influx as an explanation for why intermittency produces LTP effects where continuous stimulation fails is a good justification for calcium-based metaplasticity, as well as for the role of specific pulse rate.

(6) Circuit resonance conclusion is interesting as a modulating factor; the paper supports this hypothesis well.

(7) The analysis of corticothalamic dampening and intrathalamic enhancement in the 3D XYZ loop gain space is a strong aspect of the paper.

Weaknesses:

(1) Overall, the paper is difficult to follow narratively - the motivation (formulated as a specific research question) for each section can be a bit unclear. The paper could benefit from a minor rewrite at the start of each section to justify each section's reasoning. The Discussion is too long and should be shortened and limited to the main points.

(2) While the paper refers to modelling and data in discussion, there is no direct comparison of the simulations in the figures to data or other models, so it's difficult to evaluate directly how well the modelling fits either the existing model space or data from this region. Where exactly the model/plasticity parameters from Table 5 and the NFTsim library come from is not easy to find. The authors should make the link from those parameters to experimental data clearer. For example, which clinical or experimental data are their simulations of the resting-state broadband power suppression based on?

(3) The figures should be modified to make them more understandable and readable.

(4) The claim in the abstract that the paper introduces "a novel paradigm for individualizing iTBS treatments" is too strong and sounds like overselling. The paper is not the first computational modelling of TBS - as acknowledged also by the authors when citing previous mean-field plasiticity modelling articles. Btw. the authors could briefly mention and include also references also to biophysically more detailed multi-scale approaches such as https://doi.org/10.1016/j.brs.2021.09.004 and https://doi.org/10.1101/2024.07.03.601851 and https://doi.org/10.1016/j.brs.2018.03.010

(5) The modelling assumes the same CaDP model/mechanism for all excitatory synapses/afferents. How well is this supported by experimental evidence? Have all excitatory synaptic connections in the cortico-thalamic circuit been shown to express CaDP and metaplasticity? If not, these limitations (or predictions of the model) should be mentioned. Why were LTP calcium volumes never induced within thalamic relay-afferent connections se and sr? What about inhibitory synapses in the circuit model? Were they plastic or fixed?

(6) Minor point: Metaplasticity is modelled as an activity-dependent shift in NMDAR conductance, which is supported by some evidence, but there are other metaplasticity mechanisms. Altering NMDA-synapse affects also directly synaptic AMPA/NMDA weight and ratio (which has not been modelled in the paper). Would the model still work using other - more phenomenological implementation of the sliding threshold - e.g. based on shifting calcium-dependent LTP/LTD windows or thresholds (for a phenomenological model of spike/voltage-based STDP-BCM rules, see https://doi.org/10.1007/s10827-006-0002-x and https://doi.org/10.1371/journal.pcbi.1004588) - maybe using a metaplasticity extension of Graupner and Brunel CaDP model. A brief discussion of these issues might be added to the manuscript - but this is just a suggestion.

(7) Short-term plasticity (depression/facilitation) of synapses is neglected in the model. This limitation should be mentioned because adding short-term synaptic dynamics might affect strongly circuite model dynamics.

Reviewer #2 (Public review):

Transcranial magnetic stimulation is used in several medical conditions to alter brain activity, probably by induction of synaptic plasticity. The authors pursue the idea to personalise parameters of the stimulation protocol by adapting the stimulation frequency to an individual's brain rhythm. The authors test this approach in a population model connecting the cortex with deeper brain areas, the thalamocortical loop, which includes calcium-dependent plasticity for the connections within and between brain regions. While the authors relate literature-based experimental findings with their results, their results are so far not supported by experimental work.

The authors successfully highlight in their model that personalization of rTMS stimulation frequency to the brain intrinsic frequency has the potential to improve stimulation impact, and they relate this to specific changes in the network. Their arguments that this resonance improves efficacy are intuitive, and their finding that inhibition and excitation are selectively modulated is a good starting point for analysing the underlying mechanism.

As rTMS is used in clinical contexts, and the idea of aligning intrinsic and stimulation frequency is relatively easy to implement, the paper is conceptually of interest for the rTMS community, despite its weak points on the mechanistic explanation. The authors made the simulation code publicly available, which is a useful resource for further studies on the effects of metaplasticity. The same stimulation parameters have been tested in experiments, and a reanalysis of the experimental results following the idea of this paper could be influential for clinical optimisation of stimulation protocols.

A strength of the paper is that it takes into account also deeper brain areas, and their interaction with the cortex. The paper carefully measures system changes in response to different frequency differences between thalamocortical loop and stimulation. By explicitly modelling changes to connections, the authors do start dissect the mechanism underlying the observed effect. Unfortunately, the dissection of the mechanistic underpinning in the current version of the manuscript does not yet fully exploits the possibility of a computational model. Here are a couple of points related to this critique:

(1) The study reports that connections between thalamus and cortex as well as within the thalamus change, but the model is not used to separate the influence of both.

(2) The paper reports that a resonance between stimulation and brain increases stimulation effectiveness. This conclusion is solely based on the observation of strong reactions in the network to subharmonics of the brain's frequency, and lacks further support such as alternative measures of resonance, or an analysis of the role of the phase difference between stimulation and brain oscillation, which is likely changed by the stimulation. For example, for harmonic oscillators, resonance leads to a 90 degree phase difference between driving force and system response, and for rTMS, phase locking has been shown to be relevant.

(3) The authors claim that over-engagement of plasticity for HF-rTMS makes their intermittent protocol more effective. Yet, the study lacks a direct comparison between stimulation protocols that shows over-engagement of plasticity for the HF-protocol. The study also does not explore which time-scale of the plasticity mechanism rules the optimal stimulation protocol. Moreover, the study reports that only few number of pulses per burst show a good effect. This should depend on how strongly a single pulse changes the calcium volume, but this relation was not explored in the model.

(4) The authors report on the frequency spectrum of the cortical excitatory population, with the argument that the power of this population is most closely related to EEG measurements. A report of the other neuronal populations is missing, which might be informative on what is going on in the network.

Statistics:

(1) The authors do not state whether they test for assumptions of the multiple regression analysis, such as whether errors have equal variance or that residuals are normally distributed.

(2) For the statistical analysis, the authors ignore about half of their model simulations for which the change in the power was negligible. It is not clear to me which statistical analysis is meant; whether the figures show all model simulations, whether regression lines where evaluated ignoring them, and whether the multiple regression analysis used only half of the data points.

Reviewer #3 (Public review):

Summary:

This article presented a novel computer model to address an important question in the field of brain stimulation, using the magnetic stimulation iTBS protocol as an example, how stimulation parameters, frequency in particular, interfere with the intrinsic brain oscillations via plastic mechanisms. Brain oscillation is a critical feature of functional brains and its alteration signals the onset of many neuropsychiatric diseases or certain brain states. The authors suggested with their model that harmonic and subharmonic stimulations close to the individual alpha frequency achieved strong broadband power suppression.

Strengths:

The authors focused on the cortico-thalamic circuitry and managed to generate alpha oscillations in their four-population model. By adding the non-monotonic calcium-based BCM rule, they have also achieved both homeostasis and plasticity in response to magnetic stimulation. This work combined computer simulations and statistical analysis to demonstrate the changes in network architecture and network dynamics triggered by varied magnetic stimulation parameters. By delivering the iTBS protocol to the cortical excitatory population, the key findings are that harmonic and subharmonic stimulations close to the individual alpha frequency (IAF) achieved strong broadband power suppression. This resulted from increased synaptic weights of the corticothalamic feed-forward inhibitory projections, which were mediated by the calcium dynamics perturbed by iTBS magnetic stimulation. This finding endorsed the importance of applying customized stimulation to patients based on their IAFs and suggested the underlying mechanism at the circuitry level.

Weaknesses:

The drawbacks of this work are also obvious. Model validation and biological feasibility justification should be better addressed. The primary outcome of their model is the broadband power suppression and the optimal effects of (sub)harmonic stimulation frequency, but it lacks immediate empirical support in the literature. To the best of my knowledge, many alpha frequency tACS studies reported to increase but not suppress the power of certain brain oscillations. A review by Wang et al., 2024 (Frontiers in System Neuroscience) suggested hybrid changes to different brain oscillations by magnetic stimulation. Developing a model to fully capture such changes might be out of the scope of the present study and challenging in the entire field, but it undermines the quality of the present work if not extensively discussed and justified. Clarity and reproducibility of the work can be improved. Although it is intriguing to see how the calcium-dependent BCM plasticity mediates such changes, the writing of the methods part is not hard to follow. It was also not clear why only two populations were considered in the thalamus, how the entire network was connected, or how the LTP/LTD threshold alters with calcium dynamics. The figures were unfortunately prepared in a nested manner. The crowded layout and the tiny font sizes reduce the clarity. The third point comes to contextualization and comparison to existing models. It will strengthen the work if the authors could have compared their work to other TMS modeling work with plasticity rules, e.g, Anil et al., 2024. Besides, magnetic stimulation is unique in being supra-threshold and having focality compared to other brain stimulation modalities, e.g., tDCS and tACS, but they may share certain basic neural mechanisms if accounting for certain parameters, e.g., frequency. A solid literature review and discussion on this part may help the field better perceive the value and potential limitations of this work.