The brain is a complex, plastic, electrical network whose dysfunctions result in neurological disorders. Multichannel transcranial electrical stimulation (tCS) is a non-invasive neuromodulatory technique with the potential for network-oriented therapy. Challenges to realizing this vision include the proper identification of involved networks in a patient-specific context, a deeper understanding of the effects of stimulation on interconnected neuronal populations-both immediate and plastic-and, based on these, developing strategies to personalize brain stimulation interventions. For this reason, personalized hybrid biophysical and physiological models of brain networks are poised to play a key role in the evolution of networkoriented transcranial stimulation. We review some of the recent work in this emerging area of research and provide an outlook for future modeling and experimental work, as well as for developing its clinical applications in fields such as epilepsy. Research Projects Activity (IARPA), via 2014-13121700007. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. ES is supported by the Beth Israel Deaconess Medical Center (BIDMC) via the Chief Academic Officer (CAO) Award 2017, and the Defense Advanced Research Projects Agency (DARPA) via HR001117S0030. The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of Harvard University, and its affiliated academic health care centers. DECLARATION OF INTEREST Giulio Ruffini is a shareholder and works for Neuroelectrics, a company designing medical devices for brain stimulation. Roser Sanchez-Todo is a researcher at Neuroelectrics. REFERENCES

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.

Work in the last two decades has shown that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by increasing excitation and heuristically varying network inhibitory coupling parameters in the models. Based on these early studies, we provide a laminar NMM capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input into the pyramidal cell population, the model dynamics are autonomous. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically motivated algorithm for chloride dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of chloride in pyramidal cells due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals for comparison with real seizure recordings, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods based on NMMs.

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Personalization is rapidly becoming standard practice in medical diagnosis and treatment. This study is part of an ambitious program towards computational personalization of neuromodulatory interventions in neuropsychiatry. We propose to model the individual human brain as a network of neural masses embedded in a realistic physical matrix capable of representing measurable electrical brain activity. We call this a hybrid brain model (HBM) to highlight that it encodes both biophysical and physiological characteristics of an individual brain. Although the framework is general, we provide here a pipeline for the integration of anatomical, structural and functional connectivity data obtained from magnetic resonance imaging (MRI), diffuse tensor imaging (DTI connectome) and electroencephalography (EEG). We personalize model parameters through a comparison of simulated cortical functional connectivity with functional connectivity profiles derived from cortically-mapped, subject-specific EEG. We show that individual information can be represented in model space through the proper adjustment of two parameters (global coupling strength and conduction velocity), and that the underlying structural information has a strong impact on the functional outcome of the model. These findings provide a proof of concept and open the door for further advances, including the model-driven design of non-invasive brain-stimulation protocols.

Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM), which represent the mean activity of large numbers of neurons. In order to properly reproduce experimental data, these models require the addition of further elements. Here we provide a framework integrating conduction physics that can be used to simulate cortical electrophysiology measurements, in particular those obtained from multicontact laminar electrodes. This is achieved by endowing NMMs with basic physical properties, such as the average laminar location of the apical and basal dendrites of pyramidal cell populations. We call this framework laminar NMM, or LaNMM for short. We then employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. We define, based on the literature of columnar connectivity, a minimal neural mass model capable of generating amplitude and phase coupled slow (alpha, 4–22 Hz) and fast (gamma, 30–250 Hz) oscillations. The synapse layer locations of the two pyramidal cell populations are treated as optimization parameters, together with two more LaNMM-specific parameters, to compare the models with the multicontact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity of the model and data, where the FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology while selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals.

Mobile: +1 6177 899 6911 27 giulio.ruffini@neuroelectrics.com 28 128 >0.1 V/m can be observed in the wall opposite to the one where the sources are located. This is 129 observed in both the multiple and single source models, although, as expected, the area in which 130 the electric field is greater than 0.1 V/m is higher in the former than in the latter (the electric field 131 from multiple-source patches decays much slower than the single dipole source case (7), p. 37). 132 This effect was only observed in the model with sulcus width of 1 mm. Increasing the sulcus width 133 led to lower electric field values on the opposite sulcal wall. Figure 1 in Supplementary Materials 134 displays the decay of the normal component of the electric field and the electrostatic potential with 135 distance. The decays of V and En are well fit by a power function with exponents of −0.66, −0.88 136 and −2.11, −3.02, respectively, for the multiple source and single source models. 137 138

ObjectiveStereotactic-EEG (SEEG) and scalp EEG recordings can be modeled using mesoscale neural mass population models (NMM). However, the relationship between those mathematical models and the physics of the measurements is unclear. In addition, it is challenging to represent SEEG data by combining NMMs and volume conductor models due to the intermediate spatial scale represented by these measurements.ApproachWe provide a framework combining the multi-compartmental modeling formalism and a detailed geometrical model to simulate the transmembrane currents that appear in a layer 3, 5 and 6 pyramidal cells due to a synaptic input. With this approach, it is possible to realistically simulate the current source density (CSD) depth profile inside a cortical patch due to inputs localized into a single cortical layer and the consequent voltage measured by two SEEG contacts using a volume conductor model. Based on this approach, we built a framework to connect the activity of a NMM with a volume conductor model and we simulated an example as a proof of concept.Main resultsCSD depends strongly on the distribution of the synaptic inputs onto the different cortical layers and the equivalent current dipole strengths display considerable differences (of up to a factor of four in magnitude in our example). Thus, the inputs coming from different neural populations do not contribute equally to the electrophysiological recordings. A direct consequence of this is that the raw output of neural mass models is not a good proxy for electrical recordings. We also show that the simplest CSD model that can accurately reproduce SEEG measurements can be constructed from discrete monopolar sources (one per cortical layer).SignificanceOur results highlight the importance of including a physical model in NMMs to represent measurements. We provide a framework connecting microscale neuron models with the neural mass formalism and with physical models of the measurement process that can improve the accuracy of predicted electrophysiological recordings.