Abstracts

Rationale: Brain rhythms emerge from the activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities – termed neural masses – to understand in particular the origins of evoked potentials, intrinsic patterns of brain activity, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Such elements activities cannot be linked directly back to the activities of single neurons, the details of their function, genetics mutations, or linked to tissue level parameters such as extracellular potassium that are known to contribute to seizures and spreading depolarization.

Methods: We defined a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type models) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables, such as extracellular potassium, and synaptic current; and whose output is both firing rate and impact on the slow variables such as transmembrane potassium flux.

Results: Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.  Additionally, by introducing the change in function in sodium channels associated with genetic mutations associated with specific epilepsies, we similarly obtain networks that are more seizure-susceptible.   

Conclusions: We have developed a new method for building neural mass models that can be closely linked to measurement from real brain, and whose activities have the core building blocks for mechanistically reproducing dynamics associated with seizures and spreading depression. 

Funding: This work was supported under NIH grant R01 EB014641. RT's efforts were supported by Center of Advanced Systems Understanding (CASUS), which is financed by Germany’s Federal Ministry of Education and Research (BMBF) and by the Saxon Ministry for Science, Culture, and Tourism (SMWK).