Modelling cortical network dynamics.

We have investigated the theoretical constraints of the interactions between coupled cortical columns. Each cortical column consists of a set of neural populations where each population is modelled as a neural mass. The existence of semi-stable states within a cortical column is dependent on the type of interaction between the neuronal populations, i.e., the form of the synaptic kernels. Current-to-current coupling has been shown, in contrast to potential-to-current coupling, to create semi-stable states within a cortical column. The interaction between semi-stable states of the cortical columns is studied where we derive the dynamics for the collected activity. For small excitations the dynamics follow the Kuramoto model; however, in contrast to previous work we derive coupled equations between phase and amplitude dynamics with the possibility of defining connectivity as a stationary and dynamic variable. The turbulent flow of phase dynamics which occurs in networks of Kuramoto oscillators would indicate turbulent changes in dynamic connectivity for coupled cortical columns which is something that has been recorded in epileptic seizures. We used the results we derived to estimate a seizure propagation model which allowed for inversions using the Laplace assumption (Dynamic Causal Modelling). The seizure propagation model was trialed on simulated data, and future work will investigate the estimation of the connectivity matrix from empirical data. This model can be used to predict changes in seizure evolution after virtual changes in the connectivity network, something that could be of clinical use when applied to epilepsy surgical cases.

Global dynamics of neural mass models.

Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy.

Cerebellar asymmetry in a pair of monozygotic handedness-discordant twins.

Increasing evidence for a cerebellar role in human cognition has accrued with respect to anatomically and functionally distinct lobules. Questions of laterality, however, have been largely overlooked. This study therefore introduced and applied a novel measurement protocol for comparatively bias-free analysis of cerebellar asymmetries. Volumetric measurements were performed on magnetic resonance images from a single pair of monozygotic handedness-discordant twins. Against a background of functional cortical asymmetry for verbal and visuo-spatial functional magnetic resonance imaging activation, which was mirrored in the left-handed twin (Lux et al. 2008), between-twin differences in cerebellar asymmetry are described. Interestingly, asymmetry measures for the whole cerebellum did not correspond to either the direction of hand preference or to the weaker (functional magnetic resonance imaging) lateralization of the left-handed twin. The twins both showed clockwise cerebellar torques. This mirrored a counter-clockwise cerebral torque in the right-handed twin only. Selected single cerebellar lobules V and VII displayed between-twin laterality differences that partially reflected their discrepant handedness. Whole cerebellum anatomical measures appeared to be unrelated to single functional cortical asymmetries. These analyses contribute further anatomical evidence pertaining to the existence of multiple structurally and functionally distinct cortico-cerebellar networks of the healthy human brain in vivo.