3 research outputs found
Dynamical mean field modelling and estimation of neuronal oscillations
Oscillations in neural activity are a ubiquitous phenomenon in the brain. They span
multiple timescales and correlate with a myriad of physiological and pathological
conditions. Given their intrinsic dynamical nature, mathematical and computational
modelling tools have proven to be indispensible in order to interpret and formalize the
mechanisms through which these oscillations arise. In this Thesis, I developed a new
methodological framework that allows the assimilation of experimental data into
biophysically plausible models of neural oscillations.
Motivated by the fast oscillatory activity (30 ~ 130 Hz) at the onset of focal epileptic
seizures, I started by investigating, via means of bifurcation analyses, whether such fast
oscillations can be plausibly described by conductance-based neural mass models.
Neural mass models have enjoyed success in describing several forms of epileptiform
activity (e.g. spike-and-wave seizures and interictal spikes), but I found that, in order to
generate such fast oscillations, the parameters of this family of models would have to
depart significantly from biophysical plausibility. These results motivated the
exploration of full mean-field models of spiking neurons to characterise this type of
dynamics.
I hence proposed a variant of a mean-field neural population model based on the
Fokker-Planck equation of conductance-based, stochastic, leaky integrate-and-fire
neurons. This modelling approach was chosen for its capacity to describe arbitrary
network configurations and predict firing rates, trans-membrane currents and local field
potentials. I introduced a new numerical scheme that makes the computational cost of
integrating the ensuing partial differential equations scale linearly with the number of
nodes of the networks. These advances are crucial for the practical implementation of
model inversion schemes.
I then built upon the literature of Dynamic Causal Modelling to develop a Bayesian
model inversion algorithm applicable to dynamical systems in limit cycle regimes. I
applied the scheme to the mean-field models described above, using experimental data
recordings of carbachol-induced gamma oscillations, in the CA1 region of mice
hippocampal slice preparations. The estimated model was able to make accurate predictions about independent data features; namely inter-spike-interval distributions.
Also, the inverted models were qualitatively compatible with the observation that
excitatory pyramidal cells and inhibitory interneurons play equally important roles in
the dynamics of these oscillations (as opposed to interneuron-dominated gamma
oscillations). I also explored the applicability of this inversion scheme to neural mass
models of electroencephalographically recorded spike-and-wave seizures in humans.
In conclusion, the work presented in this thesis provides significant new contributions to
model based analyses of neuronal oscillatory data, and helps to bridge single-neuron
measurements to network-level interactions