Sensitivity analysis guided Bayesian parameter estimation for neural mass models : Applications in Epilepsy

Abstract It is well established that neural mass models (NMMs) can effectively simulate the mesoscopic and macroscopic dynamics of electroencephalography (EEG), including the epileptic EEG. However the use of NMMs to gain insight on the neuronal system by parameter estimation is hampered by their high dimensionality and the lack of knowledge on what NMM parameters can be reliably estimated. In this article, we analyze the parameter sensitivity of Jansen and Rit NMM (JR-NMM) in order to identify the most sensitive JR-NMM parameters for reliable parameter estimation from EEG data. We then propose a Bayesian approach for estimating the JR-NMM states and parameters based on expectation--maximization combined with unscented Kalman smoother (UKS-EM). Global sensitivity analysis methods including Morris method and Sobol method are used to perform sensitivity analysis. Results from both the Morris and Sobol method show that the average inhibitory synaptic gain, $B$ and the reciprocal of the time constant of the average inhibitory post-synaptic potentials (PSPs), $b$ have significant impact on the JR NMM output along with having the least interaction with other model parameters. The UKS-EM method for estimating the parameters $B$ and $b$ is validated using simulations under varying levels of measurement noise. Finally we apply the UKS-EM algorithm to intracranial EEG data from $16$ epileptic patients. Our results, both at individual and group-level show that the parameters $B$ and $b$ change significantly between the pre-seizure and seizure period, and between the seizure and post-seizure period, with transition to seizure characterized by decrease in average $B$ and high frequency activity in seizure characterized by an increase in $b$. These results establish sensitivity analysis guided Bayesian parameter estimation as a powerful tool for reducing the parameter space of high dimensional NMMs enabling reliable and efficient estimation of the most sensitive NMM parameters, with the potential for online and fast tracking of NMM parameters in applications such as seizure tracking and control.