Validation of a dynamic causal model of NMDA receptors: sensitivity and parameter recovery analysis

1368 

Abstract Submission 

Nikola Jajcay¹, Jakob Heinzle², Jiří Horáček³, Klaas Stephan²

¹National Institute of Mental Health, Klecany, Czech Republic, ²Translational Neuromodeling Unit (TNU), University of Zurich & ETH Zurich, Zurich, Zurich, ³National Institute of Mental Health, Klecany, Česká republika

Nikola Jajcay  
National Institute of Mental Health
Klecany, Czech Republic

Jakob Heinzle  
Translational Neuromodeling Unit (TNU), University of Zurich & ETH Zurich
Zurich, Zurich

Jiří Horáček  
National Institute of Mental Health
Klecany, Česká republika

Klaas Stephan  
Translational Neuromodeling Unit (TNU), University of Zurich & ETH Zurich
Zurich, Zurich

The NMDA receptor is essential for controlling synaptic plasticity and mediating learning and memory functions. Furthermore, its hypofunction may be one of the pathophysiological mechanisms of schizophrenia. To study dysfunctions in NMDA signalling, one can employ dynamic causal models (DCMs) that utilize mathematical models of neural ensembles to predict fluctuations in synaptic currents and their influence on postsynaptic potentials. DCMs allow us to infer the most likely parameters that generated brain activity. Before using such models to profile NMDA receptor (dys)function in actual data, we conducted a full model validation, including sensitivity and parameter recovery analyses, to explore the validity, identifiability, and robustness of various neurobiological model definitions and parameters.

DCMs are generative models representing the joint probability of data and model parameters. It is possible to "invert" the model and infer the posterior distribution of the parameters given the measured data. DCMs for EEG data consist of three modelling layers: the first layer models the average population membrane potential, the second layer models populations grouped into a single source, and the final layer represents a collection of sources. This work focuses on the first two layers and explores neural and noise sensitivity and parameter recoverability. We utilise the variance-based method for the parameter sensitivity analyses by computing Sobol indices, whereas for parameter recovery analysis, we sample model parameters from the prior and run the variational inference to check and compare posterior estimates. Here, we investigate a conductance-based DCM with two sources consisting of a canonical microcircuit. Finally, we formulate the problem in a Fourier domain by transforming the simulated data into cross-spectral densities (CSD) as a preparatory step for using the validated model on resting-state data.

We first explored the effect of neuronal, noise and connectivity parameters on the simulated CSD using one-at-a-time prior sampling, where we estimated the CSD variance and then estimated Sobol indices using a generalised chaos polynomial estimator. Most parameters affect only the amplitude of the CSD but cannot shift the frequency peaks. The notable differences are the firing rate variance, GABA time scale, and some within-source excitatory connections. The parameters with the strongest influence on the CSD are background input, GABA synaptic time scale, magnesium block sensitivity, noise amplitude, and noise colour. The Sobol sensitivity analysis in the first order showed that the effect of these parameters varies by frequency and that the most substantial effect in the low frequencies (theta and below) is due to the background input and noise parameters. In contrast, the higher frequencies (alpha and low beta) are governed by the magnesium block parameters, thus directly relating to the NMDA signalling. Finally, the parameter recovery analysis suggests relatively high recoverability of neural parameters (such as background input and synaptic time scales). At the same time, the model struggled to recover noise parameters (correlation between sampled value from the prior and MAP posterior estimate around 0.2 for noise magnitude and 0.5 for noise colour).

We have started a methodological sensitivity, parameter recovery, and robustness analysis of the conductance-based DCM. In the next step, we plan to examine parameter interactions more closely via n-order Sobol indices, although our preliminary results suggest that most parameters are orthogonal and second-order Sobol indices are generally relatively low. Finally, we plan to finish our model validation with prior and posterior predictive checks to compare with data of the animal pharmacological model of the NMDA antagonist, ketamine. This model validation is essential to arrive at a robust NMDA-R DCM model able to profile NMDA receptor (dys)functions.

Bayesian Modeling ¹

EEG/MEG Modeling and Analysis

Methods Development

Transmitter Receptors ²

Computational Neuroscience

Glutamate

Modeling

Statistical Methods

Other - NMDA receptor