Estimation and Identifiability of Model Parameters in Human Nociceptive Processing Using Yes-No Detection Responses to Electrocutaneous Stimulation

Healthy or pathological states of nociceptive subsystems determine different stimulus-response relations measured from quantitative sensory testing. In turn, stimulus-responses measurements may be used to assess these states. In a recently developed computational model, six model parameters characterize activation of nerve endings and spinal neurons. However, both model nonlinearity and limited information in yes-no detection responses to electrocutaneous stimuli challenge to estimate model parameters. Here, we address the question whether and how one can overcome these difficulties for reliable parameter estimation. First, we fit the computational model to experimental stimulus-response pairs by maximizing the likelihood. To evaluate the balance between model fit and complexity, we evaluate the Bayesian Information Criterion. We find that the computational model is better than a conventional logistic model regarding the balance. Second, our theoretical analysis suggests to vary the pulse width among applied stimuli as a necessary condition to prevent structural non-identifiability. In addition, the numerically implemented profile likelihood approach reveals structural and practical non-identifiability. Our model-based approach with integration of psychophysical measurements can be useful for a reliable assessment of states of the nociceptive system

Numerical Bifurcation Analysis of Homoclinic Orbits Embedded in One-Dimensional Manifolds of Maps

We describe new methods for initializing the computation of homoclinic orbits for maps in a state space with arbitrary dimension and for detecting their bifurcations. The initialization methods build on known and improved methods for computing one-dimensional stable and unstable manifolds. The methods are implemented in MatContM, a freely available toolbox in Matlab for numerical analysis of bifurcations of fixed points, periodic orbits, and connecting orbits of smooth nonlinear maps. The bifurcation analysis of homoclinic connections under variation of one parameter is based on continuation methods and allows us to detect all known codimension 1 and 2 bifurcations in three-dimensional (3D) maps, including tangencies and generalized tangencies. MatContM provides a graphical user interface, enabling interactive control for all computations. As the prime new feature, we discuss an algorithm for initializing connecting orbits in the important special case where either the stable or unstable manifold is one-dimensional, allowing us to compute all homoclinic orbits to saddle points in 3D maps. We illustrate this algorithm in the study of the adaptive control map, a 3D map introduced in 1991 by Frouzakis, Adomaitis, and Kevrekidis, to obtain a rather complete bifurcation diagram of the resonance horn in a 1:5 Neimark-Sacker bifurcation point, revealing new features

Bistability and stabilization of human visual perception under ambiguous stimulation

We discuss a computational model that describes stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals. Let Toff and Ton be the time that the stimulus is off and on, respectively. The behavior was studied by direct numerical simulation in a grid of (Toff, Ton) values in a 2007 paper of Noest, van Ee, Nijs, and van Wezel. They found that both alternating and repetitive sequences of percepts can appear stably, sometimes even for the same values of Toff and Ton. Longer Toff, however, always leads to a situation where, after transients, only repetitive sequences of percepts exist. We incorporate Toff and Ton explicitly as bifurcation parameters of an extended mathematical model of the perceptual choices. We elucidate the bifurcations of periodic orbits responsible for switching between alternating and repetitive sequences. We show that the stability borders of the alternating and repeating sequences in the (Toff, Ton)-parameter plane consist of curves of limit point and period-doubling bifurcations of periodic orbits. The stability regions overlap, resulting in a wedge with bistability of both sequences. We conclude by comparing our modeling results with the experimental results obtained by Noest, van Ee, Nijs, and van Wezel

A Comparison of Evoked and Non-evoked Functional Networks

The growing interest in brain networks to study the brain's function in cognition and diseases has produced an increase in methods to extract these networks. Typically, each method yields a different network. Therefore, one may ask what the resulting networks represent. To address this issue we consider electrocorticography (ECoG) data where we compare three methods. We derive networks from on-going ECoG data using two traditional methods: cross-correlation (CC) and Granger causality (GC). Next, connectivity is probed actively using single pulse electrical stimulation (SPES). We compare the overlap in connectivity between these three methods as well as their ability to reveal well-known anatomical connections in the language circuit. We find that strong connections in the CC network form more or less a subset of the SPES network. GC and SPES are related more weakly, although GC connections coincide more frequently with SPES connections compared to non-existing SPES connections. Connectivity between the two major hubs in the language circuit, Broca's and Wernicke's area, is only found in SPES networks. Our results are of interest for the use of patient-specific networks obtained from ECoG. In epilepsy research, such networks form the basis for methods that predict the effect of epilepsy surgery. For this application SPES networks are interesting as they disclose more physiological connections compared to CC and GC networks

Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status-epilepticus

The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed

A Comparison of Evoked and Non-evoked Functional Networks

The growing interest in brain networks to study the brain’s function in cognition and diseases has produced an increase in methods to extract these networks. Typically, each method yields a different network. Therefore, one may ask what the resulting networks represent. To address this issue we consider electrocorticography (ECoG) data where we compare three methods. We derive networks from on-going ECoG data using two traditional methods: cross-correlation (CC) and Granger causality (GC). Next, connectivity is probed actively using single pulse electrical stimulation (SPES). We compare the overlap in connectivity between these three methods as well as their ability to reveal well-known anatomical connections in the language circuit. We find that strong connections in the CC network form more or less a subset of the SPES network. GC and SPES are related more weakly, although GC connections coincide more frequently with SPES connections compared to non-existing SPES connections. Connectivity between the two major hubs in the language circuit, Broca’s and Wernicke’s area, is only found in SPES networks. Our results are of interest for the use of patient-specific networks obtained from ECoG. In epilepsy research, such networks form the basis for methods that predict the effect of epilepsy surgery. For this application SPES networks are interesting as they disclose more physiological connections compared to CC and GC networks