Pierre Sacré

Kick synchronization versus diffusive synchronization

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling.

Controlling the phase of an oscillator: A phase response curve approach

The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC) calculated from the linearized model. The performance is evaluated on a popular model of circadian oscillations.

Sensitivity Analysis of Oscillator Models in the Space of Phase-Response Curves: Oscillators As Open Systems

Oscillator models-whose steady-state behavior is periodic rather than constant-are fundamental to rhythmic modeling, and they appear in many areas of engineering, physics, chemistry, and biology [1]-[6]. Many oscillators are, by nature, open dynamical systems in that they interact with their environment [7]. Whether functioning as clocks, information transmitters, or rhythm generators, these oscillators have the robust ability to respond to a particular input (entrainment) and to behave collectively in a network (synchronization or clustering).

Lucky Rhythms in Orbitofrontal Cortex Bias Gambling Decisions in Humans

It is well established that emotions influence our decisions, yet the neural basis of this biasing effect is not well understood. Here we directly recorded local field potentials from the OrbitoFrontal Cortex (OFC) in five human subjects performing a financial decision-making task. We observed a striking increase in gamma-band (36–50 Hz) oscillatory activity that reflected subjects’ decisions to make riskier choices. Additionally, these gamma rhythms were linked back to mismatched expectations or “luck” occurring in past trials. Specifically, when a subject expected to win but lost, the trial was defined as “unlucky” and when the subject expected to lose but won, the trial was defined as “lucky”. Finally, a fading memory model of luck correlated to an objective measure of emotion, heart rate variability. Our findings suggest OFC may play a pivotal role in processing a subject’s internal (emotional) state during financial decision-making, a particularly interesting result in light of the more recent “cognitive map” theory of OFC function.

The Role of Associative Cortices and Hippocampus during Movement Perturbations

Although motor control has been extensively studied, most research involving neural recordings has focused on primary motor cortex, pre-motor cortex, supplementary motor area, and cerebellum. These regions are involved during normal movements, however, associative cortices and hippocampus are also likely involved during perturbed movements as one must detect the unexpected disturbance, inhibit the previous motor plan, and create a new plan to compensate. Minimal data is available on these brain regions during such “robust” movements. Here, epileptic patients implanted with intracerebral electrodes performed reaching movements while experiencing occasional unexpected force perturbations allowing study of the fronto-parietal, limbic and hippocampal network at unprecedented high spatial, and temporal scales. Areas including orbitofrontal cortex (OFC) and hippocampus showed increased activation during perturbed trials. These results, coupled with a visual novelty control task, suggest the hippocampal MTL-P300 novelty response is modality independent, and that the OFC is involved in modifying motor plans during robust movement.

The precuneus may encode irrationality in human gambling

Humans often make irrational decisions, especially psychiatric patients who have dysfunctional cognitive and emotional circuitry. Understanding the neural basis of decision-making is therefore essential towards patient management, yet current studies suffer from several limitations. Functional magnetic resonance imaging (fMRI) studies in humans have dominated decision-making neuroscience, but have poor temporal resolution and the blood oxygenation level-dependent signal is only a proxy for neural activity. On the other hand, lesion studies in humans used to infer functionality in decision-making lack characterization of neural activity altogether. Using a combination of local field potential recordings in human subjects performing a financial decision-making task, spectral analyses, and non-parametric cluster statistics, we analyzed the activity in the precuneus. In nine subjects, the neural activity modulated significantly between rational and irrational trials in the precuneus (p <; 0.001). In particular, high-frequency activity (70-100 Hz) increased when irrational decisions were made. Although preliminary, these results suggest suppression of gamma rhythms via electrical stimulation in the precuneus as a therapeutic intervention for pathological decision-making.

Winning versus losing during gambling and its neural correlates

Humans often make decisions which maximize an internal utility function. For example, humans often maximize their expected reward when gambling and this is considered as a “rational” decision. However, humans tend to change their betting strategies depending on how they “feel”. If someone has experienced a losing streak, they may “feel” that they are more likely to win on the next hand even though the odds of the game have not changed. That is, their decisions are driven by their emotional state. In this paper, we investigate how the human brain responds to wins and losses during gambling. Using a combination of local field potential recordings in human subjects performing a financial decision-making task, spectral analyses, and non-parametric cluster statistics, we investigated whether neural responses in different cognitive and limbic brain areas differ between wins and losses after decisions are made. In eleven subjects, the neural activity modulated significantly between win and loss trials in one brain region: the anterior insula (p = 0.01). In particular, gamma activity (30-70 Hz) increased in the anterior insula when subjects just realized that they won. Modulation of metabolic activity in the anterior insula has been observed previously in functional magnetic resonance imaging studies during decision making and when emotions are elicited. However, our study is able to characterize temporal dynamics of electrical activity in this brain region at the millisecond resolution while decisions are made and after outcomes are revealed.

Sensitivity Analysis of Circadian Entrainment in the Space of Phase Response Curves

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input–output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations.

Electrical neurostimulation for chronic pain: On selective relay of sensory neural activities in myelinated nerve fibers.

Chronic pain affects about 100 million adults in the US. Despite their great need, neuropharmacology and neurostimulation therapies for chronic pain have been associated with suboptimal efficacy and limited long-term success, as their mechanisms of action are unclear. Yet current computational models of pain transmission suffer from several limitations. In particular, dorsal column models do not include the fundamental underlying sensory activity traveling in these nerve fibers. We developed a (simple) simulation test bed of electrical neurostimulation of myelinated nerve fibers with underlying sensory activity. This paper reports our findings so far. Interactions between stimulation-evoked and underlying activities are mainly due to collisions of action potentials and losses of excitability due to the refractory period following an action potential. In addition, intuitively, the reliability of sensory activity decreases as the stimulation frequency increases. This first step opens the door to a better understanding of pain transmission and its modulation by neurostimulation therapies.

Matching an oscillator model to a phase response curve

The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a numerical tool based on the sensitivity analysis of the PRC to adapt initial model parameters in order to match a particular PRC shape. We illustrate the approach on a simple biochemical model of circadian oscillator.