Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

Neural mechanisms underlying breathing complexity

Breathing is maintained and controlled by a network of automatic neurons in the brainstem that generate respiratory rhythm and receive regulatory inputs. Breathing complexity therefore arises from respiratory central pattern generators modulated by peripheral and supra-spinal inputs. Very little is known on the brainstem neural substrates underlying breathing complexity in humans. We used both experimental and theoretical approaches to decipher these mechanisms in healthy humans and patients with chronic obstructive pulmonary disease (COPD). COPD is the most frequent chronic lung disease in the general population mainly due to tobacco smoke. In patients, airflow obstruction associated with hyperinflation and respiratory muscles weakness are key factors contributing to load-capacity imbalance and hence increased respiratory drive. Unexpectedly, we found that the patients breathed with a higher level of complexity during inspiration and expiration than controls. Using functional magnetic resonance imaging (fMRI), we scanned the brain of the participants to analyze the activity of two small regions involved in respiratory rhythmogenesis, the rostral ventro-lateral (VL) medulla (pre-Bötzinger complex) and the caudal VL pons (parafacial group). fMRI revealed in controls higher activity of the VL medulla suggesting active inspiration, while in patients higher activity of the VL pons suggesting active expiration. COPD patients reactivate the parafacial to sustain ventilation. These findings may be involved in the onset of respiratory failure when the neural network becomes overwhelmed by respiratory overload We show that central neural activity correlates with airflow complexity in healthy subjects and COPD patients, at rest and during inspiratory loading. We finally used a theoretical approach of respiratory rhythmogenesis that reproduces the kernel activity of neurons involved in the automatic breathing. The model reveals how a chaotic activity in neurons can contribute to chaos in airflow and reproduces key experimental fMRI findings.

Chaotic oscillations in a map-based model of neural activity

We propose a discrete time dynamical system (a map) as a phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find conditions under which this map has an invariant region on the phase plane, containing a chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking, etc.) derived from the proposed model.