Mathematics and Physical Sciences-Collaboration Grants for Mathematicians Grant uri icon

abstract

  • My research interests are in the areas of mathematical biology and computational neuroscience. I have been interested in applying mathematical and computational methods to better understand the neuronal activities of the brain. In the following, I will briefly discuss my most recent research.

    First-return map analysis: We developed a novel time-series analysis (first-return map) to explore the fine temporal structures of the synchrony at each cycle of oscillations in coupled oscillatory systems. By applying this approach, we observed that dynamics of the neural synchronies in the brains of several different mammals have a very specific temporal pattern: synchronous states are interrupted by frequent, but short desynchronization episodes. We showed that short desynchronization episodes are exhibited in general neuronal networks; these require weaker synaptic input to reach a pre-set synchrony level.

    Parkinson's disease (PD): We showed that the synchronies between the cortex and the basal ganglia in PD patients are significantly correlated. We demonstrated that the basal ganglia networks in PD patients exhibited multiple resonances in response to cortical inputs. We also studied how the cortical synchrony in PD patients is correlated with a unified Parkinson's disease rating scale motor score. We found that the neural synchrony patterning is more sensitive to the functionally important properties of the neural circuit's activity.

    Drug/alcohol addiction: We studied how neural signals become transiently synchronized and desynchronized in the prefrontal cortex (PFC) and hippocampus (HC) of awake rats undergoing a sensitization protocol through repeated injections of a psychostimulant drug. We found that the PFC-HC synchrony is decreased in the pre-injection period and increased in the post-injection period. This sensitization induces decoupling between the locomotor activity and the synchrony. Currently, we are exploring how the neural synchrony in the cortex areas of awake rats engaged in a Pavlovian conditioning task is altered with the presentation of a stimulus light that predicts the availability of alcohol.

    Social status dependent decision-making: Using a zebrafish as a model system, we showed that behavioral decisions reflect the interplay between competing neural circuits whose activation thresholds shift in accordance with social status. We also found that the neural mechanisms underlying habituation to the repeated stimuli are differentially regulated by social experience. Currently, we are exploring the cellular mechanisms for the effect of the neuromodulators on the escape and swim circuits depending on social status.

    Discrete dynamical models: We studied the discrete dynamical models of neuronal networks to explore complex and nonlinear interplays of the various components of networks. We characterized the dynamics of transients and attractors for directed Erdös-Rényi random graphs and other network architectures.

date/time interval

  • January 2018