Neuronal control of sleep-wake regulation
Collaborators: Cecilia Diniz Behn (Colorado School of Mines) and Kevin Hannay (Schreiner University)
Sleep and wake states are regulated in the brain by interactions among multiple neuronal populations, some of which promote the waking state and others that promote sleep states, including rapid eye movement (REM) sleep and non-REM sleep. Additionally the timing of sleep and wake is strongly influenced by our daily circadian rhythm. However, the specific interactions amongst these populations and with the circadian pacemaker in the Suprachiasmatic Nucleus (SCN) that initiate and maintain sleep and wake states have not been completely determined. We are constructing neurophysiologically-based, mathematical models of these population networks and their interactions to analyze state transition dynamics and responses to perturbations in sleep-wake behavior. We are particularly interested in understanding the regulation of REM sleep and circadian modulation of sleep states.
We are developing a mathematical analysis framework to understand the solution dynamics of sleep-wake regulation models under circadian control. The framework consists of computing circle maps that track the circadian phases of sleep onsets.
Talk on using maps to understand sleep-wake regulation models link
Neuromodulation of neuronal and network properties on network dynamics
Collaborator: Michal Zochowski (UM, Physics and Biophysics)
Neural spiking activity in brain networks is influenced and modulated by myriad factors, including intrinsic firing properties of individual neurons, architecture of synaptic connections among neurons, synaptic plasticity in response to firing activity, and modulation of neural and synaptic properties by external factors such as chemical neuromodulators. We implement computational modeling using simple, yet biophysical neural network models to understand how these factors interact to dictate spatio-temporal activity patterns in large-scale neuronal networks. We are particularly motivated by neuromodulation by acetylcholine which varies over sleep and wake states, and plays a key role in attention.
Pain processing in the spinal cord
Collaborators: Sofia Piltz (UM, Mathematics), Jen Crodelle (Middlebury College) and Scott Lempka (UM, Biomedical Engineering and Anesthesiology)
The processing of pain engages a wide variety of neural circuits across the nervous system including those in the spinal cord, brainstem, thalamus, and cortex. More specifically, it is thought that the dorsal horn (DH), an area of the spinal cord, serves as the initial processing center for incoming nociceptive, or painful signals, with the midbrain and cortex providing top-down modulation to that circuitry. This circuitry receives information about stimulation of peripheral tissues from several types of primary afferent nerve fibers (Aβ, Aδ and C fibers). We are developing mathematical models of DH neural circuitry to understand different aspects of pain processing, including circadian rhythmicity of pain sensitivity and the actions of external spinal cord stimulation for the alleviation of chronic pain.