| Abstract: |
| Mathematics plays an increasing role in brain research and medicine. The well-known Hodgkin-Huxley model for neurons laid a foundation for computational neuroscience. However, understanding activities in the whole brain remains a focus of active research. Full brain Electroencephalography (EEG) and its source localization is a brain imaging modality based on multi-channel EEG signals. It measures the brain field potential fluctuations on the entire scalp for a period of time, and then we can mathematically calculate the electric current density inside the brain by solving an inverse problem for a partial differential equation. In this talk, we introduce mathematical methods for the EEG imaging problems, their validations through simulations and experimental data, and discuss its applications. One application is in identifying abnormality in brain activities during seizures of an infant patient with Glucose Transporter Deficiency Syndrome. Another application is to find the neuronal signatures in response to pain stimulation. Our research shows these brain data can be further used to study the brain properties that glean into the inner working of brain functions using mathematical and statistical tools. |
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