Mathematical modeling of neuronal dynamics during disease

Thesis

We currently do not understand how neuronal activity leads to cognition. However, we can observe how neuronal activity changes as cognition becomes abnormal. Brain diseases tell us what aspects of neuronal functioning are necessary to maintain brain function and cognition. An essential step to understanding brain function is knowing how to fix it as it becomes dysfunctional. However, studying brain diseases in humans can be challenging because these conditions often span years or decades, making longitudinal studies difficult. Additionally, researchers are restricted to noninvasive measurement methods when studying human subjects. As a result, neuroscience is relying increasingly on quantitative sciences to find patterns in large and complex datasets. Mathematical modeling has become an essential tool to assimilate biological theories and test them in light of experimental data. In this thesis, we study the mathematical modeling of brain diseases. We cover various aspects of modeling, such as developing and analyzing new model formulations, simulating large-scale mathematical models of the human brain, and fitting them to data. First, we integrate mathematical models of Alzheimer’s disease progression and neuronal activity, showing that toxic proteins may cause alterations in brain activity consistent with clinical observations. Second, we develop a model for how neuronal activity affects disease progression, demonstrating the pivotal role neuronal activity plays in shaping disease trajectories. Third, we fit a model for brain-wide neuronal activity to brain cancer patients, discovering significant alterations in brain dynamics. Overall, we develop and analyze mathematical models to study brain diseases and their impact on neuronal activity, demonstrating the benefit of mathematical modeling in studying the mechanisms of brain disease.

Authors: Alexandersen, CG

• DOI: 10.5287/ora-g7qqmwbmj
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Alzheimer's disease; computational neuroscience; neurodegenerative disease; networks; dynamical systems; mathematical neuroscience
• Subjects: Dynamics; Computational neuroscience; Mathematics