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Fractional order modelling of neurons

Project Description

Fractional order calculus (integro-differential equations that are of non-integral order) is an emerging methodology with wide applications across all areas of Physics and Engineering. It enables the modelling of complex phenomena assuming simple underlying laws. Furthermore, it provides an explanation to emergent properties in dynamic systems. From this perspective, there is significant interest in capturing emergent phenomena associated with cognitive functions using these newly developed tools. The purpose of the proposed research is to develop novel signal processing modalities and better understanding of neuronal communications. The student will apply fractional order system identification techniques (time series analysis) to state space models of neuronal dynamics. Elements from linear and non-linear systems theory as well as elements of control theory (especially the work on coupled systems) will be used in the derivations. If the student is more interested in the biophysical aspects being incorporated in the models, biophysical state space models taking into consideration the physicochemical environment (elements of the chemical potential) within which the cells are placed will be developed. This will account for osmotic forces, electrical interactions between ions and the associated water potential parameters. Bond Graph theory to account for processes in different physico-chemical domains) and port-Hamiltonian formulations that account for power transfer in neuronal nodes of neuronal systems may also be developed. The models should be able to describe the dynamics of individual neurons or alternatively capture spatio-temporal emergent responses from a collection of neurons. Spatio-temporal statistical properties of neuronal responses could also be studied taking into consideration the theory of bio-dielectrics where charge hoping and trapping models have been well developed. This is a theoretical project with simulations performed in Matlab or Mathcad on theoretical models of neuronal responses to stimuli or using waveforms from data repositories, but there might be also opportunities to actually collect some data for further processing. The work is particularly relevant to current worldwide developments for modelling brain function as well as attempts to develop neuromorphic chips.

Funding Notes

Eligibility requirements: First class / upper second OR lower second with a Masters Degree in a relevant discipline


See my website for relevant publications. You may contact me directly at: [email protected]

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