A 2D Model of Cortical Spreading Depression Propagation Using Neural Field Framework: A Computational Study
Khan, Fizra (2025)
2025
Master's Programme in Biomedical Sciences and Engineering
Lääketieteen ja terveysteknologian tiedekunta - Faculty of Medicine and Health Technology
This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.
Hyväksymispäivämäärä
2025-12-09
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tuni-2025120511309
https://urn.fi/URN:NBN:fi:tuni-2025120511309
Tiivistelmä
Cortical spreading depression (CSD) is a biological event that arises as a slow wave of neuronal and glial depolarization across the cortex, in response to brain injury. The key neurochemical disturbance responsible for it is elevated potassium concentration in extracellular space. It is associated with injuries such as traumatic brain injury, subarachnoid haemorrhage and migraine. CSD induces conditions in the cortex that are physiologically unfavourable and is highly prone to recurrence causing severe damage to neurons.
Computational modelling approach has been widely used to investigate underlying mechanisms of CSD. Cell-based models are commonly used in computational neuroscience to understand biophysical details of a phenomenon. However, they become increasingly complex and computationally inefficient when extended to the spatial domains required for CSD like propagation.
Mean-field models, more specifically neural field models, provide a solid framework to model spatially extensive patterns and temporal evolutions of wave fronts without complexity. This is quite useful for capturing large-scale cortical phenomena with reduced computational burden.
The main objective of this thesis was to develop a two-dimensional (2D) model of CSD propagation based on neural field framework. The model was developed as an extension of a one-dimensional model developed by Baspinar et al. The original model includes extracellular potassium dynamics and its effect on the firing of neuronal populations within the framework.
This was achieved by implementing the neural field model on a 2D grid where each node represented a neural field unit. The equations of the model on individual node describe the coupled dynamics of two main neuronal populations, excitatory and inhibitory. Potassium concentration dependent sigmoidal transfer function was used to model the firing rate. A 2D exponential spatial kernel was used for weighted sum of signals from other populations. The stimulus was applied at three different locations to understand the spatial and temporal evolution of potassium and population dynamics in a 2D space. CSD speed was calculated with threshold-based front detection. Parameters such as number of nodes, distance between nodes and time constant were explored to find similar speed as control.
Radial curvatures and distinct ring-like patterns emerged as a result in spatial distribution. The firing rate of excitatory and inhibitory population exhibited potassium modulated behavior as modelled by Baspinar et al. The CSD speed closest to control speed (2.2 mm/min) was found to be 2.35 mm/min.
In conclusion, the 2D model was successful in capturing the CSD propagation based on potassium dynamics. The 2D model could serve as a foundation to simulate brain source activity and project the underlying neuronal activity at electroencephalography as voltages using forward projection method. This could be beneficial in finding detectable patterns in routine monitoring of CSD.
Computational modelling approach has been widely used to investigate underlying mechanisms of CSD. Cell-based models are commonly used in computational neuroscience to understand biophysical details of a phenomenon. However, they become increasingly complex and computationally inefficient when extended to the spatial domains required for CSD like propagation.
Mean-field models, more specifically neural field models, provide a solid framework to model spatially extensive patterns and temporal evolutions of wave fronts without complexity. This is quite useful for capturing large-scale cortical phenomena with reduced computational burden.
The main objective of this thesis was to develop a two-dimensional (2D) model of CSD propagation based on neural field framework. The model was developed as an extension of a one-dimensional model developed by Baspinar et al. The original model includes extracellular potassium dynamics and its effect on the firing of neuronal populations within the framework.
This was achieved by implementing the neural field model on a 2D grid where each node represented a neural field unit. The equations of the model on individual node describe the coupled dynamics of two main neuronal populations, excitatory and inhibitory. Potassium concentration dependent sigmoidal transfer function was used to model the firing rate. A 2D exponential spatial kernel was used for weighted sum of signals from other populations. The stimulus was applied at three different locations to understand the spatial and temporal evolution of potassium and population dynamics in a 2D space. CSD speed was calculated with threshold-based front detection. Parameters such as number of nodes, distance between nodes and time constant were explored to find similar speed as control.
Radial curvatures and distinct ring-like patterns emerged as a result in spatial distribution. The firing rate of excitatory and inhibitory population exhibited potassium modulated behavior as modelled by Baspinar et al. The CSD speed closest to control speed (2.2 mm/min) was found to be 2.35 mm/min.
In conclusion, the 2D model was successful in capturing the CSD propagation based on potassium dynamics. The 2D model could serve as a foundation to simulate brain source activity and project the underlying neuronal activity at electroencephalography as voltages using forward projection method. This could be beneficial in finding detectable patterns in routine monitoring of CSD.