Efficient Numerical Population Density Techniques with an Application in Spinal Cord Modelling

MIIND is a neural simulator which uses an innovative numerical population density technique to simulate the behaviour of multiple interacting populations of neurons under the influence of noise. Recent efforts have produced similar techniques but they are often limited to a single neuron model or type of behaviour. Extensions to these require a great deal of further work and specialist knowledge. The technique used in MIIND overcomes this limitation by being agnostic to the underlying neuron model of each population. However, earlier versions of MIIND still required a high level of technical knowledge to set up the software and involved an often time-consuming manual pre-simulation process. It was also limited to only two-dimensional neuron models. This thesis presents the development of an alternative population density technique, based on that already in MIIND, which reduces the pre-simulation step to an automated process. The new technique is much more flexible and has no limit on the number of time-dependent variables in the underlying neuron model. For the first time, the population density over the state space of the Hodgkin-Huxley neuron model can be observed in an efficient manner on a single PC. The technique allows simulation time to be significantly reduced by gracefully degrading the accuracy without losing important behavioural features. The MIIND software itself has also been simplified, reducing technical barriers to entry, so that it can now be run from a Python script and installed as a Python module. With the improved usability, a model of neural populations in the spinal cord was simulated in MIIND. It showed how afferent signals can be integrated into common reflex circuits to produce observed patterns of muscle activation during an isometric knee extension task. The influence of proprioception in motor control is not fully understood as it can be both task and subject-specific. The results of this study show that afferent signals have a significant effect on sub-maximal muscle contractions even when the limb remains static. Such signals should be considered when developing methods to improve motor control in activities of daily living via therapeutic or mechanical means.