Publication Summary and Abstract
Blenkinsop, A., Kadirkamanthan, V., Anderson, S., & Gurney, K. N. (2012), A firing rate model of the basal ganglia incorporating action selection with parameter estimation by approximate Bayesian computation, Presented at the Society for Neuroscience Annual Meeting, New Orleans.
The Basal Ganglia (BG) play a crucial role in motor control and it has been suggested that they act as a selection mechanism, permitting the execution of a limited set of actions or behaviours which present signal representations at their input (Redgrave et al., 1999). The action-selection hypothesis has received support in computational models (Gurney et al., 2001; Humphries et al., 2006). However, in these models, determination of some of the parameters (e.g. connection strengths between neural populations) is problematic because they do not have a clear physiological interpretation. Previous studies have tuned these parameters to ensure the models yield action-selection type behaviour, rather than inferring them from experimental data. In our current work we address this issue by developing a model of BG in which the connection strength parameters are estimated from experimental data in a Bayesian framework. The firing rate model of the BG that we develop is a 3-channel version of that developed by Gurney et al. (2001) and is well suited to bifurcation analysis using continuation methods. Using this approach we can investigate the transition to oscillations in the subthalamic-pallidial feedback loop which is a candidate for the source of the muscular tremor of Parkinson's disease. We obtain the connection strength parameters using approximate Bayesian computation (ABC). This estimation procedure is new to the field of neural modelling, and is ideally suited to the task since it is a numerical sampling, simulation-based method that does not require analytical treatment of model equations to infer distributions over parameter values. The ABC approach also has the advantage over many other optimisation procedures in that it yields information about the spread of all possible solutions, rather than just a single optimum parameter set. ABC therefore gives a measure of how robust the system is to disturbances, which is likely to be of greater value in neural systems than a single 'best-fit' solution. We use a wide variety of existing experimental data from single unit recording studies in primates to drive the ABC algorithm. While a hypothesis of BG function is not assumed in the estimation process, initial investigation shows that a subset of the ABC-derived models are consistent with hypotheses of action selection.