A Mathematical Model of Levodopa Medication Effect on Basal Ganglia in Parkinson's Disease: An Application to the Alternate Finger Tapping Task

Malfunctions in the neural circuitry of the basal ganglia (BG), induced by alterations in the dopaminergic system, are responsible for an array of motor disorders and milder cognitive issues in Parkinson's disease (PD). Recently Baston and Ursino (2015a) presented a new neuroscience mathematical model aimed at exploring the role of basal ganglia in action selection. The model is biologically inspired and reproduces the main BG structures and pathways, modeling explicitly both the dopaminergic and the cholinergic system. The present work aims at interfacing this neurocomputational model with a compartmental model of levodopa, to propose a general model of medicated Parkinson's disease. Levodopa effect on the striatum was simulated with a two-compartment model of pharmacokinetics in plasma joined with a motor effect compartment. The latter is characterized by the levodopa removal rate and by a sigmoidal relationship (Hill law) between concentration and effect. The main parameters of this relationship are saturation, steepness, and the half-maximum concentration. The effect of levodopa is then summed to a term representing the endogenous dopamine effect, and is used as an external input for the neurocomputation model; this allows both the temporal aspects of medication and the individual patient characteristics to be simulated. The frequency of alternate tapping is then used as the outcome of the whole model, to simulate effective clinical scores. Pharmacokinetic-pharmacodynamic modeling was preliminary performed on data of six patients with Parkinson's disease (both “stable” and “wearing-off” responders) after levodopa standardized oral dosing over 4 h. Results show that the model is able to reproduce the temporal profiles of levodopa in plasma and the finger tapping frequency in all patients, discriminating between different patterns of levodopa motor response. The more influential parameters are the Hill coefficient, related with the slope of the effect sigmoidal relationship, the drug concentration at half-maximum effect, and the drug removal rate from the effect compartment. The model can be of value to gain a deeper understanding on the pharmacokinetics and pharmacodynamics of the medication, and on the way dopamine is exploited in the neural circuitry of the basal ganglia in patients at different stages of the disease progression.