Quantifying deficiencies associated with Parkinson's disease by use of time-series analysis

In order to assess quantitatively the state of the disease or the effect of drugs in parkinsonian patients, it would be helpful to have at our disposal mathematical models that reflect in their parameter values the deficiencies associated with the disease. This paper proposes a class of such models that are easily obtained in practice and lend themselves to useful interpretations. A pursuit manual tracking experiment is used to derive these models for patients with Parkinson's disease undergoing drug therapy and for normal controls. The input (one-dimensional visual target) and operator's output (manual tracking) are analyzed using a time series approach aiming at obtaining an auto-regressive moving-average (ARMA) model that minimizes the mean square error between the actual and model response. This mathematical model takes the form of a difference equation expressing, in discrete time, the present output value as a linear combination of past output values and past and present input values. Our experimental results indicate that a difference equation (ARMA model) involving the two previous output values and the present and past input values fits best both patient and control data. A comparison between the mean estimated model parameters for patients and controls shows a statistically significant difference in two of these parameters. The first parameter, which is significantly increased in patients, relates the current response of the patient to the immediately preceding response which represents an increased 'damping' of the motor dynamics, reflecting the muscular rigidity associated with the disease (motor disorder). The other parameter, which is significantly decreased in patients, represents the relative degree to which the current response of the patient is influenced by the target position information at the previous point in time which points to a deficiency in sensing/processing of this information (possible a sensory disorder). Our results also showed a marked reduction in the mean-square error of a second trial of the experiment in normal subjects but failed to do so for the patients, possibly indicating learning deficiencies associated with the disease.