Assessing Manual Pursuit Tracking in Parkinson’s Disease Via Linear Dynamical Systems

Abstract

Quantitative assessment of motor performance is important for diseases of motor control, such as Parkinson's disease (PD). Manual tracking tasks are well suited for motor assessment, as they can be performed concomitantly with brain mapping techniques. Here we propose utilizing second-order linear dynamical systems to assess manual pursuit tracking performance. With the desired trajectory as the input, and the subject's actual motor response as the output, a linear model characterized by natural frequency and damping ratio is identified for each subject. We applied this method to 10 PD subjects (on and off L: -dopa medication) and 10 normal subjects performing a multi-frequency sinusoidal tracking task. Model parameters were more sensitive than overall tracking errors in determining significant differences between groups. The effect of L: -dopa medication was to reduce the damping ratio and make the range in natural frequency across individuals approach that of normal subjects. We interpret the changes in damping ratio and natural frequency as possibly related to suppression of compensatory cerebellar activity and/or improvement of motor program selection, and the changes in natural frequency as an implicit strategy to maintain settling time in the face of reduce damping ratio. Our results suggest that simple linear dynamical system models can be a powerful method to assess tracking performance in Parkinson's disease because of the additional insight they can provide into neurological processes.

Parkinson’s Disease Rigidity: Relation to Brain Connectivity and Motor Performance

“…It is important to note that these matrices completely characterize all possible system responses, that is, once tracking performance is successfully modeled, then the output y t can be predicted for any given input u t , not just those that were chosen experimentally. Previous work, including our own, has suggested that second-order models can successfully model normal and PD subjects during a tracking task (Oishi et al, 2011). …”

“…Yet, despite its potential functional importance, the implications of progressive rigidity in PD on quantitative motor performance are not currently known. Here we utilize Linear Dynamical System (LDS) models of tracking behavior collected concomitantly during the fMRI scanner session to assess motor performance, as we have previously shown this to be a more sensitive measure of motor performance than the normally used overall tracking error (Oishi et al, 2011). When PD subjects are asked to track a target, they tend to undershoot the actual target (Van Gemmert et al, 2003).…”

Perceptual control models of pursuit manual tracking demonstrate individual specificity and parameter consistency

“…Individual models of pursuit tracking performance may be effective tools in the assessment and treatment of motor deficits following neurologic injury. The pioneering research in analysis of estimated model parameters for people with Parkinson’s (Aiman Abdel-Malek et al, 1988 ; Au et al, 2010 ; Oishi et al, 2010 , 2011 ) indicates that models might be used to assess bradykinesia and other deficits in this group (Allen et al, 2007 ). In therapeutic settings, upper-limb assistive robotic devices provide force assistance in upper limb movements to those with neurological motor impairments, often during virtual-reality pursuit-tracking tasks (Maciejasz, Eschweiler, Gerlach-Hahn, Jansen-Troy, & Leonhardt, 2014 ).…”

“…Analysis of these parameters (gains, delays and damping constants, optimized to individual performance) enable discrimination between samples of people with Parkinson’s in receipt of medication, those who are non-medicated, and controls, despite the absence of a difference in overall task accuracy between the groups (Au et al, 2010 ; Oishi, Ashoori, & McKeown, 2010 ). Whilst many studies found that models accurately simulated the tracking behavior of individuals in model validation tests in both typical samples (Abdel-Malek & Marmarelis, 1988 ; Aiman Abdel-Malek & Marmarelis, 1990 ; Marken, 1991 ; Powers, 1978 ; Viviani et al, 1987 ; Viviani & Mounoud, 1990 ) and Parkinson’s disease samples (Aiman Abdel-Malek et al, 1988 ; Au et al, 2010 ; Oishi et al, 2010 ; Oishi, Talebifard, & McKeown, 2011 ; Viviani et al, 2009 ), there is a paucity of research studies that validate models with data collected at a later time point. This is problematic because the accuracy, and therefore usefulness, of a model must be dependent on the individual’s control strategy remaining stable over time in a well-practiced individual.…”

Manual Control Cybernetics: State-of-the-Art and Current Trends

“…Most of current cybernetics theory has been developed in the 1960s -for 1960s technology -and has been applied in aerospace [7]- [29], automotive [30]- [46], other vehicles [47]- [52], robotics [53]- [57] and medical applications [58]- [61]. The power of cybernetics is evident from the seminal crossover model [2]- [4], which captures the systematic adaptation of the Human Controller (HC) to the dynamics of the controlled vehicle or device, to achieve good feedback performance and robustness which are largely invariant with the controlled system.…”