Finger tapping movements of Parkinson’s disease patients automatically rated using nonlinear delay differential equations

Abstract

Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r ¼ 0.785) and significant (p < 0:0015) correlation between them. Parkinson's disease (PD) is a common disease affecting tens of millions of people worldwide. Its cardinal signs are resting tremor, bradykinesia (slowness clumsiness of movement), rigidity, and loss of postural reflexes. The disease evolves slowly and, to adjust medications to the severity of the disease, there is a need for automatic and objective evaluation of movements. Such objective movement assessments would supplement subjective clinical ratings, which are ordinal rather than metric and often show large inter-rater variability. Rather than using a spectral based technique, we rated dynamical features of each individuals' finger-tapping-one of the items from the unified Parkinson's disease rating scale (UPDRS) used for rating the severity of the disease-by using data models based on nonlinear delay differential equations (DDEs). The coefficients of the DDEs are then used to assess the severity of the disease.

Nonlinear dynamics underlying sensory processing dysfunction in schizophrenia

“…Embeddings are used in nonlinear dynamics to reveal invariant dynamical properties underlying a more extensive, largely unknown dynamical system (i.e., the brain) when only a single time series (e.g., EEG data) is available. Previous studies have shown that DDA can be used to extract disease-specific dynamical features: Parkinson's movement data (29,30), ECG recordings (27,31), sleep EEG (26), classification of Parkinson's disease EEG data (32,33), and electrocorticography data for epileptic seizure characterization (34).…”

Electrocardiogram classification using delay differential equations

“…Although quite flexible, as for any global modeling technique, there is a significant gain in accuracy by carefully selecting the structure of the model. 38–40 By structure selection or model learning, we mean retaining only those monomials that make the most significant contribution to the data dynamics. An equally important task is to select the right time-delays, since they are directly related to the primary time-scales and non-linear couplings between them of the dynamics under study.…”

“…40 used a genetic algorithm to find a single DDE model for the classification of Parkinson movement data. Here, we want to do an exhaustive search of models and delays and find the models and delays that best separate classes of data.…”

Analysing the stability of a delay differential equation involving two delays

“…If the modeling differential equation includes the past values of state variable then it is called as a delay differential equation (DDE). Basic analysis and various applications of DDE are discussed in [7,8,9,10].…”