A Parameter Selection for Differentiating Between Healthy and Parkinsonian Gait Through Modeling Parkinson's Disease From a Chaotic Viewpoint

To the Editor: Parkinson's disease (PD) is a neurodegenerative disease that is the most common disease after Alzheimer's disease among neurological diseases. Destruction of the substantia nigra pars compacta of basal ganglia (BG) is the cause of the disease. The exact cause of this destruction is not yet known.¹ Gait disorder is one of the cardinal symptoms of PD. The gait disorder in PD patients includes slowed gait, shortened length of stride, decreased rhythm and cadence, increased time of double support in the stance phase, shuffling and festinating gait, decreased swing of the arms, and disturbed regulation of the stride length. Five-minute walking can exhibit the disturbances in patients as compared with normal persons.^1,2 Researchers have focused from different perspectives on PD, some of which are: introducing animal models, introducing conceptual models, presenting cognitive symptoms, and finding novel treatments such as drugs and deep brain stimulation (DBS).^3–5 As studies shown, we can understand two main points about the brain and PD:

Considering the two facts, we propose to model the basal ganglia, using a black-box model that is obtained from one of the well-known chaotic relations so called “sin Circle Map.” We tried to model the disease using the recurrent relation (sin Circle Map) adding some other parameters to the equation, to increase its capability to model the disease. We used the recordings available in the Physionet⁶ to obtain the model parameters for each of the recordings. Our primary unpublished simulations showed that the range of variability of Omega (Ω) is considerably different in the two groups (healthy versus parkinsonian). Omega (Ω) is the main parameter in the model, and the rest of the system can be based on it.⁷ Therefore, we think that this parameter is the main factor for the model to show the state of the system (BG), and it can be used for proposing treatments for the disease.