A review of presented mathematical models in Parkinson's disease: black- and gray-box models

Parkinson's disease (PD), one of the most common movement disorders, is caused by damage to the central nervous system. Despite all of the studies on PD, the formation mechanism of its symptoms remained unknown. It is still not obvious why damage only to the substantia nigra pars compacta, a small part of the brain, causes a wide range of symptoms. Moreover, the causes of brain damages remain to be fully elucidated. Exact understanding of the brain function seems to be impossible. On the other hand, some engineering tools are trying to understand the behavior and performance of complex systems. Modeling is one of the most important tools in this regard. Developing quantitative models for this disease has begun in recent decades. They are very effective not only in better understanding of the disease, offering new therapies, and its prediction and control, but also in its early diagnosis. Modeling studies include two main groups: black-box models and gray-box models. Generally, in the black-box modeling, regardless of the system information, the symptom is only considered as the output. Such models, besides the quantitative analysis studies, increase our knowledge of the disorders behavior and the disease symptoms. The gray-box models consider the involved structures in the symptoms appearance as well as the final disease symptoms. These models can effectively save time and be cost-effective for the researchers and help them select appropriate treatment mechanisms among all possible options. In this review paper, first, efforts are made to investigate some studies on PD quantitative analysis. Then, PD quantitative models will be reviewed. Finally, the results of using such models are presented to some extent.