Parkinson's disease (PD) is a common neurodegenerative disorder with a prevalence rate estimated to 2.0% for people aged over 65 years. Cardinal motor symptoms of PD such as rigidity and bradykinesia affect the muscles involved in the handwriting process resulting in handwriting abnormalities called PD dysgraphia. Nowadays, online handwritten signal (signal with temporal information) acquired by the digitizing tablets is the most advanced approach of graphomotor difficulties analysis. Although the basic kinematic features were proved to effectively quantify the symptoms of PD dysgraphia, a recent research identified that the theory of fractional calculus can be used to improve the graphomotor difficulties analysis. Therefore, in this study, we follow up on our previous research, and we aim to explore the utilization of various approaches of fractional order derivative (FD) in the analysis of PD dysgraphia. For this purpose, we used the repetitive loops task from the Parkinson's disease handwriting database (PaHaW). Handwritten signals were parametrized by the kinematic features employing three FD approximations: Gr\"unwald-Letnikov's, Riemann-Liouville's, and Caputo's. Results of the correlation analysis revealed a significant relationship between the clinical state and the handwriting features based on the velocity. The extracted features by Caputo's FD approximation outperformed the rest of the analyzed FD approaches. This was also confirmed by the results of the classification analysis, where the best model trained by Caputo's handwriting features resulted in a balanced accuracy of 79.73% with a sensitivity of 83.78% and a specificity of 75.68%.

中文翻译：

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帕金森病书写困难分析中各种分数阶导数的探索

帕金森病 (PD) 是一种常见的神经退行性疾病，在 65 岁以上的人群中患病率估计为 2.0%。PD 的主要运动症状如僵硬和运动迟缓会影响手写过程中涉及的肌肉，导致称为 PD 书写障碍的手写异常。目前，数字化平板采集的在线手写信号（带有时间信息的信号）是目前最先进的图形运动困难分析方法。虽然基本的运动学特征被证明可以有效地量化 PD 书写困难的症状，但最近的一项研究发现，分数微积分的理论可以用来改进 Graphomotor 困难分析。因此，在这项研究中，我们跟进了我们之前的研究，我们旨在探索分数阶导数 (FD) 的各种方法在 PD 书写障碍分析中的应用。为此，我们使用了帕金森病手写数据库 (PaHaW) 中的重复循环任务。手写信号通过使用三个 FD 近似的运动学特征进行参数化：Gr\"unwald-Letnikov、Riemann-Liouville 和 Caputo。相关分析的结果揭示了临床状态与基于速度的手写特征之间的显着关系。 Caputo 的 FD 近似提取的特征优于其他分析的 FD 方法。分类分析的结果也证实了这一点，其中由 Caputo 的手写特征训练的最佳模型的平衡精度为 79。