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Mathematical model of patella T-reflex and clinical evaluation with Ashworth scales

  • Süleyman Bilgin EMAIL logo , Hamza Feza Carlak , Övünç Polat , Tunca Nüzket , Serkan Uslu and Hilmi Uysal


Spasticity is one of the major problems that arise in different neurological diseases and seriously affect the quality of human life. Research on the understanding of mechanism of spasticity remains as important as the studies on the spasticity therapy and rehabilitation. In this study, the spasticity mechanism which develops concerning the upper motor neuron lesions is investigated by modelling “Patella tendon reflex triggered patella pendulum”. The mathematical model based on the pendulum phenomenon is developed by solving the curve-fitting problem as finding the curve that best fits a set of data points. Electrophysiological and dynamic measurement data were taken from 76 spastic subjects and 20 healthy participants. The mathematical model is determined by the morphological properties of the goniometric variations. The results denote that the mathematical model containing two clinically relevant parameters –frequency component of the damped oscillatory motion defined as “f 0 ” with the maximum angle of the reflex defined as “a 0 ” ensures to distinguish spasticity from healthy subjects.

Corresponding author: Süleyman Bilgin, Department of Electrical & Electronics Engineering, Faculty of Engineering, Akdeniz University, Antalya, 07058, Turkey, E-mail:

Funding source: Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Award Identifier / Grant number: 214S175

Funding source: Akdeniz Üniversitesi


Thanks are due to co-author Suha Yagcioglu who was deceased before the completion of the article.

  1. Funding: This study was funded by TUBITAK with 214S175 project number, and also supported by the Research Project Department of Akdeniz University, Antalya, Turkey.

  2. Conflict of interest: All authors declare that there are no conflicts of interest regarding this article.

  3. Compliance with ethical standards: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. Informed consent was obtained from all individual participants included in the study.


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Received: 2019-03-20
Accepted: 2020-01-31
Published Online: 2020-06-09
Published in Print: 2020-10-25

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