Advanced Biomedical Engineering
Online ISSN : 2187-5219
ISSN-L : 2187-5219
Model-based Analysis of Knee Joint Spasticity Based on Pendulum Testing of the Lower Extremities and Independent Component Analysis
Keizo TominagaYanling PeiYuji NishizawaGoro Obinata
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2022 Volume 11 Pages 218-227


Evaluating patients with paralysis of the lower extremities resulting from diseases of the central nervous system is essential for planning appropriate treatments and evaluating their effects. For patients with paralysis, previous studies have proposed that the dynamic properties of the knee joint be evaluated based on the pendulum motion of the lower leg. However, objective measurement of joint spasticity is challenging, and previous studies have utilized a variety of indicators, making direct comparison difficult. This study aimed to develop a new method for estimating and analyzing pendulum motion based on three dynamic properties (moment of inertia, viscosity, and stiffness). Thirty-two individuals (20 men and 12 women; mean age: 69.5 ± 10.5 years) who developed spasticity in the quadriceps femoris muscle on the paralyzed side ≥ 1 month after stroke onset were included, along with 20 healthy community-dwelling individuals (10 men and 10 women; mean age: 68.4 ± 6.9 years). For the pendulum test, the end block of a goniometer was attached to the outer side of the distal thigh and lower leg of the target limb to interpose the knee joint. The malleolus lateralis and malleolus medialis of the target limb were grasped and allowed to fall from a 45° flexed position, following which the knee angles were measured. Independent component analysis (ICA) was used to obtain pure pendulum motion data without the influence of measurement errors caused by the initial angle of the knee joint and the influence of trunk posture. This study is the first to quantify knee joint viscosity and stiffness as parameters of a linear model and goodness-of-fit as a parameter representing a deviation from the linear model by applying ICA and a genetic algorithm. Because the values of various parameters affecting pendulum motion can be determined using our model, it is possible to simulate the effects of physical therapy on gait under various conditions (e.g., rehabilitation interventions, use of orthotic devices). Our objective and quantitative method, which is simple and does not require consideration of measurement error during pendulum testing, may also aid in elucidating the mechanisms underlying the development of spasticity.

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© 2022 Japanese Society for Medical and Biological Engineering

Copyright: ©2022 The Author(s). This is an open access article distributed under the terms of the Creative Commons BY 4.0 International (Attribution) License (, which permits the unrestricted distribution, reproduction and use of the article provided the original source and authors are credited.
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