**1. Introduction**

320 Viscoelasticity – From Theory to Biological Applications

Yuju, W. & Basaran, C. (2003), Thermomechanical Stress Analysis of Multi-Layered

Electronic Packaging, *Journal of Electronic Packaging*, Vol. 125, pp. 134-138.

Functional electrical stimulation (FES) is a promising way to restore mobility to individuals paralyzed due to spinal cord injury (SCI). Modelling and parameter identification of both the passive and active joint properties are needed to improve control of this nonlinear time varying system. In order to develop a suitable control strategy for the FES to move of the leg correctly, a proper model of stimulated muscle has to be used. The muscle is assumed to consist of two components: an active force generator and parallel passive properties. Riener and Edrich (1999) suggested passive muscle properties should be identified separately from active muscle properties because it is easier to consider the passive elastic forces as contributions to the total joint moment. Other researchers such as Zajac (1989) and Pandy et al. (1990) used a musculo-tendon model, in which the passive and the active forces are generated by single muscles. However, such models have too many parameters that cannot be identified non-invasively due to the muscle-joint redundancy of the musculoskeletal system (Riener and Edrich, 1999).

Conventionally the joint passive resistance is modelled as an elastic element like a torsion spring and a viscous element like a rotary damper (Lamb et al., 1991). These two resistances are non-linear, but the viscous resistance is often approached as a linear function of the joint angular velocity (Chizeck et. al., 1999; Mansour and Audu, 1986). These characteristics are important to estimate muscle load or fatigue during motion, especially in the field of biomechanics. Some researchers have shown further that these resistances influence the basis of motion effectively. For example, the resistance imposed by passive joint properties can impede the functionality of FES systems during limb movements (Amankwah, 2001).

© 2012 Ibrahim et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Segment mass of human body is an elementary inertial parameter for kinetic analyses of human motion. Many methods exist to estimate body segment properties. In the past, the most popular approach used to estimate segment parameters has been based on data obtained from elderly male cadavers. This database is quite limited in that a small number of cadavers have been studied. Thus, the database for making inertial estimates is not representative of the subjects often under investigation in many exercise and sport biomechanics studies. Dempster (1956) addressed the problem of mass model using cadaveric studies to establish segmental masses expressed as a percentage of total body mass (Winter, 1990). Other techniques have been developed in which inertial properties are directly measured for an individual. Zatsiorsky and Seluyanov (1985) used gamma mass scanning as a means of quantifying mass distribution in analyzing human body segment inertial characteristics. Both of these methods were promising and widely used but gave different measurement of the segment mass since calculated properties can vary drastically depending on the method used. Segment properties can significantly affect such variables, especially during swing phase (Doane and Quesada, 2006).

An Approach for Dynamic Characterisation of Passive Viscoelasticity and Estimation of Anthropometric Inertia Parameters of Paraplegic's Knee Joint 323

*M*i sd *M MM <sup>g</sup>* (2)

In this research the *M*<sup>i</sup> *Mg* represented by equation of motion for dynamic model of the lower limb and *M*s d *M* represented by fuzzy model as viscoelasticity. The subject was a 48 year-old T2&T3 incomplete paraplegic male with 20 years post-injury with height = 173cm

In this section, first the procedure to perform the pendulum test is presented to get the experimental data. Second, the equations of motion for dynamic model of the lower limb are introduced. Third, the estimations of anthropometric inertia parameters lower limb model are described briefly. Forth, the optimization of fuzzy model as passive viscoelasticity is outlined. Lastly new method for estimation and optimization of passive properties using GA by comparing with experimental data is elaborated. The procedure for estimation of the anthropometric inertia parameters and optimisation of FIS as passive viscoelasticity of the

Pendulum test can be used to evaluate passive properties such as viscosity and elasticity moments of the knee. Viscoelasticity is combination of elasticity and viscosity and represents passive resistances to joint motion associated with the structural properties of the joint tissue and of the muscular-tendon complex. Elasticity can be considered as an intrinsic property of the tissue to resist deformation, while viscosity is related to cohesive forces between adjacent layers of tissues. Both parameters may influence the joint range of motion affecting knee angle (Valle et. al, 2006). A genetic optimization algorithm is used to identify the unknown viscoelasticity by minimizing the error between the data obtained experimentally and from the simulation model. The pendulum test was conducted to measure the passive knee motion of an SCI patient. The subject sat on a chair, which allowed the lower leg to swing freely, while ankle joint was monitored to be at 0°. Reflexive or voluntary activation of muscles acting on the knee occurred during the pendulum test

In the pendulum test the knee was slowly extended, by having the experimenter lift it with minimal acceleration at the starting position (1) and then it was released as shown in Figure 3. The knee angle was recorded using electro-goniometer until the final position (2). A Biometric electro-goniometer was used to measure knee movements with sampling time of

The inertial ( *M*<sup>i</sup> ) and gravitational ( *M*<sup>g</sup> ) moments are represented by mathematical model

and weight = 80kg. Informed consent was obtained from the subject.

has been monitored to avoid the influence of pendulum movements.

0.05s. The electro-goniometer arrangement is shown in Figure 4.

**2.2. Equations of motion for dynamic model of the lower limb** 

of a dynamic system of the lower limb based on Kane's equations as follows:-

knee joint model are shown in Figure 1.

**2.1. Pendulum test** 

or

The pendulum test of Wartenberg is a technique commonly applied to evaluate passive properties in which the leg is allowed to drop from an initially extended position under the influence of gravity and then allowed to oscillate freely (Wartenberg, 1951). The test is very attractive in that it requires no special equipment and is very simple and the oscillatory movements of the lower leg recorded at the knee joint, are captured with electrogoniometers (Bajd and Vodovnik, 1984; Le Cavorzin et al., 2001), uniplanar video-based methods (Jamshidi and Smith, 1998) and 3D motion analysis systems (White et al., 2007). Most of the analyses of the pendulum motion depend on a second-order linear model to extract the elastic and viscous moments from the recorded leg oscillations. However a second order linear model does not provide an adequate description of the motion for either spastic or normal legs (Lin and Rymer, 1991).

In this paper a new approach for estimating passive properties of the paraplegic's knee joint based on pendulum test is described. On the basis of these experimental and optimization results, a non-linear fuzzy model is proposed which can be used to estimate the passive viscoelastic knee joint moment as a function of knee angle and knee velocity. The model of a dynamic system of the lower limb is derived using Kane's equations (Josephs and Huston, 2002) with accessibility to estimate of the foot mass, shank mass, moment of inertia about COM and position of COM along the segmental length of the subject.
