A mathematical model characterising Achilles tendon dynamics in flexion

The purpose of this study is to acquire mechanistic knowledge of the gastrocnemius muscle-Achilles tendon complex behaviour during specific movements in humans through mathematical modelling. Analysis of this muscle-tendon complex was performed to see if already existing muscle-tendon models of other parts of the body could be applied to the leg muscles, especially the gastrocnemius muscle-Achilles tendon complex, and whether they could adequately characterise its behaviour. Five healthy volunteers were asked to take part in experiments where dorsiflexion and plantar flexion of the foot were studied. A model of the Achilles tendon-gastrocnemius muscle was developed, incorporating assumptions regarding the mechanical properties of the muscle fibres and the tendinous tissue in series. Ultrasound images of the volunteers, direct measurements and additional mathematical calculations were used to parameterise the model. Ground reaction forces, forces on specific joints and moments and angles for the ankle were obtained from a Vicon 3D motion capture system. Model validation was performed from the experimental data captured for each volunteer and from reconstruction of the movements of specific trajectories of the joints, muscles and tendons involved in those movements

A passive movement method for parameter estimation of a musculo-skeletal arm model incorporating a modified hill muscle model

In this paper we present an experimental method of parameterising the passive mechanical characteristics of the bicep and tricep muscles in vivo, by fitting the dynamics of a two muscle arm model incorporating anatomically meaningful and structurally identifiable modified Hill muscle models to measured elbow movements. Measurements of the passive flexion and extension of the elbow joint were obtained using 3D motion capture, from which the elbow angle trajectories were determined and used to obtain the spring constants and damping coefficients in the model through parameter estimation. Four healthy subjects were used in the experiments. Anatomical lengths and moment of inertia values of the subjects were determined by direct measurement and calculation. There was good reproducibility in the measured arm movement between trials, and similar joint angle trajectory characteristics were seen between subjects. Each subject had their own set of fitted parameter values determined and the results showed good agreement between measured and simulated data. The average fitted muscle parallel spring constant across all subjects was 143 N/m and the average fitted muscle parallel damping constant was 1.73 Ns/m. The passive movement method was proven to be successful, and can be applied to other joints in the human body, where muscles with similar actions are grouped together

Mathematical modelling and simulation of the foot with specific application to the Achilles tendon

In this thesis, the development of an anatomically meaningful musculoskeletal model of the human foot with specific application to the Achilles tendon is presented. An in vivo experimental method of obtaining parameter values for the mechanical characteristics of the Achilles tendon and the gastrocnemius muscle is presented incorporating a Hill-type muscle model. The incentive for this work has been to enable the prediction of movement with regard to Achilles tendon motion of healthy volunteers, in order to then compare it with the movement of a pathologic gait and help in preventing Achilles tendon injuries. There are relatively few mathematical models that focus on the characterisation of the human Achilles tendon as part of a muscle-tendon unit in the literature. The mechanical properties of the Achilles tendon and the muscles connected to the tendon are usually calculated or predicted from muscle-tendon models such as the Hill-type muscle models. A significant issue in model based movement studies is that the parameter values in Hill-type muscle models are not determined by data obtained from in vivo experiments, but from data obtained from cadaveric specimens. This results in a complication when those predictive models are used to generate realistic predictions of human movement dynamics. In this study, a model of the Achilles tendon-gastrocnemius muscle is developed, incorporating assumptions regarding the mechanical properties of the muscle fibres and the tendinous tissue in series. Ultrasound images of volunteers, direct measurements and additional mathematical calculations are used to determine the initial lengths of the muscle-tendon complex as well as the final lengths during specific movements of the foot and the leg to parameterise the model. Ground reaction forces, forces on specific joints and moments and angles for the ankle are obtained from a 3D motion capture system. A novel experimental marker placement for the Achilles tendon is developed and generated in the 3D motion capture system. Movement dynamics of the foot are described using Newton’s laws, the principle of superposition and a technique known as the method of sections. Structural identifiability analyses of the muscle model ensured that values for the model parameters could be uniquely determined from perfect noise free data. Simulated model dynamics are fitted to measured movements of the foot. Model values are obtained on an individual subject basis. Model validation is performed from the experimental data captured for each volunteer and from reconstruction of the movements of specific trajectories of the joints, muscles and tendons involved in those movements. The major output of this thesis is a validated model of the Achilles tendon-gastrocnemius muscle that gives specific parameters for any individual studied and provides an integral component in the ultimate creation of a dynamic model of the human body. A new approach that was introduced in this thesis was the coupling of the Achilles tendon force from the musculoskeletal model to the muscle-tendon model and the non-linearity approach studied through a motion capture system. This approach and the new Achilles tendon marker placement is to the best of the author's knowledge, novel in the field of muscle-tendon research