A Finite Element Approach to Study Skeletal Muscle Tissue Aron Teklemariam A thesis submitted in partial fulfilment of the requirements of the Manchester Metropolitan University for the degree of Doctor of Philosophy. 2016 i Abstract This dissertation investigates force generation in muscle using a finite element (FE) approach to model electrical activity and mechanical force production within skeletal muscle. The work proposes new FE models design/formulations to answer specific research questions related to skeletal muscle properties. The focus is on two specific determinants of skeletal muscle force: the activation and the connective tissue. A FE model was created and designed to study the impact of the dielectric and geometric (pennation) properties of the muscle tissues on the electric activation signal detected on the skin surface by bipolar electrodes (surface electromyography, sEMG). The model shows that when considering parallel muscle fibres the tissue, attenuated mainly frequencies in the physiological range (92-542 Hz). This study revealed a strong impact of the muscle fibres pennation angle, on the detected signal (low pass filtering effect); suggesting that the low pass filtering behaviour observed in experimental data is due to the geometry (curvature or pennation) rather than the dielectric properties. The model informed recommendations for sEMG experimental protocol to increase the inter- electrodes distance when measuring sEMG of pennated muscles. A micromechanical model of the muscle tissue was created to explore the influence of the connective tissue properties (endomysium) on the total muscle force production. The constitutive model was used to study the mechanical consequence of clustering of fibres due to the remodelling of the motor units, which occurs with ageing. An FE model with a bundle of 19 fibres was designed and simulated activating 21% and 37% of the fibres in a distributed and clustered pattern. Results showed for both activation levels that the pattern of the strain distribution changed with an increased deformation toward the centre of the bundle. This could lead to excessive unbalanced stresses if higher deformations are involved. The micromechanical model can be used to study muscle force determinants at a fascicle level. It showed the importance of the fibre distribution during the muscle activation and the consequences of age related alterations on force production. i Declaration No portion of the work referred in this thesis has been submitted in support of an application for another degree or qualification at this, or any other university, or institute of learning. Date: Signed: ii Acknowledgement “ Glory to God, because of Your faithful love, because of Your truth.” I’d like to thank first of all, my supervisors team Dr. Glen Cooper, Dr. Emma Hodson- Tole, Prof. Neil Reeves, Dr. Nicholas Costen and recently Dr. Kirstie Andrew for giving me the opportunity to start a research/teaching career with this PhD. I thank my DoS of studies Dr. Glen Cooper for his support and encouragement, and for pushing me to develop a critical mind. A warm thank you to Dr. Emma Hodson-Tole for her pastoral support and her will to make us part of a disciplinary research team. I have tried my best to consider all your advices to become a mature researcher. Many thanks to my supervisors Neil Reeves, Nicholas Costen and Kirstie Andrew for always being available, and for giving me advices whenever it was needed. I am thankful to my office mates/friends/colleagues Canras, the sisters Elisa and Elisabetta, Andres, Ramzan, Simon, Dean, James, Mike, Gary, Prabhav, Khattab, Hassan, Fayad and Daniel. They made this journey enjoyable and full of meaning. Specifically I am very grateful to Canras, Elisa and Elisabetta for their support and caring. I wish them the best for their career and future families. This PhD was not just research, but also teaching which I have loved a lot. I am therefore very grateful to Dr. Hong Li and Dr. Sravanthi Shashikumar for giving me the opportunity to teach. I could not have had better mentors and examples. I think our department was blessed by the presence of staff that care about the research students. I was surprised and glad to see the dedication of our Head of Department Ms. iii Margaret Fowler and the Head of School Dr. Georgina Harris to provide support to us, research students. Finally yet importantly, I’d like to mention my family. My parents Teklemariam, Mehret and my sister Ruth. They taught me not to follow and believe the world but to have faith in God and the gift He gave us. If my PhD is meaningful, it is because of the relationships I have built and the people I have worked with. I hope to work with them again, and I wish them all to find their ways. iv Table of Contents Abstract .............................................................................................................................. i Acknowledgement ........................................................................................................... iii List of Figures .................................................................................................................... x List of Tables ................................................................................................................... xiii List of Abbreviations ...................................................................................................... xiv Publications based on this work .................................................................................... xvi Introduction ...................................................................................................................... 1 1 Muscle Anatomy & Modelling Fundamentals. .......................................................... 4 1.1 Skeletal Muscle Anatomy and Modelling Fundamentals ................................... 5 1.1.1 The Musculo-tendon Unit ........................................................................... 6 1.1.2 Motor Units and Activation ....................................................................... 10 1.2 Age-Related Changes in Muscle Tissue ............................................................ 12 1.3 Skeletal Muscle Modelling ............................................................................... 17 1.3.1 Hill-based Rheological Models .................................................................. 18 1.3.2 Rheological Hill-based Models .................................................................. 21 1.3.3 Neural Drive .............................................................................................. 24 1.3.4 Limitations of Classic Models and and Introduction to Finite Element Models 26 2 Literature Review:Mathematical Models of Skeletal Muscle ................................. 28 v 2.1 sEMG Models .................................................................................................... 29 2.1.1 sEMG ......................................................................................................... 29 2.1.2 EMG Modelling .......................................................................................... 32 2.1.3 Identified Research Question and Related Thesis Objectives .................. 46 2.2 Muscle Biomechanical Models ......................................................................... 48 2.2.1 Constitutive Mechanical Models .............................................................. 49 2.2.2 Identified Research Question and Related Thesis Objectives .................. 58 3 A FE Design Study of the Diele-ctric and Geometric Properties of the Muscle ...... 60 3.1 Overview ........................................................................................................... 61 3.2 Introduction ...................................................................................................... 62 3.3 Method ............................................................................................................. 67 3.3.1 FE Model ................................................................................................... 67 3.3.2 Input Data.................................................................................................. 72 3.3.3 Signal Processing ....................................................................................... 75 3.4 Results .............................................................................................................. 77 3.4.1 Properties of the iEMG Source Signal ....................................................... 77 3.4.2 Influence of inter-electrode distance & orientation ................................. 78 3.4.3 Influence of Fibre Pennation Angle ........................................................... 80 3.5 Discussion ......................................................................................................... 83 3.5.1 Orientation and IED ................................................................................... 83 vi 3.5.2 Pennation angle ........................................................................................ 84 3.6 Conclusion ........................................................................................................ 86 3.7 Acknowledgments ............................................................................................ 88 4 . Modelling the Connective Tissue Properties of the Muscle .................................. 89 4.1 Function and Properties of Skeletal Muscle Connective