Preface

During last couple of years there has been an increasing recognition, that problems arising in biology or related to medicine, really need a multidisciplinary approach. One simply cannot treat evolving and adapting living tissues as rigid rods or as a material with some inner structure. Although they do bring some insight into the treated problem, it remains a rather limited source of understanding.

For this reason some special branches of both applied theoretical physics and mathematics have recently emerged such as biomechanics, mechanobiology, mathematical biology, biothermodynamics. The ultimate goal of all these approaches and models is to help in clinical applications, to improve medicine. This is actually a very long process to follow, with many intermediate steps involving many approaches and specialists, as for example experts in theoretical biomechanics and mathematical modelling, biologists, and finally clinicians. It was intended to preserve generality in the modelling and viewpoints of problems related to biomechanics. The same holds for its applications. In this book, *Theoretical Biomechanics,* we can find contributions from experts from all mentioned backgrounds and viewpoints but with focus on theoretical aspects of this research. As such, it tries to evoke and trigger the needed discussion over those quite different approaches being used and hopefully to bring more understanding for them. It also offers an overview of methods available from quite different perspectives, and hopefully will find a wide audience from all above mentioned expertises.

This book, *Theoretical Biomechanics*, comprises from theoretical contributions in Biomechanics often providing hypothesis, reasoning or rationale for a given phenomenon that experiment or clinical study cannot provide. Namely, the first section called *General Notes on Biomechanics and Mechanobiology* starts with a review chapter on mechanical properties of living cells and tissues from various perspectives from physics such as free-energy formulation based on microscopic characteristics of a given tissue (thermodynamics), mechanics of a cell when treated as a physical system, and tensegrity theory. The following chapter is devoted to mechanobiology of fracture healing providing spatial and also temporal predictions in tissue differentiation within a fracture site. The third chapter in this section comments on evolution of locomotor trends in extinct terrestrial giants and offers a possible explanation to accommodation of long bones based on a safety factor herein defined. The second section, *Biomechanical*  *Modelling*, is devoted to the rapidly growing field of various biomechanical models and modelling approaches to improve our understanding about all kinds of processes in human body. In the beginning, a Functional Data Analysis technique is introduced as a possible and complex statistical tool for analysis of large quantities of experimental data. Further, a review chapter of computational biomechanical models is given (several examples of sophisticated finite element models of human body parts are provided) together with a description of whole chain of necessary tools for individualising the model such as image acquisition and processing, mesh generation. This is followed by a review chapter on typical modelling techniques used in soft tissue biomechanics such as fiber reinforced material's models and similarly a contribution about computational finite elements models and their role in endodontics. Three concrete models of important phenomena found in humans or human body parts follow: biomechanical model of lower extremity, biothermodynamical model of bone remodelling, and a robotical biomechanical model of a hand. The last section called *Locomotion and Joint Biomechanics,* is a collection of works on description and analysis of human locomotion and joint stability and acting forces. The first chapter describes available and commonly used methods for assessment of loading forces on lower limbs (reaction forces, inverse dynamics, forward dynamics), compares them and discusses their limitations. The next two chapters are discussing a possible explanation of quite striking generalizations about the dynamic similarity in gaits of locomotion of different-sized animals. The following chapter provides an analysis of three-dimensional joint movements enabling determination of a cause-and-effect relationship in joint torques and movements which is of high importance for high-performance athletes. The next contribution is discussing biomechanical means of assuring stability in arboreal locomotion. Sixth chapter in this section provides a review of biomechanical assessment techniques of human movement including electromyography, kinetic and kinematic recordings which is followed by a review of anterior cruciate ligament together with development of a suitable ligament substitute. The last chapter is devoted to biomechanical characteristics of neck followed by several models for injury mechanisms and tolerance are presented.

I would like to take this opportunity to acknowledge the Czech Technical University in Prague (CTU) as well as Institute of Thermomechanics, Academy of Sciences of the Czech Republic (IT AS CR) for their support. My thanks also go to prof. František Maršík from the Department of Thermodynamics at IT AS CR and to my family.

> **Asst. Prof. Dr. Vaclav Klika**  Dept. of Mathematics FNSPE Czech Technical University in Prague Czech Republic

X Preface

tolerance are presented.

*Modelling*, is devoted to the rapidly growing field of various biomechanical models and modelling approaches to improve our understanding about all kinds of processes in human body. In the beginning, a Functional Data Analysis technique is introduced as a possible and complex statistical tool for analysis of large quantities of experimental data. Further, a review chapter of computational biomechanical models is given (several examples of sophisticated finite element models of human body parts are provided) together with a description of whole chain of necessary tools for individualising the model such as image acquisition and processing, mesh generation. This is followed by a review chapter on typical modelling techniques used in soft tissue biomechanics such as fiber reinforced material's models and similarly a contribution about computational finite elements models and their role in endodontics. Three concrete models of important phenomena found in humans or human body parts follow: biomechanical model of lower extremity, biothermodynamical model of bone remodelling, and a robotical biomechanical model of a hand. The last section called *Locomotion and Joint Biomechanics,* is a collection of works on description and analysis of human locomotion and joint stability and acting forces. The first chapter describes available and commonly used methods for assessment of loading forces on lower limbs (reaction forces, inverse dynamics, forward dynamics), compares them and discusses their limitations. The next two chapters are discussing a possible explanation of quite striking generalizations about the dynamic similarity in gaits of locomotion of different-sized animals. The following chapter provides an analysis of three-dimensional joint movements enabling determination of a cause-and-effect relationship in joint torques and movements which is of high importance for high-performance athletes. The next contribution is discussing biomechanical means of assuring stability in arboreal locomotion. Sixth chapter in this section provides a review of biomechanical assessment techniques of human movement including electromyography, kinetic and kinematic recordings which is followed by a review of anterior cruciate ligament together with development of a suitable ligament substitute. The last chapter is devoted to biomechanical characteristics of neck followed by several models for injury mechanisms and

I would like to take this opportunity to acknowledge the Czech Technical University in Prague (CTU) as well as Institute of Thermomechanics, Academy of Sciences of the Czech Republic (IT AS CR) for their support. My thanks also go to prof. František Maršík from the Department of Thermodynamics at IT AS CR and to my family.

> **Asst. Prof. Dr. Vaclav Klika**  Dept. of Mathematics

> > Czech Republic

FNSPE Czech Technical University in Prague

**Part 1** 

**General Notes on Biomechanics** 

**and Mechanobiology** 
