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Biomechanical Modelling in Sports – Selected Applications

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Biomechanical Modelling in Sports – Selected Applications Biomechanical modelling in sports – selected applications U. Hartmann1, G. Berti2, J.G. Schmidt1, T.M. Buzug3 1University of Applied Sciences Koblenz, RheinAhrCampus, Germany. 2NEC Europe Ltd., C&C Research Laboratories, St. Augustin, Germany. 3University of Luebeck, Institute for Biomedical Engineering, Germany. Abstract In the past decade computer models have become very popular in the fi eld of sports biomechanics due to the exponential advancements in computer technology. Biomechanical computer models can roughly be grouped into multi-body mod- els and numerical models. The theoretical aspects of both modelling strategies will be shortly introduced. This chapter focuses on the presentation of instructive application examples each representing a specialized branch within the fi eld of modelling in sports. Special attention is paid to the set-up of individual models of human body parts. In order to reach this goal a chain of tools including medical imaging, image acquisition and processing, mesh generation, material modelling and fi nite element simulation becomes necessary. The basic concepts of these tools are thoroughly described and fi rst results presented. The chapter ends with a short outlook into the future of sports biomechanics. Keywords: biomechanical models, mesh generation, fi nite elements, sports 1 Introduction 1.1 Why models? The fi eld of sports biomechanics suffers from one very severe restriction; in general it is not possible for ethical reasons to measure forces and pressure inside the human body. Thus, typical measurement technology in biomechanics works on the interface between the body and the environment. Force platforms for instance dynamically quantify reaction forces when a person is walking or run- ning across the sensor, electromyography (EMG) monitors action potentials of contracting muscles with electrodes detached to the human skin. The information WIT Transactions on State of the Art in Science and Eng ineering, Vol 32, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/978-1-84564-064-4/07 WWITPress_CS_Ch007.inddITPress_CS_Ch007.indd 118989 22/22/2008/22/2008 110:11:430:11:43 AAMM 190 COMPUTERS IN SPORT provided by the measurement technology is very important to investigate move- ments in sports, but is not suffi cient to answer questions such as 1. How can we maximize the output (e.g. height of a jump) while minimizing the loads on the joints (e.g. during the landing phase)? Or: How can we better understand mechanisms of sports injury? These questions are related to the human body. 2. How do we have to design the sports equipment to optimally suit to the athlete’s requirements in terms of mechanical behaviour? These questions are related to the technical equipment. This optimization process has three aspects: ᭹ Ineffective and destructive loading on the athlete’s body has to be minimized (e.g. by increased damping through improved cushions in the sole of the sports shoe). ᭹ The athlete’s protection has to be maximized (e.g. by the design of a helmet for cyclists to avoid head injury caused by a crash, see section 3.2.1). ᭹ The output has to be maximized (e.g. by a concept for an optimized cricket bat, see section 3.2.2). The only possible way to answer the questions related to the human body is to set up mechanical models of the human body or at least of human body parts. The set-up of a sports-biomechanical model is the only possibility to gain insight into the mechanical behaviour of the inner human body. Thus, model- ling has become extremely popular because it, to some extent, heals the funda- mental dilemma of biomechanics that has been described at the beginning of the chapter. Therefore, a software tool chain for the automatic generation of anatomical structures is presented in Section 3.3. As we will see in Section 3.2 the set-up of models representing sports equip- ment is also an important task in sports biomechanics. Here, computer analy- ses are applied to better understand the mechanics of sports equipment during exercise. However, in the fi eld of sports biomechanics, measurement technology still plays an important role (see Figure 1): the information provided by the measure- ments is either input for a model (e.g. reaction forces acting on the foot) or used to validate the model (e.g. comparing the simulation results with EMG data). Thus, it is almost trivial to mention that models are of no scientifi c use without validation. 1.2 A classifi cation of models When looking at the progress being made in the fi eld of biomechanical modelling related to problems stemming from sports one can see two major directions of development: 1. Multi-body systems (MBS) have been set up yielding important results in gait analysis, jumping, throwing and gymnastics [1, 2, 3]. WIT Transactions on State of the Art in Science and Eng ineering, Vol 32, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) WWITPress_CS_Ch007.inddITPress_CS_Ch007.indd 119090 22/22/2008/22/2008 110:11:430:11:43 AAMM BIOMECHANICAL MODELLING IN SPORTS 191 biomechanical models numerical models multi-body (e.g. FEM, CFD) models material force/EMG anthropo- video properties measurements metric data analysis biomechanical measurements Figure 1: The relation between models and data. 2. Numerical models using fi nite elements (FEM) or computational fl uid dynam- ics (CFD) have been successfully applied to a variety of sports-biomechanical problems such as improving injury prevention [4], ameliorating the design of pieces of sports equipment [5] and better understanding and optimizing sports techniques [6]. Both types of models have their advantages and disadvantages: numerical models enable the computation of the whole body’s deformation, whereas multi- body models only provide forces at a limited number of body points. But, the price to pay for taking into account the body’s deformation is a much higher demand in terms of computer power for the fi nite element method. This fact partially explains why frequently parallel computers enter the stage in order to arrive at accurate FE results. Meanwhile, software packages are available that enable the user to use both methods MBS and FEM simultaneously. The remainder of this text is organized as follows: the next chapter deals with the basic concept of multi-body models to then discuss one MBS model in detail. Chapter 3 gives a short introduction to the fi nite element method, shows some example applications and fi nally describes a software tool chain to set up FE models of human body parts starting from medical image data. Finally a short outlook into the future of sports-related modelling is given. 2 MBS in sports biomechanics Within the last two decades multi-body models have frequently been applied to solve biomechanical problems in sports. Some selected MB applications are WIT Transactions on State of the Art in Science and Eng ineering, Vol 32, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) WWITPress_CS_Ch007.inddITPress_CS_Ch007.indd 119191 22/22/2008/22/2008 110:11:430:11:43 AAMM 192 COMPUTERS IN SPORT for instance simulations for impact analysis [1], investigations of the trampoline jumping [2], studies about walking and running [3] or the discussion of forces encountered in bicycle sports [7]. MBS can be used in two different ways: as forward or as inverse models. 2.1 Forward multi-body models Many example applications found in literature make use of the so-called forward models. Here, the physical forces and moments (e.g. gravitation and external forces, see Figure 3) are the given quantities. Together with geometric data (e.g. length of body segment) and mechanical parameters (e.g. moments of inertia J, centre of mass) the resulting body movement can be computed. The movement is fully described by the laws of Newtonian dynamics that is mathematically described by the following equations. F = ma (1) M = Jα (2) In general, F, a, M and α are three-dimensional vectors denoting force, linear acceleration, moments and angular acceleration, respectively. The mass m is a scalar and the moment of inertia J is in general a tensor represented by a 3 × 3 matrix. To be able to solve the underlying differential equations a kinematical chain of simple geometric entities (e.g. an ellipsoid representing the thigh) has to be set up (see Figure 2). In order to arrive at the quantities of interest (e.g. the load in the hip joint while landing) segment after segment has to be processed. The segments are linked by hinges whose degrees of freedom are defi ned according to those of the anatomical articulations. The rigid body motion (i.e. translation and rotation) of the current segment (e.g. the foot) can be calculated when the external forces (e.g. measured by a force platform) and the body weight of the Figure 2: Multi-body models in different visualizations. WIT Transactions on State of the Art in Science and Eng ineering, Vol 32, © 2008 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) WWITPress_CS_Ch007.inddITPress_CS_Ch007.indd 119292 22/22/2008/22/2008 110:11:430:11:43 AAMM BIOMECHANICAL MODELLING IN SPORTS 193 16 14 R 12 FG 10 8 FG 6 Multiples of body weight 4 F 2 G 0 0 5 10 Time in ms FR Figure 3: Link segment model of the human leg and calculated forces in the hip joint for different kinds of landing (dotted line = soft landing; straight line = hard landing). segment are given. The mechanical infl uence of the next segment in the chain (e.g. the shank) on the current segment is represented by a reaction force. These reaction forces are most interesting as they give a measure of the load present in the joint during sports exercise.
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