Musculoskeletal Biomechanics

Preface 1 Orthopaedic biomechanics, an important and interesting discipline at the interface between medical and natural sciences 2 Basic concepts from physics and mechanics 2.1 Force 2.2 Moment 2.3 Pressure 2.4 Mechanical stress 2.5 Mechanical work, energy and power 3 Vector algebra 3.1 The trigonometric functions sine, cosine and tangent 3.2 Representation of vectors 3.3 Addition of vectors: graphical procedure in the 2-dimensioal case 3.4 Addition of vectors: numerical procedure 3.5 Decomposition of vectors into vectors addends 3.6 Multiplication of vectors: scalar product and vector product 4 Translation and rotation in a plane 4.1 Translation 4.2 Rotation 4.3 Combined translation and rotation 4.4 Instantaneous centre of rotation 4.5 Error influences when describing a motion 5 Mechanical equilibrium 5.1 Conditions of static mechanical equilibrium 5.2 Example: calculation of an unknown moment in the state of static equilibrium 5.3 Example: calculation of an unknown force in the state of static equilibrium 5.4 Example: calculation of the joint force of a beam scale in static equilibrium 6 Material properties of solid materials 6.1 Elongation and compression 6.2 Shear 6.3 Elastic, viscoelastic and plastic deformation 6.4 Hardness 6.5 Fracture 7 Deformation and strength of structures 7.1 Experimental determination of deformation and strength 7.2 Deformation and strength of beam-like structures 7.2.1 Deformation f a beam under tension or compression 7.2.2 Bending of a beam fixed at one end 7.2.3 Torsion of a beam around its long axis 8 Estimation of the load transmitted by joints of the human locomotor system by means of a biomechanical model calculation 8.1 Calculation of a joint load in the static case, illustrated with the example of the elbow joint 8.2 Determination of the joint force in the dynamic case, illustrated with the example of the ankle joint 8.3 Determination of the joint force if more than one muscle or ligament force has to be taken into account 9 Mechanical aspects of the hip joint 9.1 Load on the hip joint in the stance phase of slow gait 9.2 Influencing the load on the hip joint by gait technique, walking aids or surgical interventions 9.3 Determination of the load on the hip joint by gait analysis 9.4 Measurement of the load on the hip joint by instrumented joint replacement 9.5 Determination of the stress distribution on the surface of the hip joint 9.6 Measurement of the pressure distribution on the surface of the hip joint 9.7 Pressure on the articular surface as a primary cause of arthrosis of the hip joint 10 Mechanical aspects of the knee 10.1 Common features to all joints, illustrated by the example of the knee joint 10.2 Motion of the knee joint 10.3 Load on the femoro-tibial and femoro-patellar joint 10.4 Pressure distribution in the femoro-patellar joint 10.5 Loading of the cruciate ligaments 11 Mechanical aspects of the lumbar spine 11.1 Rotational and translational motion of the vertebrae in flexion and extension 11.2 Calculation of the loading of the lumbar spine: 2-dimensional model 11.3 The role of intra-abdominal pressure 11.4 Calculation of the loading of the lumbar spine: 3-dimensional model 11.5 Determination of he loading of the lumbar spine from measurements of intradiscal pressure 11.6 Determination of the load on the lumbar spine from measurements of stature change 11.7 Recommendations for carrying and lifting 11.8 Mechanical properties of lumbar intervertebral discs 11.8.1 Deformation of discs under load 11.8.2 Pressure distribution over the vertebral endplates 11.8.3 Intradiscal pressure and mechanical function of the disc 11.9 Compressive strength of lumbar vertebrae 11.10 Fracture of the vertebral arch 12 Mechanical aspects of the shoulder 12.1 Joints of the shoulder girdle 12.2 Loading of the glenohumeral joint 12.3 Stability of the glenohumeral joint 13 Mechanical properties of muscles and tendons 14 Mechanical properties of bones 14.1 Architecture of the bone tissue 14.2 Stress and strain of inhomogeneous, anisotropic materials 14.3 Material properties of cortical bone 14.4 Architecture and material properties of trabecular bone 14.5 In-vivo measurement of bone density and bone mineral content 14.6 In-vivo determination of the fracture risk of proximal femur and lumbar vertebrae 14.7 Adaptation of bones to mechanical demands A1 Loading of the lumbar spine when sitting or standing A1.1 Loading of the lumbar spine determined by measurement of intradiscal pressure A1.2 Loading of the lumbar spine determined from measurement of stature change A1.3 Biomechanical model comparing spinal loading in sitting and standing A1.4 Conclusions A2 What do we know about primary mechanical causes of lumbar disc prolapse? A2.1 In-vitro studies A2.2 Influence of posture on disc bulge and prolapse A2.3 Epidemiological studies on the elation between heavy physical exertions and the prevalence of lumbar disc prolapse A2.4 Conclusions and outlook A3 Influence of physical activity on architecture and density of bones. An overview of observations on humans A3.1 Methods for measuring bone density and bone mineral content A3.2 Effects of increased mechanical loading A3.3 Effects of reduced mechanical loading A3.4 Summary and outlook B1 Mathematical description of translation and rotation in a plane B1.1 Cartesian coordinates B1.2 Translation B1.3 Rotation B1.4 Motion combining translation and rotation B1.5 Determination of the image parameters from 2 points and their images B1.6 Matrix notation B2 Mathematical description of translation and rotation in 3-dimensional space B2.1 Matrix notation B2.2 Coordinates and vectors B2.3 Coordinate transformations B2.4 Translation in 3-dimensional space B2.5 Rotation in 3-dimensional space B2.5.1 Rotations about the coordinate axes B2.5.2 Combined rotation made up of a sequence of rotations B2.5.3 Euler and Bryant-Cardan angles B2.5.4 Rotation about an arbitrary axis B2.5.5 Motion in 3-dimensional space, combined from rotation and translation. Theorem of Chasles B2.6 Calculation of the parameters of rotation and translation in 3-dimensional space from the coordinates of reference points and their images B2.6.1 Parameters of the motion of a body observed in a laboratory coordinate system B2.6.2 Parameters describing the relative motion of two bodies B3 Dealing with errors B3.1 Mean and variance B3.2 Biological variance B3.3 Comparing precision among measuring methods or among investigators B3.4 Error propagation B3.4.1 Calculation of a propagated error using the example of an angle defined by the end points of two straight lines B3.5 Method of least squares B3.5.1 Regression line B3.5.2 Fit of two sets of points by translation and rotation Notation and units Index