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Capsulitis Inflammation of the joint capsule.

Centripetal force Force directed toward the centre of rotation in a rotating body.

Chondromalacia patellae The softening and breakdown of the cartilage that lines the underside of the patella.

Coefficient of restitution The measure of elasticity of an object is a fractional value representing the ratio of velocities after and before an impact.

Collateral ligament An accessory ligament that is not part of the joint capsule.

Collective variable Simplistically, a variable that incorporates two or more other variables. Relative phase is a collective variable as it incorporates two angles and two angular velocities. In the context of this book, the collective variable should characterise coordination patterns or changes in coordination, which relative phase usually does. A collective variable is also known, in the coordination context, as an order parameter.

Comminuted fracture One in which the bone is broken into more than two pieces.

Computer-based feedback This term is used for feedback provided through a digital computer, usually in the form of computer graphics. Most augmented feedback to sports performers is provided in this way.

Conjugate cross correlations An extension of cross correlation functions to cover more than two joints. Rules of compatibility between the time lags and between the signs of the correlation peaks for the various cross correlation functions involved can be specified.

Constraints-led approach A key approach in ecological motor control, in which the solution to a motor, or sports, task for a given individual is determined not only by the constraints of the task itself and the environment but also by the individual’s organismic constraints (see glossary in Chapter 6).

Contractile component This is the component of models of skeletal muscle that incorporates the mechanisms of muscle contraction, essentially the actin and myosin filaments and their associated cross-bridge coupling mechanism.

Contusion Bruise, usually caused by an escape of blood from ruptured vessels after injury.

Coordination dynamics In essence, the science of coordination, which aims to describe, explain and predict how patterns of coordination form, adapt and change in living organisms. In the context of this book, the term can be applied to a single joint through to the entire human movement system.

Coordination patterns Whereas movement patterns express how a movement variable – for example, an angle, angular velocity, or angular acceleration – evolves, or varies, with time, coordination patterns look at how meaningful combinations of these variables co-vary. Coordination patterns include angle-angle diagrams, phase planes, continuous relative phase (itself a function of time) and cross-correlation functions.

Coordinative structures These are considered to be functional relationships between important anatomical parts of the body to perform a specific activity, such as when groups of muscles and joints temporarily function as coherent units to achieve a specific goal, such as hitting a ball.

Correlation coefficients These express the strength of the statistical relationship between two variables.

Correlation matrix A correlation matrix is a square symmetrical n x n matrix that contains correlations among n variables, where n is a positive integer greater than 1. The ith row and jth column of the matrix contains the correlation coefficient between the ith and the jth variables. The leading diagonal elements are correlations of variables with themselves and are, therefore, equal to 1.

Cortical bone Outer layer (cortex) of bone having a compact structure.

Cost function A function used to constrain the optimisation model; a feasible solution to the cost function that minimises or maximises, if that is the goal, the cost function is called an optimal solution. The minimisation of the cost functions is an attempt to imitate the body’s criteria for deciding which muscles to recruit and the order of recruitment.  We can also define the level of activation that will produce appropriate motion or posture for a specific task. The selection of the most appropriate criterion to use in the optimization process resides upon several aspects such as the type of motion under analysis, the objectives to achieve or the presence of any type of pathology (Ambrósio and Kecskeméthy, 2007).

Critical features Those key features of a movement that are required for the movement to be performed optimally. The term is used mostly in qualitative biomechanical analysis, in which case the critical features need to be observable. The identification of the critical features of a movement is the most important task of the preparation stage of qualitative biomechanical analysis.

Cross correlation functions These are obtained by calculating the correlation coefficient between two time series, then introducing various time lags between the two time series and recalculating the correlation coefficient for each time lag. Finally, the cross correlation function is the graph of the correlation coefficient as a function of the time lag.

Cross-sectional designs The term is used to refer to research designs taken at a specific time (a ‘snap-shot’). As an example, one or more trials by each finalist in the javelin throw at an international championship would be studied (see also Chapter 7).

Cumulative trauma Caused by accumulated microtrauma resulting in acute or overuse type of injury. It is assumed that the acumulated microtrauma is caused by repeated overloading and inadequate rest of the tissues involved.

Degeneration A gradual deterioration of specific tissues changing them to a lower or less funtionally active form.

Deterministic (or hierarchical) performance models These are models of the factors that influence sports performance in which the factors in the lower levels of the model completely determine (hence, deterministic) those in the higher levels. The top level is the factor by which performance is assessed, called the performance criterion - such as the time of a race or distance of a throw or jump. They resemble hierarchical models, for example in Microsoft Word, hence the alternative name (see also Chapter 6).

Diaphysis The central ossification region of long bones (adjective: ­diaphyseal).

Dislocation Complete separation of articulating bones consequent on forcing of joint beyond its maximum passive range.

Dual-screen displays Used in the context of this chapter to refer to the viewing of two still images or video sequences, usually in a qualitative movement analysis package, from different camera views, performances or performers on the computer screen at the same time, either side by side or one above the other. This can be extended to more than two images in some packages – multi-screen displays.

Ductile To be drawn out, to become thinner or narrower before breaking.

Elastic elements These are the components of models of skeletal muscle that store and release elastic energy. The series elastic element is in series with the contractile component and mainly consists of the tendons. The parallel elastic elements lie in parallel to the contractile component and consist mainly of the muscle’s various connective tissues and sarcolemma.

Empirical modelling This involves devising mathematical models, usually statistical ones, using experimental data. It is used widely in sports biomechanics and notational analysis.

Epiphysis The separately ossified ends of growing bones separated from the shaft by a cartilaginous (epiphyseal) plate.

Epiphysitis Inflammation of the epiphysis.

Etiology (or aetiology) In the context of this book, etiology is the study of the causes of sports injuries.

Euclidean distance In the context of this chapter, this is used to describe a mathematically meaningful distance between two points on the output map of an artificial neural network.

Exposure A method of quantifying injury risk due to participation in sport. Injury rates are reported as per athlete-exposures (number of practices or games where the athlete might be exposed to injury risk) or time-exposures (amount of time spent practicing or participating in risk activity). If an athlete participated in 100 practices lasting 60 minutes each, per season and sustains one injury during practice the exposure risk is said to be 1 per 100 or 1 per 1000 hours.

Finite element modelling Used to visualise a stresses and strains in a structure.  It uses a numerical technique called ‘finite element analysis’ for finding approximate solutions of partial differential equations as well as of integral equations.

Fracture A disruption to tissue (normally bone) integrity. In traumatic fracture a break will occur, whereas in a stress fracture the disruption is microscopic.

Golgi tendon organs These are small stretch receptors located at the junction of a muscle and its tendon. Their discharge causes inhibition of the muscle in which they are located (which helps to protect the muscle) and facilitation of the antagonist muscle.

Haemarthrosis Effusion of blood into a joint cavity.

Headform An instrumented system for testing head impacts.

Hemarthosis Bleeding or extravasation of blood into the joint spaces.

Hematoma An extravasation of blood outside the blood vessels, usually in liquid form within the tissue and generally the result of a haemorrhage.

Homogeneity of variance The assumption (in both ANOVA and t-tests, for example) that the variances of two or more datasets are equal.

Hooke’s Law Within the elastic limit of a solid material, the deformation or strain produced by a stress of any kind is proportional to the force. If the elastic limit is not exceeded, the material returns to it original shape and size after the force is removed. If the elastic limit is exceeded, the material remains deformed or stretched. The force at which the material exceeds its elastic limit is called the 'limit of proportionality.'

Immediate and summary feedback These terms are normally used to distinguish between augmented feedback provided after each trial of a task (immediate feedback) or only after several trials (summary feedback).

Impulse-momentum relationship An expression of Newton’s Second Law of Motion, which states that the impulse of a force (the mean force multiplied by the time during which the force acts) is equal to the change in momentum of the body on which the force acts.

Indeterminate system A system of simultaneous equations that has infinitely many solutions or no solutions at all. If there are fewer unique equations than variables, then the system must be indeterminate.

Individual specificity Term used to express the fact that any individual will find a specific solution (or set of solutions) to a movement task that fits his or her organismic constraints as well as the task and environmental constraints. The movement analyst has to be continually aware of the requirement for individual specificity when seeking to identify and correct movement faults. What works for one sports performer may not work for another.

Inequality constraints A restriction that limits the value of a dependent or independent variable. An inequality constraint is used to apply a limitation to a feature that may vary, such as joint movement, speed and torque.

Inertial reference frame A ‘frame of reference’ is a standard relative to which motion and rest may be measured. An inertial reference frame is relative to motions that have distinguished dynamical properties. An inertial frame is a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions. In Newtonian dynamics, an inertial frame is a reference frame with a time-scale, relative to which the motion of a body (disregarding external forces) is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions.

Inflammation Defensive response of tissue to injury indicated by redness, swelling, pain, loss of function and warmth.

Injury incidence The number of new cases of an injury within a specified time period divided by the size of the population initially at risk.

Injury prevalence Defined as the total number of cases of the injury in the population at a given time, or the total number of cases in the population, divided by the number of individuals in the population

Injury rate May be defined as case rates or athlete rates. Athlete rates are determined by dividing the total number of athletes injured by the total number of athletes participating. Case rates are determined by dividing the total number of reported cases occurring during the study period by the total number of population exposed to the possibility of injury.

Innervation ratio The number of muscle fibres that are stimulated, or innervated, by a single motor neuron; the number of muscle fibres in a particular motor unit. This ratio varies from as few as 10 for muscles requiring very fine control to over 1000 for the weight-bearing muscles of the lower extremities.

In-phase and anti-phase coordination In-phase coordination involves two joints (or segments) moving in an anatomically similar way. Examples would be the knee and hip flexing together in the downward movement of a standing vertical jump or the index fingers on both hands abducting. Anti-phase, or out of phase, coordination occurs when the movements are antagonistic, as when the index finger on one hand adducts while that on the other hand abducts, or when the hip flexes while the knee extends. In this context, ankle plantar flexion is considered to be in-phase with hip and knee extension.

Intra- and inter-analyst reliability Intra-analyst (also called intra-rater or intra-operator) reliability is the consistency of the analyses carried out by one analyst on several occasions. Inter-analyst reliability (also called objectivity) is the consistency of the analyses of several analysts. Intra-analyst reliability is usually better than inter-analyst reliability. Neither is easy to determine accurately for qualitative movement analysis.

Inverse dynamics A method for computing forces and moments of force based on the kinematics of a body and the body's inertial properties.

Inverse dynamics Inverse rigid-body dynamics is a method for computing forces and moments of force (torques) based on the kinematics of a body and the body's inertial properties (mass and moment of inertia).

Inverse optimisation An optimisation technique in which the ideal solution or outcome (i.e. movement) is known. We use the technique to optimise the muscle recruitment or muscle forces involved so as to simulate the known movement criteria.

Inverted-U A relationship between two variables that looks like an upside-down letter U.

Isometric force The tension (or force) developed in a muscle that is undergoing an isometric contraction – without change of length.

Joint angle conventions For two-dimensional analysis in the sagittal plane, the normal sports biomechanics convention is for a fully extended knee or elbow, for example, to be designated as 180º. Flexion then involves the joint angle decreasing and extension involves the joint angle increasing. This convention is used throughout this book. The angle conventions used by clinical biomechanists and in three-dimensional analysis are completely different. Movement analysts need to check carefully what joint angle convention is being used.

Laceration An open wound or cut.

Local and global optimums A function may have a global optimum, defined over the whole range of the function, as well as several local optimums, which are optimal only within a limited (local) range of the function. A geographical analogy would be the many local peaks within the Himalayas, whereas the top of Mount Everest is the global Himalayan peak.

Markov chains Named after A. A. Markov, a Markov chain is a random process in which one state depends only on the previous state. Markov chains are useful as tools for statistical modelling, particularly, in the context of this book, in modelling the outcomes of games, such as squash.

Mathematically indeterminate  A problem that has an infinite number of solutions, or one in which there are fewer imposed conditions than there are unknowns.

Maximum tetanic force Maximum force produced by a muscle in a state of sustained maximal tension.

Maximum voluntary contraction A measure of strength that can be expressed as a maximal exertion of force, reported either as a force or as a moment (or torque) around a joint.

Menu-driven systems In the context of this book, this is used to describe a system using drop-down menus, such as those used in many Windows user interfaces, to present the information contained in a possible Expert System for the diagnosis and correction of movement errors.

Metaphysis Region of long bone between the epiphysis and diaphysis.

Movement trajectory analysis A term normally used to refer to the analysis of the two-dimensional paths (or trajectories) taken by players over time across the surface of a sports pitch or court.

Multiple regression In multiple regression, more than one predictor variable is used to predict the value of the criterion variable. This contrasts with simple regression in which there is only one predictor variable.

Multivariate analysis of variance (MANOVA) a generalization of ANOVA to cases in which there are two or more dependent variables. It is sometimes used in the contrast approach to statistical modelling discussed in this chapter.

Muscle latency period Refers to the lack of visible change that occurs in the muscle fibre during (and immediately after) the action potential.

Musculotendinous unit A muscle tendon unit functions as a single system, whose two components contribute to force production at different times. The force is produced by a combination of muscle actions and a release of elastic energy from the tendon component.

Needs analysis In the context of this book, a needs analysis is usually a semi-formal meeting or interview, led by the movement analyst, to ascertain what the ‘clients’ need from the movement analysis to be undertaken.

Net-wall games Games involving a net or a wall. Table tennis, tennis, badminton and volleyball are net games and squash and fives are wall games. One of the three common categories of formal games, the others being striking and fielding games (such as cricket and baseball) and invasion games (such as rugby, basketball, soccer and netball).

Normal force The force component that is perpendicular to the surface of contact.

Normality The assumption (in both ANOVA and t-tests, for example) that a dataset conforms to a normal (or Gaussian) distribution (the bell-shaped curve).

Optimal performance model A somewhat discredited concept of a universal optimal set of movement patterns to perform a given movement task – such as a javelin throw - that applies to all individuals. This concept led to the idea of copying the movements of the current world champion in that task (the so-called ‘elite performer template’), completely ignoring the principle of individual specificity.

Optimisation A procedure or set of procedures that are used to make a system as functional as possible.

Optimisation See glossary in Chapter 7.

Optimisation The mathematical process of finding the optimum value of a function of several variables. Static optimisation computes the optimum values of a finite set of quantities of interest, such as a small set of input parameters. Dynamic optimisation seeks to compute optimum input functions of time.

Order parameter See collective variable above.

Organismic constraints The set of characteristics, or constraints, that an individual possesses; these constraints influence the movement solutions that individual will adopt for a particular task and environment. These are internal to the individual and include anatomical-anthropometric characteristics, strength, flexibility and fitness.

Orthogonal Two or more lines are said to be orthogonal if they are perpendicular or form right angles to each other.

Osteitis Inflammation of bone.

Osteochondrotic diseases Characterised by interruption of the blood supply of a bone, in particular to the epiphysis, followed by localised bony necrosis and, later, regrowth of the bone.

Parametric statistics assume that the data have come from a particular probability distribution; they involve assumptions about the parameters of that distribution, such as normality or homogeneity of variance. ANOVA, MANOVA and t-tests are all parametric statistical tests, as are Pearson product moment correlations (see Chapter 6).

Pearson product moment correlation This is the most common way of assessing the strength of a linear relationship between two variables. The strength of the relationship is expressed as the Pearson product moment correlation coefficient.

Pennate muscles The class of muscles, accounting for 75% of the body’s musculature, with relatively short fibres angled away from the tendon. The arrangement allows more fibres to be recruited, which provides a stronger, more powerful movement at the expense of range and speed of movement. The class includes the tibialis anterior (a unipennate muscle), flexor hallucis longus (a bipennate muscle) and the deltoid (a multipennate muscle).

Performance criterion A formal term that means the factor by which a performance is assessed – the result or outcome. Examples are the distance jumped or thrown, the time of a race and the score of a dive or gymnastics vault.

Performance variables (or performance parameters) A term used mostly in quantitative biomechanical analysis for the factors that influence the performance criterion, or outcome. They are roughly comparable to the critical features in a qualitative biomechanical analysis or the performance indicators in performance analysis.

Peritendinitis Inflammation of the tissues around a tendon (the ­peritendon).

Perturbation analysis Used in notational analysis of sports (particularly, to date, squash) to refer to disruptions to steady rhythms of play, through critical incidents or perturbations. These perturbations may then lead to the end of a rally or be smoothed out, resulting in the establishment of a new steady rhythm of play. They can often be seen by experienced observers as well as measured.

Pes cavus Also known as a ‘high arch’ is a human foot type in which the sole of the foot is distinctly hollow when bearing weight

Pes planus Also known as ‘flat footed’ is a condition in which the arch or instep of the foot collapses and comes in contact with the ground.

Phagocytosis A specific form of endocytosis involving the vesicular internalisation of solid particles, such as bacteria, and is the body’s mechanism used to remove pathogens and cell debris after injury.

Physiological cross sectional area The cross sectional area of a muscle perpendicular to the muscle fibres.

Plantar fasciitis An irritation and swelling of the thick tissue (fascia) on the bottom of the foot.

Polar second moment of area Is also known as the area moment of inertia, moment of inertia of plane area, or second moment of inertia Is a property of a cross section that can be used to predict the resistance of beams to bending and deflection, around an axis that lies in the cross-sectional plane

Polyethylene A type of polymer that is classified as a thermoplastic, meaning that it can be melted to a liquid and remoulded as it returns to a solid state. Polyethylene is chemically synthesised from molecules that contain long chains of ethylene, a monomer that provides the ability to double bond with other carbon-based monomers to form polymers.

Polypropylene A thermoplastic polymer used in a wide variety of applications. It is an addition polymer made from the monomer propylene and it can serve as both a plastic and a fibre.

Polyurethane Any polymer consisting of a chain of organic units joined by urethane links. It is an incredibly resilient, flexible, and durable manufactured material. It is made by combining a diisocyanate and a diol, two monomers, through a chemical reaction. This makes a basic material whose variations can be stretched, smashed, or scratched, and remain fairly indestructible.

Porous bound macadam The foundation layer of most artificial sports surfaces, the term macadam refers to the method of laying the stone and sand aggregates that are sprayed with the porous binding material.

Proprioceptive stretching Proprioceptive neuromuscular facilitation (PNF) is a more advanced form of flexibility training that involves both the stretching and contraction of the muscle group being targeted. Exercises are based on the stretch reflex which is caused by stimulation of the Golgi tendon and muscle spindles. This stimulation results in impulses being sent to the brain, which leads to the contraction and relaxation of muscles. After an injury, there is a delay in the stimulation of the muscle spindles and Golgi tendons resulting in weakness of the muscle. PNF exercises are used in rehabilitation programmes to re-educate the motor units that are lost due to the injury.

Right hand rule A procedure for identifying the direction of an angular motion vector.

Rotator cuff The group of muscles (supraspinatus, infraspinatus, teres minor and subscapularis) that act to stabilise the shoulder. The four muscles of the rotator cuff, along with the teres major and the deltoid, make up the six scapulohumeral muscles

Rupture or tear Complete break in continuity of a soft tissue structure.

Self-organising maps are artificial neural networks that are trained using unsupervised learning to produce a low-dimensional output space representation (sometimes called a map) of the high-dimensional input space of the training data.

Serial and parallel representations Used in the context of this book to refer to representations, or animations, of a movement presented sequentially, or frame by frame, as in a video recording, or as a series of images presented ‘in parallel’ on one ‘picture’, as in stick figure representations of a whole movement.

Shin splints The more common term for ‘medial tibial stress syndrome’, which is a slow healing and painful condition in the anterior medial tibia.

Simulation (or computer simulation) See glossary in Chapter 7.

Simulation evaluation This is the process of seeking to evaluate whether the results of a computer simulation adequately represent the real-world system that was being modelled.

Simulation or computer simulation involves the carrying out of computer experiments on a set of equations (or a simulation model) that represent an aspect of the real world. Simulation models used are based on physical laws not statistical relationships.

Sinusoidal A function having the form of a sine or cosine wave or a combination of these.

Sprain Damage to a joint and associated ligaments. The three degrees of sprain involve around 25%, 50% and 75% of the tissues, respectively. Grade I sprains are mild and involve no clinical instability; grade II are moderate with some instability; and grade III are severe with easily detectable instability. There may be effusion into the joint.

Statistical modelling Modelling data using various statistical methods such as ANOVA, MANOVA, t-tests and multiple regression (see Glossary in Chapter 7). 

Statistical power The power of a statistical test is the probability that the test will reject a null hypothesis that is false, in other words, that it will not make a Type II error. The greater the power, the less is the chance of a Type II error.

Strain Damage to muscle fibres. A grade I strain involves only a few fibres, and strong but painful contractions are possible. A grade II strain involves more fibres and a localised haematoma, and contractions are weak; as with grade I, no fascia is damaged. Grade III strains involve a great many, or all, fibres, partial or complete fascia tearing, diffuse bleeding and disability.

Stretch reflex The contraction of a muscle in response to a sudden stretching of that muscle. It occurs in the stretch-shortening cycle.

Subjective performance criterion A performance criteria (or result) that is judged subjectively, as in gymnastics, figure skating and diving.

Subluxation Partial dislocation.

Superior labrum The labrum is a lip-like piece of cartilage that deepens the glenoid of the shoulder joint that aids in stabilising the shoulder joint. The labrum is divided into superior, inferior, anterior and posterior parts.

Systematic observation strategy The development of a systematic ‘observation’ strategy pays attention to all matters that are relevant to good observation, and subsequent analysis, of movement.

Tendinitis Painful tendon with histological signs of inflammation within the tendon.

Tendinopathy Disease of the tendon including tendinitis, tendinosis and tenosynovitis.

Tendinosis Degenerative condition of a tendon.

Tenosynovitis Inflammation of the synovial sheath surrounding a ­tendon.

Thermomoldable plastics A type of plastic that can be moulded using a heat source such as a heat gun or special oven.

Tibia varum A frontal plane deformity where the distal third of the tibia is angled closer to the mid-sagittal plane than the proximal end

Topological equivalence Two shapes (such as angle-angle diagrams) are said to be topologically equivalent if one can be deformed into the other without folding or cutting. For our purposes, two shapes can be said to be topologically equivalent if they contain the same number of loops. [In the branch of mathematics called topology, topological equivalence is a bit more complicated than these simple statements might imply].

t-tests provide a test of whether the means of two groups are statistically different from each other. They are often used in the contrast approach to statistical modelling discussed in this chapter.

Type I and Type II errors A Type I error occurs when a null hypothesis that is true is rejected, incorrectly. A Type II error occurs when a null hypothesis is not rejected although it is false.

Ultimate tensile stress The maximum stress that a material can withstand while being stretched or pulled before necking, which is when the injury occurs

Valgus Abduction of the distal segment relative to the proximal one (as in genu valgum, knock-knees).

Validity In the analysis of human movement in sport, there is often a conflict between internal, or research, validity and external, or ecological, validity. Laboratory studies generally have good research validity and field-based studies generally have good ecological validity. Ecological validity is of prime importance when seeking to improve sports performance.

Varignon’s theorem Is also called the ‘principle of moments’ and it states that the moment of any force is equal to the algebraic sum of the moments of the components of that force.

Varus Adduction of the distal segment relative to the proximal one (as in genu varum, bow-legs).

Viscoelasticity This is a property of all biological materials, which exhibit both elastic and viscous behaviour when deformed. The stress-strain characteristics of viscoelastic materials are time-dependent (see also Chapter 1).

Wobbling mass model One of the assumptions of linear inverse dynamics is that the body being studied is a series of rigid segments. However, we can see from high-speed recordings of impacts, the soft parts of each segment of the human body are shifted relative to the bony parts and start to ‘wobble’ in a complex damped manner. Therefore, some researchers have developed ways of modelling the essential properties of the human body as ‘wobbling masses’, which are coupled quasi-elastically and strongly damped to each rigid bony part.  The wobbling mass model allows the researcher to study the effects of the different mechanical behaviour of the soft tissues and the rigid bony parts of the human body.