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Movement biomechanics goes upwards: from the leg to the arm
BM 1282 BALA BINNY NP
Journal of Biomechanics 33 (2000) 1207}1216
Movement biomechanics goes upwards: from the leg to the arm G. Rau, C. Disselhorst-Klug*, R. Schmidt Helmholtz-Institute for Biomedical Engineering, Aachen University of Technology, Pauwelsstr. 20, 52074 Aachen, Germany Accepted 1 March 2000
Abstract The analysis of lower limb movements has been well established in biomechanics research and clinical applications for a long time. For these studies, powerful and very advanced tools have been developed to measure movement parameters and reaction forces. The main focus of interest aims towards gait movements while the understanding of the basic concepts is supported by numerous models. De"nitions of physiological ranges and detection of pathological changes in movements open an increasingly valuable clinical "eld of application. If, however, the primary function of the upper extremities as highly variable and adaptive organ for manipulating tasks is the subject of interest, the situation becomes considerably more complex. The nature of free arm movements is completely di!erent from being restricted, repeatable or cyclic as compared to gait. Therefore, the transfer of the knowledge and experience gained in lower extremity movement analysis to the analysis of upper extremities turns out to be di$cult. A proposal for how to proceed in measurements, e.g. where to place the markers and how to calculate movements and angles of segments involved, will be discussed which results in the description of the joint movements of wrist, elbow and shoulder joint. The de"nition of the motion is a speci"c step in upper extremity motion analysis which is important in terms of repeatability and signi"cance of the results. An example of assessing movement disorders in children with plexus lesion will illustrate the implications and the potential of upper extremity movement analysis in clinical applications. 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Biomechanics of movement is * to a large extent * the application of Newtonian mechanics to the neuromuscular skeletal system: the forces that cause the movement, and the internal forces that act within the body. Movement analysis has been developed since about 1900 and speci"cally pushed during the last 30 yr by better insight in the living organisms supported by tremendous advances in research. Typical areas concern: Cellular function (metabolism, structure, mechanical properties, dynamic behavior), muscle, bone, ligaments, tendons, cartilage properties, neuromuscular control mechanisms. Also, dedicated biomechanical and sensorimotor control models have been established and re"ned. This increase in knowledge has been achieved by very advanced experiment procedures and equipment which is well described in various books and publications.
* Corresponding author. Tel.: #49-241-807011; fax: #49-2418888442. E-mail address: [email protected] (C. Disselhorst-Klug).
3D motion analysis has turned out to be a powerful tool for a quantitative assessment of the movement in all degrees of freedom. The early research on 3D motion analysis was mainly focused on the improvement of imaging techniques and 3D reconstruction algorithms in order to get an accurate and reliable tool for the detection of three-dimensional free body movements. However, the "rst developments had only little practical application. The breakthrough of 3D motion analysis in clinical application can be attributed to clinical gait analysis where it is now applied to the detailed diagnosis and treatment planning of patients with di$culties in gait. This is not surprising since gait is a well-de"ned motion type with cyclic sequences repetitive from heelstrike-toheelstrike. Several biomechanical models of the lower extremities have been developed allowing the calculation of joint angles, joint forces and moments as well as the work, the power or the energy. For movement detection, "rst applicable optoelectronic systems for gait analysis have been introduced in the early seventies and have been developed into reliable tools. Although they are still expensive their accuracy, speed and convenience made them into a standard measurement tool (Whittle, 1982). Thus, after more than 100 yr of technical development,
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3D motion analysis has succeeded to be a useful clinical tool in gait analysis (Whittle, 1995). Recently, a number of gait laboratories have been established in which gait abnormalities can be examined precisely. The transition from normal gait to moderate disorders that may end up with severely disturbed movement patterns which can hardly be classi"ed or connected to gait because the individuals may not be able to walk anymore. In#uences of pathological changes, and even structural deformations, have to be considered. Muscles may be a!ected by disease, such as dystrophy, arthrophy or pain reactions. Fibrous tissue contracture after surgical and reconstructive operations, as well as ligament or tendon diseases or cartilage injuries, may limit passive mobility. Injury of brain, spinal or peripheral nerve structures may disrupt motor control and feed back pathways. To overcome these de"ciencies, frequently alternative motions are developed by the patient. These are only a few aspects which may generate a person's walking pattern into a mixture of primary functional loss and substitutional actions. However, the clinical use of gait laboratories is rapidly increasing. One of the most popular clinical application of gait analysis is the use for diagnostic and surgical planning in treatment of children with spastic paralysis in which the orthopedic surgeons are the driving forces. However, presently, clinical applications take place mainly in those centres where a strong collaboration between clinicians and engineers is established. The available equipment and procedures can only be utilized by specialists but cannot be introduced into clinical routine * a big challenge for future development. Another obstacle to the clinical use is the lack of standardized, consistent and liable data banks which are necessary for interpreting the clinical signi"cance of the measurements. Analysis of the upper extremities is at an early stage, and introduction to clinical routine seems to be a step for the future. The use of the upper extremities in daily life is versatile as can be indicated by a few examples: we use tools, grasp, perform complex manipulations, we throw objects, point, gesticulate, etc., by using arms and hands in a coordinated and well-organised way. For analysis of such movements, the experience from decades of gait analysis is not readily transferable. In this context, a working group of the International Society of Biomechanics (ISB) has been established, specialising in shoulder movement and dealing with one of the most complicated joints. The variety, complexity and range of upper-extremity movements is a big challenge to assessment and interpretation of data, getting even more complicated in clinical application. To tackle this problem, the advanced developments in gait analysis could be a guideline for how to proceed in the upper extremity movement analysis. On the basis of the well-established procedures in gait analysis, one
could develop possible approaches for the three-dimensional analysis of free upper-extremity movements.
2. Motion analysis of gait Normal gait is well de"ned in each individual. The gait cycle shows a typical pattern which remains unchanged for subjects older than 4 yr (Sutherland et al., 1988). Especially the timing of the gait cycle has been described in detail, (Inman et al., 1981; Perry, 1992; Whittle, 1991) among others. Gait is a cyclic sequence of movements occurring from heelstrike to heelstrike of the same foot. Also, it is to a high degree symmetrical, and each cycle is highly reproducible. The interindividual variations are rather small, and this "nally allows to establish a reference for normal gait. Each gait cycle can be roughly divided into the swing phase and the stance phase of each leg. The stance phase is about 60% of the gait cycle and can be subdivided into double-leg and single-leg stance. The swing phase of the leg consists of three phases: initial swing, where the leg is accelerated, midswing and terminal swing, where the leg is decelerated (Inman, 1966). The position of the feet on the ground de"nes a number of gait parameters which are commonly used for description of gait and which can be easily obtained without the support of 3D motion analysis (Table 1). For each subject, the timing of gait and the characteristic gait parameters are highly repeatable. Therefore, the synchronised data of each gait cycle can be averaged to improve the reliability of the extracted parameters. In this way, a normative database has been set up, which contains the information about the timing and the characteristic parameters of the physiological gait (Murray, 1967). Most of the characteristic gait parameters can be measured when the movement of the trunk and the feet are traced. The available 3D movement analysis systems are suitable, and standardised procedures for the positioning of limb markers are established. Derived from the 3D
Table 1 Characteristic parameters describing the individual gait pattern (Whittle, 1995) Parameter
De"nition
Cadence Walking velocity Step length
Number of steps per time Distance walked per time Distance by which each foot is in front of the other one Distance which each foot moves forward in one gait cycle Side-to-side distance between the two feet angle between midline of the foot and direction of walk
Stride length Walking base Toe out angle
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trajectories of the markers, stick "gures can be created which re#ect the positions of the limbs during the gait cycle. However, since the stick "gures only show what can also be seen by eye, the real advantage of 3D motion analysis consists of its capacity to calculate joint angles from the marker trajectories. In contrast to the stick "gures, which only have very limited clinical application, joint angles are parameters which are closely related to the functions of muscles and joints. The combination of the available 3D movement analysis systems, standardised marker arrangements and an underlying mechanical model of the limb segments allows the calculation of the joint angles in all three dimensions. Most of these kinematic models of the lower extremities assume that the body is composed of rigid segments which are connected by ideal links. This approach suggests to assign one rigid segments to every bone (Andrews, 1995). How to design such a kinematic model will be shown for the upper-extremity movements in the next section. Utilising joint angles, a kinematic description of gait can be achieved. Although the kinematic description of gait has been introduced some time ago, normative data are still not completely available. Only for movements in the sagittal plane, a normative database about the joint angles has been collected (Perry, 1974). This is due to the fact that the greatest range of the motion occurs in the sagittal plan, and movements in the coronal and transverse plane are often neglected. However, although the kinematic description of gait by means of joint angles is commonly used in basic as well as in clinically orientated research, the information about the joint angles is still rarely used in clinical routine. The reason is, that the clinical de"nitions of 3D-joint movements, like #exion}extension, abduction}adduction and internal} external rotation, often di!er from those joint angles calculated by the kinematic model. That circumstance makes the interpretation of the kinematic data di$cult and the information is often useless for clinical routine. The information about the kinetics of gait has more importance for clinical application. The transition from the kinematic description of motion to a kinetic description needs the measurement of the forces provided by the neuromuscular system (Fig. 1) (Nigg and Herzog, 1994). In gait analysis, these forces are commonly measured by means of forceplates which detect the ground-reaction forces. If kinematics and forces are detected in a common co-ordinate system, they can be used as input into a mathematical model which calculates, e.g. joint moments and joint forces, (Bresler and Franke, 1950; Cavagna and Magaria, 1966). In contrast to the kinematic description, the kinetic description of gait provides powerful research tools with signi"cant meaning in clinical application. However, the evidence of the kinetic description is limited by the underlying biomechanical model. Even if the motion during the gait cycle is limited
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Fig. 1. Di!erent ways of the description of human gait. The more complex the description becomes the higher are the requirements to the recording set up and the underlying models. Since simpli"cations have to be made with each increment of complexity, the resulting interpretation of the parameters have to be used more carefully.
to the sagittal plane, which results in a comparatively simple motion, it is not possible to "nd a unique solution for the large number of equations which have to be ful"lled by the model. For that reason, simplifying assumptions have to be made which are more or less correct (Whittle, 1995). If the masses of the di!erent limb segments, their centres of gravity and their moments of inertia are known, the work, power and energy transfer between the di!erent body segments can be calculated. Although this information is of high relevance for clinical applications, there is only little correspondence between the received information and the physiological work or the metabolic activity. Muscles, for example, need metabolic activity even during excentric contractions, and the tendons and ligaments store passive energy which is not regarded in most models. Therefore, the calculated information about work, energy and power have to be handled with care. Besides the mechanical aspects in clinical gait analysis, information about the muscular coordination is of clinical relevance. This can be achieved by using electromyography (EMG) in which the electrical activity generated by a contracting muscle is detected. The large number of muscles involved in gait and the dynamic contractions require the use of surface electrodes. The problem herewith is that EMG is only semi-quantitative. The
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measured EMG amplitude depends not only on physiological properties like the thickness of the tissue layers between the muscle and the electrodes or the electrical impedance of the skin, but it also depends on the measurement arrangement, like the interelectrode distance or the location of the electrodes relative to the muscle. Additionally, cross-talk of muscles located distantly from the muscle of interest has to be avoided. Recently, within the European project SENIAM (surface EMG for non-invasive assessment of muscles), recommendations for electrodes and electrode placements have been worked out in order to improve the quality and reliability of surface EMG measurements (DisselhorstKlug and Rau, 1996; Hermens and Freriks, 1997). However, if the timing of the muscles is of interest, surfaceEMG is the only suitable tool to examine the &guilty motor pattern' in gait (Winter, 1985).
3. Upper extremities Comparing gait analysis to upper-extremity analysis (Table 2) reveals the nature of the problems when biomechanics goes from the leg to the arm. E The variability of upper-extremity movements makes the selection of one or more movements necessary. These may be movements taken from an activity under investigation or movements which are designed for the experiment. The demands for accuracy and details, as well as the way of interpretation and visualisation, may vary for each application. E Time normalisation and averaging based on the cyclic nature of gait is generally not applicable to the upper extremities. Inter- and intraindividual comparisons are thus more di$cult. E A 2D lateral view of gait yields a good approximation of the major movement components. Upper-extremity motions cannot be described in 2D. The 3D rotations occurring at the shoulder lead to non-intuitive descriptions of the rotational kinematics. E Force plates and foot pressure soles provide accurate data about the external forces during gait and running. Table 2 Comparison of the situation in gait analysis and upper extremity analysis Gait analysis
Upper extremities
One standard movement Cyclic Approx. 2D External forces easily measurable Limited range of motion Standard protocols exist Ready-to-use systems available
Task-dependent movements Non-cyclic 3D External forces di$cult to access Extremely large range of motion No standard protocols No adapted systems available
Net joint forces and moments can be calculated from the external forces since they are big compared to gravity and inertia. In contrast, the assessment of external hand forces is di$cult in most situations. Furthermore, there are frequently no external forces, and thus, only estimates of gravitational and inertial force are available for the &determination' of joint forces and moments. Therefore, kinetics description is even less accurate for the upper extremities than the lower extremities. E The large range of movements increases the problem of skin and soft tissue movements which is the major limitation of the accuracy of all measurement techniques which use skin-mounted sensors. Special attention needs to be paid to the large rotations around the longitudinal segment axes, not known from gait. E The variability and complexity of the tasks performed with the upper extremity has prevented the establishment of reliable and standardised procedures for the measurement of upper-extremity movements by the scienti"c community. As a consequence readily usable tools are not commercially available. The standards mentioned are not only necessary for the development of commercial tools. They provide the basis for the comparability and repeatability of results which is even more important for the future of the "eld. Therefore, the ISB promotes the de"nition of standards in motion analysis in order to bundle and accelerate the process. Standardisation proposals have been submitted by several research groups for the hand, the wrist, the elbow and the shoulder (http://isb.ri.ccf.org/standards/). The standards yet do not de"ne a measurement procedure but they give guidelines. A measurement procedure for the upper extremities must be #exible and accurate since it has to cover a wide range of applications with very di!erent motion types and varying accuracy requirements. A proposal of a marker-based measurement procedure for upper-extremity motions which ful"ls these demands is presented in the following (Schmidt et al., 1998,1999). The analysis of the upper extremities starts on a common methodological platform with gait analysis. At "rst, a kinematic model is needed which describes what is to be measured. The kinematic model of the upper extremities is based on the rigid segment approach in which each segment is assigned to one bone. However, scapula and clavicle are not accessible with skin-mounted markers. Therefore, the kinematic structure of the model is simpli"ed by omitting the scapula and connecting the clavicle directly to the humerus (Schmidt et al., 1998). The same problem occurs with the forearm. Ulna and radius are indistinguishable by external markers. One forearm segment with the pro-/supination realised at the elbow joint replaces the natural structure of two bones and two
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Fig. 2. Kinematic structure of the model of the upper-extremities.
radioulnar joints. The resulting kinematic structure of the upper-body is shown in Fig. 2. The model is made up of nine segments: the hands, the forearms, the upper-arms, the collarbones and the thorax. The joints in this model are ideal and ball-andsocket joints which do not permit translations between the segment. Since the ball-joints do not have distinct axes one co-ordinate system which is "xed in the proximal segment is assigned to every joint. Each co-ordinate axis then represents one joint axis. This implies orthogonal joint axes which means an additional simpli"cation of the model (Schmidt et al., 1998, Schmidt et al., 1999). The kinematic model needs to be transformed into a measurement set-up. All segments except the collarbone are de"ned by a set of at least three non-collinear markers. By means of triplets of markers the motions of each segment in all six degrees of freedom (dof) are assessed. The best correspondence between model and measurement is achieved when the three markers of one triplet are rigidly interconnected in order to suppress inter-marker motions due to skin movements. The de"nition of the joint co-ordinate systems is more complicated. Joint co-ordinate systems are a central issue of the existing standardisation proposals of ISB mentioned above. However, these de"nitions are based on bony landmarks which makes it impossible to directly implement it by skin markers. Even placing the markers above bony landmarks may not yield a good approximation because skin movement still disturbs the marker position. The proposed approach for upper-extremity analysis uses a combination of three di!erent procedures to deter-
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Fig. 3. Marker con"guration with segment (dark) and joint (light) markers. The marker triads of one segment may be connected by cu!s in order to reduce intermarker motions (after Schmidt et al., 1998).
mine joint co-ordinate systems from marker measurements: Procedure 1: Additional markers are used to de"ne the joint co-ordinate system of the wrist and the centre of the elbow. It is su$cient, and more accurate, to use these additional markers only during an extra static trial, because skin movement is largest at the joints. The markers are placed on the #exion/extension axes of the joints (Fig. 3). At the elbow, they just indicate the joint centre taken at the half-way between both markers. At the wrist, the joint centre, as well as the orientation of the #exion axis, is deduced from these markers. At the wrist, the anatomical axes are not clearly de"ned since the wrist joint is made up of several smaller interacting joints. Accordingly, the marker-de"ned axes correspond to the three basic functional axes more than to bony structures. The longitudinal axis is "xed at the joint centres of wrist and elbow. The #exion/extension axis is perpendicular to this axis and within the plane made up by the elbow centre and the wrist markers. The abduction axis then follows from the requirement of orthogonal axes. Procedure 2: The centre of the shoulder joint is calculated from a de"ned extra motion and an additional static trail. This is because the shoulder joint is located deep below the surface which hides most bony landmarks necessary for a static determination of the joint centre. Here, an evaluation of the movements of the upper-arm markers with respect to the thorax markers by an optimisation procedure is more reliable. A simple example would be to calculate the best "t of the centre of the spheres the upper-arm markers are moving on with re-
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spect to the thorax. More sophisticated optimisations take into account motions of the shoulder girdle. The result is an estimate of the position of the glenohumeral head "xed in the upper-arm segment. Procedure 3: The orientation of the shoulder co-ordinate system is actually arbitrary since no functional axes exist. Instead the main body axes are applied. Therefore, the thorax markers can be used to de"ne the orientation of the shoulder co-ordinate system. The two upper markers yield the transversal #exion/extension axis. The sagittal abduction axis is parallel to the perpendicular on the marker plane. The longitudinal axis follows from the condition of orthogonal axes. The elbow co-ordinate system is calculated from the shoulder centre. The longitudinal axis is given by the shoulder and the elbow centre which is known from the static trial with additional markers. The #exion/ extension axis is parallel to the perpendicular on the plane de"ned by the joint centres of shoulder, elbow and wrist. This de"nition is more robust in most cases than to use the elbow markers. Measurements of the internal and external rotations of the upper-arm are by far more accurate with this method. However, the de"nition is inaccurate when the arm is close to a straight line. This can be handled by "xing the elbow co-ordinate system at the upper-arm (markers) when the reliable range (#exion '153) is left, until the arm returns to a su$cient large #exion angle. After having de"ned the joint co-ordinate systems, the joint motions can be described as relative rotations between these co-ordinate systems. Shoulder rotations are rotations of the humerus-"xed elbow co-ordinate system with respect to the clavicula-"xed shoulder co-ordinate system. Elbow rotations are rotations of the forearm "xed wrist co-ordinate system with respect to the elbow coordinate system. Wrist rotations are rotations of the hand segment coordinate system with respect to the wrist co-ordinate system. The joint rotations can be expressed in several di!erent ways. The possibilities are helical axis, quaternions, Joint Coordinate System (JCS) and Euler/Cardan angles. Since Euler/Cardan angles are commonly used in gait analysis and the JCS is equivalent to a special case of Euler/Cardan angles (Nigg and Herzog, 1994), they have been employed in the following study. Euler/Cardan angles are obtained when the total rotations between the joint co-ordinate systems, usually given as the so-called rotation matrices, are decomposed into ordered sequences of rotations around the three joint axes. There are exactly 12 di!erent possible orders. We chose the one which is equivalent to the JCS, because it best re#ects the anatomical meaning of the rotation names. The order of rotations around axes "xed in the distal segment is: (1) #exion/extension, (2) abduction/adduction and (3) rotation around the longitudinal segment axis. The disadvantage of Euler/Cardan angles is that the
decomposition is not determined at certain points (singularities or gimbal lock). At these points, the resulting angles can jump 1803 although the joint movement is only small.
4. Normal movement The meaning of Euler/Cardan angles is explained in the following example of a motion of the complete arm. Fig. 5 shows the shoulder and elbow angles measured while the index "nger moved three times on a triangular trajectory in a paracoronal plane (Fig. 4). The joint angles of shoulder and elbow recorded during that movement are displayed in Fig. 5. The "rst curves display the #exion (#) and extension (!), the second curves show abduction (#) and adduction (!) and the third curves the internal (#) and external (!) rotation pronation (#) and supination (!), respectively. All angles are zero at the neutral position which is the straight arm hanging vertically and the palm pointing forwards. However, as in this example, the starting position of the measurements is not the neutral position. At time zero, the hand is already in front of the chest. The arm attitude at time 3 s in relation to the neutral position is reached by a 953 elbow #exion and 1153 pronation. The shoulder is "rst #exed 503, then abducted around the new abduction axis by 353, and "nally rotated internally around the current upper-arm axis by 503. The proposed procedure is the counterpart corresponding to existing procedures for gait analysis. It yields
Fig. 4. Trajectory of the index "nger resulting from the joint movements of shoulder and elbow shown in Fig. 5. At time 3 s the index "nger is in the shown position.
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Fig. 5. Shoulder and elbow angles during a triangular hand path.
a complete 3D description of upper-extremity movements over the full range of motions.
upper-extremities and can be related to muscle coordination via EMG recordings.
5. Pathological movement
6. Conclusions and outlook
First clinical applications are illustrated by a measurement of a child su!ering from a plexus lesion, caused by a birth trauma (Fig. 6). Motion analysis is used in this case to answer quite the same questions as gait analysis does for cerebral paresis children. How is the range of motion and the motion pattern altered due to the impairment? In combination with surface electromyography, the muscle co-ordination during the movements can be assessed. This enables to answer separately whether the e!ects of missing innervation, co-contraction or a mechanical block of the joint are responsible for the de"cit. This is crucial information for the planning of conservative and surgical therapies. The movements which were tested are abduction, elevation, and a hand motion from the knee to the mouth (cookie test). Fig. 6 shows a child during the cookie test. In addition to the re#ecting markers, EMG electrodes are visible at the upper-arm and the shoulder. The motion pattern of the a!ected side (Fig. 7, right curves) is clearly di!erent from the healthy side (Fig. 7, left curves). The movement of the handicapped arm is, in general, slow and irregular. The surface-EMG indicates that this could be a result of co-contraction of the biceps and the triceps. Shoulder #exion is smaller and jerkier. The pronation seems to be barely controlled which causes large variations of that joint angle. In summary, the movement analysis of the upperextremities, as proposed here, provides information which is relevant for clinical decision making. It gives detailed insight into the complex motion patterns of the
As mentioned above, in routine biomechanics analyses, gait may be considered as a gross movement with joints of limited degrees of freedom involved. The spatial dynamic movement patterns are frequently and satisfactorily assessed by a 2D-observation, and in special cases, this has been extended to 3D-analysis. Standardized equipment and procedures in gait analysis are elaborate and available. Kinematic and kinetic models have been developed in order to assess joint angles, joint forces, and moments. If masses, centres of gravity, and moments of inertia are available, work, energy and power can be calculated. Besides the limiting simpli"cations made in the models, the movement of gait can be described almost completely. Although the movement of upper extremities is much more complicated, it has been shown that some of the knowledge from gait analysis can be used in the analyses of upper-extremity motions. However, in both lower and upper-extremity movement some basic questions and some restrictions in application are still present.
7. Basic questions Movements can be considered from various point of views. First of all, they are observed as motion in time and space. The observation can be re"ned by adequate measurement procedures and equipment as a time-varying imagery or image sequence. Understanding the movements needs a model-based description, but also an
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Fig. 6. Measurement of upper-extremity movements of a child su!ering from a plexus lesion.
adequate biomechanical model. It is not su$cient to generate a computer model of the human body as utilized presently in synthetically animated movies where rigid body parts connected by rotary joints with 1, 2 or 3 degrees of freedom are used (Hodgins, 1998; Hodgins et al., 1998; Dubois and Huang, 1998). So far, it has some natural look but still does not teach us the underlying mechanisms and properties of the biomechanics. As already mentioned, gait movements have been analyzed thoroughly on the basis of measurements with high accuracy, and the interpretation supported by biomechanical models is very advanced. Recently, re"ned
models which also include the main muscles involved are being developed. However, gait movements are well de"ned, and the joints' characteristics can be simpli"ed adequately for a gross movement description. Of course, if one looks into the biomechanics of the knee µscopically' the situation may become very complicated. In essence, gait analysis and interpretation by modeling is already well developed. Similarly, for a better understanding of upper-extremity movements, we need an adequate model approach where the knowledge of the shoulder joint movement is an integral part. Everybody who is familiar with the
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Fig. 7. Comparison of the healthy arm (left) with the handicapped arm (right). The joint motions of the a!ected side are slower and jerkier.
anatomy, muscle mechanics, viscoelastic elements, and sensory}motor control will tend to ask: Are there solutions existing at all in such over-de"ned systems?
8. Restriction by application Of course, if a very high precision is requested, the problems will pile up exponentially. Therefore, one can look into speci"c applications and then design movement patterns to be performed by the subject accordingly in such a way that we can get answers to our questions. It is well known that repetitive movements with the arm/hand/"nger system can be executed highly reproducibly; even time and amplitude invariance have been described in literature. Interesting "elds of application are in Ergonomics and in Medicine. Again, the free arm}hand}"nger gesture movements as input media in man}machine interaction need a rather high-resolution recognition of the movements but not a biomechanical model. Handtracking algorithms have been demonstrated already during the Telekon Fair in Geneva in 1995, and recently, "rst commercial products have become available which are utilized for man}machine communications by gestures. Medical applications are speci"cally embedded in clinical routine and, therefore, need to ful"ll some di!erent characteristics. The "rst requirement which has to be ful"lled is that the detected movement is repeatable with high reliability. This does not necessarily mean high precision, but the results must be comparable, independent of the investigating clinic. As a consequence, a certain degree of standardization is indispensable. This situation becomes more complicated if movement analysis has to be introduced into clinical routine. All tasks have to be simple, easy to be applied, reliable, not time consuming, and clear in the result. The personnel
involved is critical: how many minutes of a doctor, a technician or nurse are necessary? The duration of a measurement is also essential because patients, especially children and elderly persons, may not be loaded very much, dependent on their de"ciencies. And some of the patients are, in principle, not able to reproduce a movement at all as, e.g., in the case of spasticity. Here, completely di!erent procedures of pattern recognition have to be developed. In spastic phenomena, primarily not dramatic deformations of the biomechanics structure, but typical abnormal changes in the neuromuscular control, are responsible for the disease. In this context, the EMG patterns will contribute essentially to the understanding of the situation, and it may be extremely helpful for planning operations and interventions, while it may clarify why that physiotherapy does not improve the spasticity of the movements. In essence, the understanding and assessment of movements of the upper extremities need the transfer of procedures, knowledge and expertise gained from gait analyses. Applications in the occupational or ergonomic context, in sports, and in daily life situations will be a challenge to biomechanics research while the clinical applications may increase the complexity of the movement as well as its di$culties of detection and interpretation.
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Disselhorst-Klug, C., Rau, G., 1996. Acquisition of surface EMG signals: an overview of the state of the art. In: Hermens, H., Merletti, R., Freriks, B. (Eds.), European Activities on Surface Electromyography. RRD, Enschede, pp. 83}89. Dubois, E., Huang, T.S., 1998. Motion estimation. IEEE Signal Processing Magazine, 15, 51}56. Hermens, H., Freriks, B., 1997. The State of the Art on Sensors and Sensor Placement Procedures of Surface Electromyography: A Proposal for Sensor Placement Procedures. RRD, Enschede. Hodgins, J.K., 1998. Animating human motion. Scienti"c American 278, 46}51. Hodgins, J.K., O'Brien, J.F., Tumblin, J., 1998. Perception of human motion with di!erent geometric models. IEEE Transactions on Visualisation and Computer Graphics 4, 307}316. Inman, V.T., 1966. Human locomotion. Journal of Canadian Medical Association 94, 1054}1064. Inman, V.T., Ralston, H.J., Todd, F., 1981. Human Walking. Williams & Wilkins, Baltimore. Perry, P., 1974. Kinesiology of the lower extremity bracing. Clinical Orthopaedics & Related Research 63, 21}31. Perry, P., 1992. Gait Analysis: Normal and Pathological Function. Slack, New York. Murray, M.P., 1967. Gait as a total pattern of movement. American Journal of Physical Medicine 46, 290}333.
Nigg, B.M., Herzog, W., 1994. Biomechanics of the Musculo-Skeletal System. Wiley, Chichester. Schmidt, R., Di{elhorst-Klug, C., Silny, J., Rau, G., 1998. A Measurement procedure for the quantitative analysis of free upper-extremity movements. Proceedings of the Fifth International Symposium on 3-D Analysis of Human Movement. Chattanooga, USA, pp. 47}50. Schmidt, R., Di{elhorst-Klug, C., Silny, J., Rau, G., 1999. A marker based measurement procedure for unconstrained wrist and elbow motions. Journal of Biomechanics 32 (6), 615}621. Sutherland, D.H., Olshen, R.A., Biden, E.N., Wyatt, M.P., 1988. The Development of Nature Walking. Mac Keith Press, London. Whittle, M.W., 1982. Calibration and performance of three-dimensional television system for kinematic analysis. Journal of Biomechanics 15, 185}196. Whittle, M.W., 1991. Gait Analysis: an Introduction. ButterworthHeinemann, Oxford. Whittle, M.W., 1995. Musculoskeletal applications of three-dimensional analysis. In: Allard, P., Stokes, A.F., Blanchi, J.-P. (Eds.), Three-Dimensional Analysis of Human Movement. Human Kinetics, Montreal, pp. 295}309. Winter, D.A., 1985. Concerning the scienti"c basis for the diagnosis of pathological gait and for rehabilitation protocols. Physiotherapy Canada 37, 245}252.
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Movement biomechanics goes upwards: from the leg to the arm G. Rau, C. Disselhorst-Klug*, R. Schmidt Helmholtz-Institute for Biomedical Engineering, Aachen University of Technology, Pauwelsstr. 20, 52074 Aachen, Germany Accepted 1 March 2000
Abstract The analysis of lower limb movements has been well established in biomechanics research and clinical applications for a long time. For these studies, powerful and very advanced tools have been developed to measure movement parameters and reaction forces. The main focus of interest aims towards gait movements while the understanding of the basic concepts is supported by numerous models. De"nitions of physiological ranges and detection of pathological changes in movements open an increasingly valuable clinical "eld of application. If, however, the primary function of the upper extremities as highly variable and adaptive organ for manipulating tasks is the subject of interest, the situation becomes considerably more complex. The nature of free arm movements is completely di!erent from being restricted, repeatable or cyclic as compared to gait. Therefore, the transfer of the knowledge and experience gained in lower extremity movement analysis to the analysis of upper extremities turns out to be di$cult. A proposal for how to proceed in measurements, e.g. where to place the markers and how to calculate movements and angles of segments involved, will be discussed which results in the description of the joint movements of wrist, elbow and shoulder joint. The de"nition of the motion is a speci"c step in upper extremity motion analysis which is important in terms of repeatability and signi"cance of the results. An example of assessing movement disorders in children with plexus lesion will illustrate the implications and the potential of upper extremity movement analysis in clinical applications. 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Biomechanics of movement is * to a large extent * the application of Newtonian mechanics to the neuromuscular skeletal system: the forces that cause the movement, and the internal forces that act within the body. Movement analysis has been developed since about 1900 and speci"cally pushed during the last 30 yr by better insight in the living organisms supported by tremendous advances in research. Typical areas concern: Cellular function (metabolism, structure, mechanical properties, dynamic behavior), muscle, bone, ligaments, tendons, cartilage properties, neuromuscular control mechanisms. Also, dedicated biomechanical and sensorimotor control models have been established and re"ned. This increase in knowledge has been achieved by very advanced experiment procedures and equipment which is well described in various books and publications.
* Corresponding author. Tel.: #49-241-807011; fax: #49-2418888442. E-mail address: [email protected] (C. Disselhorst-Klug).
3D motion analysis has turned out to be a powerful tool for a quantitative assessment of the movement in all degrees of freedom. The early research on 3D motion analysis was mainly focused on the improvement of imaging techniques and 3D reconstruction algorithms in order to get an accurate and reliable tool for the detection of three-dimensional free body movements. However, the "rst developments had only little practical application. The breakthrough of 3D motion analysis in clinical application can be attributed to clinical gait analysis where it is now applied to the detailed diagnosis and treatment planning of patients with di$culties in gait. This is not surprising since gait is a well-de"ned motion type with cyclic sequences repetitive from heelstrike-toheelstrike. Several biomechanical models of the lower extremities have been developed allowing the calculation of joint angles, joint forces and moments as well as the work, the power or the energy. For movement detection, "rst applicable optoelectronic systems for gait analysis have been introduced in the early seventies and have been developed into reliable tools. Although they are still expensive their accuracy, speed and convenience made them into a standard measurement tool (Whittle, 1982). Thus, after more than 100 yr of technical development,
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3D motion analysis has succeeded to be a useful clinical tool in gait analysis (Whittle, 1995). Recently, a number of gait laboratories have been established in which gait abnormalities can be examined precisely. The transition from normal gait to moderate disorders that may end up with severely disturbed movement patterns which can hardly be classi"ed or connected to gait because the individuals may not be able to walk anymore. In#uences of pathological changes, and even structural deformations, have to be considered. Muscles may be a!ected by disease, such as dystrophy, arthrophy or pain reactions. Fibrous tissue contracture after surgical and reconstructive operations, as well as ligament or tendon diseases or cartilage injuries, may limit passive mobility. Injury of brain, spinal or peripheral nerve structures may disrupt motor control and feed back pathways. To overcome these de"ciencies, frequently alternative motions are developed by the patient. These are only a few aspects which may generate a person's walking pattern into a mixture of primary functional loss and substitutional actions. However, the clinical use of gait laboratories is rapidly increasing. One of the most popular clinical application of gait analysis is the use for diagnostic and surgical planning in treatment of children with spastic paralysis in which the orthopedic surgeons are the driving forces. However, presently, clinical applications take place mainly in those centres where a strong collaboration between clinicians and engineers is established. The available equipment and procedures can only be utilized by specialists but cannot be introduced into clinical routine * a big challenge for future development. Another obstacle to the clinical use is the lack of standardized, consistent and liable data banks which are necessary for interpreting the clinical signi"cance of the measurements. Analysis of the upper extremities is at an early stage, and introduction to clinical routine seems to be a step for the future. The use of the upper extremities in daily life is versatile as can be indicated by a few examples: we use tools, grasp, perform complex manipulations, we throw objects, point, gesticulate, etc., by using arms and hands in a coordinated and well-organised way. For analysis of such movements, the experience from decades of gait analysis is not readily transferable. In this context, a working group of the International Society of Biomechanics (ISB) has been established, specialising in shoulder movement and dealing with one of the most complicated joints. The variety, complexity and range of upper-extremity movements is a big challenge to assessment and interpretation of data, getting even more complicated in clinical application. To tackle this problem, the advanced developments in gait analysis could be a guideline for how to proceed in the upper extremity movement analysis. On the basis of the well-established procedures in gait analysis, one
could develop possible approaches for the three-dimensional analysis of free upper-extremity movements.
2. Motion analysis of gait Normal gait is well de"ned in each individual. The gait cycle shows a typical pattern which remains unchanged for subjects older than 4 yr (Sutherland et al., 1988). Especially the timing of the gait cycle has been described in detail, (Inman et al., 1981; Perry, 1992; Whittle, 1991) among others. Gait is a cyclic sequence of movements occurring from heelstrike to heelstrike of the same foot. Also, it is to a high degree symmetrical, and each cycle is highly reproducible. The interindividual variations are rather small, and this "nally allows to establish a reference for normal gait. Each gait cycle can be roughly divided into the swing phase and the stance phase of each leg. The stance phase is about 60% of the gait cycle and can be subdivided into double-leg and single-leg stance. The swing phase of the leg consists of three phases: initial swing, where the leg is accelerated, midswing and terminal swing, where the leg is decelerated (Inman, 1966). The position of the feet on the ground de"nes a number of gait parameters which are commonly used for description of gait and which can be easily obtained without the support of 3D motion analysis (Table 1). For each subject, the timing of gait and the characteristic gait parameters are highly repeatable. Therefore, the synchronised data of each gait cycle can be averaged to improve the reliability of the extracted parameters. In this way, a normative database has been set up, which contains the information about the timing and the characteristic parameters of the physiological gait (Murray, 1967). Most of the characteristic gait parameters can be measured when the movement of the trunk and the feet are traced. The available 3D movement analysis systems are suitable, and standardised procedures for the positioning of limb markers are established. Derived from the 3D
Table 1 Characteristic parameters describing the individual gait pattern (Whittle, 1995) Parameter
De"nition
Cadence Walking velocity Step length
Number of steps per time Distance walked per time Distance by which each foot is in front of the other one Distance which each foot moves forward in one gait cycle Side-to-side distance between the two feet angle between midline of the foot and direction of walk
Stride length Walking base Toe out angle
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trajectories of the markers, stick "gures can be created which re#ect the positions of the limbs during the gait cycle. However, since the stick "gures only show what can also be seen by eye, the real advantage of 3D motion analysis consists of its capacity to calculate joint angles from the marker trajectories. In contrast to the stick "gures, which only have very limited clinical application, joint angles are parameters which are closely related to the functions of muscles and joints. The combination of the available 3D movement analysis systems, standardised marker arrangements and an underlying mechanical model of the limb segments allows the calculation of the joint angles in all three dimensions. Most of these kinematic models of the lower extremities assume that the body is composed of rigid segments which are connected by ideal links. This approach suggests to assign one rigid segments to every bone (Andrews, 1995). How to design such a kinematic model will be shown for the upper-extremity movements in the next section. Utilising joint angles, a kinematic description of gait can be achieved. Although the kinematic description of gait has been introduced some time ago, normative data are still not completely available. Only for movements in the sagittal plane, a normative database about the joint angles has been collected (Perry, 1974). This is due to the fact that the greatest range of the motion occurs in the sagittal plan, and movements in the coronal and transverse plane are often neglected. However, although the kinematic description of gait by means of joint angles is commonly used in basic as well as in clinically orientated research, the information about the joint angles is still rarely used in clinical routine. The reason is, that the clinical de"nitions of 3D-joint movements, like #exion}extension, abduction}adduction and internal} external rotation, often di!er from those joint angles calculated by the kinematic model. That circumstance makes the interpretation of the kinematic data di$cult and the information is often useless for clinical routine. The information about the kinetics of gait has more importance for clinical application. The transition from the kinematic description of motion to a kinetic description needs the measurement of the forces provided by the neuromuscular system (Fig. 1) (Nigg and Herzog, 1994). In gait analysis, these forces are commonly measured by means of forceplates which detect the ground-reaction forces. If kinematics and forces are detected in a common co-ordinate system, they can be used as input into a mathematical model which calculates, e.g. joint moments and joint forces, (Bresler and Franke, 1950; Cavagna and Magaria, 1966). In contrast to the kinematic description, the kinetic description of gait provides powerful research tools with signi"cant meaning in clinical application. However, the evidence of the kinetic description is limited by the underlying biomechanical model. Even if the motion during the gait cycle is limited
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Fig. 1. Di!erent ways of the description of human gait. The more complex the description becomes the higher are the requirements to the recording set up and the underlying models. Since simpli"cations have to be made with each increment of complexity, the resulting interpretation of the parameters have to be used more carefully.
to the sagittal plane, which results in a comparatively simple motion, it is not possible to "nd a unique solution for the large number of equations which have to be ful"lled by the model. For that reason, simplifying assumptions have to be made which are more or less correct (Whittle, 1995). If the masses of the di!erent limb segments, their centres of gravity and their moments of inertia are known, the work, power and energy transfer between the di!erent body segments can be calculated. Although this information is of high relevance for clinical applications, there is only little correspondence between the received information and the physiological work or the metabolic activity. Muscles, for example, need metabolic activity even during excentric contractions, and the tendons and ligaments store passive energy which is not regarded in most models. Therefore, the calculated information about work, energy and power have to be handled with care. Besides the mechanical aspects in clinical gait analysis, information about the muscular coordination is of clinical relevance. This can be achieved by using electromyography (EMG) in which the electrical activity generated by a contracting muscle is detected. The large number of muscles involved in gait and the dynamic contractions require the use of surface electrodes. The problem herewith is that EMG is only semi-quantitative. The
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measured EMG amplitude depends not only on physiological properties like the thickness of the tissue layers between the muscle and the electrodes or the electrical impedance of the skin, but it also depends on the measurement arrangement, like the interelectrode distance or the location of the electrodes relative to the muscle. Additionally, cross-talk of muscles located distantly from the muscle of interest has to be avoided. Recently, within the European project SENIAM (surface EMG for non-invasive assessment of muscles), recommendations for electrodes and electrode placements have been worked out in order to improve the quality and reliability of surface EMG measurements (DisselhorstKlug and Rau, 1996; Hermens and Freriks, 1997). However, if the timing of the muscles is of interest, surfaceEMG is the only suitable tool to examine the &guilty motor pattern' in gait (Winter, 1985).
3. Upper extremities Comparing gait analysis to upper-extremity analysis (Table 2) reveals the nature of the problems when biomechanics goes from the leg to the arm. E The variability of upper-extremity movements makes the selection of one or more movements necessary. These may be movements taken from an activity under investigation or movements which are designed for the experiment. The demands for accuracy and details, as well as the way of interpretation and visualisation, may vary for each application. E Time normalisation and averaging based on the cyclic nature of gait is generally not applicable to the upper extremities. Inter- and intraindividual comparisons are thus more di$cult. E A 2D lateral view of gait yields a good approximation of the major movement components. Upper-extremity motions cannot be described in 2D. The 3D rotations occurring at the shoulder lead to non-intuitive descriptions of the rotational kinematics. E Force plates and foot pressure soles provide accurate data about the external forces during gait and running. Table 2 Comparison of the situation in gait analysis and upper extremity analysis Gait analysis
Upper extremities
One standard movement Cyclic Approx. 2D External forces easily measurable Limited range of motion Standard protocols exist Ready-to-use systems available
Task-dependent movements Non-cyclic 3D External forces di$cult to access Extremely large range of motion No standard protocols No adapted systems available
Net joint forces and moments can be calculated from the external forces since they are big compared to gravity and inertia. In contrast, the assessment of external hand forces is di$cult in most situations. Furthermore, there are frequently no external forces, and thus, only estimates of gravitational and inertial force are available for the &determination' of joint forces and moments. Therefore, kinetics description is even less accurate for the upper extremities than the lower extremities. E The large range of movements increases the problem of skin and soft tissue movements which is the major limitation of the accuracy of all measurement techniques which use skin-mounted sensors. Special attention needs to be paid to the large rotations around the longitudinal segment axes, not known from gait. E The variability and complexity of the tasks performed with the upper extremity has prevented the establishment of reliable and standardised procedures for the measurement of upper-extremity movements by the scienti"c community. As a consequence readily usable tools are not commercially available. The standards mentioned are not only necessary for the development of commercial tools. They provide the basis for the comparability and repeatability of results which is even more important for the future of the "eld. Therefore, the ISB promotes the de"nition of standards in motion analysis in order to bundle and accelerate the process. Standardisation proposals have been submitted by several research groups for the hand, the wrist, the elbow and the shoulder (http://isb.ri.ccf.org/standards/). The standards yet do not de"ne a measurement procedure but they give guidelines. A measurement procedure for the upper extremities must be #exible and accurate since it has to cover a wide range of applications with very di!erent motion types and varying accuracy requirements. A proposal of a marker-based measurement procedure for upper-extremity motions which ful"ls these demands is presented in the following (Schmidt et al., 1998,1999). The analysis of the upper extremities starts on a common methodological platform with gait analysis. At "rst, a kinematic model is needed which describes what is to be measured. The kinematic model of the upper extremities is based on the rigid segment approach in which each segment is assigned to one bone. However, scapula and clavicle are not accessible with skin-mounted markers. Therefore, the kinematic structure of the model is simpli"ed by omitting the scapula and connecting the clavicle directly to the humerus (Schmidt et al., 1998). The same problem occurs with the forearm. Ulna and radius are indistinguishable by external markers. One forearm segment with the pro-/supination realised at the elbow joint replaces the natural structure of two bones and two
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Fig. 2. Kinematic structure of the model of the upper-extremities.
radioulnar joints. The resulting kinematic structure of the upper-body is shown in Fig. 2. The model is made up of nine segments: the hands, the forearms, the upper-arms, the collarbones and the thorax. The joints in this model are ideal and ball-andsocket joints which do not permit translations between the segment. Since the ball-joints do not have distinct axes one co-ordinate system which is "xed in the proximal segment is assigned to every joint. Each co-ordinate axis then represents one joint axis. This implies orthogonal joint axes which means an additional simpli"cation of the model (Schmidt et al., 1998, Schmidt et al., 1999). The kinematic model needs to be transformed into a measurement set-up. All segments except the collarbone are de"ned by a set of at least three non-collinear markers. By means of triplets of markers the motions of each segment in all six degrees of freedom (dof) are assessed. The best correspondence between model and measurement is achieved when the three markers of one triplet are rigidly interconnected in order to suppress inter-marker motions due to skin movements. The de"nition of the joint co-ordinate systems is more complicated. Joint co-ordinate systems are a central issue of the existing standardisation proposals of ISB mentioned above. However, these de"nitions are based on bony landmarks which makes it impossible to directly implement it by skin markers. Even placing the markers above bony landmarks may not yield a good approximation because skin movement still disturbs the marker position. The proposed approach for upper-extremity analysis uses a combination of three di!erent procedures to deter-
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Fig. 3. Marker con"guration with segment (dark) and joint (light) markers. The marker triads of one segment may be connected by cu!s in order to reduce intermarker motions (after Schmidt et al., 1998).
mine joint co-ordinate systems from marker measurements: Procedure 1: Additional markers are used to de"ne the joint co-ordinate system of the wrist and the centre of the elbow. It is su$cient, and more accurate, to use these additional markers only during an extra static trial, because skin movement is largest at the joints. The markers are placed on the #exion/extension axes of the joints (Fig. 3). At the elbow, they just indicate the joint centre taken at the half-way between both markers. At the wrist, the joint centre, as well as the orientation of the #exion axis, is deduced from these markers. At the wrist, the anatomical axes are not clearly de"ned since the wrist joint is made up of several smaller interacting joints. Accordingly, the marker-de"ned axes correspond to the three basic functional axes more than to bony structures. The longitudinal axis is "xed at the joint centres of wrist and elbow. The #exion/extension axis is perpendicular to this axis and within the plane made up by the elbow centre and the wrist markers. The abduction axis then follows from the requirement of orthogonal axes. Procedure 2: The centre of the shoulder joint is calculated from a de"ned extra motion and an additional static trail. This is because the shoulder joint is located deep below the surface which hides most bony landmarks necessary for a static determination of the joint centre. Here, an evaluation of the movements of the upper-arm markers with respect to the thorax markers by an optimisation procedure is more reliable. A simple example would be to calculate the best "t of the centre of the spheres the upper-arm markers are moving on with re-
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spect to the thorax. More sophisticated optimisations take into account motions of the shoulder girdle. The result is an estimate of the position of the glenohumeral head "xed in the upper-arm segment. Procedure 3: The orientation of the shoulder co-ordinate system is actually arbitrary since no functional axes exist. Instead the main body axes are applied. Therefore, the thorax markers can be used to de"ne the orientation of the shoulder co-ordinate system. The two upper markers yield the transversal #exion/extension axis. The sagittal abduction axis is parallel to the perpendicular on the marker plane. The longitudinal axis follows from the condition of orthogonal axes. The elbow co-ordinate system is calculated from the shoulder centre. The longitudinal axis is given by the shoulder and the elbow centre which is known from the static trial with additional markers. The #exion/ extension axis is parallel to the perpendicular on the plane de"ned by the joint centres of shoulder, elbow and wrist. This de"nition is more robust in most cases than to use the elbow markers. Measurements of the internal and external rotations of the upper-arm are by far more accurate with this method. However, the de"nition is inaccurate when the arm is close to a straight line. This can be handled by "xing the elbow co-ordinate system at the upper-arm (markers) when the reliable range (#exion '153) is left, until the arm returns to a su$cient large #exion angle. After having de"ned the joint co-ordinate systems, the joint motions can be described as relative rotations between these co-ordinate systems. Shoulder rotations are rotations of the humerus-"xed elbow co-ordinate system with respect to the clavicula-"xed shoulder co-ordinate system. Elbow rotations are rotations of the forearm "xed wrist co-ordinate system with respect to the elbow coordinate system. Wrist rotations are rotations of the hand segment coordinate system with respect to the wrist co-ordinate system. The joint rotations can be expressed in several di!erent ways. The possibilities are helical axis, quaternions, Joint Coordinate System (JCS) and Euler/Cardan angles. Since Euler/Cardan angles are commonly used in gait analysis and the JCS is equivalent to a special case of Euler/Cardan angles (Nigg and Herzog, 1994), they have been employed in the following study. Euler/Cardan angles are obtained when the total rotations between the joint co-ordinate systems, usually given as the so-called rotation matrices, are decomposed into ordered sequences of rotations around the three joint axes. There are exactly 12 di!erent possible orders. We chose the one which is equivalent to the JCS, because it best re#ects the anatomical meaning of the rotation names. The order of rotations around axes "xed in the distal segment is: (1) #exion/extension, (2) abduction/adduction and (3) rotation around the longitudinal segment axis. The disadvantage of Euler/Cardan angles is that the
decomposition is not determined at certain points (singularities or gimbal lock). At these points, the resulting angles can jump 1803 although the joint movement is only small.
4. Normal movement The meaning of Euler/Cardan angles is explained in the following example of a motion of the complete arm. Fig. 5 shows the shoulder and elbow angles measured while the index "nger moved three times on a triangular trajectory in a paracoronal plane (Fig. 4). The joint angles of shoulder and elbow recorded during that movement are displayed in Fig. 5. The "rst curves display the #exion (#) and extension (!), the second curves show abduction (#) and adduction (!) and the third curves the internal (#) and external (!) rotation pronation (#) and supination (!), respectively. All angles are zero at the neutral position which is the straight arm hanging vertically and the palm pointing forwards. However, as in this example, the starting position of the measurements is not the neutral position. At time zero, the hand is already in front of the chest. The arm attitude at time 3 s in relation to the neutral position is reached by a 953 elbow #exion and 1153 pronation. The shoulder is "rst #exed 503, then abducted around the new abduction axis by 353, and "nally rotated internally around the current upper-arm axis by 503. The proposed procedure is the counterpart corresponding to existing procedures for gait analysis. It yields
Fig. 4. Trajectory of the index "nger resulting from the joint movements of shoulder and elbow shown in Fig. 5. At time 3 s the index "nger is in the shown position.
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Fig. 5. Shoulder and elbow angles during a triangular hand path.
a complete 3D description of upper-extremity movements over the full range of motions.
upper-extremities and can be related to muscle coordination via EMG recordings.
5. Pathological movement
6. Conclusions and outlook
First clinical applications are illustrated by a measurement of a child su!ering from a plexus lesion, caused by a birth trauma (Fig. 6). Motion analysis is used in this case to answer quite the same questions as gait analysis does for cerebral paresis children. How is the range of motion and the motion pattern altered due to the impairment? In combination with surface electromyography, the muscle co-ordination during the movements can be assessed. This enables to answer separately whether the e!ects of missing innervation, co-contraction or a mechanical block of the joint are responsible for the de"cit. This is crucial information for the planning of conservative and surgical therapies. The movements which were tested are abduction, elevation, and a hand motion from the knee to the mouth (cookie test). Fig. 6 shows a child during the cookie test. In addition to the re#ecting markers, EMG electrodes are visible at the upper-arm and the shoulder. The motion pattern of the a!ected side (Fig. 7, right curves) is clearly di!erent from the healthy side (Fig. 7, left curves). The movement of the handicapped arm is, in general, slow and irregular. The surface-EMG indicates that this could be a result of co-contraction of the biceps and the triceps. Shoulder #exion is smaller and jerkier. The pronation seems to be barely controlled which causes large variations of that joint angle. In summary, the movement analysis of the upperextremities, as proposed here, provides information which is relevant for clinical decision making. It gives detailed insight into the complex motion patterns of the
As mentioned above, in routine biomechanics analyses, gait may be considered as a gross movement with joints of limited degrees of freedom involved. The spatial dynamic movement patterns are frequently and satisfactorily assessed by a 2D-observation, and in special cases, this has been extended to 3D-analysis. Standardized equipment and procedures in gait analysis are elaborate and available. Kinematic and kinetic models have been developed in order to assess joint angles, joint forces, and moments. If masses, centres of gravity, and moments of inertia are available, work, energy and power can be calculated. Besides the limiting simpli"cations made in the models, the movement of gait can be described almost completely. Although the movement of upper extremities is much more complicated, it has been shown that some of the knowledge from gait analysis can be used in the analyses of upper-extremity motions. However, in both lower and upper-extremity movement some basic questions and some restrictions in application are still present.
7. Basic questions Movements can be considered from various point of views. First of all, they are observed as motion in time and space. The observation can be re"ned by adequate measurement procedures and equipment as a time-varying imagery or image sequence. Understanding the movements needs a model-based description, but also an
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Fig. 6. Measurement of upper-extremity movements of a child su!ering from a plexus lesion.
adequate biomechanical model. It is not su$cient to generate a computer model of the human body as utilized presently in synthetically animated movies where rigid body parts connected by rotary joints with 1, 2 or 3 degrees of freedom are used (Hodgins, 1998; Hodgins et al., 1998; Dubois and Huang, 1998). So far, it has some natural look but still does not teach us the underlying mechanisms and properties of the biomechanics. As already mentioned, gait movements have been analyzed thoroughly on the basis of measurements with high accuracy, and the interpretation supported by biomechanical models is very advanced. Recently, re"ned
models which also include the main muscles involved are being developed. However, gait movements are well de"ned, and the joints' characteristics can be simpli"ed adequately for a gross movement description. Of course, if one looks into the biomechanics of the knee µscopically' the situation may become very complicated. In essence, gait analysis and interpretation by modeling is already well developed. Similarly, for a better understanding of upper-extremity movements, we need an adequate model approach where the knowledge of the shoulder joint movement is an integral part. Everybody who is familiar with the
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Fig. 7. Comparison of the healthy arm (left) with the handicapped arm (right). The joint motions of the a!ected side are slower and jerkier.
anatomy, muscle mechanics, viscoelastic elements, and sensory}motor control will tend to ask: Are there solutions existing at all in such over-de"ned systems?
8. Restriction by application Of course, if a very high precision is requested, the problems will pile up exponentially. Therefore, one can look into speci"c applications and then design movement patterns to be performed by the subject accordingly in such a way that we can get answers to our questions. It is well known that repetitive movements with the arm/hand/"nger system can be executed highly reproducibly; even time and amplitude invariance have been described in literature. Interesting "elds of application are in Ergonomics and in Medicine. Again, the free arm}hand}"nger gesture movements as input media in man}machine interaction need a rather high-resolution recognition of the movements but not a biomechanical model. Handtracking algorithms have been demonstrated already during the Telekon Fair in Geneva in 1995, and recently, "rst commercial products have become available which are utilized for man}machine communications by gestures. Medical applications are speci"cally embedded in clinical routine and, therefore, need to ful"ll some di!erent characteristics. The "rst requirement which has to be ful"lled is that the detected movement is repeatable with high reliability. This does not necessarily mean high precision, but the results must be comparable, independent of the investigating clinic. As a consequence, a certain degree of standardization is indispensable. This situation becomes more complicated if movement analysis has to be introduced into clinical routine. All tasks have to be simple, easy to be applied, reliable, not time consuming, and clear in the result. The personnel
involved is critical: how many minutes of a doctor, a technician or nurse are necessary? The duration of a measurement is also essential because patients, especially children and elderly persons, may not be loaded very much, dependent on their de"ciencies. And some of the patients are, in principle, not able to reproduce a movement at all as, e.g., in the case of spasticity. Here, completely di!erent procedures of pattern recognition have to be developed. In spastic phenomena, primarily not dramatic deformations of the biomechanics structure, but typical abnormal changes in the neuromuscular control, are responsible for the disease. In this context, the EMG patterns will contribute essentially to the understanding of the situation, and it may be extremely helpful for planning operations and interventions, while it may clarify why that physiotherapy does not improve the spasticity of the movements. In essence, the understanding and assessment of movements of the upper extremities need the transfer of procedures, knowledge and expertise gained from gait analyses. Applications in the occupational or ergonomic context, in sports, and in daily life situations will be a challenge to biomechanics research while the clinical applications may increase the complexity of the movement as well as its di$culties of detection and interpretation.
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