Springer-Verlag 1998
Exp Brain Res (1998) 119:493±503
RESEARCH ARTICLE
Helge Topka ´ Jürgen Konczak ´ Klaus Schneider Andreas Boose ´ Johannes Dichgans
Multijoint arm movements in cerebellar ataxia: Abnormal control of movement dynamics
Received: 28 October 1996 / Accepted: 30 September 1997
Abstract In cerebellar ataxia, kinematic aberrations of multijoint movements are thought to originate from deficiencies in generating muscular torques that are adequate to control the mechanical consequences of dynamic interaction forces. At this point the exact mechanisms that lead to an abnormal control of interaction torques are not known. In principle, the generation of inadequate muscular torques may result from an impairment in generating sufficient levels of torques or from an inaccurate assessment and prediction of the mechanical consequences of movements of one limb segment on adjacent joints. We sought to differentiate the relative contribution of these two mechanisms and, therefore, analyzed intersegmental dynamics of multijoint pointing movements in healthy subjects and in patients with cerebellar degeneration. Unrestrained vertical arm movements were performed at three different target movement velocities and recorded using an optoelectronic tracking system. An inverse dynamics approach was employed to compute net joint torques, muscular torques, dynamic interaction torques and gravitational torques acting at the elbow and shoulder joint. In both groups, peak dynamic interaction forces and peak muscular forces were largest during fast movements. In contrast to normal subjects, patients produced hypermetric movements when executing fast movements. Hypermetric movements were associated with smaller peak muscular torques and smaller rates of torque change at elbow and shoulder joints. The patients deficit in generating appropriate levels of muscular force were prominent during two different phases of the pointing movement. Peak muscular forces at the elbow were reduced during the initial phase of the movement when simultaneous shoulder joint flexion generated an extensor influence upon the elbow joint. When attempting to terminate
)
H. Topka ( ) ´ J. Konczak ´ A. Boose ´ J. Dichgans Department of Neurology, University of Tübingen, Hoppe-Seyler-Strasse 3, D-72076 Tübingen, Germany e-mail:
[email protected], Fax: +49-7071-29-6507 K. Schneider Institute of Sport Science, Hochschule der Bundeswehr, Neubiberg, Germany
the movement, gravitational and dynamic interaction forces caused overshooting extension at the elbow joint. In normal subjects, muscular torque patterns at shoulder and elbow joint were synchronized in that peak flexor and extensor muscular torques occurred simultaneously at both joints. This temporal pattern of muscular torque generation at shoulder and elbow joint was preserved in patients. Our data suggest that an impairment in generating sufficient levels of phasic muscular torques significantly contributes to the patients difficulties in controlling the mechanical consequences of dynamic interaction forces during multijoint movements. Key words Cerebellar ataxia ´ Limb movements ´ Dynamics ´ Human
Introduction Previous studies on multijoint movements in cerebellar limb ataxia have shown characteristic kinematic abnormalities that are associated with cerebellar function. Patients tend to move slower than normal subjects and exhibit reduced peak hand acceleration and deceleration (Bastian et al. 1996; Massaquoi and Hallett 1996). Motions about the shoulder and elbow joints are hypermetric compared with normal subjects and, as a consequence, the curvature of the hand path increases (Goodkin et al. 1993; Massaquoi and Hallett 1996). These kinematic abnormalities are only subtle when moving at slow or moderate velocities but are marked when subjects attempt fast movements (Massaquoi and Hallett 1996; Topka et al. 1994). To understand the nature of the tasks that have to be resolved by the central nervous system when performing accurate multijoint movements, it is helpful to consider the mechanical characteristics of the human arm and to investigate the dynamics of limb movements. Mechanically, the human arm represents a multisegmented limb of linked bodies. In order to perform accurate movements, task-adequate intersegmental coordination is required. To achieve coordination among limb segments, muscle torques at each joint have to be adjusted to account for the
494
effects of gravitation (Virji-Babul et al. 1994). In addition, in a multiple-link mechanical structure, motion of any one part of the linkage exerts forces (passive reaction forces or motion-dependent interactive forces) on the remaining parts (Hollerbach and Flash 1982; Schneider and Zernicke 1990; Virji-Babul and Cooke 1995). It is well documented that, by means of passive reaction forces, muscles are able to cause movement about joints they do not span (Almeida et al. 1995; Zajac 1993). For example, in standing humans, activation of the soleus muscle not only generates extensor torques at the spanned ankle joint but simultaneously accelerates the unspanned knee into extension. If the body is near the upright vertical position, the induced acceleration of the knee joint may be 2 times larger than the acceleration at the ankle joint (Zajac and Winters 1990). Physiological studies in healthy subjects have shown that reaction forces arising during multijoint movements are sufficiently large to influence movement trajectories if not compensated for (Ghez and Sainburg 1995; Hollerbach and Flash 1982; Sainburg et al. 1995; Virji-Babul and Cooke 1995). Previous studies on multijoint movements in cerebellar limb ataxia have largely focused on the analysis of movement kinematics (Becker et al. 1990; Massaquoi and Hallett 1996). Only recently, the issue of cerebellar control of dynamic movement variables has been addressed (Bastian et al. 1996; Topka et al. 1994). Bastian and colleagues (Bastian et al. 1996) studied multijoint reaching movements in patients with various cerebellar disorders and in normal subjects and demonstrated a mismatch between muscular torque production at the elbow joint and dynamic interaction torques acting at this joint. These findings strongly suggest that a major role of the cerebellum is to coordinate motions of adjacent joints by adapting muscular torques at a joint according to predicted interaction torques being generated at other moving joints. At this point, it is unclear what the exact mechanisms of cerebellar involvement in controlling dynamic interactions among limb segments are. In principle, two different mechanisms are conceivable. First, cerebellar dysfunction may result in an impairment in generating levels of muscular forces that are sufficient to cancel dynamic interaction forces at a given joint. Second, cerebellar dysfunction may degrade the ability to properly assess and anticipate the kinematic effects of dynamic interaction forces and, as a consequence, result in inadequate assignment of muscular forces at a given joint. In this situation, the difficulties of cerebellar patients in compensating for dynamic interaction forces may originate primarily from a deficiency in maintaining or updating an internal model of the dynamic properties of the limb and may resemble those that have been observed in deafferented patients (Ghez and Sainburg 1995; Sainburg et al. 1993). In the present experiments, we sought experimental evidence that may help to judge upon the relative contribution of these two mechanisms. To this end, we performed a quantitative analysis of intersegmental dynamics of multijoint pointing movements in patients with cerebellar disorders and healthy subjects.
Patients and methods We studied nine patients with cerebellar degenerative disorders, aged 25±62 years (mean 46 16 years; three women, six men) and ten age- and sex-matched healthy subjects (mean 47 14 years). Patients were diagnosed as having autosomal-dominant ataxia (ADCA I, n = 3; ADCA III, n = 1), idiopathic ataxia (IDCA, n = 2), and early-onset cerebellar ataxia (EOCA, n = 3) according to clinical findings, magnetic resonance imaging findings, and patterns of inheritance as proposed by Harding (Harding 1993) and Klockgether (Klockgether et al. 1993). Mean duration of the disease was 8.5 5 years (range 3±20 years). Clinical signs of cerebellar dysfunction included upper or lower limb ataxia and midline ataxia, dysarthria, and mild cerebellar oculomotor dysfunction. The degree upper limb ataxia was graded minor (slightly dysmetric finger-tonose test, irregular finger-tapping, only minor motor problems in the activities of every-day life), moderate (dysmetric finger-to-nose test, marked irregularities in finger-tapping, noticeable motor problems in some activities of every-day life with respect to fine motor control and steadiness of force production), or severe (markedly dysmetric finger-to-nose test, marked irregularities in finger-tapping test, problems in virtually all motor tasks involving the upper limbs). In the majority of patients (n = 8), upper limb ataxia was graded mild to moderate. Only one patient was graded severe, and none of the patients were wheelchair-bound. All but one patient exhibited cerebellar atrophy on imaging studies and, in one patient, there were signs of additional brain stem atrophy. Patients showing signs of extracerebellar involvement in the upper extremities such as rigidity, upper motor neuron signs, or peripheral neuropathy were excluded. None of the patients presented with severe tremor. Patients and healthy controls did not differ with respect to their anthropometric data (total body weight, total arm length, and length of upper and lower arm segments). All subjects gave informed consent before participating. Apparatus and experimental procedures Vertical pointing movements were recorded in three dimensions using an infrared optoelectronic tracking system (ELITE, Milan, Italy) with reflective markers overlying the rotational axes of the wrist, elbow and shoulder joint of the subjects right arms. Subjects were seated and comfortably restrained in order to allow only for shoulder and elbow movements. To map the entire range of movement velocities, subjects were encouraged to alter movement velocities and to move at ªcomfortable velocity,º ªas fast as possible,º and ªslow.º As a target, an additional reflective marker was attached to a metal rod at a distance of 85% of total arm length. The target was positioned in front of the subject s right shoulder such that movements about the shoulder joint could, in principle, be restricted to the anterior-posterior plane. The height of the chair the subjects were seated on was not adjusted. Thus, depending on the length of upper and lower arm segments, the initial joint positions for shoulder and elbow joint varied between subjects to some extent. However, statistical comparisons of shoulder and elbow angle at the start position did not show differences between groups. Shoulder angle (mean 1 SD): healthy subjects 130.1 6.9 , patients 131.3 5.2 , P = 0.508, Wilcoxon; elbow angle: healthy subjects 129.7 10.9 , patients 126.8 3.9 , P = 0.402, Wilcoxon. Subjects were allowed practice trials in order to familiarize themselves with the apparatus and the experimental protocol. We considered the pointing task a simple and overlearned multijoint movement and, therefore, did not record and analyze practice trials. Prior to the data acquisition, total body weight and lengths of limb segments were taken. Based on these measurements, standard procedures (Hatze 1980) were used to compute the anthropometric data required for the inverse dynamics analysis. The algorithm computes segment volumes and masses, moments of inertia, and coordinates of the mass centroid with an estimated maximum error of about 5%.
495 Data analysis Time-position data were sampled at 100 Hz, digitally filtered (D Amico and Ferrigno 1992), and stored on a hard disk for later off-line analysis using a standard laboratory microcomputer. Angular kinematics at the elbow and shoulder joint were analyzed by computing planar angles from time-position data, the elbow angle representing the planar angle between humerus and ulna (shoulder marker ± elbow marker ± hand marker), the shoulder angle representing the angle between the humerus and the upper vertical of the shoulder joint. Angular velocity and acceleration at both joints were calculated by differentiating planar angle time series. For analysis of trajectories, a custom-written software package was employed. The start of the movement was defined as point in time at which the linear velocity of the hand marker exceeded 50 mm/s. The end of the movement was defined as point in time at which the linear velocity of the hand marker dropped below 50 mm/s after passing through peak linear velocity of the hand marker. In trials in which linear velocity of the hand marker did not drop below this criterion, we defined the local minimum between the first and the second velocity peak as end of the movement. This definition was chosen to restrict the analysis to the first segment of the movement that occurs prior to corrective movements with subsequent velocity peaks. The threshold was not changed for different subjects. Active and passive torques acting at shoulder and elbow joint were calculated from spatial coordinate-time data using an inverse dynamics approach (Schneider and Zernicke 1990; Schneider et al. 1989). The upper limb is modeled as three interconnected rigid links or segments (upper arm, forearm, wrist) with frictionless joints (shoulder, elbow, wrist). The model employed uses equations of motions that allow for quantification of effects of gravity (GRA), muscle influences on limb motion (MUS), and passive reaction forces (motion-dependent forces, MDT) acting at the shoulder and elbow joint and renders four torque-time series (Fig. 1): 1. Net joint (NET) torque: the sum of all positive and negative torque components (gravitational, muscle, interactive), where NET is given by NET = MUS + MDT + GRA 2. Gravitational (GRA) torque: a passive torque arising from gravity acting at the center of mass of each segment 3. Motion-dependent interactive (MDT) torques: passive torques arising from angular acceleration of a specific joint, dynamic interactions between linked segments, centripetal forces, and Coriolis forces 4. Generalized muscle (MUS) torque: a residual term that represents a torque that includes forces arising from active muscle contractions and from passive deformations of muscles, tendons, ligaments, and other periarticular tissues. Rates of MUS torque change were computed by differentiating MUS torque time-series data. The equations of motions used in our analysis render joint torque estimates for both shoulder and elbow joints. Algorithms that compute dynamic movement variables based on recordings of planar arm movements bear the potential risk of inaccurate torque estimates if the actual movement deviates from the defined plane of motion. Being aware of this limitation and expecting a tendency in subjects to deviate from a given movement plane, we used the algorithm by Schneider and Zernicke (1990) that introduces a moving local plane in order to maintain the validity of the computation of joint torques for three-dimensional movements. In this algorithm, the shoulder angle is defined relative to the projection of the upper arm in a moving local plane passing through the shoulder, elbow, and wrist joints. This method is limited in one respect, however. Shoulder torques are computed relative to the moving plane, which combines motion of the shoulder in the abduction/ adduction and in the anterior-posterior plane. Thus, in some instances, it may be difficult to relate the direction of shoulder torques to movements of the shoulder in either plane. To account for this limitation, the target marker was positioned such that shoulder adduction or abduction was not required to reach the target and we encour-
aged subjects to restrict their shoulder movements to the sagittal plane. Other differences between the algorithm used in our study and previously used methods are addressed in the Discussion section. Joint torques were computed for both the shoulder and the elbow joints. However, in order to simplify the presentation of our results, statistical comparisons between groups and data shown in figures are largely restricted to elbow joint torques. By definition, torques that exert flexor effects were assigned positive values, torques that exert extensor effects were assigned negative values. To allow for group comparisons despite differences in muscle strength, torque magnitudes were normalized for body weight gravity. Torque magnitudes, therefore, are reported in newton-meters per newton. Statistical analysis All data represent means 1 SD. For statistical analyses, a commercial software package was used (JMP 3.1, SAS Institute, Apple Macintosh version). Comparisons between patients and healthy subjects were performed using a 2 3 repeated-measures ANOVA with the factors Group and Movement Velocity. Student s t-test was used for post hoc tests. Bonferroni adjustments were applied with the significance level set to 0.05.
Results Angular kinematics and dynamics at the elbow joint for a fast pointing movement of a normal subject are summarized in Fig. 1 (left panels). Analyses of angular kinematics revealed that the pointing movement as prescribed by our task required combination of two movement segments about the elbow joint (Fig. 1, upper and middle panels). An initial flexion was followed by a second movement phase in which the elbow was extended. The elbow angular velocity profile was roughly symmetric in that velocities of initial elbow flexion and subsequent extension were of similar amplitudes, albeit with different temporal characteristics. The underlying NET torques (Fig. 1, lower panel) acting at the elbow joint consist of an initial flexor torque associated with elbow flexion and a second extensor torque component reflecting subsequent extension of the elbow. Partitioning the forces acting at the elbow joint into MUS forces, GRA forces, and MDT forces revealed a marked asymmetry of flexor and extensor torque influences upon the elbow joint during the pointing movement. GRA force exerted an extensor torque at the elbow joint throughout the movement that was only slightly modulated when flexing and extending the elbow (Fig. 1, lower panel). Consequently, GRA torque opposed the initial flexion of the elbow joint and assisted the subsequent extension. Thus, much larger muscular torques were required to generate the initial flexion of the elbow joint as compared to the subsequent extension of the elbow joint, which could partly be achieved by giving way to the influence of gravitation. In addition, muscular torques during elbow flexion had to be adjusted in order to compensate for passive (extensor) reaction forces originating in inertial, Coriolis, and centripetal forces opposing initial flexion of the elbow joint to some extent (MDT torque; Fig. 1, lower panel). Thus, in order to perform this particular pointing movement accurately, muscular torques had
496 Fig. 1 Kinematics and intersegmental dynamics of a vertical multijoint pointing movement in a normal subject and in a cerebellar patient. Subjects were instructed to move ªas fast as possible.º Upper panel Displacement of shoulder and elbow joint during the movement. Middle Panel Angular velocity at the elbow joint. Net torques (NET) acting at the elbow joint during the pointing movement are partitioned into generalized muscular torques (MUS), motion-dependent interactive torques (MDT), and gravitational forces (GRA). For all traces, flexor torques are represented as positive values, extensor torques as negative. Shaded areas represent flexor or extensor NET torques. Overshooting extension of the elbow in the patient is indicated by the vertical arrow. Dotted vertical line Point in time at which elbow displacement passes through the targeted elbow joint position for the first time
Fig. 2A, B Patterns of intersegmental dynamics at the elbow joint associated with different hand velocities in healthy subjects. A Flexor and extensor MUS torques, and GRA torques at the elbow joint during a vertical arm movement of a single normal subject. The abscissa indicates hand velocities. The dashed line indicates zero torques. Each symbol represents a single movement. Lines represent quadratic (flexor and extensor MUS, r = 0.977 and r = 0.984) or linear (GRA, r = 0.751) fit. B Relationship between hand velocity and magnitudes of flexor MUS torques (upper panel) and extensor MDT torques (lower panel) at the elbow joint. Each symbol represent a single movement of a normal subject. Data are pooled from ten healthy controls. Lines represent quadratic fit (flexor MUS, r = 0.906; extensor MDT, r = 0.903)
to be dimensioned to counterbalance the effects of GRA and MDT forces. Figure 1 (right panel) illustrates disordered kinematics and dynamics during a fast pointing movement in a single cerebellar patient. Movement kinematics were character-
ized by overshooting angular motion at the elbow joint, while peak angular velocities during flexion and extension of the elbow were reduced. Initial peak flexor MUS torque was slightly smaller than normal, resulting in reduced peak angular velocity when performing the initial flexion of the elbow. As is depicted in Fig. 1 (upper panel), in this example, the patient starts the movement by beginning to flex the shoulder joint. Flexion of the shoulder joint results in extensor interaction torques acting at the elbow joint. Thus, in contrast to the healthy subject, who starts the movement by lifting the hand and flexing the elbow joint without moving the shoulder joint, in the patient the muscular torques generated at the elbow joint are sufficient to counteract the extensor interaction torques, yet the torque amplitude is not sufficient to accelerate the elbow joint to a normal extent. When attempting to terminate the movement, MUS torque exerted an extensor influence at the elbow joint inappropriate to support
497 Fig. 3 Effects of increasing MUS and MDT torques on amplitudes of elbow joint motion during fast and slow vertical pointing movements in healthy subjects (n = 10) and patients with degenerative cerebellar disorders (n = 9). Empty symbols represent data from healthy subjects, filled symbols represent data from cerebellar patients. Subjects were instructed to perform their movements at ªslowº or ªmoderateº velocity, or ªas fast as possible.º The ordinate indicates peak-to-peak amplitudes of angular motion about the elbow joint. MDT and MUS torques were grouped into High, Medium and Low magnitudes of torques. Data represent mean 1 SD deviation. Depicted are flexor MUS torques (upper left), extensor MUS torques (upper right), flexor MDT (lower left), and extensor MDT (lower right). Asterisks indicate P < 0.05 two-sample t-test, Bonferroni adjusted
flexor MDT torque and compensate for extensor GRA torque. Thus, extensor NET torques were applied at the elbow joint (Fig. 1, dotted vertical line) when a zero NET torque would have been required at this point in time to stop extension of the elbow and to prevent overshoot. In normal subjects, altering peak hand velocities profoundly affected the underlying patterns of flexor and extensor MUS torques at the elbow joint, although the task did not require altering the spatial layout of the arm movement. At slow movement velocities, extension of the elbow joint was chiefly accomplished by taking advantage of the extensor influence of gravitational forces. In order to control the velocity of elbow extension, subjects applied flexor MUS torques throughout the movement to partly counterbalance the passive extension of elbow due to gravitational effects (Fig. 2A). Fast movements not only required an increase in peak flexor MUS torques in order to support larger accelerations of the limb segments but also required an extensor MUS torque at the elbow joint during the extension of the arm to assist passive extension of the elbow due to gravitational effects. In addition, increasing movement velocities were associated with a nonlinear increase in MDT torques (flexor MUS torque, r = 0.906; extensor MDT torque, r = 0.903; Fig. 2B). Thus, in order to maintain similar spatial characteristics of the movement trajectory during slow and fast movements, the dynamic strategies involved differ. Group comparisons revealed that increasing MUS and MDT torque levels had different effects on angular kinematics in patients and healthy subjects. For statistical comparisons, peak flexor and extensor MUS torques and peak flexor and extensor MDT torques were grouped into three categories (Low, Medium, and High) of torque magnitudes. To allow for determination of differences in
angular kinematics between groups for similar magnitudes of joint torques, the torque values that were categorized as Low, Medium, and High were chosen to be similar for both groups. Normal subjects maintained amplitudes of elbow angular motion when performing faster movements irrespective of the magnitude of muscular torques or motion-dependent interactional torques acting at the joint (Fig. 3). In contrast, in patients increasing levels of muscular forces (MUS torque and MDT torque) were associated with an increasing amount of hypermetria (peak flexor and extensor MUS torque Group effect, P £ 0.001; peak flexor and extensor MDT torque Group effect, P £ 0.01). Detailed analysis of movemet dynamics revealed that, in general, cerebellar patients, similarly to healthy subjects, were able to modify MUS torque when fast movements required compensation of larger magnitudes of MDT torque (Table 1). In particular, changes in dynamic movement patterns that required switching from flexor MUS torque to extensor MUS torque when increasing movement velocities (see Fig. 2A, peak extensor MUS torque) were normal. In both groups, peak MUS torques had a positive sign during slow and moderate velocity movements, indicating a flexor MUS torque influence at the elbow joint throughout the movement, whereas during fast movements peak MUS torques had a negative sign. Magnitudes of flexor MUS torque and extensor MDT torque acting at the elbow joint during initial flexion of the movements, however, were smaller in the patients (peak flexor MUS torque Group effect, P £ 0.03; peak extensor MDT torque Group effect, P £ 0.03). Post hoc statistics revealed that differences between patients and healthy subjects were most pronounced when fast movements were requested. Magnitudes of extensor MUS torque and flexor MDT torque associated with extension of the elbow were not
498 Table 1 Magnitudes of MUS and MDT torques and MUS torque rates at the elbow joint Slow Controls Peak Flexor MUS (Nm/N103) Peak Extensor MUS (Nm/N103) Peak Flexor MDT (Nm/N103) Peak Extensor MDT (Nm/N103) Peak Flexor MUS Torque change (Nm/N s103) Peak Extensor MUS Torque change (Nm/N103)
Moderate Patients
Controls
Fast Patients
Controls
Patients
3.570.52
3.780.59
4.680.66
4.110.78
11.224.66
7.692.05**
1.450.30
1.070.57
0.990.27
0.980.45
2.121.41
1.241.31
0.460.01
0.540.01
0.780.16
0.650.02
2.781.09
2.280.89
0.870.02
1.090.04
1.730.03
1.360.04
6.623.20
4.221.57*
13.123.23
18.447.01
26.898.53
22.838.17
184.42143.57
12.532.53
17.725.74
23.354.67
21.377.39
88.5935.04**
209.96162.54 ±106.8344.45*
* P0.05). Thus, patients were limited in their capacity to oppose gravitational and dynamic interaction forces during initial elbow flexion when performing fast movements (peak flexor MUS torque), but showed normal peak MUS torques when assisting gravitational effects that forced passive elbow extension (peak extensor MUS torque). Patients not only exhibited reduced peak flexor MUS torque compared with normals, but also generated smaller rates of flexor and extensor MUS torque (flexor MUS torque change Group effect, P = 0.06; interaction term, P = 0.03; extensor MUS torque change Group effect, P = 0.08; interaction term, p = 0.04; Table 1). The patients limitation in generating normal levels of
MUS torque rates was also present at the shoulder joint (flexor MUS torque change Group effect, P = 0.29; interaction term, P = 0.008; extensor MUS torque change Group effect, P = 0.56; interaction term, P = 0.01). Similar to abnormalities in production of peak MUS torques, differences between patients and healthy subjects in MUS torque rates at shoulder and elbow joints were not detectable during slow and moderate velocity movements but were marked if subjects performed fast movements. Hypermetric movements associated with reduced peak flexor MUS torque and reduced MUS torque change suggest that kinematic abnormalities in patients were related to an abnormal influence of MDT or GRA torques. As outlined in the Patients and methods section, MDT torque as computed in our analysis represents a summary term,
499 Fig. 5 Muscular torque patterns generated at shoulder and elbow joints in one normal subject and one cerebellar patient. Subjects were instructed to move fast, at moderate velocities, and slowly. To allow for comparisons across movement velocities, movement times are normalized
Fig. 6 Relative timing of peak muscular torques at shoulder and elbow joint during vertical pointing movements in normal subjects and patients with cerebellar degeneration. Each symbol represents a single trial. Solid lines indicate linear fit for normal subjects, dotted lines, for cerebellar patients. SLOW, MODERATE, and FAST denote the subjects instructions
which includes torques arising from dynamic interactions between linked segments as well as torques that arise from motion of the joint in question. Thus, an abnormal influence of MDT torque on movement kinematics in patients may, in principle, arise from deficient coordination of adjacent joints or from deficient compensation of MDT torque components that originate from and affect a specific single joint or a combination of both. Figure 4 illustrates the relative contribution of selected MDT torque
components to the sum of MDT torque for the elbow joint in a normal subject and a cerebellar patient. In our particular pointing movement, intersegmental MDT torque components originating from simultaneous motion of the adjacent shoulder joint opposed (Sh-AA, elbow torques due to shoulder angular acceleration) the execution of voluntary elbow flexion. Note that in both healthy subject and patient during initial elbow flexion the largest single component of MDT torque acting at the el-
500
bow were torques that originated from angular acceleration of the elbow joint itself. In comparison, inertial torque components originating from motion of the adjacent shoulder joint were of similar magnitude or tended to be slightly smaller. In patients, the overall temporal pattern of torque profiles was preserved, however, pointing movements associated with kinematic abnormalities were characterized by more irregular torque patterns (Fig. 4, right), affecting all components of MDT torque. In addition to reduced amplitudes of muscular torques, an abnormal influence of MDT torque on movement kinematics in patients may also be due to deficient temporal coordination of muscular torques acting at shoulder and elbow joint. Figure 5 illustrates the temporal relationship of muscular torque generation at these two joints during our pointing task. In both healthy subjects and cerebellar patients, muscular torque patterns at each joint were organized such that peak flexor and extensor MUS torques at the shoulder joint coincided with peak flexor and extensor MUS torques at the elbow joint. The normal pattern of shoulder and elbow joint MUS torques was preserved in patients (Fig. 6). The pattern was also preserved across movement velocities in both groups. However, the temporal relationship of shoulder and elbow MUS torques was slightly more variable during the braking phase of the movement and when subjects moved at slow velocities.
Discussion Previous studies of multijoint movements both in healthy subjects and in patients have largely focused on the analysis of movement kinematics. In these studies, kinematic variables were used to deduce planning variables that may govern the control of limb movements. Kinematic analyses of movements, however, may not suffice to fully explain the strategies employed by the nervous system to execute accurate multijoint movements, in particular if one tries to relate movement characteristics to their neuroanatomical substrates and to understand the pathophysiology of disordered motor performance. Although kinematic coordinates may play a significant role in movement planning, to execute accurate multijoint movements in three-dimensional space, the neural commands that finally cause activation of muscles have to account for the constraints that are posed by the physics of movement such as the mechanical properties of the human arm or the magnitude and orientation of the gravitational field. As opposed to single-joint movements, for multijoint movements, force and acceleration of limb segments are no longer proportional but are influenced by intersegmental dynamic interactions (Hollerbach 1984; Kaminski and Gentile 1989). In their recent study, Bastian and colleagues analyzed intersegmental dynamics in cerebellar limb ataxia (1996). Cerebellar patients produced inappropriate levels of shoulder and elbow muscle torque ªthat did not vary appropriately with the dynamic interaction torques that occurred at the elbow.º From these findings, the authors hy-
pothesized that the cerebellum plays an important role in generating muscle torques at a joint that will predict the interaction torques being generated by other moving joints and compensate for them as they occur. In principle, two different mechanisms of cerebellar involvement in controlling dynamic interaction forces are conceivable. The generation of inadequate muscular torques may result from an impairment in generating sufficient levels of torques, or alternatively from an inaccurate assessment and prediction of the mechanical consequences of movements of a given limb segment on adjacent joints, or a combination of both. Our findings support the notion of abnormal control of dynamic movement variables as a major source of kinematic movement abnormalities in cerebellar limb ataxia, as suggested earlier (Bastian et al. 1996). Direct comparisons between Bastian s study and our findings, however, are difficult to perform for several reasons. First, at this point, there is no widely accepted standard for the analysis of movement dynamics. Physically, the equations of motions that are used for the computation of joint torques, in particular, if parsing NET torques into MUS torques, MDT torques, and GRA torques is included, can be formulated in several ways. As a consequence, previous studies that analyzed movement dynamics such as the study by Bastian and colleagues or the studies by Sainburg and coworkers (1995; Ghez and Sainburg 1995) in deafferented patients differ from each other and differ from ours in several respects. Most importantly, the definition of interaction torques labeled MDT in our study, dynamic interaction torques in the study by Bastian et al., or interaction torques by Sainburg and colleagues differ from each other slightly. For example, in our study, motion-dependent torques include the torques that originate from motion of the joint in question, whereas in the study by Sainburg the torque components that arise from acceleration of the joint in question (self-torque) are separated from interaction torques. Another difficulty arises from differences in the motor task that is studied. As pointed out by Bernstein (1967), normal control of movement may not only compensate for but may also exploit the mechanical consequences of dynamic limb interactions, depending on the requirements of the task. Thus, abnormal control of interaction torques in one motor task may consist in an insufficient compensation for dynamic interactions, whereas in another task abnormal control of interaction torques may consist in insufficient exploitation of dynamic interaction torques. Thus, when comparing dynamic movement variables obtained with different computational methods, different definitions of torque terms and in different motor tasks, these limitations have to be taken into account. In our study, patients exhibited dynamic movement variables during slow- or moderate-velocity pointing movements that were similar to normal subjects and showed marked abnormalities when fast movements were executed. These findings are consistent with the notion of an abnormal influence of dynamic interaction between limb segments in cerebellar limb ataxia. Hollerbach and
501
Flash, in their theoretical work (1982), have shown that for planar arm movements the absolute magnitude of interaction torques increases with movement speed, while the significance of the velocity interaction torques relative to the inertial interaction torques does not vary with the speed of movement. They explicitly excluded the effects of gravity and, therefore, their scaling factor r2, which described the relationship between movement velocity and magnitudes of interaction torques, may not describe the dynamics of vertical limbs movements accurately. However, it is clear that also, for vertical limb movements, the magnitude of interaction torques increases with movement speed in a nonlinear fashion. In addition, for vertical movements as studied in our paradigm, the relative contribution of gravity and interaction torques to NET torques varies with movement speed. During slow vertical movements, muscular torques have to be generated to primarily move the limb in question and to counteract the (roughly constant) effects of gravity. In contrast, to support fast movements, muscular torques have to be scaled in order to achieve rapid acceleration and to counteract interaction torques with magnitudes that are relatively more significant than gravity (see example in Fig. 2). Thus, the finding that the patients difficulties in executing pointing movements were most prominent during fast movements is compatible with the notion of an insufficient compensation of dynamic interaction forces in cerebellar limb ataxia. Our findings suggest that an impairment in generating sufficient levels of MUS torques significantly contributes to the patients difficulties in adequately controlling interaction forces during multijoint movements. Compared with normal subjects, the most striking abnormality in our study was a reduction in peak muscular torques during the initiation of fast movements and a marked reduction in peak torque rates both at the shoulder and the elbow joints, occurring during both initiation and termination of fast movements. It is well documented that maximal isometric force production in general is not impaired in chronic cerebellar ataxia (Mai et al. 1988). However, optimal movement execution, in particular if performed at high velocities, requires adequate temporal control and rapid force production. In our particular task, the patients limitations in MUS torque production were most prominent during movement segments that required large MUS torques such as the initial flexion of the elbow. To accomplish initial fast elbow flexion, subjects had to generate MUS torques appropriate to compensate for GRA effects and for MDT torques associated with elbow flexion and simultaneous flexion of the shoulder joint. To generate the subsequent extension of the elbow, smaller levels of elbow muscular torques were sufficient to assist the effects of gravitation, and thus, peak muscular torques were within the normal range during this phase of the movement. During this phase of the movement, a marked reduction in peak torque-change rates was the primary deficit in patients compared with normal subjects. In addition, MUS torque patterns, even though of normal peak magnitudes, may be inadequately shaped or timed to
serve the purpose of the task. When attempting to terminate elbow extension, patients appeared to generate patterns of muscular torques inadequate to compensate for the effects of gravitation or dynamic interaction forces (Fig. 1). Our finding of an impairment in generating normal levels of phasic muscular activity during multijoint movements in cerebellar patients also relates well to previous findings in single-joint movement studies. The mechanics of single-joint movements differ from multijoint movements in that the contributions of dynamic interactions between limb segments to dynamic interaction forces are relatively minor and forces related to inertia of the moved limb predominate. However, similar to our finding of reduced rates of muscular torques during multijoint pointing movements, single-joint movements in cerebellar ataxia in both animal (Flament and Hore 1986) and human experiments (Hallett et al. 1975, 1991; Hore et al. 1991; Wild et al. 1996) were characterized by decreased peak acceleration and a more gradual buildup of agonist electromyographic activity. The notion that a quantitative deficit in MUS torque production may lead to the ataxic appearance of multijoint movements receives some indirect support from an earlier study that analyzed the kinematics of initiating a two-joint arm movement (Massaquoi and Hallett 1996). In this study, the patients trajectory aberrations were characterized by an increased curvature of their trajectories when high-speed movements were requested. Though not measuring or computing joint torques directly, the authors hypothesized that this kinematic abnormality may be related to a deficient torque production at the shoulder and elbow joint. Becker and colleagues (1990) pointed out that multijoint throwing movements in cerebellar patients were characterized by an increased variability to produce the appropriate hand direction in response to a visual target, yet stated that ªother aspects of coordinationº were normal as compared to healthy controls. Our findings argue against the hypothesis of an increased variability of motor performance as the main sequelae of cerebellar dysfunction. Instead, the inability to generate sufficiently large MUS torques points to a systematic failure in patients. Our finding of normal temporal coordination of muscular torque generation at shoulder and elbow joints in patients supports this view. Remarkably, the synchronicity of shoulder and elbow joint torques that characterized pointing movements in healthy subjects was preserved in patients, indicating that the principle of linear covariance of shoulder and elbow muscular torques (Gottlieb et al. 1996) that governs a wide variety of limb movements in healthy subjects appears not to be violated in the presence of cerebellar dysfunction. Our data may not allow to directly address the question of whether inadequate assessment and prediction of the mechanical consequences of movement contributes to inadequate control of dynamic interaction forces in cerebellar limb ataxia. Neuroanatomical evidence of extensive sensory inputs to the cerebellum, in particular from pro-
502
priospinal pathways, as well as other sources, is consistent with the notion that a major role of the cerebellum is in evaluating the sensory consequences of movement. In particular, the fractured somatotopy of mossy fiber inputs to cerebellar cortex (Welker 1987; Woolston et al. 1981) may be relevant to relay sensory inputs from a wide variety of sources to a particular set of Purkinje cells involved in a voluntary movement. For example, extending the arm when standing upright will cause a shift of the center of gravity that requires preceding preparatory and simultaneous coactivation of leg and truncal muscle in order to ensure stable stance. Divergent afferent cerebellar input from mossy fibers could, in principle, provide a means to monitor local and remote sensory effects of a particular voluntary movement, hereby enabling the central nervous system to provide for appropriate activation of muscles that directly support a particular voluntary movement (e.g., muscles that span adjacent joints) as well as muscles that indirectly support focal voluntary movement, such as truncal muscles. Previous studies on mechanisms of postural control during voluntary arm movement are consistent with this hypothesis, demonstrating that the normal sequence of muscle activation during movement preparation and execution is profoundly disturbed in the presence of cerebellar dysfunction (Diener et al. 1989). Findings that may help to judge upon the relative role of cerebellar processing of sensory afferents originate from studies that investigated the kinematics and dynamics of multijoint movements in patients with severely disordered proprioception due to sensory neuropathies (Ghez and Sainburg 1995; Sainburg et al. 1993, 1995). In these studies degraded proprioception was associated with abnormalities in movement kinematics and dynamics that were remarkably similar to the ones observed in cerebellar patients. In both patient groups, kinematic movement abnormalities as compared to normal subjects were shown to result to a large extent from an abnormal influence of dynamic interaction torques (Bastian et al. 1996; Ghez and Sainburg 1995; Sainburg et al. 1995). Sainburg and colleagues (1995) hypothesized that planning and execution of accurate multijoint movements depends on the integrity of an internal model of the biomechanic characteristics of the limb. From their findings in deafferented patients, they concluded that afferent sensory information may be required to maintain and update such an internal model of limb dynamics. Similarities between both patient groups are compatible with the notion that both cerebellar pathways and sensory afferents are involved in the process of maintaining such an internal model. Characteristic differences in the behavior and the patterns of abnormalities observed in deafferented patients and in patients with cerebellar disorders, on the other hand, suggest that afferent and cerebellar pathways are supporting different aspects of an internal model of limb dynamics. Deafferentation and cerebellar dysfunction seem to predominantly affect different phases of movement execution. In a mimed slicing gesture, the main motor sequel of deafferentation was an impairment in coordinating shoulder and elbow joint motion during segments
of the movement that required abrupt reversals of movement direction while movement initiation appeared to be normal in patients. The patients kinematic errors at movement reversals were shown to be related to deficiencies in timing muscles activation adequately with respect to the effects of interaction torques (Sainburg et al. 1995). Similarly, previous studies have shown that deafferentation chiefly affects movement variables related to the termination of movement while initial agonist activation and isometric torque pulses on average were scaled normally (Forget and Lamarre 1987). In contrast, our findings and pertinent earlier findings in single- and planar multijoint movements (Massaquoi and Hallett 1996) demonstrate significant impairment in generating normal levels of phasic muscular torques, agonist electromyographic activity (Flament and Hore 1986; Hallett et al. 1975, 1991; Hore et al. 1991; Wild et al. 1996) or joint acceleration also during early phases of the movement. There are also differences between deafferentiation and cerebellar dysfunction with respect of the effects of visual feedback on motor performance. Motor deficits in deafferented patients were most prominent when visual feedback was removed, whereas movements were only mildly affected if performed under visual guidance or if executed immediately after allowing visual control of initial limb position. In contrast, cerebellar patients do not benefit from visual feedback or exhibit even more severe motor deficits when using visual guidance (Beppu et al. 1987; Brown et al. 1993; Donkelaar and Lee 1994). The patterns of abnormalities in controlling dynamic movement variables observed in deafferented patients and in patients with cerebellar degeneration are compatible with the notion of an internal model of limb dynamics that is employed to adapt muscular torques to the mechanics of moving a multi-segmented limb such as the human arm. Cerebellar pathways may be involved in implementing such an internal biomechanical model of the limb within the nervous system. Sensory afferents are providing feedback and may serve to update the model. Deficits in maintaining such an internal model of limb biomechanics in cerebellar ataxia could also explain the observation that visual feedback improves motor performance in deafferented patients but not in patients with cerebellar dysfunction. The finding that cerebellar dysfunction affects both movement initiation and termination suggests that deficiencies in providing accurate feedforward and feedback control of limb dynamics contribute to cerebellar limb ataxia. Acknowledgements The authors wish to thank Dr. Mark Hallett for critically reviewing an earlier version of the manuscript and helpful comments. This work was supported by a grant from Deutsche Forschungsgemeinschaft (German Science Foundation) SFB 307/A3.
503
References Almeida GL, Hong DA, Corcos D, Gottlieb GL (1995) Organizing principles for voluntary movement: extending single-joint rules. J Neurophysiol 74:1474±1481 Bastian AJ, Martin TA, Keating JG, Thach WT (1996) Cerebellar ataxia: abnormal control of interaction torques across multiple joints. J Neurophysiol 76:492±509 Becker WJ, Kunesch E, Freund HJ (1990) Coordination of a multijoint movement in normal humans and in patients with cerebellar dysfunction. Can J Neurol Sci 17:264±74 Beppu H, Nagaoka M, Tanaka R (1987) Analysis of cerebellar motor disorders by visually guided elbow tracking movement. 2. Contribution of the visual cues on slow ramp pursuit. Brain 110:1±18 Bernstein NA (1967) The coordination and regulation of movement. Pergamon Press, New York Brown SH, Kessler KR, Hefter H, Cooke JD, Freund HJ (1993) Role of the cerebellum in visuomotor coordination. I. Delayed eye and arm initiation in patients with mild cerebellar ataxia. Exp Brain Res 94:478±488 D Amico M, Ferrigno G (1992) Comparison between the more recent techniques for smoothing and derivative assessment in biomechanics. Med Biol Eng Comp 30:193±204 Diener HC, Dichgans J, Guschlbauer B, Bacher M, Langenbach P (1989) Disturbances of motor preparation in basal ganglia and cerebellar disorders. Prog Brain Res 80:481±488 Donkelaar P van, Lee RG (1994) Interactions between the eye and hand motor systems: disruptions due to cerebellar dysfunction. J Neurophysiol 72:1674±1685 Flament D, Hore J (1986) Movement and electromyographic disorders associated with cerebellar dysmetria. J Neurophysiol 55:1221±1233 Forget R, Lamarre Y (1987) Rapid elbow flexion in the absence of proprioceptive and cutaneous feedback. Human Neurobiol 6:27± 37 Ghez C, Sainburg R (1995) Proprioceptive control of interjoint coordination. Can J Physiol Pharmacol 73:273±284 Goodkin HP, Keating JG, Martin TA, Thach WT (1993) Preserved simple and impaired compound movement after infarction in the territory of the superior cerebellar artery. Can J Neurol Sci [Suppl 3] 20:S93±S104 Gottlieb GL, Song Q, Hong D, Almeida GL, Corcos DM (1996) Coordinating movement at two joints: a principle of linear covariance. J Neurophysiol 75:1760±1764 Hallett M, Shahani B, Young RR (1975) EMG analysis in patients with cerebellar deficits. J Neurol Neurosurg Psychiatry 38:1163±1169 Hallett M, Berardelli A, Matheson J, Rothwell J, Marsden CD (1991) Physiological analysis of simple rapid movements in patients with cerebellar deficits. J Neurol Neurosurg Psychiatry 54:124±133 Harding AE (1993) Clinical features and classification of inherited ataxias. Adv Neurol 61:1±14 Hatze H (1980) A mathematical model for the computational determination of parameter values of anthropometric segments. J Biomech 13:833±843
Hollerbach JM (1984) Dynamic scaling of manipulator trajectories. ASME J Dyn Syst Meas Control 106:102±106 Hollerbach JM, Flash T (1982) Dynamic interactions between limb segments during planar arm movement. Biol Cybern 44:67±77 Hore J, Wild B, Diener HC (1991) Cerebellar dysmetria at the elbow, wrist and fingers. J Neurophysiol 65:563±571 Kaminski TR, Gentile AM (1989) A kinematic comparison of single and multijoint pointing movements. Exp Brain Res 78:547±556 Klockgether T, Wüllner U, Dichgans J, Grodd W, Nägele T, Petersen D, Schroth G, Schmidt O, Voigt K (1993) Clinicial and imaging correlations in inherited ataxias. Adv Neurol 61:77±96 Mai N, Bolsinger P, Avarello M, Diener HC, Dichgans J (1988) Control of isometric finger force in patients with cerebellar disease. Brain 111:973±998 Massaquoi SG, Hallett M (1996) Kinematics of initiating a two-joint arm movement in patients with cerebellar ataxia. Can J Neurol Sci 23:3±14 Sainburg RL, Poizner H, Ghez C (1993) Loss of proprioception produces deficits in interjoint coordination. J Neurophysiol 70:2136±2147 Sainburg RL, Ghilardi MF, Poizner H, Ghez C (1995) Control of limb dynamics in normal subjects and patients without proprioception. J Neurophysiol 73:820±835 Schneider K, Zernicke RF (1990) A Fortran package for the planar analysis of limb intersegmental dynamics from spatial coordinate-time data. Adv Eng Software 12:123±128 Schneider K, Zernicke RF, Schmidt RA, Hart TJ (1989) Changes in limb dynamics during the practice of rapid arm movements. J Biomech 22:805±817 Topka H, Konczak J, Schneider K, Dichgans J (1994) Analysis of intersegmental dynamics in cerebellar limb ataxia. Soc Neurosci Abstr 20:712.10 Virji-Babul N, Cooke JD (1995) Influence of joint interactional effects on the coordination of planar two-joint arm movements. Exp Brain Res 103:451±459 Virji-Babul N, Cooke JD, Brown SH (1994) Effects of gravitational forces on single joint arm movements in humans. Exp Brain Res 99:338±346 Welker W (1987) Comparative study of cerebellar somatosensory representations: the importance of micromapping and natural stimulation. In: Glickstein M, Yeo C, Stein J (eds) Cerebellum and neuronal plasticity. Plenum Press, New York, pp 109±118 Wild B, Klockgether T, Dichgans J (1996) Acceleration deficit in patients with cerebellar lesions. A study of kinematic and EMG parameters in fast wrist movements. Brain Res 713:186±191 Woolston DC, Kassel J, Gibson JM (1981) Trigemino-cerebellar mossy fiber branching to granule cell layer patches in the rat cerebellum. Brain Res 209:255±269 Zajac FE (1993) Muscle coordination of movement: a perspective. J Biomech 26:109±124 Zajac FE, Winters JM (1990) Modeling musculoskeletal movement systems: joint and body segmental dynamics, musculoskeletal actuation, and neuromuscular control. In: Winters JM, Woo SL-Y (eds) Multiple muscle systems: biomechanics and movement organisation. Springer, Berlin Heidelberg New York, pp 121±148
