Cerebellar ataxia: Quantitative assessmentand cybernetic interpretation

Vittorio Sanguineti a,b,*, Pietro G. Morasso a,b, Luigi Baratto b,Giampaolo Brichetto c, Giovanni Luigi Mancardi c,

Claudio Solaro c

a Department of Informatics, Systems, Telematics, University of Genova, Via Opera Pia 13, 16145 Genova,

Italyb Center of Bioengineering, Hospital La Colletta, Via Giappone 3, 16011 Arenzano, Italy

c Department of Neurological and Vision Sciences, University of Genova, Via A. De Toni 5,

16132 Genova, Italy

Abstract

To assess neuromotor disorders clinicians often rely on rating scales. Unfortunately, these

scales lack the sensitivity and accuracy needed to detect the small changes in motor coordina-

tion that reflect the clinical progression of the disease on the basis of which treatment pro-

grammes can be adjusted. As a contribution to this topic, the present paper proposes a

straightforward kinematic and kinetic analysis of reaching movements of patients with cere-

bellar ataxia in conjunction with a cybernetic interpretation of the data. The aim of the ap-

proach is to capture key deficits in the underlying motor control processes. We suggest that

cerebellar ataxia may be characterized by defective feedforward control.

� 2002 Elsevier Science B.V. All rights reserved.

PsycINFO classification: 2330; 3297

Keywords: Reaching movements; Cerebellar ataxia; Kinematics; Feedforward control; Feedback control

* Corresponding author. Address: Department of Informatics, Systems, Telematics, University of Genova,

Via Opera Pia 13, 16145 Genova, Italy.

E-mail address: sangui@dist.unige.it (V. Sanguineti).

0167-9457/03/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0167-9457(02)00159-8

Human Movement Science 22 (2003) 189–205

www.elsevier.com/locate/humov

1. Introduction

Understanding the mechanisms that allow the brain to construct and control

complex motor patterns remains a fundamental challenge for biological cybernetics,

neuroscience, and rehabilitation engineering. Even though many question are stillunanswered, a consensus is emerging that such mechanisms are based on adaptive

interactions of feedforward and feedback control systems. Indeed, two control mo-

dalities seem to coexist in the motor system (Sainburg, Ghez, & Kalakanis, 1999): (1)

an anticipatory (feedforward) component in which the motor commands (i.e. the ex-

citation of motor neurons and the inhibition of spinal reflexes) required for a desired

movement are pre-programmed and (2) a feedback component, responsible for the

correction of the outgoing motor commands on the basis of sensory (typically visual

and proprioceptive) information. Experimental evidence suggests that both com-ponents may use some form of �internal model� of body dynamics (Bhushan & Shad-

mehr, 1999). The view of the cerebellum as a computing machinery that has

competence as regards the physics of the body (Ito, 1984; Kawato & Gomi, 1992;

Marr, 1969) suggests that the cerebellar circuitry is likely to play an important

role in carrying out these tasks. Therefore, cerebellar syndromes, i.e. ataxias, form

a useful case study to improve our understanding of the mechanisms underlying

sensorimotor coordination. Furthermore, a model-driven interpretation of the char-

acteristic symptoms of this motor dysfunction might help to design reliable rehabil-itation strategies.

Ataxia is the main sign of cerebellar dysfunction. According to the classic descrip-

tion by Holmes (1917, 1939), the term indicates multiple problems in the planning

and execution of movements, including: (1) delay in movement initiation, (2) inaccu-

racy in achieving a target (dysmetria), (3) inability to perform movements of con-

stant force and rhythm (dysdiadochokinesia), and (4) inability to coordinate

movements at more than one joint. Additional cerebellar symptoms are diminished

resistance to passive limb displacement (hypotonia) and kinetic tremor (a patternwhich appears at movement onset and increases in amplitude while approaching

the target). Severe tremor may, by itself, preclude functional movements, although

it is most often associated with other impairments.

Clinical assessment of ataxia is based on a number of qualitative neurological

tests. One of these tests concerns a standardized, semi-quantitative scale called the

International Cooperative Ataxia Rating Scale (see Trouillas et al., 1997), which

compartmentalizes the symptoms of ataxia into four categories: (1) posture and

stance, (2) limb movements, (3) speech, and (4) eye movements. In this paper, wefocus on the �arm� section of the second component, which alone contributes 52%of the final score. The arm section of the test includes four tasks, each aimed at as-

sessing different features of the underlying control process: (i) the finger-to-nose task

(to assess decomposition, dysmetria, and intentional tremor); (ii) the finger-to-finger

task (to assess action tremor and instability); (iii) alternating pronation–supination

movements (to assess movement speed and rhythm); and (iv) drawing an Archime-

des� spiral on a predetermined pattern (to assess dysmetria and decomposition).

These rather coarse evaluations inevitably lack the sensitivity and accuracy that

190 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

are required to detect small changes in motor coordination, capable to reflect the

clinical progression of the disease, and thus to fine tune the treatment strategy (cf.

Notermans, van Dijk, van der Graaf, van Gijn, & Wokke, 1994; Sullivan, Ornstein,

& Swayne, 1994). The clinical interest for better and more accurate experimental

tools is further motivated by the fact that the standard medical and rehabilitationtherapies for cerebellar dysfunctions are of very limited efficacy (cf. Gilman, 1997).

Quantitative methods for movement analysis have a long history. (In fact, the

classic description of ataxia made by Holmes (1939) is based on an ingenious tech-

nique for recording hand trajectories.) Methods based on kinematic and/or kinetic

analysis of movements may potentially allow one to identify more subtle aspects

of movement disorders as well as small changes in the degree of the involved impair-

ments over time. This could not only help improve the diagnosis but also refine the

monitoring of the effects of pharmacological and/or rehabilitation therapies. More-over, kinematic/kinetic analysis of movements may help to elucidate the defining

mechanisms of movement disorders and their progression, as was recently demon-

strated in patients with Huntington�s disease (see Smith, Brandt, & Shadmehr, 2000).

Kinematic measurements in patients with cerebellar ataxia based on single-joint

arm movements (Brown, Hefter, Mertens, & Freund, 1990) have provided a precise

description of the alteration of the temporal structure of these movements. While pa-

tients preserved the linear relationship between peak velocity and movement ampli-

tude as is typical for normal subjects, the speed profiles were asymmetric, with alonger deceleration phase. The asymmetry of the speed profiles was also observed

in multi-joint arm movements (Becker, Kunesch, & Freund, 1990, 1991), together

with an inability to reproduce the same movement direction from trial to trial.

Joint-kinematic and EMG analyses in throwing movements (Becker et al., 1990) re-

vealed a defective coordination among agonist and antagonist muscles, and among

the different joints.

In general, multi-joint movements tend to enhance pathological features of the

movements such as the incoordination of shoulder and elbow joints, the curvatureof hand paths, and dysmetria (Bastian, Martin, Keating, & Thach, 1996; Gordon,

Ghilardi, Cooper, & Ghez, 1994). These authors found evidence that speed asymme-

try is mainly due to an abnormal timing between the different joint rotations, because

the individual joints exhibit almost normal angular speed profiles. They also pointed

out the importance of interaction torques, that is the components of joint torques

associated with the multi-link structure of the human arm, consisting of a combina-

tion of centripetal, Coriolis and inertial components. These torque components need

to be explicitly accounted for by the controller, otherwise the resulting trajectorieswould be significantly distorted. A related observation is that in healthy subjects

the total muscle torque in each joint is highly correlated with the interaction torques

whereas in cerebellar patients this correlation is absent. This finding can be inter-

preted as a result of a defective compensation of interaction torques (which only oc-

cur in multi-joint movements). Moreover, Massaquoi and Hallett (1996) found that

movement inaccuracies related to partially unaccounted interaction torques are also

present, in healthy subjects performing fast movements, even though its extent is

much smaller.

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 191

Another typical feature of many cerebellar patients, viz. the decomposition of

movements into separated segments (Bastian et al., 1996; Topka, Konczak, & Dich-

gans, 1998; Topka, Konczak, Schneider, Boose, & Dichgans, 1998), can also be as-

sociated with interaction torques because by moving the joints one at a time such

torques can be eliminated. In fact, interaction torques express the dynamical cou-pling among the joints due to the biomechanics of the arm, and uncoupling the joint

motions by whatever mechanism may contribute to reduce the effects of these inter-

action torques. On the other hand, neutralizing interaction torques by means of

movement decomposition has the obvious drawback of worsening the overall

smoothness of the movement patterns. Also the recent finding by Boose, Dichgans,

and Topka (1999), that in cerebellar patients there is a deficient level of phasic muscle

forces, can be attributed to a defective compensation of interaction torques, partic-

ularly in the higher speed part of the movements.Summing up, the reported studies provide a reliable background for the present

focused, quantitative assessment of the movements of patients with cerebellar ataxia

followed by a model-driven interpretation of the defining features of this particular

motor impairment.

2. Methods and experiments

To investigate this problem (see also preliminary reports in Sanguineti, Spada,

Baratto, Morasso, & Sarti (1999) and Solaro et al. (2000)) we performed an exper-

iment with seven patients (48� 11 years of age; two males and five females), six with

idiopathic cerebellar ataxia (IDCA) and one with Friedreich�s ataxia (FRDA). Theirperformance was compared with young controls (nine subjects, 33� 10 years of age,

seven males, two females). Diagnosis of FRDA was confirmed by genetic analysis.

Diagnosis of IDCA was based on neuroradiologic evidence of cerebellar atrophy,

negative genetic analysis for spino-cerebellar ataxias (SCA1–6), and absence of toxicor metabolic causes. Experiments were carried out at the Bioengineering Center of

the Hospital La Colletta, and all subjects were informed about the purpose of the

study and gave their informed consent in agreement with the regulations of the hos-

pital.

Subjects sat on a chair in front of a grid of six circular targets (1 cm size), arranged

in two rows on an horizontal table at the level of the shoulder joint. (See Fig. 1, left

panel; the target distance was 17 cm in the medio-lateral direction and 26 cm in the

antero-posterior direction.) Torso, wrist and finger movements were restrained, andthe forearm was suspended from the ceiling in order to restrict the motion to planar

two-degrees-of-freedom patterns without the influence of gravity. The position of the

subjects was adjusted in such a way that, with the finger pointing at the center of the

grid, the elbow and the shoulder joints were flexed about 90� and 45�, respectively.Subjects were requested to perform fast and accurate point-to-point reaching move-

ments, under visual control. The experiment included four blocks of trials involving,

respectively, the following pairs of movements: (1) from target 2 to target 6 and

back; (2) from target 2 to target 4 and back; (3) from target 2 to target 5 and back;

192 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

(4) from target 4 to target 6 and back. It is worth noting that in this way the experi-

ments involved movements with four different starting positions. Subjects had to

rest for at least 1 s before initiating backward movements. Each pair of movements

was repeated 5–10 times. The four movement patterns were executed in the order just

described and the command for each movement was given verbally by the experi-

menter. The experimental protocol was applied to both arms.Arm trajectories were recorded by means of a stereo-photogrammetric system

(MacReflex, Qualisys) with two cameras; three reflective markers were placed, re-

spectively, at the shoulder, the elbow and the finger tip. The recorded trajectories

(sampled at 50 Hz), together with an estimate of the anthropometric parameters,

allowed a full kinematic and kinetic analysis of the movements.

Fig. 1 compares the performance of two typical subjects for a subset of the re-

corded movements. Visual inspection of the data shows that the performance of nor-

mal subjects (central panel) is characterized by straight trajectories with a symmetric,bell-shaped speed profile (Morasso, 1981). Cerebellar subjects (right panel) have a

number of abnormal features: (i) longer duration, (ii) asymmetry of the speed profile

with a prolonged deceleration phase, (iii) lateral deviations in the hand path that de-

pend on the movement direction, (iv) reduced smoothness of the trajectory. In order

to translate these qualitative observations into quantitative estimates, the data were

analyzed by computing a suitable set of indexes of movement coordination:

1. Linearity index, or indicator of path curvature, defined as the percent increment ofthe total length of the hand path with respect to the nominal movement amplitude.

2. Smoothness index, computed as the logarithm of the normalized time integral of

the squared norm of the jerk (third time derivative of hand trajectory). The mo-

tivation of this choice is that in reaching movements, hand trajectories seem to

minimize the jerk integral (Flash & Hogan, 1985).

Fig. 1. Planar reaching movements. Left panel: schematic experimental setup. Central panel: hand trajec-

tories (top) and speed profile (bottom) in a typical control subject. Right panel: hand trajectories (top) and

speed profile (bottom) in a typical cerebellar patient.

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 193

3. Asymmetry index, related to the shape of the speed profile: it was computed by

detecting the time of peak velocity and dividing the duration of the deceleration

phase by the duration of the acceleration phase.

Finally, we analyzed the data in order to compare patients and controls from thepoint of view of the organization of the control system. In particular, we defined two

simple indicators:

1. Indicator of early inaccuracy, computed by considering the aiming error, i.e. the

angular difference between the starting direction of the hand trajectory (estimated

by linear regression over the first 120 ms of movement), and the direction of the

target point. As in the initial part of the movement there is no time for feedback

intervention, we may take this indicator as a measure of inaccuracy of the feed-forward component of control. In particular, we estimated the overall size of

the error, by computing the standard deviation of the error distribution over

all movement directions, as well as the dependence of the aiming error upon

the different movement directions.

2. Indicator of inaccurate corrective control, computed as the ratio of the jerk inte-

grals computed, respectively, over the deceleration and the acceleration phases.

Fig. 2. Distribution of the linearity index in cerebellar and control patients. Triangles (M) and squares (�)

denote, respectively, left and right hand movements.

194 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

This indicator, first proposed by Smith et al. (2000), is motivated by the observa-

tion that, if the corrective responses to self-generated errors were inappropriate,

they would result in a decreased smoothness in the late part of the movement.

In other words, this indicator may be seen as a measure of the ability of the feed-

back component of the control to deal with movement errors.

For each index, we performed a 3-way ANOVA, involving one between-subjects

condition (disease: cerebellar vs. control) and two within-subjects conditions (hand:

dominant vs. non-dominant; trajectory: eight different paths), and took p < 0:05 asthe limit for significance. In the case of the aiming error, we also performed a 2-way

ANOVA (disease and hand) on its standard deviation, computed over the different

trajectories. This can be considered as a measure of how much the aiming error

changes with the different movement directions.

3. Results

Figs. 2–4 show the distribution of the indexes of movement coordination defined

in the previous section. Statistical analysis of the data confirmed what was expected,

Fig. 3. Distribution of the smoothness index (jerk integral) in cerebellar and control patients. Triangles

(M) and squares (�) denote, respectively, left and right hand movements.

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 195

i.e. that cerebellar patients have significantly more curved (24.9% vs. 4.13%,

F ð1; 14Þ ¼ 12:26; p < 0:0035) and less smooth (8.28 vs. 5.66, F ð1; 14Þ ¼ 60:46;p < 0:00001) hand paths, with a more asymmetric (1.92 vs. 1.25, F ð1; 14Þ ¼ 26:93;p < 0:00001) speed profile. However, the right panel of Fig. 4 also shows that, al-

Fig. 4. Distribution of the asymmetry index (ratio of the durations of the deceleration and the acceleration

phase) in the patients and controls (top panel). Triangles (M) and squares (�) denote, respectively, left and

right hand movements. The bottom panel shows the relation between the acceleration phase and deceler-

ation phase in the patients (j,N) and the controls (�,M). The 45� dashed line would correspond to move-ments with the asymmetry index equal to 1.

196 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

though in patients the speed profile is more asymmetric and the total movement du-

ration is significantly longer (0.727 vs. 1.24 s, F ð1; 14Þ ¼ 63:70; p < 0:00001), the ef-fect is less marked in the acceleration (0.325 vs. 0.447 s, F ð1; 14Þ ¼ 21:91; p < 0:0004)than in deceleration phase (0.398 vs. 0.781 s, F ð1; 14Þ ¼ 63:64; p < 0:00001). Thissuggests that in cerebellar patients the timing of the later part of the movement ismore affected than that of the initial one.

While there were no significant effects of hand dominance, significant effects of the

trajectory direction were found in the linearity (F ð7; 98Þ ¼ 2:15; p < 0:0457),

Fig. 5. Indicator of early inaccuracy. Evaluation of the ‘‘size’’ of the aiming error in the patients and con-

trols, averaged over all the movement directions (top panel), computed as the standard deviation of the

distribution. In the bottom panels the average aiming error is plotted against the movement direction (with

respect to the medio-lateral axis): controls in the left part of the panel; patients in the right part. Triangles

(M) and squares (�) denote, respectively, left and right hand movements. The dashed line (zero aiming

error for any movement direction) would indicate a perfect calibration of the feedforward motor com-

mand, at least in the initial part.

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 197

smoothness (F ð7; 98Þ ¼ 10:58; p < 0:00001), and asymmetry indexes (F ð7; 98Þ ¼3:26; p < 0:0038); in the total duration (F ð7; 98Þ ¼ 14:47; p < 0:00001), as well asin the durations of the acceleration (F ð7; 98Þ ¼ 10:88; p < 0:00001) and of the decel-eration phases (F ð7; 98Þ ¼ 6:85; p < 0:00001). In the case of durations, the effect islikely to be a consequence of the Fitts� law (smaller durations correspond to shorterpaths); in the case of the other indexes, the dependencies on trajectory do not suggest

any clear interpretation and we put them aside in the context of this study. Signifi-

cant group interactions were also found in those indicators which relate to the timing

of the movement. In particular, in the asymmetry index there is a significant disease–

hand–trajectory interaction (F ð7; 98Þ ¼ 2:25; p < 0:036), whereas in total and accel-eration duration there is a significant disease–trajectory interaction (F ð7; 98Þ ¼ 2:25;p < 0:036 and F ð7; 98Þ ¼ 2:642; p < 0:015, respectively). Total duration also displaysa significant hand–trajectory interaction (F ð7; 98Þ ¼ 2:189; p < 0:042).

Fig. 6. Indicator of corrective control. Scatter diagram of the jerk integral in the initial part of the move-

ment (pre-peak) vs. the jerk integral in the late part of the movement (post-peak). Open and filled triangles

and squares indicate, respectively, control and cerebellar subjects. The 45� dashed line would indicateequal pre- and post-peak jerk integrals.

198 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

Fig. 5 shows the results concerning the early inaccuracy indicator. The size of the

aiming error is obviously much larger in the patients than in the controls (top panel).

However, if the errors are plotted as a function of the movement direction (bottom

panel), the resulting patterns are similar: the errors are positive for positive directions

and negative for negative directions – angles are measured with respect to the medio-lateral axis (X ). Statistical analysis confirms this empirical observation: the aver-age aiming error (i.e. the aiming bias) is quite small, and does not significantly differ

between patients and controls, as well as between dominant and non-dominant

hands. However, there is a marked effect of trajectory direction (F ð7; 98Þ ¼ 9:54;p < 0:00001), whose range of variation, as shown in Fig. 5 (top), differs signifi-

cantly in patients and controls (26.4� vs. 10.7�, respectively; F ð1; 14Þ ¼ 13:21;p < 0:0027).Fig. 6 displays the results for the corrective control indicator and, in a sense, ex-

tends the finding of Fig. 3 that in cerebellar subjects the hand paths are less smooth.

By itself, this feature might be attributed to unspecific factors of performance degra-

dation, such as a higher level of noise in the control system. However, Fig. 6 allows

us to go one step further, because it shows that degradation of smoothness affects in

the same way the acceleration and the deceleration phases. This finding supports the

view that, in addition to larger noise levels in the system, feedback control is not spe-

cifically disrupted in cerebellar patients, as defective feedback control would predict

a variation of jerk in the later part of the trajectory.

4. Discussion

In summary, the above results suggest that kinematic analysis, in spite of its sim-

plicity, is sensitive enough to detect subtle abnormalities in movement coordination,

which cannot be revealed by standard neurologic examination. It is also worth men-

tioning that, although significantly �abnormal�, the movement patterns of the pa-tients are rather consistent and repeatable. Thus the source of abnormality, in

addition to some kind of excess �noise�, must also have a �cybernetic� nature relatedto the organization of the motor controller.

4.1. Toward a cybernetic interpretation

In Section 1, we already mentioned the plausible coexistence in the motor control

system of feedforward and feedback modalities. If this is true, then both control mo-dalities may use some form of �internal model� of the body (Bhushan & Shadmehr,

1999). In particular, two kinds of internal models may be identified: a forward and a

backward or inverse model (Fig. 7).

A forward internal model is a set of neural circuits which can predict the fu-

ture state of the body, starting from a copy of the motor command (the efference

copy) and the available sensory information (visual, proprioceptive, tactile). In con-

trast, an inverse internal model is capable of determining the motor commands

required to go from the specified present state to a future state. Several studies

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 199

(Flanagan & Lolley, 2001; Gribble & Ostry, 1999; Lackner & Dizio, 1994, among

others) have demonstrated that the brain is able to anticipate with precision and

compensate for the dynamic features of arm movements such as inertial, Coriolis

and centripetal forces. An inverse internal model is the main component of a feed-

forward controller, whose aim is to produce suitable control patterns, uðtÞ, on thebasis of a desired state trajectory, xdðtÞ. This control modality may, in principle, al-low the actual trajectory, xðtÞ, to track xdðtÞ without using the available sensory in-formation about the actual movement outcome, i.e. in a open-loop modality of

operation. Although deprived of a direct control function, sensory information still

has a role in the adaptation of the control and planning modules to changes in the

body or the environment.

In contrast, in a feedback controller motor commands are generated on the basis

of real-time estimates of the error between the desired and the actual trajectory. One

major problem with feedback control is the transmission delay with which sensory

information is made available to the controller. Basic system theory predicts that thisdelay, if exceeding a critical value 1 and left uncorrected, would inevitably cause in-

stability of the control system. To prevent this, a forward model is necessary, with

the purpose of compensating the delays by means of a mechanism of prediction of

the current state on the basis of the delayed sensory afference and the concurrent ef-

ference copy. The notion that the brain uses forward models is supported by studies

Fig. 7. Schematic diagrams of feedforward control (top) and feedback control (bottom) of movements.

Feedforward control requires an inverse model of the body, feedback control a forward model.

1 A propagation delay yields a phase shift which is proportional to frequency. The condition of stability

of a closed loop system is that such phase delay, added to the phase delays induced by the mechanical and

neural transfer functions in the loop, must not exceed 180� at the frequency for which the loop gain is 1.

200 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

of patterns of motor responses to perturbations (see e.g. Desmurget & Grafton,

2000; Wolpert, Miall, & Kawato, 1998).

Studies on motor learning have shown that separate kinematic and dynamic mod-

els are constructed simultaneously based on errors computed in different coordinate

frames, and possibly, in different sensory modalities, using separate working-mem-ory systems (Krakauer, Ghilardi, & Ghez, 1999). This suggests that they involve,

at least partly, different anatomical structures. According to this computational de-

scription of the motor system, a deficit in movement execution may due to the abnor-

mal behavior of any of the neural components, as well as the corresponding

interconnections. Therefore, it makes sense to devise experimental protocols that at-

tempt (i) to dissociate the contributions of the different components of control (i.e.

feedforward and feedback), (ii) to assess the effects of their abnormal behaviors,

and (iii) to characterize the degree of adaptivity of the corresponding internal mod-els. For example, Smith et al. (2000) have shown that Huntington�s disease is char-acterized, at onset, by a defective behavior of the feedback component of movement

control, whereas the feedforward component appears to be intact. With regard to

cerebellar ataxia, the findings of Bastian et al. (1996) and those of Boose et al.

(1999) point to abnormalities in the internal representations of body dynamics,

but do not clarify whether the disorder involves the feedforward or the feedback

component of control (or both).

4.2. Feedforward control

Based on the assumption that the early phase of a movement is exclusively under

feedforward control, our finding of an abnormal movement initiation suggests that

the feedforward component of control is significantly affected in patients with cere-

bellar ataxia. Information about the nature of this abnormality may come from the

analysis of the relationship between the pattern of aiming errors and the directional

characteristics of the arm inertia tensor. In the case of a planar arm with two de-grees-of-freedom, the principal axis of the corresponding inertia ellipse is aligned

with the forearm (Winter, 1990): 2 see Fig. 8, top panel. In this direction the force

and acceleration vectors are collinear, whereas they are not collinear in the other di-

rections. This means that, if a force vector is generated in a given direction, the cor-

responding acceleration vector has a sideway component which tends to deviate the

movement from its intended path, with the exception of the principal directions.

If Fig. 5 (bottom panel) is re-plotted in such a way to display, for each subject, the

relationship between the aiming error and the movement direction relative to theprincipal direction of the inertia ellipse, we can see that the error tends to vanish in

the principal direction and is characterized by sideways deviations in the other direc-

tions which are consistent with the directional characteristics of the inertia (see Fig.

8, bottom panel). Remarkably, the trend emerges from the data in spite of two

2 Note that the orientation of the inertia ellipse is determined only by mechanics and has nothing to do

with the physiology of muscles and/or the motor control strategy.

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 201

potentially disturbing features of the experimental protocol: (1) the fact that the re-

corded movements had four different starting positions and thus four different orien-tations of the inertia ellipse; (2) the fact that the movement sequence was not

randomized and the same back-forth pattern was repeated several times. It is known

indeed (Ghilardi, Gordon, & Ghez, 1995) that learning visuomotor transformations

may produce directional biases in different parts of the workspace. Thus, the rela-

tionships between the aiming errors and the directional characteristics of the arm in-

ertia seems to be a robust effect that supports the hypothesis of a biomechanic

explanation, related to the cybernetic task of compensating the interaction torques.

This finding also rules out interpretations of cerebellar deficits based on an inabilityto generate sufficiently large torques, because in this case the largest errors would be

expected in the principal direction. Moreover, we can observe from the data that

both patients and controls exhibit a similar pattern of aiming errors, and this fact

further support the above interpretation.

4.3. Feedback control

The indicator of inaccurate corrective control does not suggest any specific prob-lems in on-line corrections in response to self-generated trajectory errors. As ex-

Fig. 8. Top panel: orientation of the inertia ellipse. Bottom panel: dependence of the aiming error on the

direction of the movement with respect to the principal axis of the inertia ellipse, which is aligned along the

forearm.

202 V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205

plained in Section 2, a post-peak to pre-peak jerk ratio greater than one would reflect

abnormal feedback control. However, from this finding alone it cannot be concluded

that feedback control is normal in cerebellar subjects. More direct experiments

would be necessary, involving external rather than self-generated perturbations.

4.4. Motor learning

As a final point in the discussion of a cybernetic interpretation of the kinematic

features of the movements of patients with cerebellar ataxia, we wish to briefly con-

sider the computational problem of motor learning, particularly as regards the in-

verse dynamic model used by the feedforward control scheme. A leading proposal

in the literature on motor learning is the feedback error learning hypothesis (Kawato

& Gomi, 1992). The main idea of this mechanism is that two controllers operate inparallel: a basic (imprecise) feedback controller and a trainable feedforward control-

ler. The former controller operates as a bootstrap system which is progressively

taken over by the latter one as the training proceeds (Fig. 9). The scheme is plausible

because it is self-organizing, without any need of an external teacher. However, the

implementation with the �biological hardware� is rather unfeasible due to the

substantial transmission delays in the feedback loop that would probably cause an

instability of the controlled system without compensation of the delays. A straight-

forward alternative is to substitute the explicit feedback loop with the implicit feed-back provided by the tunable stiffness of the muscles, which has the obvious

advantage of being instantaneous and computationally �cheap�. In the original feed-back error learning scheme the learning signal is the output of the standard control-

ler, whereas in the proposed modification it is the result of the corollary discharge,

i.e. the difference between the efference copy and the reafferent sensory information.

A null or small difference would signal a well learned feedforward controller. In

Fig. 9. Classic feedback error learning scheme.

V. Sanguineti et al. / Human Movement Science 22 (2003) 189–205 203

other words, the intrinsic muscle feedback, due to the viscous–elastic nature of mus-

cle forces, might operate at the same time as a zero-lag approximate load compensa-

tor and, via the sensory reafference, as an effective load estimator.

5. Concluding remarks

The proposed method of analysis of reaching movements, based on the estimation

of simple indicators, provides a robust experimental framework for complementing

currently available rating scales of cerebellar ataxia with quantitative measurements.

The proposed cybernetic interpretation is a plausible starting point because, in our

opinion, measurements are of little help, even in clinical research, unless they are

given sense by plausible computational models which are the guide for analyzingthe data and planning future experiments.

Acknowledgements

This research was supported by grants of the Italian Ministry of Research, and

the Italian Multiple Sclerosis Foundation.

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