Assessment of human hemiplegic spasticity by a resonant frequency method

Clinical

Biomechanics

1988; 3: 173-l 78

Assessment of human hemiplegic spasticity by a resonant frequency method M Lakie PhD E G Walsh* G W Wright* Department *Department

MD FRSE

of Biology

and Preclinical

of Physiology,

Edinburgh

Medicine, University

University Medical

of St Andrews, School,

Fife, Scotland,

Edinburgh,

Scotland,

UK. UK.

Summary The resonant frequency of the wrist has been measured in hemiplegic subjects and was higher on the spastic side, indicating greater stiffness. The increased stiffness is associated with stretch reflex activity, which is absent in normal subjects. The increased stiffness of spasticity in most of the patients did not exaggerate the sharpness of tuning as there was a compensatory rise in damping. Increased damping will contribute to the subjective assessment of muscular hypertonicity. Measurements of resonant frequency and damping are essential in assessing muscular hypertonicity.

Relevance A method for investigating the muscular hypertonicity of spastic hemiplegic patients is described. Such a method is very useful for monitoring long term changes in the condition, or for quantifying the effects of drug therapy or physiotherapy. Key words: Hemiplegic

spasticity, Resonant frequency,

Stiffness, Hypertonicity

Introduction The assessment of muscle stiffness (tone) by instrumental means has attracted considerable attention since the original observations of Mosso’. He used weights and a pulley to dorsiflex the ankle. One test sometimes used to assess spasticity was devised by Wartenburg’, a method recently extended”. The person being investigated lies on his back on a couch and the foot of the side under examination is swung as a pendulum about the knee, coming to rest after a few oscillations. In spasticity the oscillations are more rapid. The procedure has the merit of simplicity, but interpretation is complicated because the restoring force due to the musculature cannot readily be separated from the restoring force due to gravity. A more satisfactory elementary method which has been used for assessing hip stiffness is to take the weight of the limb by a cord fastened to the ceiling, so that it is free to oscillate about the hip in the horizontal plane without S~thmittedc19 October

1987 Retwxed for revision: 26 November 1987 Accepted; 21 January 1988 Correspondence and reprint requests to: Dr E G Walsh, Department of Physiology, University Medical School, Teviot Place, Edinburgh EH8 9AG, UK @ 1988 Butterworth & Co (Publishers) Ltd 0248~033/88/030173 -06 $03.00

rising and fallingA. The restoring force is then purely due to the stretching of the musculature and a more rigorous analysis is possible; the method has not so far been applied to the analysis of spasticity. Both techniques can only be applied to the parts of the body which are significantly underdamped. Carmichael and Green’ attempted to measure muscular hypertonus of the arm by moving the limb with a falling weight. Timberlake’ also used a gravity driven ergograph, but the methods seem to have had only a modest success. Similar limitations evidently arose in a method devised by Springer’. In this, a light hammer rebounded from the biceps muscle. The time of the rebound was measured electrically and was found to be faster with stiffer muscles. Kerr and Scott* measured the pressure in muscles by a saline-filled manometer, the idea being that the greater the tonus the greater the pressure. Such quantitative information is valuable in the evaluation and treatment of patients suffering from muscle hypertonia of various pathological types. Stiffness, defined as stress/strain, can be measured in two ways, either by the imposition of position changes or the application of controlled forces to the limb. The first approach has been referred to as ‘stretching’ and the second as ‘pulling’“. Work with the muscles of the decere-

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brate cat has revealed different results using these alternative procedures. With ‘stretching’ the limb is usually coupled to a powerful geared electric motor, which moves the limb to and fro while the reactive tension generated between the limb and the instrument is measured (e.g. ‘” and ‘I). This method imposes a limit on the frequency and velocity that can be used; the effect of inertia increases with frequency, and a movement of 1 radian, which might be reasonable at 0.5 Hz, would be potentially damaging at 5.0 Hz. We have recently employed the alternative strategy, using rhythmic ‘pulling’ to study wrist muscle tone in normal subjects”. As the size of the movement is not fixed, high frequencies can be studied. This technique has revealed the existence of striking thixotropic effects, for under certain conditions the stiffness of the wrist depends on the past history of movement. Thus a single perturbation may loosen the system and several seconds of rest may be needed for the initial stiffness to be fully regained. If the hand has been immobile for 2 seconds or more the system is very stiff when small forces are applied. If, however, the limb is maintained in almost continuous rapid motion its apparent stiffness is much reduced. Similar results have been reported at the elbow where ‘a major component of stiffness appears to decay within 1 s”‘. The slow movements necessarily used with stretching instruments would be such that significant thixotropic stiffening would occur and the calculated stiffness that these techniques yield may be much greater than that obtained by a pulling technique. Some of the complex properties of muscle are consequently masked by a stretching approach.

Methods varying torques at freWe have applied sinusoidally quencies up to 15 Hz and recorded the resultant rhythmic excursions of position and velocity. In normal subjects there is invariably a resonance with maximal motion at about 2-2.5 Hz: voluntary stiffening raises the resonant frequency to a degree that is dependent on effort. A primary purpose of the present investigation was to establish whether a corresponding elevation of resonant frequency is found in hemiplegic patients. As the inertia of the moving parts in any one subject does not change. the resonant frequency reflects the component of stiffness which is behaving in a spring-like manner. The normal wrist has been shown to behave as a torsional pendulum. The standard formula has been found to be a most useful description of the biodynamics over a wide range of oscillation amplitudes”. It is:

where f is the resonant the inertia.

frequency,

K the stiffness

and J

Some of the resistance to movement is not due to spring properties but to damping. Opposing forces are generated proportional to the velocity of movement. Such viscous resistance can also be evaluated by this method, for at resonance the effects of K and J are equal and opposite and the motion is constrained solely by the damping. In this study we have compared the stiffness and damping of paralysed and normal limbs. For these experiments use is made of a ‘printed motor’ - type G9M4 (Printed Motors Ltd). Such a device transmutes electrical currents into the corresponding torques; the properties of these motors were discussed by Knights”. The moving parts are light, for the armature consists solely of a plastic disc on which are positioned flat copper wires (Figure 1). As there is no iron in the armature the inductance is minimal. The use of rapidly alternating currents is thus not impeded. The hand is coupled to the motor, which provides the force and which is equipped with a potentiometer for recording the resulting oscillation in the horizontal plane. The motor is supplied with sinusoidal currents of exponentially rising frequency. Recordings of the e.m.g. are obtained with suction cup electrodes. For the right side an upwards movement of the torque, position or velocity trace corresponds to extension (flexion for the left side). The use of this procedure for studying normal subjects has been described in detail”. Thirteen children aged S-15 were tested and were at the same time examined neurologically. The patients had dense hemiplegia; voluntary movements were absent or very slow and laboured. Twenty-one adults, up to 72 years old, were also studied; some investigations were repeated over a period of 5 years. None were in the acute phase and all the patients investigated were on a clinical ‘plateau’. The control group was the unaffected limbs of the hemiplegic patients; there are known

Figure 1. Part of the armature of a printed motor. Current is taken to the wires by carbon brushes and the armature is in a strong magnetic field. The passage of the current produces a corresponding turning moment.

Lakie et al.: Human

to be some neurological abnormalities in the nonaffected limbs of certain hemiplegic patients but comparison with data from normal age-matched controls revealed no differences. Patients who presented with wrist clonus or subclonic reflexes were excluded from the series.

Table 1. Resonant frequencies hemiplegic children

No.

Results Resonant frequency The phenomenon under investigation is illustrated in Figure 2. The peak level of force applied to the limb remains constant throughout the sweep but the rate at which it is applied varies. This form of torque input is referred to as a ‘chirp’. At the resonant frequency the motion is greatest and the oscillations of position and velocity reach a maximum. In this example the spasticity is quite minor; the elevation of resonant frequency above normal is small but definite. Sometimes we recorded the phase. Below resonance, torque lagged behind velocity; at resonance, torque and velocity were in phase whilst above resonance, torque led velocity. The resonant frequency of the normal side was in general substantially lower than that of the paralysed side. Such differences are illustrated in Figure 3. The rate at which the frequency rose could be varied over a wide range. For the purpose of illustration relatively rapid rates are shown in Figures 2 and 3. The resonant frequency measured at much slower sweep rates was identical. Over a wide range the results are insensitive to the variation of the experimental conditions in this way. TtwmlcN

10.5

-

N m

Il.0

-

rad

11 rad

1.0

Is

s

Figure2.A’chirpf.Asinusoidallyvaryingforcewhich has a fixed maximum value and an exponentially increasing frequency is applied to the wrist. The resonant frequency (where the oscillations of position and velocity are maximal) is 2.7 Hz in this slightly spastic subject; the nonaffected side was 2.0 Hz. Bursts of firing phase locked to the motion are visible in the flexor e.m.g.

Ex emg.

FIemg.

p 1.0

s

Figure3. The normal limb compared with the spastic. The spastic wrist (rightpanel) has a considerably higher resonant frequency and there is activity in flexor and extensor e.m.g. which is absent on the normal side.

9 10 11 12 13

hemiplegic

spasticity

of the wrist of 13

Side of Resonant frequency (H,) lesion Hemiplegic Normal side side

Sex

Age

M F M F M M F F

5.5 8 10 10 13 14 15 15

R R R R R R R R

4.5 3.0 3.5 7.0 7.5 2.0 6.0 3.5

2.5 2.5 3.0 2.5 1.5 2.0 2.2 2.0

F F F F M

6 7.5 13 15 15.5

L L L L L

9.5 7.5 5.0 2.5 2.5

2.5 3.0 2.5 2.0 2.0

Mean + sd.

175

4.9k2.3

2.3kO.4

For 13 children who were tested in this way the resonant frequency was compared with that of the normal side (Table 1). The clinical findings with this group of patients are described elsewhere’“. The mean values show that on average the frequency on the spastic side has rather more than doubled; the stiffness has thus increased fully 4-fold. The difference in the mean values is highly significant. (Using the f-test, P~0.01.) There is naturally a scatter of results in the hemiplegic limbs depending on the severity of the condition: this is much greater than the scatter of data from the normal wrists. Above a certain level of peak torque the resonant frequency is constant at about 2.2 Hz in normal wrists and the system is linear. With small peak forces, however, the normal wrist stiffens and the resonant frequency rises (Figure 4, right). This rise reflects intrinsic properties of the tissues, for it occurs in anaesthetised and The discontinuity is very clear paralysed patients”. when period (at resonance) is plotted against torque. The change in properties is the justification for describing the results in terms of two lines. We examined 21 adult hemiplegics at seven levels of peak force. The results (Figure 4, left) show that the mean values are clearly greater than the normal values. As the resonant frequency was essentially the same at all levels of force, the limb was behaving in a linear manner and not stiffening progressively as the movement became smaller, as it does in normal subjects; this is evidence that Hooke’s law is obeyed. It follows that equation (1) (above) is applicable. Not all subjects with hemiplegia are spastic; our series included some usually termed hypotonic, although the resonant frequency was never below the normal range and this word may thus be misleading. It is usual in neurological literature to refer to muscle tone as increased, normal or decreased. We have already thrown doubt on whether there can ever be an acute

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reduction in muscle tone below normal for the resonant frequency of the wrist is not lowered by anaesthesia and neuromuscular blocking drugs”. The situation may of course be different in chronic conditions if there is muscle wasting. Electromyography

The procedure in normal people is commonly associated with virtual silence in the e.m.g., and it is generally recognized that normal people at rest shut off any neural discharges to supported limbs. Sometimes, however, the e.m.g. shows shortening reactions. When the hand is swung into extension the extensors become active; when swung into flexion the flexors become active. We believe from our earlier studies that this activity takes in the slack in the musculature, but has only trivial biomechanical effects. The shortening reactions in any event only occur with the larger peak torques, in the neighbourhood of resonance when the swings are large and the velocity high. A different form of e.m.g. activity was regularly seen in patients with paralysed limbs. The most characteristic feature was a rhythmic modulation of flexor activity which occurred at the rate of the applied force close to resonance (Figures 2 and 3). Sometimes this modulation was seen throughout most of the chirp. At times there was continuous tonic activity in the flexor musculature on which the modulation was superimposed. The timing of the modulation at, or close to, resonance showed that it occurred as the muscle was being stretched and it represented stretch reflex activity. Stretch reflex activity is never seen in normal relaxed subjects. In the extensor musculature the discharges were variable and often inconspicuous. In keeping with the tonic activity in the flexor musculature, most of the wrists showed some tendency to be

flexed when free to move and supported in the horizontal plane by the apparatus. In some patients the flexed position was striking. We have repeatedly observed the effects of voluntary stiffening of the wrist in normal people. There is co-contraction of the flexor and extensor musculature and with moderate degrees of stiffening the resonant frequency rises. Accentuation of the stretch reflexes does not occur with voluntary stiffening. The spastic state is thus very different from that of a voluntarily stiffened limb. Damping

In assessing muscular stiffness by manipulation the physician will be influenced not only by the elasticity of the muscles but, inter alia, by the viscous resistance which controls the damping in the system. The wrist evidently behaves as a second order resonant system; the mathematics involved has been well established by engineers I6. The sharpness of tuning (Q) is given by the equation:

where c is the damping coefficient. At resonance the amplitude of the motion is dependent solely on the damping. The damping coefficient is the ratio of the force applied to the velocity attained. If the damping was constant, the peak velocity would remain the same with varying degrees of stiffness. We have accordingly divided the velocity at resonance on the normal side by that on the hemiplegic side at the same peak force level. The value thus obtained expresses the damping in terms of normal. The results with eight children are shown in

10

10

9

9

8

8

7

7

6

6

5

5

L

L

3

3

2

2

1

1

0

0.1

0.2 Torque

0.3

0.4

0

0.1

(N m)

Figure4. Resonantfrequencyversus torque, whereas normal subjects falls below about 0.2 Nm.

0.2 Torque

peaktorque. The spastic limbs (IeftJshow stiffen considerably (shown by an elevation

littlevariation of resonant

0.3 (N

0.L

ml

of resonantfrequencywith frequency) when peak torque

Lakie et al.: Human hemiplegic

Figure 5. The damping increases with increasing resonant frequency. It is possible that this is due to the phasic stretch reflexes seen with electromyography, for these will provide negative velocity feedback. This change in c offsets the effects of increasing stiffness (K) in equation (2) and inspection of the records confirmed that the sharpness of tuning was little different from that of the relaxed wrist. In Figure 3 too, it will be seen that the peak velocity at resonance is lower on the spastic side. In a perfectly linear system with viscous damping there would be a linear relationship between torque and peak velocity at resonance. This is approximately the situation with normal subjects. We measured this relationship in nine adult subjects with hemiplegia and the results are shown in Figure 6. There is a slight departure from linearity, as the relationship is not a perfect straight line. Such non-linear damping does not significantly compromise the analysis of the system based on equation (1). ‘Even when the damping is known not to be viscous, approximating it as such often leads to a good practical estimate of the behaviour of the system’16.

spasticity

177

Discussion The clinician manipulates a limb to ascertain muscle tone. This apparently simple procedure is actually quite complex. In active or passive movements the following resistive forces are inevitably encountered: 1) inertia, related to acceleration; 2) elastic, related to displacement; 3) viscous, related to velocity; and 4) thixotropic, related to the history of movement. We have discussed in a previous paper” how the apparatus used here can analyse these different factors. Measurements of limb inertia and stiffness are possible by increasing the stiffness or inertia of the apparatus by a known amount and performing a simple calculation’7.‘x. Furthermore, by the use of electromyography during the examination it is possible to form a judgement as to the role of reflex action or voluntary control. The method described here can in principle be applied to any part of a limb. The procedure has previously been used to follow changes in muscle tone in Parkinsonism’” and in head injury’“. We know of no other system which has been successfully used to discriminate between these different components of muscle tone.

7-

6Damplng 250%

5Velocity rad s-’

L-

3-

2-

50%

l-

o%1

0

10

20

Resonant

I

30

frequency

40

50

squared

Figure 5. The relationship between damping (expressed in terms of normal) and stiffness (expressed as resonant frequency squared). As stiffness increases there is a concomitant increase in damping.

60

0

0.1

I

I

0.2 TORQUE Nm

Figure 6. In a linear system there is a straight line relationship between peak torque and peak velocity. relationship that is found approximates to this.

0.3

The

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C/in. Biomech. 1988; 3: No 3

There are, from the above investigations, two biodynamic parameters which are relevant to the evaluation of muscular hypertonicity. The first is the resonant frequency, related to muscular stiffness. Secondly, the peak velocity at resonance is proportional to the inverse of the damping. We have clearly shown that both the stiffness and the damping are increased in hemiplegia. The resistance felt on manipulating a limb will be related to both of these factors; both need to be evaluated in any particular patient at a number of different torque levels. None of the systems discussed in the Introduction used

References Mosso A. Description d’un myotonometre pour etudier la tonicite des muscles chez I’homme. Arch Ital de Biol 1896;25:349-84 Wartenburg R. Pendulousness of the legs as a diagnostic test. Neurology 1951;1:18-24 Bajd T. Vodovnik L. Pendulum testing of spasticity. J Biomed Eng 1984;6:Y-16 Walsh EG, Wright GW. Postural thixotropy at the human hip. J Exp Physiol 1988:73:369-77 Carmichael EA, Green FHK. Parkinsonian rigidity. A clinical and instrumental study of the effect of stramonium. hyoscine and other alkaloids. QJ Med 1928;22:51-8 Timberlake WH. Evaluation of hypertonia with the use of a gravity driven ergograph. Clin Pharm Ther 1964$(6):879-X2 Springer R. Untersuchungen uber die Resistenz (die sogenannte Harte) menschlicher Muskeln. Zeitschr fur Biol 19 14;63:201-22 Kerr JDO, Scott LDW. The measurement of muscle tonus. BMJ 1936;3:758-60 Roberts TDM. Rhythmic excitation of a stretch reflex rcvcaling (A) hysteresis and (B) a difference between the responses to pulling and stretching. QJ Exp Physiol 1963;107:328-45 10 Webster DW. The dynamic quantitation of spasticity with automated integrals of passive motion resistance. Chn Pharm Ther 1964;5(6):900-8

by previous workers has separated these factors. It is more difficult to decide how far these changes are due to reflex action - prominent in our patients - or purely due to increased motoneurone activity, except by the combination of the biomechanical and electromyographic evidence. Acknowledgements We wish to thank the Chest, Heart and Stroke Association for financial support, Dr Keith Brown (paediatric neurologist) and the patients who acted as subjects.

11 Duggan TC, McLellan DL. Measurement of muscle tone: a method suitable for clinical use. Electroencephologr Clin Neurophysiol 1973;35:654-8 12 Lakie M, Walsh EG, Wright GW. Resonance at the wrist demonstrated by the use of a torque motor: an instrumental analysis of muscle tone in man. J Physiol 1984;353:265-85 13 MacKay WA, Crammond DJ, Kwan HC, Murphy JT. Measurements of human forearm viscoelasticity. J Biomech 1986;19(3):231-8 14 Knights DE. Prospects for the printed motor. Engineer Lond 1975;215(3):199-202 15 Brown JK, van Rensburg F, Walsh EG, Lakie M, Wright GW. A neurological study of hand function of hemiplegic children. Dev Med Child Neural 1987;29:287-304 16 Burton R. Vibration and impact. New York: Dover, 1968 17 Lakie M, Walsh EG. Wright GW. Measurementsof inertia of the hand, and the stiffness of the forearm muscles using resonant frequency methods, with added inertia or position feedback. J Physiol 1981;310:3_4P 18 Walsh EG, Wright GW. Inertia, resonant frequency, stiffness and kinetic energy of the human forearm. QJ Exp Physiol 1987;72:161-70 19 Gillingham FJ. Walsh EG, Wright GW. Resonance at the wrist in parkinsonism - changes induced by stereotactic surgery. J Physiol 1974;238:37P 20 Tsementzis SA. Gillingham FJ. Gordon A, Lakie M. Two methods of measuring muscle tone applied in patients with decerebrate rigidity. J Neurol Neurosurg Psychiatr 1980:43:25-36