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RIGINAL ARTICLE

he Use of a Portable Muscle Tone Measurement Device toeasure the Effects of Botulinum Toxin Type A on Elbow

lexor Spasticity

ia-Jin Jason Chen, PhD, Yi-Ning Wu, PT, Sheng-Chih Huang, MS, Hsin-Min Lee, PhD, Yu-Lin Wang, MD

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ABSTRACT. Chen J-JJ, Wu Y-N, Huang S-C, Lee H-M,ang Y-L. The use of a portable muscle tone measurement

evice to measure the effects of botulinum toxin type A onlbow flexor spasticity. Arch Phys Med Rehabil 2005;86:655-60.

Objective: To use a portable muscle tone assessment deviceo measure spasticity after a botulinum toxin type A (BTX-A)njection.

Design: Before-after trial.Setting: Hospital.Participants: Ten chronic stroke patients with upper-limb

pasticity.Intervention: BTX-A was injected in the biceps brachii.Main Outcome Measures: The biomechanic parameters,

iscous component, and averaged viscosity derived from thecquired reactive resistance and angular displacements, as wells the reflex electromyographic threshold of biceps brachii,ere used for spasticity evaluation.Results: A statistically significant decrease in averaged vis-

osity and a significant increase in reflex electromyographichreshold (P�.05) both indicated reduction in spasticity owingo BTX-A intervention. There was no clear reflex electromyo-raphic activity detected at lower stretch frequencies.

Conclusions: Our portable design allows for the convenientse of the device for quantifying spasticity in clinics. Alluantitative measurements suggest that BTX-A decreases spas-icity within 2 weeks of injection. Our portable muscle toneeasurement device may be useful for the clinical assessment

f elbow flexor spasticity.Key Words: Botulinum toxin type A; Muscle spasticity;

ortable system; Rehabilitation.© 2005 by the American Congress of Rehabilitation Medi-

ine and the American Academy of Physical Medicine andehabilitation

PASTICITY, A COMPLEX SYMPTOM, is usually seen inpatients with upper moto neuron dysfunctions such as ce-

ebrovascular accidents (CVAs), spinal cord injuries, and mul-iple sclerosis.1,2 The mechanism of spasticity is commonlyhought of as an exaggerated stretch reflex, which is a velocity-ependent increase in the resistance to the passive move-

From the Institute of Biomedical Engineering, National Cheng Kung University,aiwan (Chen, Wu, Huang); Department of Physical Therapy, I-Shou University,aohsiung, Taiwan (Lee); and Chi-Mei Hospital, Tainan, Taiwan (Wang), ROC.Supported by the Chi Mei Foundation Hospital (grant no. CMFHR9326).No commercial party having a direct financial interest in the results of the research

upporting this article has or will confer a benefit upon the authors(s) or upon anyrganization with which the author(s) is/are associated.Reprint requests to Yu-Lin Wang, MD, Rehabilitation Dept, Chi-Mei Foundation

ospital, Yung Kang City, Tainan County, Taiwan, ROC, e-mail: d8101080@ms2.inet.net.

p0003-9993/05/8608-9557$30.00/0doi:10.1016/j.apmr.2005.03.019

ent.3,4 Spasticity in conjunction with excessive muscle tonerequently interferes with the voluntary motor function in patientsith residual muscle power, causing difficulties with daily activ-

ties. Muscle pain or discomfort, as well as contracture, can alsoccur at the joint surrounded by spastic muscles.5,6

To alleviate spasticity, various interventions such as medi-ation, surgery, and physical therapy techniques have beenommonly used.2,7 Recently, botulinum toxin type A (BTX-A)as been used for spasticity reduction because of its localizedffect and convenience.8,9 Nevertheless, in a number of ran-omized and open studies for stroke patients,3,10-13 evidenceupporting the clinical efficacy of BTX-A still is not convinc-ng, because the dosage for each person still cannot be accu-ately decided and there is a lack of a suitable assessment tool.ecent studies3,10-13 have investigated the treatment effect ofTX-A for spasticity suppression in upper limbs for adult

troke patients; however, these approaches often used func-ional outcome measures, self-report questionnaires, and mus-le force or range of motion as the semiquantitative assessmentethods. Few previous studies used quantitative assessment

echniques to evaluate the treatment effects of BTX-A in re-ucing spasticity.Previous studies14-16 have shown higher velocity-dependent

eflex response in both torque and electromyographic activityor quantifying muscle tone in spastic muscles, based on mo-or-driven systems. To assess BTX-A injection, Miscio et al17

uantified the stiffness in the upper limb of stroke patients afternterventions by using mechanical wrist displacements inducedy a torque motor. Although motor-driven muscle assessmentystems are very sensitive and accurate in quantifying velocity-ependent properties, their bulky size makes motor-driven sys-ems unsuitable for routine clinical trials.

In our previous studies,16,18 we developed a portable deviceor quantifying the velocity-dependent property of spasticity inhe upper limbs. This device shows high reliability in valida-ion studies.18 Compared with the motor-driven approach, theain feature of this portable system is that it is easily manip-

lated in the clinic for the objective quantification of the spasticlbow joint. Our aim in this study was to use the portableuscle tone measurement device, combined with surface elec-

romyography, to investigate the changes in muscle tone afternjecting BTX-A on the spastic elbow flexor.

METHODS

nstrumentThe portable muscle tone assessment device was developed

o provide precise biomechanic measurements of reactive re-istance and stretch velocity in the elbow joint during sinusoidtretches. The portable spasticity assessment device consists ofmajor parts: air bags for stretching torque and a light-weight

ensor for angular rate measurements (fig 1). The air bags arexed on both the ventral and dorsal sides of the wrist forensing reactive torque, which is recorded using a differential

ressure sensor.a We assumed that there was no relative dis-

Arch Phys Med Rehabil Vol 86, August 2005

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1656 QUANTIFICATION OF BOTULINUM TOXIN TYPE A EFFECTS, Chen

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lacement between the air bags and each subject’s limb—inther words, the moment arm was constant. Under these con-itions, the recorded differential pressure value could be takens a proportion of the reactive torque. We used light-weightngular rate sensorb mounted on the dorsal side of the middleorearm to measure the stretch velocity, which we furtherrocessed to obtain the joint trajectory. In addition to biome-hanic measurements, we recorded an electrophysiologic mea-urement of the electromyographic signals of the 2 targeteduscles, biceps brachii and triceps brachii, via 2 surface elec-

romyography electrodesc with a gain of 380 during passiveinusoid stretches of the limb. The reactive resistance, angularate, and electromyographic signals were sampled at 1000Hznd sent to a laptop computer through an analog-to-digitalonverterd with 12-bit resolution. Interfacing programs of datacquisitions were constructing using LabView,d and off-lineata were further processed and analyzed using Matlab.e

xperimental ProceduresParticipants. A sample of 10 stroke patients with moderate

o severe upper-limb spasticity was recruited in this study.ubjects had BTX-A (Botox) treatment in the Department ofehabilitation at Chi-Mei Hospital, Tainan, Taiwan. The eval-ations both before and after treatment were conducted by theame experienced physical therapist in the same consultingoom at the same time of day. Included participants (1) were ateast 6 months from the onset of CVA, (2) had no contractureround the elbow joint, (3) had no severe cognitive or affectiveysfunction, and (4) were above Brunnstrom stage III, a clin-cal criterion for evaluating the severity of the hemiplegia.19

ubjects were 36 to 70 years old (mean � standard deviationSD], 57.3�12.2y). All patients were diagnosed and evaluatedy a qualified physician before participating in the experiment.he subjects gave informed consent before undergoing BTX-A

njections, which followed the clinical protocol approved byhe Education Commission of Chi-Mei Hospital. The subjects’linical data are summarized in table 1. To avoid influencerom other treatments, subjects received the same rehabilitationrotocols before and after BTX-A injection.Treatment and evaluation. Subjects received intramuscu-

ig 1. The portable muscle tone measurement system consists ofhe air bags, a differential pressure sensor, and an angular velocityensor. The muscle activities are recorded by using 2 surface elec-romyography electrodes. The reactive resistance, angular displace-ent, and electromyographic activities are recorded by an analog-

o-digital converter during the quasisinusoidal movement limitedetween 60° and 120° of flexion by an elbow limiter. Abbreviations:D, analog-to-digital; BB, biceps brachii; EMG, electromyographicctivity; TB, triceps brachii.

ar BTX-A injections (mean dose, 57.5U; range, 25–100U) A

rch Phys Med Rehabil Vol 86, August 2005

nly to the biceps brachii and some other forearm muscles. Theocation of BTX-A injection was guided by needle electromyo-raphy, and the same physician who carried out the injectionsetermined the dose.Two assessment sessions were performed, one 2 weeks

efore the BTX-A injection and one 2 weeks afterward. Forach assessment session, the clinical scale, biomechanic, andlectrophysiologic electromyographic assessments were exam-ned. At first, the investigator assessed the subjects by using a

odified Ashworth Scale (MAS) of 6 scores (range, 0–5). Theanked scores were compared with those taken from biome-hanic and neurophysiologic measurements later.

For biomechanic assessment, subjects lay down comfortablyn a bed with slight abduction of the shoulder. Stretch reflexesere elicited by stretching the elbow in a back-and-forth man-er, approximately in a sinusoid movement. An elbow braceas used to limit the elbow’s movement range between 60° and20° of flexion with full forearm supination. In a sinusoidovement, the zero degree is defined as when the elbow is at

0° of flexion. Thus, a stretch range of �30° to �30° can beefined in which the positive direction stands for extendingrom 0° (fig 1). Before the portable muscle tone measurementystem was used, the surface electromyography electrodesere placed on the primary flexor and extensor of the elbow,iceps brachii, and triceps brachii. During the whole experi-ent, subjects were requested to relax entirely, a state moni-

ored by an electromyographic recording.Four different stretching velocities (1⁄3, ½ 1, 3⁄2Hz) were

mposed on the elbow manually. Between each trial, eachubject rested for at least 30 seconds. After a brief instructionnd with the assistance of a metronome and range limiter (anlbow brace as shown in fig 1), the investigator was easily ableo apply a regular sinusoid displacement stretch. We selectedhe stretching frequency (maximum, 3⁄2Hz; with peak velocitybout 280°/s) based on the criteria that the stretch velocity beufficient to elicit the stretch reflex in a spastic limb and notause discomfort in subjects.15

ata AnalysisOur analytic methods were designed to estimate the velocity-

ependent viscous component from the reactive torque and dis-lacement of biomechanic data, as well as to observe the stretcheflex threshold from the electromyographic data. The estimationf the viscous component is based on the relation between thexternally imposed joint displacements and the correspondingoint resistance, which is generally modeled as a second-orderystem. From the biomechanic model (appendix 1), the viscousomponents, measured at 4 stretching frequencies—that is, 1⁄3, 1⁄2,

Table 1: Summary of the Subjects’ Clinical Data

Subject Age (y) SexMonths

PostinjuryAffected

SideBrunnstrom

Stage

A 35 F 16 Right VB 64 F 31 Left VC 65 F 24 Left VD 71 M 90 Left VE 50 F 9 Left IVF 61 M 61 Left IIIG 68 M 43 Left IIIH 38 F 14 Right IIII 70 M 20 Right IIIJ 55 F 69 Left IV

bbreviations: F, female; M, male.

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1657QUANTIFICATION OF BOTULINUM TOXIN TYPE A EFFECTS, Chen

, and 3⁄2Hz—are denoted as B�1⁄3, B�1⁄2, B�1, and B�3⁄2, respec-ively. From the viscous components measured at the 4 stretchingelocities, 1 viscosity parameter (B) (see appendix 1, equation 1)an be derived from a linear fitting process for each subject. Moreetailed information is presented in our previous publication.18

For electromyography analysis to determine the stretch re-ex, the raw electromyogram was fed to a notch filter toliminate 60-Hz interference and to a band-pass (10–400Hz)lter to remove the motion artifacts and high-frequency noise.he filtered electromyographic data were processed in a linearnvelope representation20 to determine the reflex threshold. Inhe continuous sinusoid movements, we divided the electro-yographic data into extension and flexion phases. The zero

osition is defined as 90° of elbow flexion; the negative andositive values represent the corresponding flexion and exten-ion movements of the elbow. The reflex electromyographichreshold was defined as the angle at which the sustainedlectromyographic activity surpassed 3 SDs of the backgroundignal taken before stretching. The threshold electromyo-raphic activity at varied stretch velocities was normalized toe a percentage of the total range.After acquiring the biomechanic and electromyographic data

efore and after intervention, the Student paired t test was usedo compare the reflex electromyographic threshold at differentrequencies in the same subject. A nonparametric test (Wil-oxon signed-rank test) was applied to the clinical MAS scoresnd the biomechanic variables of 2 assessment stages. Com-arisons of the reflex electromyographic thresholds amongtretch frequencies and assessment sessions were performedsing the Mann-Whitney U test. P values of less than .05 wereonsidered statistically significant. The SPSS softwaref wassed to perform statistical analyses.

RESULTSTable 2 lists the MAS scores before and after intervention

or all subjects. Before injection, MAS scores ranged from 1 to(median, 3). All subjects exhibited either the same score or a

ecrease in MAS score 2 weeks after the BTX-A injection.efore treatment, 5 subjects had MAS scores of 3 and the 2

ubjects had a score of 4; after treatment most subjects (n�6)ad MAS scores of 2, and none of them had the high score of. We noted no obvious side effects in the subjects.

ssessment of Muscle Tone From Biomechanic DataWe manually applied a regular sinusoid displacement stretch

t 4 different frequencies on the subjects’ elbows. Figure 2hows a portion of the reactive resistance and displacementeasurements taken when stretched at 3⁄2Hz stretching fre-

uency. We observed that the phase lag between the angularisplacement and the reactive torque, which represents theargeted muscle, has a damper effect. The values of the phasehift can be derived from the phase spectra of both sets of data.he displacement-resistance plot and the complex modulus

Table 2: Clinical Assessment of Spastic Elbow Flexor Before (Pre)and 2 Weeks After BTX-A Injection (Post) Using the MAS

MAS Score

Subject

A B C D E F G H I J

Pre 1 2 3 1 4 4 3 3 3 3Post 1 2 2 1 3 2 2 3 2 2

OTE. Significant difference of the MAS was found using the Wil-oxon signed-rank sum test (P�.05).

lot (after � phase shift of displacement) can be observed ints

gures 2C and D. A typical subject with spasticity usuallyhows a hysteretic loop in his/her displacement-resistance plotsee fig 2C). After the calculation of the averaged complexodulus (slope of X[t��] and T[t]) and the phase lag, the

elocity-dependent viscous component (B�) can be derived.his is the index used for each stretch frequency.After obtaining the B� from 4 different stretching frequen-

ies (1⁄3, ½ 1, 3⁄2Hz), we could derive the averaged viscosity ofhe spastic muscle from the linear fitting of measured viscousomponents. Figure 3 illustrates the averaged viscosity of 2epresentative stroke patients with severe (MAS score 3) andild (MAS score 1) spasticity. Our results indicate that the

hange of viscous components in response to stretch velocity isigher (ie, at a steeper slope or more sensitive to stretchelocity) when the subject has severe spasticity. Thus, we usedhe averaged viscosity as an index for spasticity evaluationefore and after intervention.The viscous components of each subject at 4 different stretch

requencies show that the viscous component of each subjectecreases after BTX-A injection at each stretching frequency,xcept for subject I and subject F at 1⁄3 and ½Hz, respectively.he derived viscosity—that is, the slope fitting the viscousomponents across varied frequencies—is listed in table 3.omparing the preinjection values with those 2 weeks after

ig 2. Typical examples of (A) reactive resistance and (B) displace-ent measurements stretched at 3⁄2Hz. The dotted lines determinecomplete stretch cycle from the peak values of angular displace-ent. Obvious phase shift can be observed between reactive resis-

ance and angular displacement, which shows the viscous propertyf the targeted muscle. From the displacement-resistance plot (C),he viscous component can be obtained by fitting a straight line to

he displacement-resistance plot after phase shift, (D), in a typicalpastic patient.

Arch Phys Med Rehabil Vol 86, August 2005

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njection, all assessments showed a significant decrease inveraged viscosity value.

eflex Electromyographic ThresholdFigure 4 shows representative electromyographic activity insession of sinusoid stretch. Among these stretches, 15 cycles

f data were selected for determining the stretch reflex elec-romyographic threshold. We can clearly observe raw electro-yographic activity in the biceps brachii (agonist) comparedith the triceps brachii (antagonist). The electromyography

inear envelope form was used to determine the onset point ofhe reflex electromyographic activity, which is represented ashe middle vertical dotted line in figure 5. We could observe thebvious activity in spastic biceps brachii muscles at highertretching frequencies (1, 3⁄2Hz) but not at lower stretchingrequencies (1⁄3, ½Hz), at which some reflex electromyographicctivity is not evident because of lower stretch velocity. Figureshows representative examples of reflex electromyographic

ctivity in the same subject stretching at 3⁄2Hz before and afterBTX-A injection. The electromyographic threshold before

reatment occurred at 64.1% of the stretch cycle, comparedith 78.3% after treatment. This indicates that a lower thresh-ld can be found before treatment—that is, reflex electromyo-raphic activity happened earlier at a smaller stretch angle.Among the 15 cycles selected from a trial at each stretching

requency, there were at least 5 cycles of electromyography

ig 3. The viscosity (B) (slopes of the dotted and the solid lines) iserived from a regression line of the viscous component parametercross 4 different stretch frequencies for 2 representative CVA sub-ects with severe (MAS score 3) (circle data) and mild (MAS score 1)pasticity (cross data), respectively. The viscosity of subject withevere spasticity (dotted line) is higher than that of subject withild spasticity (solid line).

Table 3: Quantification of Spasticity Using Viscosity Before (Pre)and After (Post) Injection

Viscosity

Subject

A B C D E F G H I J

Pre .078 .164 .364 .180 .366 .136 .170 .207 .292 .137Post .064 .101 .206 .098 .091 .007 .138 .091 .077 .128

aOTE. Significant difference was found using the Wilcoxon signed-

ank sum test (P�.05).

rch Phys Med Rehabil Vol 86, August 2005

inear envelope that reached our preset electromyographichreshold, (eg, �3 SDs for a certain duration) which would bencluded in further analysis. Because most of the reflex elec-romyographic activity in the ½-Hz stretching frequency wasot evident, we only compared the electromyographic activitiesf 1- and 3⁄2-Hz frequencies for our different subjects. Table 4ummarizes the mean and SD values of the reflex electromyo-raphic threshold for stretch frequencies of 1 and 3⁄2Hz for eachubject. A lower electromyographic threshold can be found at⁄2Hz, a higher stretching frequency compared with those of-Hz stretch frequency for both preinjection and postinjectioneasurements. This implies that the reflex electromyographic

ctivity is induced earlier at a higher stretch velocity. Compar-ng the preinjection and postinjection results, all of the testshowed either a significant increase (7/10 subjects at bothrequencies) or maintained about the same levels. None ofhem decreased in reflex electromyographic threshold at 1 and⁄2Hz.

DISCUSSIONIn our previous study,18 the portable muscle tone measure-ent device was calibrated and validated by the motor-driven

ystem, and it had high correlation of measurement results. Theiscous components under each stretching frequency and theveraged viscosity across 4 frequencies have been derived tostimate the velocity-dependent properties of the elbow joint.oreover, the reflex electromyographic threshold derived from

he electromyography linear envelope was adopted herein torovide electrophysiologic evidence of the stretch reflex. Ourtudy combines these 2 assessment methods to observe thehanges in muscle tone after BTX-A treatment.

We first compared the viscous components at 4 differentrequencies before and after BTX-A injections. We found thathe viscous components of the major subjects clearly decreasedfter treatment for each stretching frequency. Similarly, we

ig 4. A complete session of 15 sinusoid stretching cycles can bebserved from (A) the angular displacement. Clear electromyo-raphic activities are found in (B) the biceps brachii compared withC) triceps brachii.

lso observed that the viscosity (subjects B in table 4) of the

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1659QUANTIFICATION OF BOTULINUM TOXIN TYPE A EFFECTS, Chen

pastic muscle in all subjects had a declining trend after inter-ention. These results show that the severity of the hypertoniaf the biceps brachii muscle is reduced after intervention.As indicated in figure 5, we observed evident electromyo-

raphic activity in the biceps brachii muscle when the elbowexor was stretched. At least 7 of the 15 selected cycleshowing evident reflex electromyographic activity were ob-erved in all subjects when stretched at 1- and 3⁄2-Hz stretchingrequencies. However, the stretching electromyographic activ-ty is not evident at lower stretching frequencies, that is, 1⁄3 andHz. In their previous study, Pisano et al15 suggest that the

elocity of 100°/s represents a cutoff value that discriminatesetween patients and controls. In our study, the stretchingange for elbow movement was 60°, from which 1-Hz stretch-ng frequency represents an equivalent stretching velocity of20°/s, sufficient to elicit the stretch reflex. However, stretchest 1⁄3 and ½Hz with equivalent stretching velocities of 40°/s and0°/s are insufficient to activate the spastic muscle spindle.herefore, we used only reflex electromyographic thresholdseasured at the 1- and 3⁄2-Hz stretching frequencies to assess

he BTX-A intervention. From these 2 stretching frequencies,e also observed that the reflex electromyographic thresholds

re all lower at stretching frequencies of 3⁄2Hz (7/10 subjectsith significant decrease, as shown in table 5), which is con-

istent with the velocity-dependent properties of spasticity. Inddition, the electromyographic thresholds are either main-ained at the same level or significantly increased after treat-

ig 5. The electromyographic activities and their correspondingtretch angles are processed to determine the reflex electromyo-raphic threshold (vertical dotted line) for subject E at 3⁄2Hz oftretch frequency for (A) preinjection and (B) 2 weeks after BTX-Anjection. Abbreviation: LE, linear envelope.

Table 4: Comparison of Reflex Electromyographic Threshold (%)3⁄2-Hz Stret

Stretch Frequencies A B C D

1Hz Pre 77.1�9.6 60.1�6.4 50.3�7.4 66.9�

Post 92.3�4.7 74.4�7.5 67.6�7.2 76.5�

Mann-Whitney U test * * * *3⁄2Hz Pre 68.8�7.9 55.4�4.5 48.9�8.9 61.9�

Post 78.4�2.7 68.8�5.3 64.9�5.5 75.5�

Mann-Whitney U test * * * *

OTE. Values are mean � SD.

Significant difference (P�.05) before and after injection.At each frequency, 3 subjects had no significant difference (P�.05).

ent in 7 of 10 subjects at both 1 and 3⁄2Hz. The increase inlectromyographic threshold also indicates a decrease in mus-le tone after treatment.

Although the clinical scale (see table 2) shows the severity ofuscle tone in all subjects who either maintained the same

core or decreased by at least 1 point on the MAS after BTX-Anjection, it is difficult to observe the delicate changes from the

AS, as compared with our biomechanic and reflex electro-yographic threshold assessments. Other research also indi-

ated a weak correlation between the MAS score and neuro-hysiologic indices of spasticity, observed from the excitabilityf alpha motoneurons.21 It is believed that the MAS is alinically useful grade assessment; however, it can providenly semiquantitative assessment of muscle tone21,22 and isrone to subjective evaluation. For example, some subjects’AS assessments (subjects A, B, D, G) in table 2 show no

hange, although their viscosity and reflex electromyographicctivity indicated significant improvement in muscle tone.

Comparing the 2 quantitative measurements used in ourtudy, we found that the viscous parameters could be usedor muscle tone assessment when the reflex electromyo-raphic activity is not evident, especially at 2 weeks afternjection. The possible causes for this are 2-fold. First, theeflex electromyographic activity is not obvious at slowtretch velocities and with lower muscle tone by using theurface electromyographic measurement. Second, the vis-ous components measure the change in the mechanicalroperties of spastic muscle that have induced secondaryuscle stiffness due to spasticity.23 However, the sensitivity

f the biomechanic and electrophysiologic measurementsnd their clinical acceptance should be further investigatedfter many clinical trials over longer periods of assessmentime. We also suggest that our quantitative measurementsan be used for monitoring the changes in muscle tone in aime course manner that can determine the effect of BTX-An varied subjects and can provide useful information toetermine a personally tailored therapeutic plan.

CONCLUSIONSOur study shows that a convenient portable muscle toneeasurement device can be used to assess muscle tone changes

fter BTX-A injection. Compared with the scale-based evalu-tion of the MAS, our results indicate that viscosity decreasesnd electromyographic thresholds increase after BTX-A treat-ent, which provides a quantitative assessment of muscle tone

hange after injection. We believe that the treatment effect ofTX-A would decay with passing time, but the accurate lastingffective duration and the progressive changes are still unclear.sing such a portable device for a time course study of BTX-A

reatment should increase the knowledge about treatment effectn the future. By applying sensitive and quantitative evaluation

e (Pre) and After (Post) Injection for Each Subject During 1- andequencies

Subject

E F G H I J

66.9�7.7 67.5�5.2 84.5�7.2 53.0�4.9 74.7�7.5 80.5�5.876.4�6.8 81.0�6.9 86.5�5.3 77.4�9.9 73.0�5.7 82.4�6.6

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ethods, not only can the treatment effect of BTX-A beetermined, but also the optimal effective dose of BTX-Areatment can be established3 in clinical studies.

APPENDIX 1: BIOMECHANIC MODEL OFJOINT MOVEMENT

In a sinusoid stretch, the measured reactive resistance resultsrom inertial (I), viscous (B), elastic (K) contributions andnitial constant offset. The offset in reactive resistance can beemoved by detrending the measured resistance. Thus, theynamic equation of movement can be written as:

T(t)�IX(t)�BX(t)�KX(t) (1)

here T(t) is reactive torque and X(t) is joint displacement,˙ (t) and X(t) denote the joint angular velocity and accelera-ion, respectively; and t stands for time. Because we tookinusoid movement as the assessed method, we could substitutesin(�t) for X(t). Equation 1 can be rewritten as:

(t)�A[(K�I�2)sin(�t)�B�cos(�t)]

�A sin(�t��)[(K�I�2)2�(B�)2]1⁄2 (2)

here ��tan�1[(B�)/(K–I�2)]. After fast Fourier transforma-ion of the recorded torque data, we could find the different �phase l) at different stretch angular frequency (�). Utilizingnown reactive torque value, angular frequency (�) and de-ived phase lag (�), the viscous components (B�) could bestimated.

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