muscle and joint elastic properties during elbow flexion in duchenne

Duchenne muscular dystrophy (DMD) is characterized bya direct effect on muscle fibres leading to muscle atrophyand weakness due to a lack of muscle dystrophin.Dystrophin is a sarcolemma cytoskeletal protein whosedeficit leads to segmental necrosis of the muscle fibre.DMD is thus characterized by a decrease in the number ofmuscle fibres, which are progressively replaced by fibro-adipose tissue. The first observed clinical signs relate todifficulties in running or climbing stairs and calfhypertrophy. Gait then becomes lordotic and waddling.Between 6 and 11 years of age, limb and torso musclesprogressively and steadily decrease in strength. Loss ofambulation occurs (average 10.5 years of age) and all torsoand limb muscles decrease in size.

The assessment of muscle mechanical properties in DMDpatients is mostly limited to a more or less sensitiveevaluation of strength production, generally in staticconditions and occasionally during a locomotor act. Twokinds of non-invasive technique are generally used tocharacterize muscle functional properties in DMDpatients. (i) Semi-quantitative measurements (manual

testing, timed scores during motor acts) are performed inroutine clinical practice and afford a functionalevaluation (Edwards & Hide, 1977; Brooke et al. 1981;Aitkens et al. 1989). For instance, manual testing (scoredfrom 0 to 5) is based on an international graduated scaleof muscle ability: MRC scale (Medical Research Council,1943) reorganized from 0 to 10 (Brooke et al. 1981).(ii) Quantitative measurements (manual dynamometry)can be performed in some muscle groups and give amaximal voluntary contraction (MVC) measurement(Munsat, 1989).

Understanding of the mechanisms responsible for muscleadaptation to altered functional demand (pathology ortraining) requires quantification of muscle mechanicalproperties. For instance, muscle contractility and muscleelasticity were experimentally found to be sensitive toperiods of hyperactivity as well as hypoactivity (Goubel& Marini, 1987; Almeida Silveira et al. 1994; Canon &Goubel, 1995). The same holds for viscoelastic propertiesof joints (Heerkens et al. 1986; Tipton et al. 1986). It cantherefore be hypothesized that muscle elastic properties

Muscle and joint elastic properties during elbow flexion inDuchenne muscular dystrophy

Christophe Cornu *†, Francis Goubel * and Michel Fardeau †

*Département de Génie Biologique UMR – CNRS 6600, Université de Technologie,BP 20529, F-60205 Compiègne Cedex and † Institut de Myologie, Groupe Hospitalier

Pitié-Salpêtrière, F-75651 Paris, Cedex 13, France

(Received 27 November 2000; accepted 29 December 2000)

1. Maximal voluntary contraction (MVC), series elastic stiffness and total joint stiffness duringelbow flexion were investigated in healthy boys and in boys with Duchenne musculardystrophy (DMD) in order to assess changes in mechanical properties induced by the disease.

2. Two methods were used to perform stiffness measurements: (i) the application of sinusoidalperturbations to the joint during flexion efforts, allowing the calculation of total jointstiffness; (ii) the use of quick-release movements of the elbow, which had previously beenmaintained in isometric contraction, allowing the calculation of series elastic stiffness. In eachcase, stiffness was linearly related to torque, leading to the calculation of a normalized stiffnessindex as the slope of this stiffness–torque relationship.

3. As expected, mean MVC was found to be much higher for healthy boys (20.02 ± 5.20 N m) thanfor DMD patients (3.09 ± 2.44 N m). Furthermore, the results showed that it was possible tocharacterize healthy and DMD children by virtue of the mechanical properties measured. Meanseries elastic stiffness index was higher for DMD children (142.55 ± 136.58 rad_1) than forhealthy subjects (4.39 ± 2.53 rad_1). The same holds for mean total joint stiffness index:43.68 ± 67.58 rad_1 for DMD children and 2.26 ± 0.70 rad_1 for healthy subjects. In addition,increases in stiffness were more marked in DMD patients exhibiting high levels of muscleweakness.

4. These changes are interpreted in terms of the adaptation of the properties of the muscles andjoint involved, i.e. muscle fibres, tendons, peri- and intra-articular structures.

Journal of Physiology (2001), 533.2, pp.605–61611986 605

and joint characteristics are modified by alterationsinduced by DMD. This was shown regarding the musclestiffness of knee extensors (Cornu et al. 1998). A classicalmethod of obtaining quantitative information on isolatedmuscle series elastic component (SEC) behaviour is thequick-release movement first used by Hill, who specifiedthe concept of SEC from his muscle model (Hill, 1938).The same technique can be applied in human musclegroups with some protocol modifications (Goubel &Pertuzon, 1973; Pousson et al. 1990; Hof, 1997; Tognellaet al. 1997; Cornu et al. 1998). Another widely usedapproach to measure viscoelastic properties is to applysinusoidal disturbances over a range of frequencies.Considering displacement and force parameters,frequency-dependent changes in compliance and phaseshifting reflect the classical features of mixed mechanicalcontributions from inertia, viscosity and elasticity of theconsidered structures (Cannon & Zahalak, 1982; Winterset al. 1988; Kearney & Hunter, 1990). The existence ofviscoelastic behaviour during sinusoidal perturbationswas first quantified in the soleus muscle of the cat byRack (1966). In humans, an identical goal was pursued: to

develop a tool to characterize musculo-articular behaviourin order to determine the role played by muscles, tendonsand joints in movement. For this purpose, Joyce et al.(1974) applied sinusoidal perturbations to the elbow jointand Agarwal & Gottlieb (1977) and Kearney & Hunter(1990) to the ankle joint.

The present study was designed to determine andcompare SEC stiffness and total joint stiffness changes inDMD children during elbow flexion. This was done usingthe quick-release technique and the sinusoidalperturbation method, respectively, to give stiffnessindices, which were examined for changes related to thestage of the disease.

METHODSMaterials

Experiments were performed with an ergometer especially designedto test the mechanical properties of the muscle groups and jointduring elbow flexion and extension on both sides in children (Fig. 1).Briefly, this ergometer consists of a platform supporting a powerunit and a seat associated with a driving unit. The seat, including

C. Cornu, F. Goubel and M. Fardeau606 J. Physiol. 533.2

Figure 1. Elbow ergometer

restraining systems, is adaptable to child morphology, and is three-dimensionally adjustable to optimize the subject’s position. A fixedcolumn supports: (i) a direct drive actuator (NSK Megatorque) with arotation axis held in the vertical position; (ii) a forearm supportdirectly fixed onto the rotor, allowing the subject’s forearm to bemaintained in the horizontal plane such that the elbow rotation axiscoincides with that of the actuator; (iii) specific transducers: angularposition is measured by an ‘absolute coding’-type transducer givingthe instantaneous absolute position of the rotor. The resolution of thedisplacement measurement is one-tenth of a degree. Angular velocityis recorded from the resolver of the actuator except for velocitiesgreater than 3 laps s_1, which require a tachometer (Minimotor).Torque is obtained by a torque transducer whose axis coincides withthe motor axis. Its sensitivity in measuring strength non-perpendicular to the main shaft is virtually nil. In the quick-releasetest, inertia of the moving part must be as low as possible in order toobtain release in a few milliseconds (Goubel & Pertuzon, 1973;Tognella et al. 1997). This was achieved by using an electromagneticclutch allowing quick coupling/uncoupling of the actuator and of theforearm support.

The driving unit was composed of a PC equipped with a specific12-bit A/D converter and a timer board allowing ergometer pilotingand data acquisition after signal conditioning. The computercontrolled the position of the actuator according to a specific softwaremenu. The software controlled all procedures, from the choice of testto real-time commands, signal acquisition and storage. Motor controlwas mediated by transistor–transistor logic lines plus one RS 232link, connected to the driver unit of the actuator. Mechanicalvariables were also stored in the computer. Signals were processed byspecific software allowing expression of the results in terms ofcharacteristic parameters.

Experimental protocol

The main experiment was designed as follows. A full test session,including rest periods, lasted about 1 h and comprised: (i) anexplanation of the tests, (ii) preparation of the subject, (iii)habituation to the tests, (iv) the actual tests.

For the tests, the subject was placed on the seat and maintained byspecial restraint systems in order to keep his body and head againstthe seat back and headrest, respectively. The subject’s legs weresupported by an adjustable foothold so that the knee joint angle wasnear 90 deg in order to prevent potential circulatory compression.The seat was adjusted by means of a moving system near the fixedcolumn so that the subject’s forearm rested on the forearm support.The motor rotation axis was aligned with the epitrochlea–epicondyleaxis of the humerus, which gives the elbow a remarkably constantradius of rotation (Wilkie, 1950). The hand was placed in the proneposition by taking a horizontal grip, the distance of which from the

motor rotation axis could be adjusted. A crucial point was to prevent,during either quick-release or sinusoidal perturbation tests,movement of the wrist in the horizontal plane when moving theelbow joint; wrist movement would lead to changes in inertia andthen in stiffness. This was achieved by virtue of the raised edge ofthe forearm support, which kept the hand immobilized, and withrestraint systems holding the forearm to its support. The generalposture of the subject during the experiment was with the arm andforearm in the horizontal plane, with an angle of 45 deg between thefrontal plane and the arm, and the elbow joint angle set at 90 deg.

MVC was first measured for the elbow flexors under isometricconditions. Three tests were performed and the best was retained asthe real elbow flexor MVC. Quick-release movements (QR) duringelbow flexion were then performed at three submaximal isometrictorques (35, 50 and 75 % MVC), with three measurements per torque.Lastly, sinusoidal perturbations (SP) were imposed on the right elbow(4–12 Hz , 3 deg peak-to-peak harmonic angular displacement),during which the subject developed a mean constant torque equal to35, 50 or 75 % MVC. Each trial lasted 4 s. The trials were separatedby a rest period to prevent muscle fatigue. Instructions to thesubjects were displayed on a PC screen and an oscilloscope for QR andSP, respectively.

In order to improve the comparison between normal and DMDsubjects, an additional experiment was designed in which normalsubjects had to develop torques in a similar range to DMD subjects.The same tests (i.e. QR and SP) were performed at three submaximalisometric torques (1, 4 and 7 N m).

Subjects

Twenty-two DMD boys (mean age, 13.55 ± 3.03 years; range,9–21 years) and fifteen healthy boys (mean age, 11.02 ± 1.66 years;range, 9–15 years) volunteered for the main experiment, whilst nineboys (mean age, 11.44 ± 1.99 years; range, 8–15 years) volunteeredfor the additional experiment. Some physical characteristics of thesubjects are shown in Table 1. All children and their legal guardianswere informed of the nature and the aim of this study and signed aconsent form. The study was authorized by the Ethics Committee ofthe Hôpital de la Pitié-Salpêtrière (Paris, France) and was carried outin accordance with the Declaration of Helsinki.

Data processing

Quick-release movement: stiffness index calculation (SIQR). Foreach QR trial, the parameters collected (see Fig. 2) were (i) isometrictorque before the release (T), and (ii) changes in angular position (∆)and changes in angular acceleration (∆fifi) calculated from thederivation with respect to time of the angular speed signal. These twoparameters were characterized at the very beginning of the quickrelease of the system (30 ms after the acceleration peak). Series elastic

Stiffness in Duchenne muscular dystrophyJ. Physiol. 533.2 607

Table 1. Physical characteristics of the experimental subjects

Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

DMDH (m) 1.40 1.25 1.51 1.32 1.65 1.57 1.55 1.40 1.34 1.54 1.57 1.52 1.50 1.25 1.36 1.34 1.65 1.60 1.25 1.38 1.51 1.62 — —W (kg) 43.0 23.0 52.0 36.0 70.0 34.5 30.0 45.0 26.5 31.0 33.5 50.0 55.0 24.5 36.0 37.0 77.5 56.0 24.5 31.5 51.0 50.0 — —I 0.058 0.031 0.049 0.053 0.097 0.047 0.045 0.033 0.030 0.052 0.026 0.032 0.061 0.033 0.027 0.019 0.067 0.0660.026 0.029 0.026 0.046 — —

HealthyH (m) 1.27 1.45 1.40 1.38 1.29 1.40 1.48 1.31 1.50 1.38 1.58 1.45 1.47 1.55 1.68 1.62 1.65 1.25 1.70 1.50 1.45 1.20 1.45 1.22W (kg) 29.0 51.0 40.0 39.0 31.0 38.0 39.0 28.0 53.0 37.5 56.0 40.0 39.0 39.5 55.0 50.0 50.0 25.0 50.0 42.0 34.0 29.0 30.0 26.5I 0.032 0.035 0.047 0.043 0.027 0.038 0.041 0.026 0.023 0.029 0.023 0.037 0.042 0.030 0.056 0.037 0.035 0.0160.029 0.022 0.021 0.018 0.019 0.015

Elbow inertia (I; N m s2 rad_1) is the mean value of that estimated from QR and SP experiments.Abbreviations: H, height; W, weight.

stiffness (SQR) is conventionally calculated at the start of motion(Goubel & Pertuzon, 1973; Tognella et al. 1997), i.e. when the serieselastic component (SEC) is supposed to recoil. Thus the stiffness index(SIQR) is expressed as the ratio between changes in angularacceleration (∆fifi) and angular displacement (∆), multiplied by thecorresponding inertia value (I):

SQR = I (∆fifi/∆). (1)

In this equation, inertia is assumed to be constant. This can be easilycalculated by considering the transition between the static phase andthe dynamic phase of the test. At this moment, static torque (T)equals dynamic torque and acceleration is maximal (fifimax). Then:

Ififimax = T

and I = T/fifimax. (2)

SQR was related to the corresponding isometric torque (T) exerted bythe subject. The slope of the linear stiffness–torque relationship so

obtained gave the series elastic stiffness index (SIQR), which was usedto normalize stiffness data. In addition, I was related to T in order toassess its constancy.

Sinusoidal perturbations: stiffness index calculation (SISP).During a SP trial the recorded variables were angular displacementand torque (Fig. 3). The mechanical analysis only considered torquemodulated at the driving frequency, and non-linearities weretherefore neglected (Kearney & Hunter, 1990). For each maintainedtorque, averaged position-to-torque amplitude ratios (compliancecurve) and position-to-torque difference in phase (phase curve) wereplotted against the imposed frequencies on a Bode diagram aftercompensation for actuator dynamics. As in other studies (see forreview Kearney & Hunter, 1990), frequency-dependent changes incompliance and phase shifting reflected the classical features of amixed mechanical contribution from inertia (I), viscosity (B) andelasticity (K) of the musculo-articular system. Such a feature can beobserved providing that a frequency range of 4–12 Hz is imposed. So,by using identification techniques (Levy, 1959), a second-order modelincluding such parameters was adjusted to the Bode diagrams asexpressed by the formula:

d2(t) d (t)I——— + B——— + K(t) = T(t), (3)

dt 2 dt

where T is the external torque (N m) and is the angular position(rad).

So, for each level of torque, the stiffness, K (N m rad_1), the viscosity,B (N m s rad_1), and the inertia, I (N m s2 rad_1), can be determined.

The K values were related to the maintained torque by using dataobtained at 35, 50 and 75 % of MVC. The slope of the linear stiffnessrelationship so obtained gave the total joint stiffness index (SISP),which was used to normalize the stiffness data. In addition, I wasrelated to T in order to assess its constancy.

Manual testing

Manual testing data were collected during medical consultation byspecialized physiotherapists using an international standardizedscale (Medical Research Council, 1943). This semi-quantitativemethod estimates disease severity using a scale between 5 for healthysubjects and 0 when no movement is possible. Muscle grades werethen reorganized in order to build a numerical scale between 10(healthy subjects) and 0 (no movement) according to the methodproposed by Brooke et al. (1981).


Figure 3. Typical raw data for sinusoidalperturbation test

A, healthy subject; B, DMD patient. Position-to-torque amplitude ratio (a/b) and position-to-torquedifference in phase (q) were calculated for eachimposed frequency.

Figure 2. Typical raw data for quick-released movement

A, healthy subject; B, DMD patient. Changes in acceleration (∆fifi) and position (∆) were calculated duringthe first 30 ms after release.

Statistics

A correlation coefficient, r 2, was calculated for each plotted fit, andalso when plotting Bode diagrams in order to determine, for eachfrequency, the scattering with regard to the theoretical behaviourgoverned by eqn (3). A Cochran t test was used for comparison of theglobal values presented with standard deviation (S.D.). An analysis ofvariance (ANOVA) was performed for comparison of the meanvalues. The level of significance was set at P < 0.05.

RESULTSMaximal voluntary contraction (MVC)

MVC was always much lower for DMD patients than forhealthy subjects. Mean MVC was significantly higher forhealthy boys (20.02 ± 5.20 N m) than for DMD patients(3.09 ± 2.44 N m). When associating healthy and DMDsubjects, an exponential relationship was found betweenmean MVC and the corresponding manual testing score(r 2 = 0.92, P < 0.05).

Series elastic stiffness: SQR and SIQR

Inertia determined during QR experiments was found tobe independent of torque (Fig. 4). For the healthysubjects, the mean slope of the I–T relationship was0.0021 ± 0.0018 s2 rad_1, i.e. nearly horizontal. The sameholds for DMD patients, for whom the mean slope was0.027 ± 0.034 s2 rad_1. This allowed us to estimate theinertia of each subject by subtracting the contribution ofthe apparatus, leading to mean values of 0.037 ± 0.013and 0.038 ± 0.021 N m s2 rad_1 for healthy and DMDsubjects, respectively.

SQR increased linearly with torque irrespective of thesubject (Fig. 4). This relationship was also linear for datapooled for healthy subjects from the main experimentand gave a global SIQR of 5.14 ± 0.29 rad_1 (r 2 = 0.74,

P < 0.05). The global relationship between SQR and torquefor DMD patients showed a clear dissociation into twopopulations (Fig. 5). One population with lower stiffnessand exercising higher torque corresponded to DMDpatients with test scores ≥ 5. The global stiffness–torquerelationship for this population was linear and gave aglobal SIQR of 3.41 ± 0.57 rad_1 (r 2 = 0.46, P < 0.05). Asecond population with higher stiffness and exercisinglower torque corresponded to DMD patients with testscores < 5. For this population, the stiffness–torquerelationship was also linear and gave a global SIQR of138.36 ± 10.67 rad_1 (r 2 = 0.70, P < 0.05). Moreover,stiffness calculated for healthy subjects from theadditional experiment, i.e. developing low torques, was ina lower range than stiffness calculated for healthysubjects from the main experiment. Pooling the data forall healthy subjects (main and additional experiments) ledto a linear stiffness–torque relationship that gave a globalSIQR of 3.85 ± 0.22 rad_1 (r 2 = 0.61, P < 0.05; Fig. 6). Inspite of inter-individual variations, mean SIQR wassignificantly lower for healthy subjects (4.39 ± 2.53 rad_1)than for DMD patients (142.55 ± 136.58 rad_1; P < 0.05).More precisely, mean SIQR was significantly lower forhealthy subjects in both experiments (5.44 ± 2.40 rad_1 inthe main experiment; 2.48 ± 1.34 rad_1 in the additionalexperiment) and for DMD subjects with test scores ≥ 5(5.31 ± 2.87 rad_1) than for DMD subjects with test scores< 5 (220.97 ± 109.20 rad_1; P < 0.05). Moreover, nosignificant difference in mean SIQR was found betweenhealthy subjects of both experiments and DMD subjectswith test scores ≥ 5 (P > 0.05). A mean SIQR value wascalculated for each available grade of manual testing, andindicated a large increase in SIQR with the severity of thedisease when the test score of the elbow flexors droppedbelow 5 (Table 2).


Figure 4. Typical series elastic stiffness–torque and inertia–torque relationships

Stiffness (8) and inertia (9) for a DMD patient. Stiffness (•) and inertia (ª) for a healthy subject.

Total joint stiffness: SSP and SISP

Inertia determined during SP experiments was found tobe independent of torque (Fig. 7). For the healthypopulation, the mean slope of the I–T relationship was0.0004 ± 0.0003 s2 rad_1, i.e. nearly horizontal. The sameholds for DMD patients, for whom the mean slope was0.047 ± 0.059 s2 rad_1. This allowed us to estimate theinertia of each subject by subtracting the contribution ofthe apparatus. These inertias were not significantlydifferent from those deduced from QR experiments.

In Bode diagrams, the compliance curve in healthysubjects from the main experiment showed a peak for theresonant frequency followed by a linear decrease with aslope of _40 dB decade_1 and the phase diagram showeda _90 deg phase lag for the resonant frequency (Fig. 8A).In DMD subjects, the resonant frequency was shiftedtowards lower values, resulting in truncated diagrams(Figs 8B and 9). The same holds for healthy subjectsdeveloping low torques (Fig. 9). Moreover, Fig. 9 showsthat fitting a second-order model equation to theexperimental data revealed a resonant frequency for


Figure 6. Global series elastic stiffness–torque relationship for healthy subjects

r 2 = 0.61, global SIQR = 3.85 rad_1.

Figure 5. Global series elastic stiffness–torque relationship for DMD patients

A clear dissociation of the population is observed. 0, linear relationship for DMD patients with test scores< 5 (r 2 = 0.70, SIQR = 138.36 rad_1). 1, linear relationship for DMD patients with test scores ≥ 5(r 2 = 0.46, SIQR = 3.41 rad_1).

subjects developing low torques that was not observablewithin the frequency range used for the experiments.Finally, for every subject, the second-order model gave asatisfactory fit: the correlation coefficient, r 2, wasbetween 0.71 and 0.99 for DMD patients and between0.77 and 0.98 for healthy subjects from both experiments.

SSP increased linearly with torque irrespective of thesubject (Fig. 7). This relationship was also linear for data

pooled for all healthy subjects from the main experiment,giving a global SISP of 2.89 ± 0.33 rad_1 (r 2 = 0.63, P <0.05). The global relationship between SSP and torque forDMD patients showed a dissociation into two populations(Fig. 10). In fact, a linear relationship for DMD patientswith test scores ≥ 5 gave a global SISP of 3.75 ± 1.15 rad_1

(r 2 = 0.32, P < 0.05). No obvious relationship wasobserved between stiffness and torque for DMD patients


Figure 7. Typical total joint stiffness–torque and inertia–torque relationships

Stiffness (8) and inertia (9) for a DMD patient. Stiffness (•) and inertia (ª) for a healthy subject.

Figure 8. Bode diagrams

A, typical compliance and phase diagrams for healthy subjects. The compliance curve shows a peak in theresonant frequency followed by a linear decrease with a slope of _40 dB decade_1 (r 2 = 0.95). B, typicalcompliance and phase diagrams for DMD patients. Resonant frequency shifted towards lower frequencies,leading to truncated diagrams (r 2 = 0.90).

with test scores < 5 (r 2 = 0.028, P > 0.05). Stiffnesscalculated for healthy subjects from the additionalexperiment, i.e. developing low torques, was in a lowerrange than stiffness calculated for healthy subjects from

the main experiment. Pooling data for all healthy subjects(main and additional experiments) led to a linearstiffness–torque relationship that gave a global SISP of2.74 ± 0.23 rad_1 (r 2 = 0.67, P < 0.05; Fig. 11). In spite ofinter-individual variations, no significant difference inmean SISP was found between healthy subjects from thetwo experiments (2.50 ± 0.45 rad_1 in the main experiment;2.16 ± 0.79 rad_1 in the additional experiment).Furthermore, mean SISP was significantly lower forhealthy subjects from both experiments (2.26 ± 0.70 rad_1)than for DMD subjects (43.68 ± 67.58 rad_1; P < 0.05).More precisely, significant differences in mean SISP werefound for three groups (P < 0.05): healthy subjects, DMDsubjects with test scores ≥ 5 (4.96 ± 2.21 rad_1) and DMDsubjects with test scores < 5 (65.81 ± 76.98 rad_1). A meanSISP was calculated for each available grade of manualtesting. This indicated a large increase in SISP with theseverity of disease when the test score of the elbowflexors dropped below 5 (Table 2).

Series elastic stiffness index and total joint stiffnessindex comparison

Mean SISP (2.26 ± 0.70 rad_1) was significantly lower thanmean SIQR (4.39 ± 2.53 rad_1) in healthy subjects(P < 0.05). The same holds for DMD patients, whose meanSISP was 43.68 ± 67.58 rad_1 and mean SIQR was 142.55 ±136.58 rad_1 (P < 0.05).

DISCUSSIONThe present experiment was designed to quantify bothmuscle and joint mechanical properties in healthy andDMD boys during elbow flexion. As expected, mean MVCwas considerably higher for healthy subjects than forDMD patients. Moreover, considering mean MVC and thecorresponding test score for the elbow flexors for allsubjects, a clear exponential relationship was noted,confirming the loss of strength with the severity ofdisease (see for review Engel et al. 1994). Furthermore, forthe first time to our knowledge, elastic characteristicswere calculated during elbow flexion in DMD patients bymeans of two methods, allowing the determination of twokinds of stiffness index, SIQR and SISP.

Series elastic stiffness: SQR and SIQR

The results demonstrate that the quick-release techniquecan be used to follow disease progression. In an isolatedmuscle, the initial phase of the quick-release movement


Figure 9. Simulated Bode diagrams from thesecond-order model obtained by virtue ofexperimental data for a DMD patient and ahealthy subject working at low torque

A, compliance diagram; B, phase diagram.ª, experimental data for a DMD patient exerting amean torque of 0.95 N m (r 2 = 0.99). 1, experimentaldata for a healthy subject exerting a mean torque of1.14 N m (r 2 = 0.97). Simulated data in the 1–50 Hzfrequency range are shown for a DMD patient (dottedline) and a healthy subject (continuous line).

Table 2. Changes in mean series elastic stiffness index (SIQR) and in mean total joint stiffnessindex (SISP) with test score

Test score 10 7 5 4 3 2n 24 3 5 2 7 5Mean SIQR (rad_1) 4.39 ± 2.53 3.75 ± 1.03 6.25 ± 1.53 186.69 ± 52.98 197.77 ± 51.86 267.15 ± 62.44Mean SISP (rad_1) 2.26 ± 0.70 6.67 ± 0.95 3.94 ± 0.90 29.90 ± 2.79 28.41 ± 6.18 132.54 ± 50.90

A score of 10 corresponds to healthy subjects and a score of 0 is given when no movement is possible.n, number of subjects with the corresponding test score.

corresponds to a SEC recoil (Wilkie, 1956). The SECconsists of an active fraction that is located in the cross-bridges (Huxley & Simmons, 1971) and a passive fractionthat is located in the tendon (Jewell & Wilkie, 1958). Theuse of the quick-release technique in humans differs insome regards from its use in isolated muscle (Goubel &Pertuzon, 1973). In fact, the stiffness measurement isperformed during the SEC recoil, which is very brief inisolated muscle (1–5 ms) but longer in the case of in situhuman experiments (40–50 ms): this is due to inertiaopposed to the movement (limb and experimental device),

which does not permit an instantaneous shortening ofelastic elements. However, it was necessary to performmeasurements before the appearance of an unloadingreflex (Angel et al. 1965), which is known to occur about30 ms after the release. For the low levels of torque whenthe SEC stiffness is low, the passive resistance of theantagonistic muscles and passive structures can interferewith the SEC recoil. Agonistic compliance can then beminimized, i.e. SEC stiffness increased (Shorten, 1987).However, the quick-release estimate of human SECstiffness is in fair agreement with those obtained with


Figure 10. Global total joint stiffness–torque relationship for DMD patients

No obvious global relationship is observed whereas a linear relationship can be observed for DMD patientswith test scores ≥ 5 (1; r 2 = 0.32, SISP = 3.78 rad_1). 0, DMD patients with test scores < 5.

Figure 11. Global total joint stiffness–torque relationship for healthy subjects

r 2 = 0.67, global SISP = 2.74 rad_1.

alternative methods such as small amplitude oscillationexperiments (Cannon & Zahalak, 1982) and the freevibration technique (Shorten, 1987). Furthermore, thecharacteristics of SEC stiffness of human muscle werealso found to change according to the functional demand(Pousson et al. 1990; Goubel, 1997; Lambertz et al. 2001).This coherence in the reported data suggests that thequick-release method can be satisfactorily applied to invivo human experiments.

The increasing linear relationship between SQR and torqueirrespective of the subject shows that SEC stiffnessdepends on activated contractile elements (Goubel &Pertuzon, 1973). The same kind of relationship can bededuced from the compliance–force relationship of theelbow equivalent flexor (Goubel & Pertuzon, 1973;Pousson et al. 1990) or compliance–torque of triceps surae(Tognella et al. 1997). This yields a stiffness index (SIQR),which characterizes the musculo-tendinous behaviour of asubject in terms of normalized stiffness. Interestingly,the global SQR–torque relationship for DMD patientsclearly dissociated the whole population into two groupsaccording to test scores of ≥ 5 and < 5. This shows thesensitivity of the quick-release method. On the otherhand, no dissociation into two groups was found for theglobal SQR–torque relationship for healthy subjects whenincluding additional results obtained for low torques. Thisreinforces the differences in SIQR observed between DMDand healthy subjects.

Total joint stiffness: SSP and SISP

Mechanical responses were studied after elimination ofchanges in torque signal due to the reflex responseresulting from sinusoidal perturbations. Thus,neurophysiological aspects of the musculo-articularstructure’s behaviour were not taken into account. Bodediagrams obtained in this study for healthy children arein accordance with those reported in the literature(Agarwal & Gottlieb, 1977; Kearney & Hunter, 1990).Moreover, the low torques exercised by DMD patients andhealthy subjects in the additional experiment shifted theresonant frequency in Bode diagrams towards lowfrequencies. A second-order model fitted the datasatisfactorily, despite the lack of experimental data forfrequencies below the resonant frequency.

The increasing linear relationship between SSP and torqueirrespective of the subject is in accordance with datareported in the literature (Joyce et al. 1974; Zahalak &Heyman, 1979; Cannon & Zahalak, 1982). This dependencebetween SSP and active torque indicates that musclestructures contribute to stiffness measured by using SP. Itwas used to calculate a stiffness index (SISP)characterizing the joint behaviour of a subject in terms ofnormalized stiffness. DMD patients were separated intotwo groups (test scores ≥ 5 and < 5) by the globalSSP–torque relationship. Nevertheless, a linearrelationship was only found for DMD patients with a testscore ≥ 5. For these DMD subjects, a significant

difference in mean SISP compared with that of healthysubjects pointed to the sensitivity of the sinusoidalperturbation method. Furthermore, additional results forhealthy subjects developing low torques did not changethe global SISP. This reinforces the differences in SISP

observed between healthy subjects and DMD patients.

Stiffness indices and muscle weakness

When considering either healthy subjects or DMDpatients, mean SISP was significantly lower than meanSIQR (P < 0.05). This shows that these two kinds ofstiffness have different origins. SIQR reflects SEC muscleability to release potential energy stored during aprevious contraction. SISP indicates musculo-tendinousand joint structure abilities to react to an imposeddisplacement disturbance. In the present study, bothmean stiffness indices were significantly higher for DMDpatients than for healthy subjects. These indicesincreased substantially as the disease worsened: theincrease in stiffness was more marked for children withlower scores on Brooke’s scale (Brooke et al. 1981).Surprisingly, and especially for quick-release results,stiffness–torque relationships separated the DMDpopulation into two groups, whereas DMD is known to bea progressive dystrophy. Nevertheless, these results arein accordance with those presented in Table 2, showingexponential increases in stiffness index with the stage ofdisease. In fact, a large increase in stiffness index isobserved from the test score threshold value of 5. This isnot easily explainable in terms of genetic factors butcould be due to a more marked increase in the balancebetween fibro-adipose tissue and muscle tissue from thisstage of the disease.

In terms of SEC stiffness, SIQR changes are explainable interms of structural changes in DMD muscles reported inthe literature. More precisely, increases in SIQR can beexplained by changes in active structures (muscle fibres)as well as passive structures (tendons, surroundingtissues). Regarding active structures, the contractilecomponent, located in cross-bridges, is known to bemodified according to changes in functional demand(Fitts & Holloszy, 1977; Almeida Silveira et al. 1994).Moreover, several studies have shown that it was possibleto induce fibre-type transitions and SEC stiffnesschanges simultaneously in the rat soleus muscle inresponse to training (Goubel & Marini, 1987) or disuse(Canon & Goubel, 1995). However, data on skinned fast-twitch and slow-twitch fibres indicate no differences inthe elastic characteristics of cross-bridges whatever themyosin heavy chain isoform (Galler et al. 1996). It is alsoconceivable that elastic structures in series with slow-twitch fibres and those in series with fast-twitch fibreshave different stiffness characteristics. This couldexplain discrepancies between the results obtained withskinned fibres and whole muscle. Nonetheless, when awhole muscle decreases its proportion of fast-twitchfibres, its SEC stiffness increases in proportion. Type I


fibres are considered to predominate in DMD muscles(Dubowitz & Brooke, 1973) and it is generally accepted thatduring disease progression the proportion of type I fibresincreases whereas type IIB fibre deficiency is observed(Nonaka et al. 1981; Webster et al. 1988). Such changes cancontribute to the observed increase in SEC stiffness.

Regarding passive structures, DMD is characterized by adirect effect on muscle fibres leading to a deficit andmuscular atrophy. The primary muscular process issegmentary necrosis of muscle fibres, which isincompletely compensated by fibre regeneration bynecrosis-activated satellite cells. Marked interstitialfibrosis then progressively develops. The observed muscleweakness parallels the progressive loss of muscular tissueand its replacement by fibro-adipose tissue (Bell & Conen,1968). This can obviously explain the observed increase inSEC stiffness with disease progression. Furthermore, theincrease in joint resistance could interfere with SEC recoilduring the initial phase of the quick-release movement,leading to an increase in SEC stiffness. This couldpartially explain the gap observed in the stiffness indexbetween test scores of 5 and 4. In fact, from a test score of≤ 4, patients have contractures that cause an additionalresistance to movement. All of these features concerningchanges in both active and passive structures in DMDsubjects can explain the increase in SIQR with disease-related changes characterized by the quick-release method.

In terms of total joint stiffness, changes in SISP may resultfrom structural changes in DMD muscle, tendon and inperi- and intra-articular structures. Then, the parallelelastic component (PEC) of Hill’s muscle model has to beconsidered (Hill, 1938). PEC comprises the sarcolemma,connective tissue and titin (Horowits, 1992). Itscharacteristics can be modified according to functionaldemand (Kovanen et al. 1989). Moreover, as aconsequence of the disease, the relative immobilization ofthe musculo-articular structures can lead to an increase inpassive resistance of the joint. It is well known that intra-articular and peri-articular structures are moreresponsive to disuse than to an increase in use (Tipton etal. 1986). Noyes (1977) found a decrease in elasticitymodules of a bone–ligament–bone preparation afterimmobilization. This result was confirmed by Klein et al.(1982). Immobilization was also found to increaseconsiderably the passive resistance of the human kneejoint (Heerkens et al. 1986). Such changes due to relativeimmobilization of the elbow joint contribute to theobserved increase in SISP with disease. Furthermore, ashas been previously shown with the quick-releasemethod, the increase in total joint stiffness in DMDresults at least partly from the increase in SEC stiffness.

In this study, it has been shown that SIQR and SISP

increased as the disease progressed. This suggests thatthese parameters can be used to monitor DMD progressionand may be of use in other muscle diseases. Both quick-release and sinusoidal perturbation methods are

sufficiently sensitive to characterize DMD changes,giving information about changes in series elasticstiffness and in total joint stiffness. This should completethe clinical picture obtained by using devices wherestiffness is only evaluated in terms of rigidity, i.e.resistance to motion performed by the examiner (Ghika etal. 1993; Caligiuri, 1994; Prochazka et al. 1997). However,further experiments combining mechanical andneurophysiological approaches are needed to improveknowledge of the predominant behaviour of passive andactive structures that leads to the functionalconsequences observed in DMD.

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Acknowledgements

We are very grateful to J. Paulus and M. Meunier who performed themanual muscle tests. This work was supported by grants from theA.F.M. (Association Française contre les Myopathies). The authorsthank David Marsh for correcting the English.

Corresponding author

F. Goubel: Département de Génie Biologique UMR-CNRS 6600,Université de Technologie de Compiègne, BP 20529, F-60205Compiègne Cedex, France.

Email: [email protected]


muscle and joint elastic properties during elbow flexion in duchenne

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