Gait and Posture 12 (2000) 243– 250 www.elsevier.com/locate/gaitpost

Motion of the body centre of gravity as a summary indicator of the mechanics of human pathological gait C. Detrembleur a,*, A. van den Hecke b, F. Dierick a,b a

Uni6ersite´ catholique de Lou6ain, Unite´ de Re´adaptation, Tour Pasteur 5375, A6enue Mounier 53, B-1200 Brussels, Belgium b Cliniques uni6ersitaires Saint-Luc, Ser6ice de Me´decine Physique, A6enue Hippocrate 10, B-1200 Brussels, Belgium Received 28 February 2000; received in revised form 23 March 2000; accepted 11 July 2000

Abstract Abnormal movements of the body segments due to lowest level gait disorders such as musculoskeletal disorders, peripheral neuropathies and radiculopathies or middle-level disorders such as hemiplegia, paraplegia and dystonia influence the motion of the centre of gravity (CG) during walking. The translation of the CG can be studied by the work done by muscles (WExt) with respect to the ground. The efficacy of gait’s mechanism can be quantified by the energy transferred between gravitational potential and kinetic energies (recovery). WExt and recovery were investigated in lowest and middle-level gait disorders during level walking. No statistical significant difference was observed between patients with lowest-level gait disorders and normal subjects. However, WExt was increased for the patients with middle-level gait disorders and recovery decreased up to 20%. The measurement of changes in mechanical energy of the CG might be a summary indicator for the mechanics of pathological gait. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Pathological gait; Mechanics; External work; Recovery

1. Introduction The mechanism of human gait can be examined mainly by a biomechanical and/or a neurophysiological approach. The biomechanical approach [1] proposes that the mechanics of gait (mechanical characteristics of the body segments and the external forces) dictate the locomotor mechanism while the neurophysiological approach [2] emphasises the importance of neural networks (central pattern generator networks, CPGs) that are located within the spinal cord and modulated by peripheral afferents and descending influences. From a mechanical standpoint [1], combined movements of different body segments during locomotion are the result of the interaction between muscle activity, dictated by the CNS, and the mechanical demands of the locomotor activity. The motion of the centre of gravity (CG) of the body, representing the whole body system in movement, is the ultimate result of both * Corresponding author. Tel.: +32-2-7645375; fax: +32-27645360. E-mail address: [email protected] (C. Detrembleur).

energy expenditure and motions of the body segments. The work done by muscles to translate the CG (external work) with respect to the ground is one determinant of the energy expenditure of gait [3]. Central nervous system disorders affecting the pyramidal or extrapyramidal systems and musculoskeletal disorders disturb normal movements of the body segments during gait. These abnormal movements influence the motion of the CG of the body. In this way, a detailed analysis of how lowest-level [4] (musculoskeletal disorders, peripheral neuropathies or radiculopathies) or middle-level [4] (hemiplegia, paraplegia or dystonia) gait disorders alter the motion of the CG may be a summary indicator of the mechanism of walking. During level walking, the CG motion may be compared to the motion of an inverted pendulum. At each step, the CG is successively behind, or in front of the point of contact with the foot on the ground. When the CG is behind the point of contact, the link to the ground causes a forward deceleration (therefore a decrease in the kinetic energy due to the forward speed) and a vertical rise in the CG (therefore an increase in gravitational potential energy). Some of the kinetic

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energy due to the forward speed is converted into gravitational potential energy. As the CG moves forward of the point of contact on the ground, the link to the ground allows a decrease in height of the CG and a concomitant increase in the forward velocity, as some of the gravitational potential energy is converted back into the kinetic energy due to the forward speed. If the movements of the CG were equal to that of an ideal frictionless pendulum, the fluctuations of the kinetic energy due to the forward speed and gravitational potential energy would be equal and opposite, the total energy of the CG would be constant, and no external work would be required to maintain the motion [5]. However, humans are not ideal frictionless pendulums, the kinetic and potential energy is not perfectly conserved, and consequently the total energy of the CG fluctuates. Nevertheless, the increments of total energy of the CG are below the sum of the increments of the kinetic energy due to the forward and lateral speeds and gravitational potential energy indicating that at least some energy is conserved. The recovery expresses the amount of muscular work through the pendular exchange between potential and kinetic energy. In an ideal frictionless pendulum, the recovery would be 100%; in normal subjects, the recovery attains a maximum of 60% during unloaded gait at the optimal speed [5]. The aim of this study was to evaluate the mechanics of human pathological gait among patients with lowest or middle-level gait disturbances. We hypothesised that the measurement of the mechanical energy changes of the CG of the body might be a summary indicator of the consequences of the lowest or middlelevel gait disorders. Only few studies have focused on the analysis of the body’s CG during neurological [6,7] or orthopaedic disorders [6,8]. In addition, none of these studies tried to compare different levels of gait disorders with the mechanics of gait.

2. Patients, subjects and methods

2.1. External mechanical energy of the body Data recording and processing followed the principles defined and adopted by Cavagna (1975) [9] and used by other investigators [6,8,10 – 12]. A straingauge platform (1.8 m long and 0.6 m wide), made of seven plates of different sizes (insert Fig. 1; Pharos System Inc., MA) was mounted at ground level in the middle of a walkway (10 m long). The plates had a natural frequency of 125 Hz for the three small plates and 250 Hz for the remainder. All plates had linear response within 1% of the measured value for masses up to 100 kg. The differences in electrical response to

a given force applied at different points on the surface of the seven plates was less than 4.5% in all directions. The ‘cross-talk’ between the vertical, forward and lateral axis was, at worst, 1–2.5% of the applied force. The plate signal was sampled at 50 Hz, digitized by 12-bit A/D converter (RTI800-Analog Devices converter, MA) and summed in all three directions by software. The subject’s weight, measured on a precision scale, was subtracted from the vertical forces. The sagittal, transverse and vertical accelerations were obtained from the respective forces and were then integrated to give the speed changes of the CG in all three directions, relative to constants of integration. These constants were the average velocities in the vertical, lateral and forward directions [9]. The records of the speed changes in all directions were used to decide whether or not a record was acceptable for analysis. The criterion for rejecting the trials was that, within the selected steps, the sum of the increments of forward, vertical and lateral velocity change exceeded by more than 40% the sum of the corresponding decrements, thus revealing a clear trend toward increase or decrease of the average velocity [8]. From the instantaneous velocity in forward, lateral and vertical directions, the instantaneous kinetic energy Ekf = 0.5(m V 2f ), Ekl = 0.5(m V 2l ) and Ekv = 0.5(m V 2v) can be calculated. The sum of the increments of the kinetic energy represents the positive work required to accelerate the CG of the body. Whereas Ekf and Ekl represent respectively the total mechanical energy of forward (i.e. Ef = Ekf) and lateral (i.e. El = Ekl) directions, the vertical motion also involves changes of gravitational potential energy (Ep). Ep was calculated from vertical displacement and added to Ekv to obtain the total mechanical energy of vertical motion (i.e., Ev = Ep + Ekv). However, at low and intermediate walking speeds (less than 4 km h − 1), Ekv is very small in normal gait [13] and in pathological gait, Ekv = 2.9%9 2.7% of Ev, so that Ev  Ep. The increments of Ef, El and Ev represent the positive work necessary to accelerate the CG in forward and lateral directions and to lift the CG (Wf, Wl, Wv) and were calculated for each step of the stride. Ef, El and Ev were added to obtain the total mechanical energy of the CG (Etot = Ef + Ev +El = Ekf + Ekl + Ekv + Ep). The positive external work done by muscles, WExt, was obtained by adding the increments of Etot in each step of the stride. It is known that WExt can be smaller than Wf + Wl + Wv because of a transfer between Ep and Ef, such as it occurs in a pendulum. The percent of recovery of mechanical energy, R, due to the passive exchange between Ef, Ev and El was then calculated according to the equation: R=100*(Wf + Wv + Wl − WExt)/(Wf + Wv + Wl).

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2.2. Kinematics and electromyographic data recording

EMG as described by Van Boxtel et al. [15].

Kinematics and electromyographic data from patients were recorded simultaneously to force signals. Timing of left and right ground contacts was recorded through dedicated foot-switch soles at 1000 Hz (Elite System 5.0, BTS, Milan, Italy). Kinematics data were recorded by four infrared cameras measuring the co-ordinates of passive markers at 50 Hz (Elite System 5.0, BTS, Milan, Italy). Movements of pelvis, hip, knee and ankle in sagittal, transversal and frontal planes were determined using the three-dimensional-segmental model of Davis et al. [14]. Myoelectrical activity of rectus femoris, semitendinosus, triceps surae, tibialis anterior was recorded by surface electrodes (MediTrace, Graphics Controls Corporation, Buffalo, NY). The electromyogram (EMG) was recorded with a telemetry system (Telemg, BTS, Milan, Italy). The signal was digitalized at 1000 Hz and filtered (band-pass 25 – 300 Hz). The onset and cessation of muscle activity were determined by computing the threshold voltage of

2.3. Patients and subjects

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Twenty-eight patients (12 men and 16 women) participated in the study. Informed consent was obtained for each subject. The main characteristics of the 28 patients are shown in Table 1. Patients were divided into two groups: lowest-level and middle-level gait disorders. The patients with lowest-level gait disorders (4 men and 10 women) had an average age of 47.8 (S.D. 12) years, height of 1.68 (0.08) m, and weight of 71.7 (15) kg. Five patients were affected bilaterally and nine patients unilaterally (four right and five left sides). The patients with middle-level gait disorders (eight men and six women) had an average age of 39.9 (S.D. 18) years, height of 1.63 (0.15) m, and weight of 68.4 (20) kg. Seven patients were affected bilaterally and seven patients unilaterally (four right and three left sides). All patients suffered from disturbances which were functionally detrimental to gait from visual gait observa-

Fig. 1. Typical kinematics, electromyographic activity and external work across normal subject and two patients. Hip (Fig. 1A), knee (Fig. 1B) and ankle (Fig. 1C) motions in sagittal plane plotted with the percentage of gait cycle. The mean ( 9 1 S.D.) is plotted for normal subject (Elite Software reference— thin line), for patient with orthopaedic disorder (Table 1: number 14, female, 34 yrs, 1.82 m, 64 kg) and for patient with neurological disorder (Table 1: number 28, male, 20 yrs, 1.80 m, 67 kg). The subjects walked in same range of speed (between 2.9 and 3.3 km h − 1). Electromyographic data (Fig. 1D) are displayed in normalised to 100% of stride. The horizontal bars indicate the normal (white bars) and pathological (black bars and grey bars) phasic activity of the muscles sampled. Fig. 1E shows WExt who represents the muscular work done to sustain the changes of the total mechanical energy of the centre of gravity of the body. Fig. 1F gives the pendular recovery of muscular work, R, due to passive exchange between kinetic and potential energy. Values are averaged into following forward speed classes from 0.5 km h − 1 between 1 and 4 km h − 1. Vertical and horizontal bars represent the standard deviations for normal subjects. Symbols indicate the mean values obtained for the two patients. Insert shows a view of the platform.

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tions and quantitative gait analysis. Patients were instructed to walk at their spontaneous speed. Each patient made an average of 69 2 trials. Kinetics, kinematics and electromyographic data were recorded simultaneously and synchronised by two photocells. All of the signals were processed by an IBM compatible personal computer using customised software (Elite System 5.0, BTS, Milan, Italy). Control data (n= 26 strides obtained in eight normal subjects walking at different speeds from 1 to 4 km h − 1) were taken from a previous study [16]. For normal subjects and patients, 66 strides were analysed. As WExt and recovery varied with walking speed, results were grouped into following forward speed classes: 1–1.49 km h − 1 (n = 7 strides), 1.5 –1.99 km h − 1 (n= 8 strides), 2 – 2.49 km h − 1 (n = 8 strides), 2.5 – 2.99 km h − 1 (n = 16 strides), 3 – 3.49 km h − 1 (n = 16 strides), 3.5 – 3.99 km h − 1 (n = 11 strides). In each range of speed, the result was expressed as the mean for the same subject. Results were also grouped following the classification of gait syndromes [4]: lowest-level gait disorders (n =18 strides), middle-level gait disorders (n=22 strides) and normal gait (n =26 strides). A two-way measures ANOVA with Tukey test (SigmaStat for Windows V2.0, SPSS Sciences Software Gmbh, Erkrath, Germany) was performed to evaluate the effect of pathology and walking speed on gait recovery.

3. Results Fig. 1 (A,B,C) shows mean hip, knee and ankle motions in the sagittal plane for two patients and normal reference data (Elite System 5.0, BTS, Milan, Italy). Walking speed was in same range between 2.9 – 3.3 km h − 1. The patient with the lowest-level gait disorder (number 14, female, 34 yrs, 1.82 m, 64 kg) had equinus resulting from a laceration of the Achilles tendon. Ankle plantar flexion was exaggerated throughout gait cycle (Fig. 1C — thick black line). The patient with the middle-level gait disorder (number 28, male, 20 yrs, 1.80 m, 67 kg) had an acquired right hemiplegia. Ankle plantar flexion was also exaggerated throughout gait cycle (Fig. 1C — thick grey line). For both patients, a stiff knee and an abnormal flexion in stance phase and restriction of hip extension in toe-off were observed secondary to the equinus (Fig. 1A, B). Abnormal muscle activity of the lower limb was also observed for each patient (Fig. 1D). Overactivity of rectus femoris was noticed in stance. Semitendinosus activity was prolonged throughout gait cycle for patient with the middle-level gait disorder, triceps surae activity was exaggerated in swing and tibialis anterior was silent in terminal swing. The consequences of disturbed movements and abnormal muscle activity on the mechanism

of gait are illustrated in Fig. 1E, F. The patient with lowest-level gait disorder was able to move her body in such a way to allow a normal amount of external muscular work to be performed per unit distance (Fig. 1E). The pendular exchange between potential and kinetic energy was intact (Fig. 1F). The patient with the middle-level gait disorder moved his body with an excessive amount of external muscular work performed per unit distance. The pendular exchange between potential and kinetic energy was more affected. Fig. 2 shows three typical experimental recordings from a normal subject (Fig. 2A female, 36 yr, 1.5 m height, 50 kg weight), a patient with right knee arthritis (Fig. 2B —patient number 12 (Table 1), female, 41 yr, 1.56 m height, 93 kg weight) and a patient with familial spastic paraparesis (Fig. 2C—number 21 (Table 1), male, 45 yr, 1.8m height, 101 kg weight). The overlapping curves, reading from top to bottom, give, on the ordinate, the time-course of the mechanical energy of the CG in the forward, vertical and lateral directions (Ef = Ekf, Ev = Ep + Ekv and El = Ekl, respectively), and their sum Etot during one stride. Recordings from successive trials (normal: n= 3, arthritis: n= 4, paraparesis: n=4) were superimposed. Stride duration was normalised. In normal gait, the maximum of Ef and El is reached during the double-stance period, whereas the maximum of Ev is reached during the single stance period. A substantial pendulum-like energy transfer can thus take place, and the Etot curve has smaller increments than either of its main components, Ef, Ev and El. The exchange between Ef, El and Ev, however is not sufficient to maintain constant the total mechanical energy. The overall pattern of patient with knee arthritis (Fig. 2B) was closely similar to the one observed in normal subject (Fig. 2A). A substantial pendulum –like energy transfer took place between Ef, El and Ev. However, increments of El and Ev were greater than normal values. The overall pattern of the patient with familial spastic paraparesis (Fig. 2C) was radically different from the one observed in a normal subject. The changes of Ev were 10-fold greater than normal values and no substantial pendulum –like energy transfer took place between Ef, El and Ev. The weight-specific positive work done per unit distance to sustain various energy increments during gait is plotted in Fig. 3 as a function of speed. In the left panel, from top to bottom the figure shows Wf, Wv, Wl. In the right panel, from top to bottom the figure shows WExt and the recovery of mechanical energy due to the pendular transfer between gravitational potential energy and kinetic energy of the CG. Vertical and horizontal bars give the standard deviations of the averages within each group speeds. The dots represent mean values obtained for normal subjects [16]. Black circles represent the mean values obtained for patients with lowest-level gait disorders. White circles represent the

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Fig. 2. Mechanical energy changes of the centre of gravity during walking. A. Normal subject was a woman, 36 yr, 1.5 m height, 50 kg weight. B. Orthopaedic patient was a woman, 41 yr, 1.56 m height, 93 kg weight (number 12 — Table 1). C. Neurological patient was a man, 45 yr, 1.8 m height, 101 kg weight (number 21 — Table 1). From top to bottom, the curves refer to the mechanical energy changes of the centre of gravity of the body due to the motion in forward, vertical and lateral directions (Ef =Ekf, Ev =Ep +Ekv, El =Ekl) and their sum, Etot =Ef +Ev + El. Several entire strides are presented for each patient. Curves from different strides, performed at about the same average speed ( 9 10%), are superimposed.

mean values obtained for patients with middle-level gait disorders. Taking speed into account, the difference in the mean values of Wf among the different groups was not statically significant difference (Table 2, p =0.624). However, Wv and Wl (Table 2, p =0.001) were statistically greater than normal values for all patients. WExt was statistically greater than normal values for patients with middle-level gait disorders and the recovery statistically smaller (Table 2, p =0.001). For patients with middle-level gait disorders, WExt was five times greater than normal values and recovery was twice less. Moreover, the recovery was constant at all speeds (R = 20% between 1.1 and 3.2 km h − 1) (Fig. 3). No statistical difference was observed between patients with the lowest-level gait disorders and normal subjects for WExt (Table 2, p=0.06) and recovery (Table 2, p = 0.86).

4. Discussion The neurophysiological control of locomotion can be divided into three functional systems. Firstly, locomotion has to be initiated and speed controlled. Secondly, locomotion has to be in the desired direction, the feet have to be placed properly, and obstacles avoided. Thirdly, equilibrium has to be maintained during the movements of the body [2]. In our study, only the first system is considered and discussed. Our mechanical

approach does not allow us to consider the second and third systems. Neurophysiological investigations relating to the spinal contribution involved in the locomotor mechanism have been and are largely dependent on animal work [17]. We used an original model of human pathological gait in an attempt to gain a better understanding of pathological gait in the lowest and middlelevel gait disorders. An effective pendulum-like mechanism may be obtained by widely varying patterns of motion of the body segments [18]. Impaired motion secondary to orthopaedic pathologies, inducing lowest-level gait disturbances, did not reduce the recovery of mechanical energy during gait. These patients conserved the energy between the kinetic energy of forward motion and the potential energy of their CG. Their mechanical system, i.e. inverted pendulum was not affected by musculoskeletal pathologies and a normal amount of muscular external work was performed per unit distance. This finding is similar to that found in African women who can carry head-supported loads up to 20% of their body weight without increasing their external mechanical work of walking [19]. These results suggest that gait can adapt to some musculoskeletal disorders or extra loads. In our study, we did not investigate peripheral neuropathic gait disorders. As these patients are classified in the lowest-level gait disorders [4], it seems reasonable to assume that the motion of the CG could be the same

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as in musculoskeletal disorders. In this case, WExt and recovery variables could be a sensitive indicator to distinguish between central and peripheral neurological disorders. Further investigations of peripheral neuropathic gait disorders will be needed to confirm this hypothesis. On the other hand, central nervous system pathologies causing middle-level gait disturbances, profoundly modified the recovery of gait. In this case, the mechanical system was altered: external mechanical work increased and the recovery did not exceed 20%. Thus there appeared to be little adaptation of gait recovery to central neurological disorders. A hypothesis involving central pattern generators (CPGs) in the spinal cord may explain this observation. These consist of a neuronal network that allows rhythmical signals to the muscles to be generated without sensory input from the moving body [2]. This CPG network could generate a simple pattern with alternation between flexor and extensor muscles or complex motor patterns, e.g. locomotion in the lamprey [20]. The CPG network controlling locomotion must be sufficiently robust to avoid disruption of the locomotor activity. The musculoskeletal pathology in the patients with lowest-level gait disor-

ders did not appear to affect the CPG network and the mechanism of locomotion was intact. However, the CPGs can be influenced by neural pathways descending from the brain to the spinal cord and could, in turn, influence locomotor performance. The experiments of Orlovsky [21] suggest that the corticospinal system has the potential to influence the cycling of the spinal CPGs. In our patients with middle-level gait disorders, the cerebral cortex and the pyramidal or extrapyramidal tracts were damaged. The CPGs network were thus affected and the mechanism of locomotion altered. Our findings suggest that the three-dimensional motion of the CG may be a new tool for clinical practice. The measurement of external work may be a useful tool to evaluate the effect of interventions on gait recovery. This summary indicator could be particularly useful for patients with middle-level gait disturbances which profoundly modify the recovery of gait and may help validate new procedures to improve function of patients with lower limb spasticity. We believe that the assessment of the external work is a summary indicator for the mechanics of gait. This is easy to measure and may be obtained from the output of an ergometer. It must be recalled that the

Table 1 Patient’s biometrics data and clinical features. Number° Lowest-level gait disorders 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Middle-level gait disorders 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Sex

Age(yrs)

Height(m)

Weight(Kg)

F M F M F F F M F F M F F F

50 35 52 43 63 53 41 31 46 70 66 41 44 34

1.65 1.70 1.68 1.82 1.60 1.58 1.65 1.70 1.65 1.60 1.79 1.56 1.67 1.82

60 70 82 83 90 63 50 49 85 60 72 93 83 64

F F M F M M M F F M M M F M

18 18 18 39 43 69 45 40 38 33 67 64 47 20

1.46 1.50 1.40 1.60 1.73 1.60 1.80 1.58 1.58 1.88 1.70 1.75 1.50 1.80

43 45 40 59 84 61 101 61 54 88 75 74 105 67

Etiology

Bilateral gonarthrosis Right ankle sprain (trauma) Bilateral gonarthrosis Left gonarthrosis Left gonarthrosis Left hip arthrosis Bilateral amputation of toes (trauma) Left knee sprain (trauma) Left ankle sprain (trauma) Bilateral gonarthrosis Right hip fracture (trauma) Right gonarthrosis Bilateral gonarthrosis Right tendon Achilleus’ cutting (trauma) Left hemiplegia Familial spastic paraparesis Familial spastic paraparesis Right hemiplegia Spastic tetraparesis Normal pressure hydrocephalus Familial spastic paraparesis Familial spastic paraparesis Left hemiplegia Right hemiplegia Normal pressure hydrocephalus Left hemiplegia Right hemiplegia Right hemiplegia

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Fig. 3. Work done by muscles to move the centre of gravity and the recovery. Muscular work (W) done to sustain the changes of the mechanical energy of the centre of gravity of the body in all directions is calculated as the sum of the positive increments on each curve on Fig. 2. On the left and from top to bottom, Wf, Wv, Wl represent the work done per unit distance and weight during gait to sustain respectively the forward accelerations, the vertical lifts, and the lateral accelerations of the centre of gravity as function of speed. On the right, WExt represents the muscular work done to sustain the changes of the total mechanical energy of the centre of gravity of the body (Etot, see Fig. 1). The lower panel gives the pendular recovery of muscular work, R, due to passive exchange between kinetic and potential energies. Values are averaged into following forward speed classes from 0.5 km h − 1 between 1 and 4 km h − 1. Vertical and horizontal bars represent the standard deviations. Table 2 Results of a two-way measures ANOVA with post hoc results (Tuckey Test). Wf, Wv, Wl, WExt are expressed in J kg−1 m−1a df WfFactor group’’Factor ‘‘speed’’ WvFactor ‘‘group’’Factor ‘‘speed’’ WlFactor ‘‘group’’Factor ‘‘speed’’ WExtFactor ‘‘group’’Factor ‘‘speed’’ Reco6eryFactor ‘‘group’’Factor ‘‘speed’’ a b

F

Tuckey test on factor ‘‘group’’

p

25

0.483.46

0.6240.008b

25

33.702.45

B0.001b0.044b

Normal vs lowest-level, pB0.001bNormal vs middle-level, p =0.022bLowest vs middle-level, pB0.001b

25

20.951.96

B0.001b0.097

Normal vs lowest-level, pB0.001bNormal vs middle-level, pB0.001bLowest vs middle-level, p = 0.66

25

36.502.69

B0.001b0.030b

Normal vs lowest-level, p =0.06Normal vs middle-level, pB0.001bLowest vs middle-level, pB0.001b

25

14.776.45

B0.001bB0.001b

Normal vs lowest-level, p =0.86Normal vs middle-level, pB0.001bLowest vs middle-level, pB0.001b

Recovery is expressed in%; df=degrees of freedom. Statically significant.

work done to move the CG can only account for a fraction of the total work during gait. More research is necessary to evaluate the internal work expended to move the limbs or energy expenditure are necessary to gain a better understanding of the mechanisms of pathological gait

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