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The 3-D motion of the centre of gravity of the human body during level walking. II. Lower limb amputees
Clinical Biomechanics Vol. 13, No. 2, pp. 83-90, 1998
© 1998ElsevierScienceLtd.All rightsreserved Printed in Great Britain 0268-0033/98$19.00+ 0.(X)
ELSEVIER PII: S0268-0033(97)00081-8
The 3-D motion of the centre of gravity of the human body during level walking. II. Lower limb amputees L Tesio 1,2, D Lanzi 2, C Detrembleur 3 l"Salvatore Maugeri" Foundation, IRCCS, Department of Research, Functional Assessment and Quality Assurance in Rehabilitation, and the Department of Rehabilitation, Pavia, Italy 2"San Raffaele" Hospital, IRCCS, Servizio di Fisiatria, Milan, Italy 3Service de M~decine Physique, Cliniques Universitaires Saint-Luc, Bruxelles, Belgium
Abstract
Objective. To analyse the motion of the centre of gravity (CG) of the body during gait in unilateral lower limb amputees with good kinematic patterns. (below-knee, BK) and four transfemoral (above-knee, AK) amputees were required to perform successive walks over a 2.4 m long force plate, at freely chosen cadence and speed. Background.In previous studies it has been shown that in unilateral lower limb amputee gait, the motion of the CG can be more asymmetric than might be suspected from kinematic analysis. Methods. The mechanical energy changes of the CG due to its motion in the vertical, forward and lateral direction were measured. Gait speed ranged 0.75-1.32 m s 1 in the different subjects. This allowed calculation of (a) the positive work done by muscles to maintain the motion of the CG with respect to the ground ('external' work, Wext) and (b) the amount of the pendulum-like, energy-saving transfer between gravitational potential energy and kinetic energy of the CG during each step (percent recovery, R). Step length and vertical displacement of the CG were also measured. Results. The recorded variables were kept within the normal limits, calculated in a previous work, when an average was made of the steps performed on the prosthetic (P) and on the normal (N) limb. Asymmetries were found, however, between the P and the N step. In BK amputees, the P step R was 5% greater and We×t was 21% lower than in the N step; in AK amputees, in the P step R was 54% greater and We×t was 66% lower than in the N step. Asymmetries were also found in the relative magnitude of the external work provided by each lower limb during the single stance as compared with the double stance: a marked deficit of work occurred at the P to N transition.
Design. Three transtibial
Relevance
In either BK or AK, amputees during gait may conceal-severe overlaoding of the healthy lower limb and underloading of the prosthetic lower limb, despite a good kinematics. The power provided by the prosthetic limb is minimal. The reduction of these ergometric asymmetries might be porposed as an index of effectiveness of the prosthetic treatment. © 1998 Elsevier Science Ltd. All rights reserved Key words: Walking, amputation, lower limb, prosthesis work, centre of gravity
C/in. Biomech. Vol 13, No. 2, 83-90, 1998 Introduction
Materials and design of prosthetic components for lower limb amputation undergo continuous technical improvements. These have fostered the adaptive Received. 13 November 1996;Accepted: l0 September 1997 Correspondence and reprint requests to: Dr Luigi Tesio, Department
of Rehabilitation, Fondazione "Salvatore Maugeri", via A. Ferrata, 8, 27111[)Pavia, Italy. e-mail: [email protected]
capacities of the patients. In transtibial (below-knee, BK) and transfemoral (above-knee, AK) unilateral amputations the energy cost of gait may be kept within normal limits I. Gait kinematics (step length and frequency, joint rotations) has also been shown to approximate normality 2,3. We propose that a more sensitive indicator of the consequences of the amputation on the overall mechanics of gait might be represented by the
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C/in. Biomech. Vol. 13, No. 2, 1998
measurement of the mechanical energy changes of the body system as a whole, represented by its centre of gravity, CG. On one hand, the mechanical energy changes of the CG can be easily synchronized with and interpreted in the light of other variables relating to body segments during motion (e.g. joint forces and angles, EMG tracings etc.); on the other hand, since they represent the end result of the positive work done by many muscles, the energy changes of the CG can be meaningfully related to the overalle nergy expenditure of gait. The purpose of this paper is to investigate the motion of the CG of the body in above- and below-knee amputees, as an example of application of this approach to the clinical evaluation of pathological gait.
Methods
Patients Table 1 summarizes the clinical information of the patients involved in this study. Patients w e r e all volunteers. They gave their informed consent to participate in the study. There were three BK and four AK adult amputees, comprising five men and two women, age between 20 and 39 years (median 33 years). The cause of amputation was a trauma for six of them, and osteosarcoma for one of them (subject a3). The amputation had occurred between 2 and 17 years (median 3 years) ago. Six of them had been using the prosthesis for 3 months-5 years (median 1 year). One subject (a3, 20 years since amputation) had been fitted with the present prosthesis 3 days earlier. Her new prosthesis, however, just replicated the previous one, which she had used for 2 years. All subjects walked independently and felt very comfortable with their devices. On visual inspection the gait pattern looked quite symmetric between the left and the right step. All of the patients were actively employed and presented with no other impairments.
Testing procedure
Clinical testing Patients were all under the care of the same physiatrist. In all cases the stump appeared hypotrophic, compared to the sound lower limb, with no skin lesions. R a n g e of motion was, in general, well preserved. In BK patients, the knee lacked 10-15 ° of full extension (goniometric measurement). In AK patients, hip excursion was 5-15 ° less than the neutral position. The isometric strnegth of the stump was graded 5 (hold against gravity and maximum pressure) according to the 0-5 Kendall's scoring4 in all movements. No motion anomalies were detected in the sound lower limb. While standing with the prosthesis on, six of the seven patients showed no
asymmetries ( > 0.5 cm) of leg length measured from great trochanter to ground. In subject a4 (AK amputation), the trochanter was found to be 1.5 cm higher on the amputated side. The prosthesis length was the one he preferred and currently adopted.
Methodology. Subjects wore a shirt and short pants and gym shoes with embedded switches signalling the foot-floor contacts (see below). Weight and height were measured on preicsion scales. Patients became accustomed to the experimental procedure by walking 4-5 times back and forth at their freely chosen cadence and speed over a force platform 0.6 m wide, 2.4 m long. In the experimental trials the subjects were invited to start about 2 m before the platform system, to walk at constant, freely-chosen, speed and cadence, and to stop no less than 2 m after the plates. The gait direction was reversed after each trial. Depending on the reproducibility of the tracings, 12-30 successive trials were requested, each followed by a rest of at least 4 min. The whole session lasted 2-4 h.
Data acqu&ition and processing. Data acquisition and processing followed the basic principles defined and adopted by Cavagna 5,~' and the methods described in a companion paper providing on healthy subjects y. The mechanical energy changes of the CG in the forward, vertical and lateral directions were calculated from the ground reactions recorded by a 2.4 m long force platform over which the ground reactions recorded by a 2.4 m long force platform over which the subject performed several subsequent steps. The average forward speed, Vf, was calculated through an optoelectronic system (see Ref. 7 for technical details). From each of the seven patients, 4-10 strides were found to be acceptable. The individual mean values were plotted, for comparison, over control values (mean+confidence limits, 7, see Figures 2 and 3).
Analysis of mechanical energy changes: within-step comparisons As described in a companion paper y, the changes in kinetic energy of the CG due to the motion in the forward (Ekf), lateral (Ekj) and vertical (Ekv) direction, the changes of gravitational potential energy (Ep), the changes of energy due to the vertical motion (Ev=Ekv+Ep) and the changes of total mechanical energy (E,,t = Ekf+Ekl+Ev) were calculated from the force paltform records. The sum of the energy increments during each step was calculated as work: Wr for Ekf, WI for Ekl, Wv for Ev, Wcxt, Wcx!for Etot. (1)
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The amount of muscular work recovered (R) through the pendular exchange between kinetic and potential energy (Ref. 7, eqn (1)), the step length, Si, and the vertical displacement, Sv, were measured. As a rule, Sv during the step performed mainly on the prosthetic limb (P step) was lower, compared to the step mainly performed on the normal limb (N step). Frequently the CG remained high, rather than being lowered and raised again, at the N/P transition, thus giving a false impression of symmetry in the work done against gravity between the two steps. For this reason, the highest level (Hv) reached during each step with respect to the lowest level reached during the stride was calculated independently from Sv. The a and b fractions of Wext (Figure 1) were measured separately on each step. The b increment is due to an upward push of the limb on ground during the single stance, while the subsequent a increment is due to the same lower limb, now in rear position during the double stance. The sum of increment b during, say, the stance on the left leg, and the subsequent increment a (at the left/right step transition) gives the
muscular work provided by the left leg to keep the body in motion. The average power provided during the a and the b increments can be calculated by dividing each energy increment by its duration. In healthy subjects, over the same speed range adopted by the patients (0.75-1.32m s ~) the a/b ratio for muscular power ranged 2.7-3.9, independent of speed (see Figure 5 in Ref. 7). It was hypothesized that (a) this ratio is not the same in amputees and that (b) it is not the same in the P step, compared to the N step. Four increments of Etot were independently measured: the b increments taking place during the single stance over the prosthetized (P) and the normal (N) limb and the a increments taking place at the P to N and the N to P transition (Figure
1). Results
Figure 1 shows typical experimental records from BK (left) and AK (right) patients. From top to bottom, the overlapping curves give, on the ordinate, the
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T i m e (s) Figure 1. From top to bottom the curves refer to the mechanical energy changes of the CG due to the motion in the forward, vertical and lateral direction (Ekf, Ev, Ekl), and their sum, Etot = Ekf+Ekl+Ev (note the 10-fold more sensitive scale for Ekl), as a function of time (normalized)• One entire stride (two subsequent steps), beginning with the step performed over the prosthetized (P) limb, was analysed in a transtibial prosthetized amputee (below-knee, BK, left) and in a transfemoral prosthetized amputee (AK, right) walking at their preferred speed. Each step begins when Ekf reaches a maximum (usually, while both feet are on ground). Curves from different strides, performed at about the same average speed ( + 10%), are superimposed. The bottom horizontal lines mark the time intervals in which the prosthetized, P, or the normal, N, foot is on ground. During the double stance and during the single stance phases of the stride an increment of Etot occurs (a and b, respectively), which must be necessarily sustained by positive muscle work. In amputee patients these increments can hardly be distinguished from each other in the P step.
Tesio et al: 3-D motion o f centre o f gravity during walking - - II
time-course of the mechanical energy changes of the CG in the forward, vertical and lateral directions (Ekf, Ev and Ekl, respectively), and their sum Etot during one stride (two subsequent steps). Records from successive trials were superimposed. The left and the right columns of tracings refer to a BK and an AK amputees, respectively. For clarity, the tracings referring to strides beginning with the P step were superimposed (5 and 7 strides for the BK and the AK amputee, respectively). Conventionally,
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Walking speed (m s -I) Figure 2. The four upper panels give the positive work done per unit mass and distance (on the ordinate) to sustain the changes of mechanical energy of the centre of gravity (CG) of the body during walking as a function of the average forward speed (on the abscissa). From top to bottom: Wf, Wv and W~ (note the 10-fold more sensitive scale) represent the work done to sustain the forward accelerations, the vertical lifts and the lateral accelerations of the CG, respectively. Wext is the muscular work done to sustain the increments of the total mechanical energy of the CG (Etot, see Figure 1). The bottom graph gives the amount of recovery, R, of mechanical energy. The crosses give the average and the 95% confidence limits in both axes calculated, in a previous work 7, in 125 steps performed by eight healthy subjects at various gait speeds. Each cross is centred over the mean speed recorded in one of the nine nearly-equally spaced bins, from 0.2 to 1.8 m s 1. The solid symbols give the mean values recorded in the seven amputees described in Table 1 (bl to b3 = below-knee amputees; al to a4 = above-knee amputees).
the step period begins when E k f reaches a maximum, after the ground contact of the P foot. Stride duration was normalized. The bottom horizontal lines mark the time intervals during which the P and the N lower limits were on ground. The overall pattern resembled that observed in normal subjects 7,s. A substantial pendulum-like energy transfer took place between (Ekf+Ekl) and Ev. In fact Etot, which in is the sum of Ekf, Ekl and Ev, had smaller increments than the sum of the increments of its components. Unlike normal subjects, substantial asymmetries were found between the two steps. During the P step, much lower increments (both a and b) of Eto t take place, compared to the N step. This reveals that during this step little muscle positive work is done to keep the body in motion, thanks to a nearly passive, pendulum-like oscillation over the prosthetic limb. Conversely, large increments of Etot do occur during the N step, suggesting that most of the work needed to keep the body in motion is provided by the unaffected lower limb. Note that the AK patient (right column of graphs) shows less consistent tracings. The positive work done to sustain the mechanical energy changes of the CG, and the pendular recovery of mechanical energy, R, are given as a function of speed in Figure 2. The crosses provide means and 95% confidence limits on both axes for 8 normal subjects over an 0.2-1.8ms 1 speed range 7. For
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Clin. Biomech. Vol. 13, No. 2, 1998
each variable, patients' values were averaged between the P and the N step and were superimposed on the corresponding graphs. Each subject was labelled as in Table 1. It can be seen that, on average, patients' values were within the confidence limits of the controls. In particular, Wext did not overcome the upper normal confidence limits. No distinct patterns for BK and AK patients could be seen. The same was true for the kinematic variables of the motion of the CG, shown in Figure 3: step length (Sb upper graph) and vertical displacement (Sv, lower graph), averaged between the P and the N step. The difference between the pathological and the normal step is illustrated in Figure 4, which gives the index of gait asymmetry6'7. The ordinate gives, on log scale, the ratio between the values recorded in the P and the N step, with respect to the variables given on the abscissa. The average of this ratio is 1 for normal subjects 6. Values above 1 indicate that more of a given variable was recorded in the P step, with respect to the N step. Records from all patients were presented together (BK, left graph, and AK, right graph). Data were graphically summarized in box-plot form. They showed that values of AK patients were more variable and less symmetrically distributed, compared to BK patients. This is consistent with the inconsistency of the energy tracings from successive trials in the AK subjects (see an example in Figure
1). Figure 4 shows that asymmetries did exist between the P and the N step, in both BK or AK patients, Wf, Wv and Wex t w e r e lower in the P step, whereas W~ tended to be higher in the P step. Absolute values of WI, however, were minimal (see Figure 2) so that they influenced either R or Wext minimally. During the P step R was, as a mean, 5% (median 8%) higher in BK patients and 54% (median 47%) higher in AK patients. On the contrary, the work, We×t, done by
muscles to translate the body system during the P step was, as a mean, 21% (median 40%) lower in BK patients and 66% (median 76%) lower in AK patients, compared to the N step. The kinematic variables, Sn and Hv, also showed lower values in the P step, but were much less asymmetric than Wcx t and R. In fact, all subjects walked without any gross asymmetry of kinematics. Figure 5 gives, on the ordinate, the average power provided by muscles to sustain the a and the b increments of Etot (see Figure 1) during an entire stride. Each data point refers to the mean values recorded in the various patients, labelled as in Table 1. The increments taking place at the transition between the normal and the prosthetic step (type-a increments, see Figure 1) give rise to the values plotted above the N/P label, on the abscissa. The same increments taking place at the transition between the P and the N step give rise to the values plotted over the P/N label. The increments taking place during the single stance (type-b increments, see Figure 1) on the prosthetic and the normal lower limb gave rise to the values plotted over the P and the N labels, respectively. The N/P,P,P/N,N,N/P sequence on the abscissa matches the prosthetized-normal step sequence depicted in Figure 1. From Figure 5 it is evident that the power provided by the P lower limb (P+P/N power values) was much smaller than the power provided by the N lower limb (N+N/P power values). This is in agreement with the asymmetry of We×t shown in Figure 4. The double stance/single stance (a/b) power ratios were smaller than normal, and differed between the two steps. Over the speed range of 0.75-1.32 m s recorded in our patients the normal subjects provided as an average 2.7-3.9 more power during the double stance (a increment of Etot, powered by the rear limb) than in the single stance (b increment of Etot, Above-Knee Amputation
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Tesio et al: 3-D motion of centre of gravity during walking - - II
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powered by the supporting limb; see Figure 5 in Ref. 7). In our patients the average a/b ratio of the power provided by the P limb (P/N step transition over P single stance) was, as a median, 0.35, while the average a/b ratio for the power provided by the N limb (N-P step transition over N single stance) limb was 1.7.
Discussion Our sample of amputee subjects was rather small, compared to the variety of the clinical pictures seen in this pathology. Therefore, caution must be taken in generalising the results. All of our amputee patients were able to move the body system in a way allowing a normal amount of muscular external work to be performed per unit distance (Figure 2). This is consistent with the evidence that the energy expenditure per unit distance can be normal in amputees walking at their preferred speed, when patients and normals are compared at the same speed ~,9. The highly asymmetric way the patients translated their body system, however, is evident (Figure 4). This seems to be in contrast with the good kinematic quality of gait which can be visually appreciated in properly fitted patients (Figure 3, see also Refs 2 and 3). On the other hand, the analysis of displacements of anatomical body segments cannot reveal, in itself, the energy changes of the CG, which is a virtual point representing the body system as a whole from a mechanical standpoint. Furthermore, most of the
work to propel the body system is done by each limb during ground contact, when much smaller joint rotations occur, with respect to the subsequent swing. In moving their stump, patients usually show a high level of skill, which has an interesting counterpart in the enlarged cortical representation of the stump itself 1°. One would expect that stumps become hypertrophic, to compensate for the lost muscle mass. Actually, stumps were atrophic, typical of these subjects. Furthermore, beyond hypotrophy, weakness of the stump, compared to the sound lower limb, is also a well known findingll,12: and this, despite the evidence for adaptive changes in the time course of the activation of hip flexors at pull-off, and of hip extensors at push-off3. Furthermore, our results show that limbs amputated either below or above the knee and provided with different types of prostheses worked much less than the normal lower limb (see the asymmetry of Wcxt in Figure 4). This fits with the finding that the total cost of gait shows few changes, if any, as a function of the prosthetic components and mechanisms~3 15. From a purely speculative perspective, one might say that stump atrophy is the consequence, rather than the cause, of a sort of 'locomotory neglect' made possible by the highly efficient energy-saving, pendulum-like oscillation over the prosthetic limb. In a previous ergometric study 1¢,, the underloading of the impaired limb was found also in patients with hemiplegia and unilateral hip arthritis. We suggest that this phenomenon is another example of 'learned non use', suspected to underlie
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Clin. Biomech. Vol. 13, No. 2, 1998
the lack of recovery of the paretic arm in hemiplegics 17't8. As a rule, in unilateral impairments 'learned non use' and contralateral compensation may be favoured over the 'intrinsic' recovery, whenever a task can be successfully completed by the unaffected side ~9. This might well be the case for gait which, as amputees demonstrate, can be sufficiently powered by the unaffected limb, only. It remains to be determined whether the results provided by this method can contribute to the clinical assessment of these patients. A more symmetric movement of the CG seems to be a desirable goal in itself, as far as it should indicate a greater reliance upon the prosthetic limb. These ergometric data consistently matched, and thus validated and complemented, the clinical findings. For example, more muscle mass remained in the amputated limb in BK, compared to A K patients. Correspondingly, the prevalence of the external work done during the N step, compared to the P step, was less evident in BK patients (Figure 4). More of the prosthetic lower limb remained under neural control in BK compared to A K patients. Correspondingly, the motion of the CG was more reproducible from trial to trial in BK compared to AK patients (Figure 1 and Figure 4). This suggests that knowledge of the mechanics of the CG may prove useful in tailoring the prosthesis and the exercise program on the needs of the individual patient, and in assessing the functional outcome. Nevertheless, a full understanding of the gait anomalies can only arise from multifactorial analyses. It must be recalled that the work done to move the CG can only account for a fraction of the total work done during gait, which is inclusive of the work done to move the limbs with respect to the CG itself"e°. Lengthening (so called 'negative' work) and isometric muscle contractions also contribute substantially the total energy expenditure, which is worthy of further research. Furthermore, the motion of the CG does not describe the underlying movements nor the neural control of individual body segments: these should also be analyzed 3.
Acknowledgements We thank A. Panini and the Officine Ortopediche Rizzoli, orthotists in Milan, for introducing their patients to us.
References 1. Tesio, L., Roi, G. S. and M611er, F. Pathological gaits: inefficiency is not a rule. Clin Biomech, 1991, 6, 47-50. 2. Frigo, C. and Tesio, L. Speed-dependent variations of lower-limb joints angles during walking. A graphic computerized method showing individual patterns. Am J Phys Med, 1986, 65(2), 51-62.
3. Winter, D. A., Olney, S. J., Conrad, J., White, S. C., Ounpuu S. and Gage, J. R. Adaptability of motor patterns in pathological gait. In Multiple Muscle Systems: Biomchanics and Movewment Organization, eds Woo, S. L. and Winters, J. M. Springer-Verlag, New York, 1990, pp. 680-693. 4. Kendall, F. P. and McCreary, E. K. Muscle Testingand Function, 3rd edn, Ch. 1. Williams & Wilkins, Baltimore, 1983. 5. Cavagna, G. A. Force platforms as ergometers. JAppl Physiol, 1975, 39(1), 174-179. 6. Cavagna, G. A., Tesio, L., Fuchimoto, T. and Heglund, N. C. Ergometric evaluation of pathological gait. JAppl Physiol, 1983, 55(2), 606-613. 7. Tesio, L., Lanzi, D. and Detrembleur, C. The 3-D motion of the centre of gravity of human body during level walking. I. Normal subjects at low and intermediate walking speeds. Mechanics of normal gait at low and intermediate speeds. Clin Biomech 1998 (submitted). 8. Cavagna, G. A., Thys, H. and Zamboni, A. The sources of external work in level walking and running. J Physiol, 1976, 262, 639-657. 9. Jaegers, S. M. H. J., Vos, L. D. W., Rispens, P. and Hof, A. L. The relationship between comfortable and most metabolically efficient walking speed in persons with unilateral above-knee amputation. Arch Phys Med Rehabil, 1993, 74, 521-525. 10. Fuhr, P., Cohen, L. G., Dang, N., Findley, T. W., Haghogji, S., Oro, J. and Hallett, M. Physiological analysis of motor reorganization following lower limb amputation. EEG Clin Neurophysiol, 1992, 85, 53-60. 11. Isakov, E., Burger, H., Gregoric, M. and Marincek, C. Isokinetic and isometric strength of the thigh muscles in below-knee amputees. Clin Biomech, 1996, 11(4), 233-235. 12. Burger, H., Valencic, V., Marincek, C. and Kogovsek, N. Properties of musculus gluteus maximus in aboveknee amputees. Clin Biomech, 1996, 11(1), 35-38. 13. Lehmann, J. F., Price, R., Boswell-Bessette, S., Dralle, A. and Questad, K. Comprehensive analysis of dynamic elastic response feet: Seattle ankle/lite foot versus SACH foot. Arch Phys Med Rehabil, 1993, 74, 853-861. 14. Boonstra, A. M., Schrama, J., Fidler, V. and Eisma, W. H. Energy cost during ambulation in transfemoral amputees: a knee joint with a mechanical swing phase control vs. a knee joint with a pneumatic swing phase control. Scand J Rehabil Med, 1995, 27, 77-81. 15. Czerniecki, J. M. and Gitter, A. J. Gait analysis in the amputee: has it helped the amputee or contributed to the development of improved prosthetic components?. Gait & Posture, 1996, 4, 258-268. 16. Tesio, L., Tessari, L. and Civaschi, P. Motion of the center of gravity of the body in clinical evaluation of gait. Am J Phys Med, 1985, 64(2), 57-70. 17. Wolf, S., Lecraw, D., Barton, L. and Jann, B. Forced use of hemiplegic upper extremities to reverse the effect of learned nonuse among chronic stroke and head-injured patients. Exp Neurol, 1989, 104, 125-132. 18. Taub, E., Miller, N., Novack, T., Cook, E., Fleming, W., Nepomuceno, C., Connell, J. and Crago, J. Technique to improve chronic motor deficit after stroke. Arch Phys Med RehabU, 1993, 74, 347-354. 19. Tesio, L. From neuroplastic potential to actual recovery after stroke: a call for cooperation between drugs and exercise (Letter). Aging, 1991, 3, 97-98. 20. Willems, P. A., Cavagna, G. A. and Heglund, N. C. External, internal and total work in human locomotion. J Exp Biol, 1995, 198(2), 379-393.
© 1998ElsevierScienceLtd.All rightsreserved Printed in Great Britain 0268-0033/98$19.00+ 0.(X)
ELSEVIER PII: S0268-0033(97)00081-8
The 3-D motion of the centre of gravity of the human body during level walking. II. Lower limb amputees L Tesio 1,2, D Lanzi 2, C Detrembleur 3 l"Salvatore Maugeri" Foundation, IRCCS, Department of Research, Functional Assessment and Quality Assurance in Rehabilitation, and the Department of Rehabilitation, Pavia, Italy 2"San Raffaele" Hospital, IRCCS, Servizio di Fisiatria, Milan, Italy 3Service de M~decine Physique, Cliniques Universitaires Saint-Luc, Bruxelles, Belgium
Abstract
Objective. To analyse the motion of the centre of gravity (CG) of the body during gait in unilateral lower limb amputees with good kinematic patterns. (below-knee, BK) and four transfemoral (above-knee, AK) amputees were required to perform successive walks over a 2.4 m long force plate, at freely chosen cadence and speed. Background.In previous studies it has been shown that in unilateral lower limb amputee gait, the motion of the CG can be more asymmetric than might be suspected from kinematic analysis. Methods. The mechanical energy changes of the CG due to its motion in the vertical, forward and lateral direction were measured. Gait speed ranged 0.75-1.32 m s 1 in the different subjects. This allowed calculation of (a) the positive work done by muscles to maintain the motion of the CG with respect to the ground ('external' work, Wext) and (b) the amount of the pendulum-like, energy-saving transfer between gravitational potential energy and kinetic energy of the CG during each step (percent recovery, R). Step length and vertical displacement of the CG were also measured. Results. The recorded variables were kept within the normal limits, calculated in a previous work, when an average was made of the steps performed on the prosthetic (P) and on the normal (N) limb. Asymmetries were found, however, between the P and the N step. In BK amputees, the P step R was 5% greater and We×t was 21% lower than in the N step; in AK amputees, in the P step R was 54% greater and We×t was 66% lower than in the N step. Asymmetries were also found in the relative magnitude of the external work provided by each lower limb during the single stance as compared with the double stance: a marked deficit of work occurred at the P to N transition.
Design. Three transtibial
Relevance
In either BK or AK, amputees during gait may conceal-severe overlaoding of the healthy lower limb and underloading of the prosthetic lower limb, despite a good kinematics. The power provided by the prosthetic limb is minimal. The reduction of these ergometric asymmetries might be porposed as an index of effectiveness of the prosthetic treatment. © 1998 Elsevier Science Ltd. All rights reserved Key words: Walking, amputation, lower limb, prosthesis work, centre of gravity
C/in. Biomech. Vol 13, No. 2, 83-90, 1998 Introduction
Materials and design of prosthetic components for lower limb amputation undergo continuous technical improvements. These have fostered the adaptive Received. 13 November 1996;Accepted: l0 September 1997 Correspondence and reprint requests to: Dr Luigi Tesio, Department
of Rehabilitation, Fondazione "Salvatore Maugeri", via A. Ferrata, 8, 27111[)Pavia, Italy. e-mail: [email protected]
capacities of the patients. In transtibial (below-knee, BK) and transfemoral (above-knee, AK) unilateral amputations the energy cost of gait may be kept within normal limits I. Gait kinematics (step length and frequency, joint rotations) has also been shown to approximate normality 2,3. We propose that a more sensitive indicator of the consequences of the amputation on the overall mechanics of gait might be represented by the
84
C/in. Biomech. Vol. 13, No. 2, 1998
measurement of the mechanical energy changes of the body system as a whole, represented by its centre of gravity, CG. On one hand, the mechanical energy changes of the CG can be easily synchronized with and interpreted in the light of other variables relating to body segments during motion (e.g. joint forces and angles, EMG tracings etc.); on the other hand, since they represent the end result of the positive work done by many muscles, the energy changes of the CG can be meaningfully related to the overalle nergy expenditure of gait. The purpose of this paper is to investigate the motion of the CG of the body in above- and below-knee amputees, as an example of application of this approach to the clinical evaluation of pathological gait.
Methods
Patients Table 1 summarizes the clinical information of the patients involved in this study. Patients w e r e all volunteers. They gave their informed consent to participate in the study. There were three BK and four AK adult amputees, comprising five men and two women, age between 20 and 39 years (median 33 years). The cause of amputation was a trauma for six of them, and osteosarcoma for one of them (subject a3). The amputation had occurred between 2 and 17 years (median 3 years) ago. Six of them had been using the prosthesis for 3 months-5 years (median 1 year). One subject (a3, 20 years since amputation) had been fitted with the present prosthesis 3 days earlier. Her new prosthesis, however, just replicated the previous one, which she had used for 2 years. All subjects walked independently and felt very comfortable with their devices. On visual inspection the gait pattern looked quite symmetric between the left and the right step. All of the patients were actively employed and presented with no other impairments.
Testing procedure
Clinical testing Patients were all under the care of the same physiatrist. In all cases the stump appeared hypotrophic, compared to the sound lower limb, with no skin lesions. R a n g e of motion was, in general, well preserved. In BK patients, the knee lacked 10-15 ° of full extension (goniometric measurement). In AK patients, hip excursion was 5-15 ° less than the neutral position. The isometric strnegth of the stump was graded 5 (hold against gravity and maximum pressure) according to the 0-5 Kendall's scoring4 in all movements. No motion anomalies were detected in the sound lower limb. While standing with the prosthesis on, six of the seven patients showed no
asymmetries ( > 0.5 cm) of leg length measured from great trochanter to ground. In subject a4 (AK amputation), the trochanter was found to be 1.5 cm higher on the amputated side. The prosthesis length was the one he preferred and currently adopted.
Methodology. Subjects wore a shirt and short pants and gym shoes with embedded switches signalling the foot-floor contacts (see below). Weight and height were measured on preicsion scales. Patients became accustomed to the experimental procedure by walking 4-5 times back and forth at their freely chosen cadence and speed over a force platform 0.6 m wide, 2.4 m long. In the experimental trials the subjects were invited to start about 2 m before the platform system, to walk at constant, freely-chosen, speed and cadence, and to stop no less than 2 m after the plates. The gait direction was reversed after each trial. Depending on the reproducibility of the tracings, 12-30 successive trials were requested, each followed by a rest of at least 4 min. The whole session lasted 2-4 h.
Data acqu&ition and processing. Data acquisition and processing followed the basic principles defined and adopted by Cavagna 5,~' and the methods described in a companion paper providing on healthy subjects y. The mechanical energy changes of the CG in the forward, vertical and lateral directions were calculated from the ground reactions recorded by a 2.4 m long force platform over which the ground reactions recorded by a 2.4 m long force platform over which the subject performed several subsequent steps. The average forward speed, Vf, was calculated through an optoelectronic system (see Ref. 7 for technical details). From each of the seven patients, 4-10 strides were found to be acceptable. The individual mean values were plotted, for comparison, over control values (mean+confidence limits, 7, see Figures 2 and 3).
Analysis of mechanical energy changes: within-step comparisons As described in a companion paper y, the changes in kinetic energy of the CG due to the motion in the forward (Ekf), lateral (Ekj) and vertical (Ekv) direction, the changes of gravitational potential energy (Ep), the changes of energy due to the vertical motion (Ev=Ekv+Ep) and the changes of total mechanical energy (E,,t = Ekf+Ekl+Ev) were calculated from the force paltform records. The sum of the energy increments during each step was calculated as work: Wr for Ekf, WI for Ekl, Wv for Ev, Wcxt, Wcx!for Etot. (1)
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The amount of muscular work recovered (R) through the pendular exchange between kinetic and potential energy (Ref. 7, eqn (1)), the step length, Si, and the vertical displacement, Sv, were measured. As a rule, Sv during the step performed mainly on the prosthetic limb (P step) was lower, compared to the step mainly performed on the normal limb (N step). Frequently the CG remained high, rather than being lowered and raised again, at the N/P transition, thus giving a false impression of symmetry in the work done against gravity between the two steps. For this reason, the highest level (Hv) reached during each step with respect to the lowest level reached during the stride was calculated independently from Sv. The a and b fractions of Wext (Figure 1) were measured separately on each step. The b increment is due to an upward push of the limb on ground during the single stance, while the subsequent a increment is due to the same lower limb, now in rear position during the double stance. The sum of increment b during, say, the stance on the left leg, and the subsequent increment a (at the left/right step transition) gives the
muscular work provided by the left leg to keep the body in motion. The average power provided during the a and the b increments can be calculated by dividing each energy increment by its duration. In healthy subjects, over the same speed range adopted by the patients (0.75-1.32m s ~) the a/b ratio for muscular power ranged 2.7-3.9, independent of speed (see Figure 5 in Ref. 7). It was hypothesized that (a) this ratio is not the same in amputees and that (b) it is not the same in the P step, compared to the N step. Four increments of Etot were independently measured: the b increments taking place during the single stance over the prosthetized (P) and the normal (N) limb and the a increments taking place at the P to N and the N to P transition (Figure
1). Results
Figure 1 shows typical experimental records from BK (left) and AK (right) patients. From top to bottom, the overlapping curves give, on the ordinate, the
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T i m e (s) Figure 1. From top to bottom the curves refer to the mechanical energy changes of the CG due to the motion in the forward, vertical and lateral direction (Ekf, Ev, Ekl), and their sum, Etot = Ekf+Ekl+Ev (note the 10-fold more sensitive scale for Ekl), as a function of time (normalized)• One entire stride (two subsequent steps), beginning with the step performed over the prosthetized (P) limb, was analysed in a transtibial prosthetized amputee (below-knee, BK, left) and in a transfemoral prosthetized amputee (AK, right) walking at their preferred speed. Each step begins when Ekf reaches a maximum (usually, while both feet are on ground). Curves from different strides, performed at about the same average speed ( + 10%), are superimposed. The bottom horizontal lines mark the time intervals in which the prosthetized, P, or the normal, N, foot is on ground. During the double stance and during the single stance phases of the stride an increment of Etot occurs (a and b, respectively), which must be necessarily sustained by positive muscle work. In amputee patients these increments can hardly be distinguished from each other in the P step.
Tesio et al: 3-D motion o f centre o f gravity during walking - - II
time-course of the mechanical energy changes of the CG in the forward, vertical and lateral directions (Ekf, Ev and Ekl, respectively), and their sum Etot during one stride (two subsequent steps). Records from successive trials were superimposed. The left and the right columns of tracings refer to a BK and an AK amputees, respectively. For clarity, the tracings referring to strides beginning with the P step were superimposed (5 and 7 strides for the BK and the AK amputee, respectively). Conventionally,
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Walking speed (m s -I) Figure 2. The four upper panels give the positive work done per unit mass and distance (on the ordinate) to sustain the changes of mechanical energy of the centre of gravity (CG) of the body during walking as a function of the average forward speed (on the abscissa). From top to bottom: Wf, Wv and W~ (note the 10-fold more sensitive scale) represent the work done to sustain the forward accelerations, the vertical lifts and the lateral accelerations of the CG, respectively. Wext is the muscular work done to sustain the increments of the total mechanical energy of the CG (Etot, see Figure 1). The bottom graph gives the amount of recovery, R, of mechanical energy. The crosses give the average and the 95% confidence limits in both axes calculated, in a previous work 7, in 125 steps performed by eight healthy subjects at various gait speeds. Each cross is centred over the mean speed recorded in one of the nine nearly-equally spaced bins, from 0.2 to 1.8 m s 1. The solid symbols give the mean values recorded in the seven amputees described in Table 1 (bl to b3 = below-knee amputees; al to a4 = above-knee amputees).
the step period begins when E k f reaches a maximum, after the ground contact of the P foot. Stride duration was normalized. The bottom horizontal lines mark the time intervals during which the P and the N lower limits were on ground. The overall pattern resembled that observed in normal subjects 7,s. A substantial pendulum-like energy transfer took place between (Ekf+Ekl) and Ev. In fact Etot, which in is the sum of Ekf, Ekl and Ev, had smaller increments than the sum of the increments of its components. Unlike normal subjects, substantial asymmetries were found between the two steps. During the P step, much lower increments (both a and b) of Eto t take place, compared to the N step. This reveals that during this step little muscle positive work is done to keep the body in motion, thanks to a nearly passive, pendulum-like oscillation over the prosthetic limb. Conversely, large increments of Etot do occur during the N step, suggesting that most of the work needed to keep the body in motion is provided by the unaffected lower limb. Note that the AK patient (right column of graphs) shows less consistent tracings. The positive work done to sustain the mechanical energy changes of the CG, and the pendular recovery of mechanical energy, R, are given as a function of speed in Figure 2. The crosses provide means and 95% confidence limits on both axes for 8 normal subjects over an 0.2-1.8ms 1 speed range 7. For
88
Clin. Biomech. Vol. 13, No. 2, 1998
each variable, patients' values were averaged between the P and the N step and were superimposed on the corresponding graphs. Each subject was labelled as in Table 1. It can be seen that, on average, patients' values were within the confidence limits of the controls. In particular, Wext did not overcome the upper normal confidence limits. No distinct patterns for BK and AK patients could be seen. The same was true for the kinematic variables of the motion of the CG, shown in Figure 3: step length (Sb upper graph) and vertical displacement (Sv, lower graph), averaged between the P and the N step. The difference between the pathological and the normal step is illustrated in Figure 4, which gives the index of gait asymmetry6'7. The ordinate gives, on log scale, the ratio between the values recorded in the P and the N step, with respect to the variables given on the abscissa. The average of this ratio is 1 for normal subjects 6. Values above 1 indicate that more of a given variable was recorded in the P step, with respect to the N step. Records from all patients were presented together (BK, left graph, and AK, right graph). Data were graphically summarized in box-plot form. They showed that values of AK patients were more variable and less symmetrically distributed, compared to BK patients. This is consistent with the inconsistency of the energy tracings from successive trials in the AK subjects (see an example in Figure
1). Figure 4 shows that asymmetries did exist between the P and the N step, in both BK or AK patients, Wf, Wv and Wex t w e r e lower in the P step, whereas W~ tended to be higher in the P step. Absolute values of WI, however, were minimal (see Figure 2) so that they influenced either R or Wext minimally. During the P step R was, as a mean, 5% (median 8%) higher in BK patients and 54% (median 47%) higher in AK patients. On the contrary, the work, We×t, done by
muscles to translate the body system during the P step was, as a mean, 21% (median 40%) lower in BK patients and 66% (median 76%) lower in AK patients, compared to the N step. The kinematic variables, Sn and Hv, also showed lower values in the P step, but were much less asymmetric than Wcx t and R. In fact, all subjects walked without any gross asymmetry of kinematics. Figure 5 gives, on the ordinate, the average power provided by muscles to sustain the a and the b increments of Etot (see Figure 1) during an entire stride. Each data point refers to the mean values recorded in the various patients, labelled as in Table 1. The increments taking place at the transition between the normal and the prosthetic step (type-a increments, see Figure 1) give rise to the values plotted above the N/P label, on the abscissa. The same increments taking place at the transition between the P and the N step give rise to the values plotted over the P/N label. The increments taking place during the single stance (type-b increments, see Figure 1) on the prosthetic and the normal lower limb gave rise to the values plotted over the P and the N labels, respectively. The N/P,P,P/N,N,N/P sequence on the abscissa matches the prosthetized-normal step sequence depicted in Figure 1. From Figure 5 it is evident that the power provided by the P lower limb (P+P/N power values) was much smaller than the power provided by the N lower limb (N+N/P power values). This is in agreement with the asymmetry of We×t shown in Figure 4. The double stance/single stance (a/b) power ratios were smaller than normal, and differed between the two steps. Over the speed range of 0.75-1.32 m s recorded in our patients the normal subjects provided as an average 2.7-3.9 more power during the double stance (a increment of Etot, powered by the rear limb) than in the single stance (b increment of Etot, Above-Knee Amputation
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Tesio et al: 3-D motion of centre of gravity during walking - - II
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powered by the supporting limb; see Figure 5 in Ref. 7). In our patients the average a/b ratio of the power provided by the P limb (P/N step transition over P single stance) was, as a median, 0.35, while the average a/b ratio for the power provided by the N limb (N-P step transition over N single stance) limb was 1.7.
Discussion Our sample of amputee subjects was rather small, compared to the variety of the clinical pictures seen in this pathology. Therefore, caution must be taken in generalising the results. All of our amputee patients were able to move the body system in a way allowing a normal amount of muscular external work to be performed per unit distance (Figure 2). This is consistent with the evidence that the energy expenditure per unit distance can be normal in amputees walking at their preferred speed, when patients and normals are compared at the same speed ~,9. The highly asymmetric way the patients translated their body system, however, is evident (Figure 4). This seems to be in contrast with the good kinematic quality of gait which can be visually appreciated in properly fitted patients (Figure 3, see also Refs 2 and 3). On the other hand, the analysis of displacements of anatomical body segments cannot reveal, in itself, the energy changes of the CG, which is a virtual point representing the body system as a whole from a mechanical standpoint. Furthermore, most of the
work to propel the body system is done by each limb during ground contact, when much smaller joint rotations occur, with respect to the subsequent swing. In moving their stump, patients usually show a high level of skill, which has an interesting counterpart in the enlarged cortical representation of the stump itself 1°. One would expect that stumps become hypertrophic, to compensate for the lost muscle mass. Actually, stumps were atrophic, typical of these subjects. Furthermore, beyond hypotrophy, weakness of the stump, compared to the sound lower limb, is also a well known findingll,12: and this, despite the evidence for adaptive changes in the time course of the activation of hip flexors at pull-off, and of hip extensors at push-off3. Furthermore, our results show that limbs amputated either below or above the knee and provided with different types of prostheses worked much less than the normal lower limb (see the asymmetry of Wcxt in Figure 4). This fits with the finding that the total cost of gait shows few changes, if any, as a function of the prosthetic components and mechanisms~3 15. From a purely speculative perspective, one might say that stump atrophy is the consequence, rather than the cause, of a sort of 'locomotory neglect' made possible by the highly efficient energy-saving, pendulum-like oscillation over the prosthetic limb. In a previous ergometric study 1¢,, the underloading of the impaired limb was found also in patients with hemiplegia and unilateral hip arthritis. We suggest that this phenomenon is another example of 'learned non use', suspected to underlie
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Clin. Biomech. Vol. 13, No. 2, 1998
the lack of recovery of the paretic arm in hemiplegics 17't8. As a rule, in unilateral impairments 'learned non use' and contralateral compensation may be favoured over the 'intrinsic' recovery, whenever a task can be successfully completed by the unaffected side ~9. This might well be the case for gait which, as amputees demonstrate, can be sufficiently powered by the unaffected limb, only. It remains to be determined whether the results provided by this method can contribute to the clinical assessment of these patients. A more symmetric movement of the CG seems to be a desirable goal in itself, as far as it should indicate a greater reliance upon the prosthetic limb. These ergometric data consistently matched, and thus validated and complemented, the clinical findings. For example, more muscle mass remained in the amputated limb in BK, compared to A K patients. Correspondingly, the prevalence of the external work done during the N step, compared to the P step, was less evident in BK patients (Figure 4). More of the prosthetic lower limb remained under neural control in BK compared to A K patients. Correspondingly, the motion of the CG was more reproducible from trial to trial in BK compared to AK patients (Figure 1 and Figure 4). This suggests that knowledge of the mechanics of the CG may prove useful in tailoring the prosthesis and the exercise program on the needs of the individual patient, and in assessing the functional outcome. Nevertheless, a full understanding of the gait anomalies can only arise from multifactorial analyses. It must be recalled that the work done to move the CG can only account for a fraction of the total work done during gait, which is inclusive of the work done to move the limbs with respect to the CG itself"e°. Lengthening (so called 'negative' work) and isometric muscle contractions also contribute substantially the total energy expenditure, which is worthy of further research. Furthermore, the motion of the CG does not describe the underlying movements nor the neural control of individual body segments: these should also be analyzed 3.
Acknowledgements We thank A. Panini and the Officine Ortopediche Rizzoli, orthotists in Milan, for introducing their patients to us.
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