A BALLISTIC SWING PHASE MODEL OF NORMAL AND TRANSFEMORAL AMPUTEE WALKING
T. M. Bach, O. M. Evans, I. G. A. Robinson
La Trobe University, Melbourne, Australia
INTRODUCTION
The purpose of this investigation was to examine the extent to which a ballistic swing phase model (Mochon and McMahon, 1980) could predict characteristics of normal walking and deviations from this pattern observed in transfemoral amputee gait. The investigation was prompted by recent debate about optimal inertial characteristics of prosthetic limbs.
REVIEW OF LITERATURE
Biomechanical models of human walking have been used mainly to describe the normal locomotor pattern while fewer attempts have been made to construct theoretical models or to identify performance objectives in walking (Marshall et al. 1989). Research which attempts to identify the underlying nature of human walking is essential to the development predictive biomechanical models.
Investigators dating back to Borelli have suggested that swing phase in human walking is an essentially ballistic action. Support for this concept comes from electromyographic and kinetic analyses of gait (eg. Winter, 1991) and from computer optimization studies which have suggested that joint torque minimization is the performance objective during swing phase (Marshall et al. 1989). Mochon and McMahon (1980) have demonstrated, using a computer simulation, that an entirely ballistic swing phase could be achieved by establishing appropriate initial conditions.
Because of evidence that the gait pattern is related to inertial characteristics of the limbs, it has been suggested that altered inertial characteristics of prosthetic limbs may be responsible in part for the asymmetric gait pattern of amputees and that a prosthetic limb should be inertially matched to the sound limb for optimal function (Mena et al., 1981; Tsai and Mansour, 1986). However, these studies have used kinematic and kinetic data obtained from normal subjects to drive models in which inertial characteristics were manipulated. The models therefore failed to account for the possibility of adaptive responses to altered inertial conditions.
The present investigation extended the ballistic model developed by Mochon and McMahon (1980) through more accurate representation of segment dimensions and inertial characteristics, improved numerical methods and more extensive comparisons with normative data. A method for estimating energy expenditure was developed and application of the model to transfemoral amputee gait was explored. The model offers advantages for investigations of inertial effects in amputee locomotion in that it is adaptive and does not require assumptions about driving functions.
METHOD
The model consisted of four segments: three distributed mass segments representing the stance limb (thigh and shank), the swing thigh and the swing shank/foot and a point mass representing the head, arms and trunk (HAT). Dimensions and inertial characteristics of the segments were based on data of Chandler et al. (1975). Joints were unconstrained except that the knee of the swing limb was prevented from hyperextending by a linear torsional spring. Equations of motion were derived (Marshall et al., 1985) and implemented in a computer program which solved for the motion of the system given initial positions and angular velocities of the segments. Duration of the simulated swing phase was from toe off until heel contact. The initial position was constrained by specifying step length and by assuming that the stance limb had rotated as far forward as possible consistent with the toe maintaining contact with the ground. Algorithms were constructed to choose initial angular velocities subject to the constraints that (1) at the completion of swing, the knee was fully extended, (2) the step length achieved was the same as the previous step and (3) the minimal toe clearance was equal to a specified value (1 cm, Winter, 1991). Double support duration was estimated by modelling the HAT as an inverted simple pendulum and integrating backward from the initial conditions to the stance limb angle at heel contact. Energy expenditure was estimated by summing the energy changes needed within each limb during double support in order to satisfy energy levels required at the beginning of the next swing phase. Energy exchanges were allowed within but not between limbs. For purposes of comparison, oxygen consumption per unit distance was estimated assuming standing oxygen consumption of 4.24 ml·kg-1min-1, an overall efficiency of 65% (Pierrynowski et al., 1980) and an oxygen equivalent of 20.3 J·ml-1.
RESULTS AND DISCUSSION
Model predictions of gait characteristics and energy expenditure are depicted in Figures 1, 2 and 3. In Figure 1 the predicted relationship between step length and walking velocity is compared to normative data from Dean (1965) and Grieve and Gear (1966). In Figure 2, predicted swing phase and double support phase duration are compared with normative data reported by Murray (1967) and Finley et al. (1975, cited in Inman et al. 1981). In Figure 3, predicted oxygen consumption is compared to regression equations reported by Zarrugh et al. (1974) and by Waters et al. (1990). Overall, very good agreement was obtained between predicted and observed characteristics.
Amputee simulations were performed by substituting prosthetic limb inertial characteristics based on measurements of a sample of nine transfemoral amputees. Simulations were performed using the same toe clearance constraint as normal walking (AMP1 in Figures 4 and 5) and using a toe clearance constraint of 5 cm (AMP5 in Figures 4 and 5) based on observations by Murray (1983). In Figure 4, the predicted relationship between step length and walking velocity for the normal limb and the prosthetic limb are illustrated. The results suggest that for a constant walking velocity, prosthetic step length would be longer than sound step length or that for equal prosthetic and sound step lengths, walking velocity would be greater during sound swing than during prosthetic swing. In amputees, Murray et al. (1983) have observed a combination of these asymmetries. In Figure 5, predicted swing and double support duration for sound and prosthetic limbs are plotted. Predicted swing phase duration was greater for the prosthetic limb than for the sound limb. Murray et al. (1983) reported sound swing phase durations of 0.43 s and prosthetic swing phase durations between 0.49 s and 0.57 s for free-speed walking. Prosthetic step lengths were 6 cm to 9 cm greater than sound step lengths. Although AMP1 and AMP5 simulations both predicted changes in the same direction as those reported by Murray et al., the AMP5 simulation provided much better predictions of the magnitude of these changes.
Attempts were made to estimate energy expenditure for amputee gait based on similar assumptions to those used for normal gait and including the possibility of changes in HAT total energy as a result of changes in velocity between prosthetic and sound stance phase. Predicted energy expenditure was similar to or lower than predictions for normal gait contrary to the universal observation of increased metabolic cost in amputee locomotion. It is probable that the high overall efficiency reported for normal locomotion (Pierrynowski et al., 1980) does not apply to amputee gait in part because of the loss of elastic structures in the lower limb. It is also probable that movements in the coronal plane not considered in the simple planar model contribute to higher mechanical work in amputees.
CONCLUSIONS
Despite the simplicity of the model, very good agreement with published data was obtained for characteristics of normal and amputee gait and for energy requirements in normal walking. This investigation suggests that the underlying nature of the gait pattern is related to an essentially ballistic swing phase with appropriate initial conditions established during double support.
Results of amputee simulations suggested that altered inertial parameters of prosthetic limbs contribute in part to asymmetries observed in amputee gait. However, increased toe clearance during prosthetic swing appeared to be a more important factor in determining differences between sound and prosthetic limbs. Increased toe clearance may be a result of a conscious attempt by the amputee to ensure safety during swing phase or may be a result of an inability to establish appropriate initial conditions due to the loss of muscular control of the knee.
The goal of continuing research in our laboratory is to optimize amputee gait using the model to suggest changes in inertial parameters and adjustments of knee componentry.
REFERENCES
Chandler, R. F. et al. (1975). Tech. Report AMRL-TR-74-137. Wright-Patterson Air Force Base, Aerospace Medical Research Laboratories.
Dean, G. A. (1965). Ergonomics 8:31-47.
Grieve, D. W. and R. J. Gear (1966). Ergonomics 5:379-399.
Inman, V. T. et al. (1981). Human Walking. Baltimore, Williams and Wilkins.
Marshall, R. N. et al. (1985). J. Biomech. 18:359-367.
Marshall, R. N. et al. (1989). Hum. Movement Sci. 8:571-594.
Mena, D. et al. (1981). J. Biomech. 14:823-832.
Mochon, S. and T. A. McMahon (1980). J. Biomech. 13:49-57.
Murray, M. P. et al. (1983). Arch. Phys. Med. Rehabil. 64:339-345.
Murray, M. P. (1967). Am. J. Phys. Med. 46:290-333.
Pierrynowski, M. R. et al. (1980). Ergonomics 23:147-156.
Tsai, C. S. and J. M. Mansour (1986). J. Biomech. Eng. 108:65-72.
Waters, R. L. et al. (1990). J. Orthop. Res. 9:253-257.
Winter, D. A. (1991). The Biomechanics and Motor Control of Human Gait. Waterloo, University of Waterloo Press.
Zarrugh, M. Y. et al. (1974). Eur. J. App. Physiol. 33:293-306.
Amputee simulations were performed by substituting prosthetic limb inertial characteristics based on measurements of a sample of nine transfemoral amputees. Simulations were performed using the same toe clearance constraint as normal walking (AMP1 in Figures 4 and 5) and using a toe clearance constraint of 5 cm (AMP5 in Figures 4 and 5) based on observations by Murray (1983). In Figure 4, the predicted relationship between step length and walking velocity for the normal limb and the prosthetic limb are illustrated. The results suggest that for a constant walking velocity, prosthetic step length would be longer than sound step length or that for equal prosthetic and sound step lengths, walking velocity would be greater during sound swing than during prosthetic swing. In amputees, Murray et al. (1983) have observed a combination of these asymmetries. In Figure 5, predicted swing and double support duration for sound and prosthetic limbs are plotted. Predicted swing phase duration was greater for the prosthetic limb than for the sound limb. Murray et al. (1983) reported sound swing phase durations of 0.43 s and prosthetic swing phase durations between 0.49 s and 0.57 s for free-speed walking. Prosthetic step lengths were 6 cm to 9 cm greater than sound step lengths. Although AMP1 and AMP5 simulations both predicted changes in the same direction as those reported by Murray et al., the AMP5 simulation provided much better predictions of the magnitude of these changes.
Attempts were made to estimate energy expenditure for amputee gait based on similar assumptions to those used for normal gait and including the possibility of changes in HAT total energy as a result of changes in velocity between prosthetic and sound stance phase. Predicted energy expenditure was similar to or lower than predictions for normal gait contrary to the universal observation of increased metabolic cost in amputee locomotion. It is probable that the high overall efficiency reported for normal locomotion (Pierrynowski et al., 1980) does not apply to amputee gait in part because of the loss of elastic structures in the lower limb. It is also probable that movements in the coronal plane not considered in the simple planar model contribute to higher mechanical work in amputees.