T. M. Bach, O. M. Evans and I. G. A. Robinson
La Trobe University, Melbourne, Australia

INTRODUCTION

The purpose of this investigation was to apply a computer simulation of swing phase in human walking to transfemoral (TF) amputee gait in order to determine the extent to which the simulation could predict characteristics of TF amputee gait and to determine whether the simulation could be used to predict optimal inertial loading of a TF prosthesis.

Accumulating evidence suggests that because inertial characteristics of limbs are important determinants of the normal gait pattern (Mochon and McMahon, 1980; Mena et al., 1981; Bach et al., 1993a), altered inertial characteristics in TF prosthetic limbs (Bach et al., 1993b) may be responsible, at least in part, for gait abnormalities observed in TF amputees. A number of investigators have demonstrated that the gait pattern could be improved (Menkveld et al., 1981; Tashman et al., 1985; Hale, 1990) and energy expenditure reduced (Skinner and Mote, 1989) with addition of mass to a TF prosthesis. However, only Skinner and Mote (1989) have attempted to identify an optimal inertial loading.

Computer simulation studies have also suggested that improved function could be obtained with heavier prostheses (Mena et al., 1981; Menkveld et al., 1981; Tsai and Mansour, 1986). The conclusions of these studies have been that the inertial characteristics of the prosthesis should be matched to the sound limb for best function. However, these computer simulation studies have utilized forward dynamic models with normal data (joint trajectories or muscle moments) as driving functions. It is therefore not unexpected that the closest match to normal function would be obtained with inertial characteristics matched to the sound limb. These models have failed to account for likely adaptive behaviours of the amputee designed to accommodate the drastic structural changes accompanying amputation and prosthetic replacement.

A ballistic model of swing phase in human walking has proved successful in predicting characteristics of normal and TF amputee gait (Bach et al., 1993a). The purpose of this paper is to describe a modified version of the model which can be used to predict optimal inertial loading for a TF prosthesis based on individual anthropometry and measured dimensions and inertial characteristics of the prosthetic limb. The model is adaptive in that it assumes that the amputee will establish different initial conditions at the end of double support in order to accomplish swing phase in an essentially ballistic manner.

METHOD

Two slightly different models were considered in this investigation. The version 1 model described previously (Bach et al, 1993a) consisted of four segments: three distributed mass segments representing the stance limb (thigh and shank), the swing thigh and the swing shank-foot with a point mass representing the head-arms-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 torsional spring. Equations of motion (Marshall et al., 1985) were implemented in a computer program which solved the equations and computed the motion of the system given initial positions and angular velocities of the segments. The problem is a two-point boundary value problem requiring six equations of constraint in order to determine a unique solution. Three of these equations constrained the initial positions of the three distributed mass segments such that, at toe off, step length was a specified distance and the stance limb had rotated as far forward as possible consistent with the toe of the swinging limb remaining in contact with the ground. Algorithms were constructed to compute initial angular velocities which satisfied three additional constraints that (1) at the completion of swing, the knee was fully extended, (2) step length achieved was the same as the previous step and (3) toe clearance during swing was equal to 1 cm for the sound limb (Winter, 1991) and 5 cm for the prosthetic limb (Murray et al., 1980). Energy expenditure for each step 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 each limb but not between limbs or between the limbs and the HAT.

The version 2 model differed only in that the toe clearance constraint (2 above) was replaced by a constraint which required that the initial angular velocity of the prosthetic thigh was equal and opposite to that of the prosthetic shank-foot. This assumption was based initially on theoretical considerations and was subsequently verified by experimental data.

A version 1 simulation was used to predict the gait pattern for the sound limb and both version 1 and version 2 models were used to predict the gait pattern for the prosthetic limb. Anthropometry was based on an individual of 82.4 kg mass and 1.78 m stature and prosthetic limb inertial parameters reported by Bach et al. (1993b) for an endoskeletal TF prosthesis. Two approaches to the optimization of inertial loading were considered: a mechanical energy cost approach and a gait symmetry approach. In the former, added mass and mass location were varied in order to determine a combination which minimized mechanical energy cost. In the latter approach a combination which minimized the difference between predicted sound and prosthetic limb swing phase duration was determined. A multi-dimensional downhill simplex method was used to determine the optimum in both cases.

RESULTS AND DISCUSSION

Both the version 1 and 2 models predicted relationships between step length and walking velocity and between swing phase duration and cadence which were consistent with observed characteristics of amputee gait (James and Öberg, 1973; Murray et al., 1980, 1983). The version 2 model predicted a relationship between toe clearance and walking velocity which was consistent with the observations of Murray et al. (1980, 1983). Predicted mechanical energy cost of amputee gait was substantially higher than the prediction for normal gait, a finding which is difficult to reconcile with limited empirical data (Winter, 1979; Goldbrandson and Writa, 1981)

The version 1 model failed to optimize using either of the approaches tested. For the energy cost approach, the optimization predicted zero added mass. For the symmetry approach, the optimization tended toward large masses added distally but eventually the model failed to solve because the boundary conditions could not be satisfied with the large added masses. The version 2 model could be optimized using either the energy cost approach or the symmetry approach. Optimal loads predicted by the simulation varied between 1kg and 2kg located between 10% and 50% of shank length below the knee. In both cases the predictions were sensitive to individual anthropometry and to walking velocity. There were, however, substantial differences in predicted masses and mass locations for the two approaches. Predictions of the two optimization approaches were similar to the empirical results reported by Skinner and Mote (1989). However, it was not possible to differentiate between the two optimization approaches based on the limited published empirical data.

Overall, the simulation results provided good evidence of construct and predictive validity of the model and provided an elegant explanation of observed behaviour in amputee locomotion. The optimization results have profound implications for the design and fabrication of TF prosthetic limbs.

REFERENCES

Bach, T. M. et al. (1993a) Proceedings of the IVth International Symposium on Computer Simulation in Biomechanics, France. pp BMR2-BMR5.
Bach, T. M. et al. (1993b) Proceedings of the XIVth International Congress on Biomechanics, France. pp130-131.
Chandler, R. F. et al. (1975). Tech. Report AMRL-TR-74-137. Wright-Patterson Air Force Base, Aerospace Medical Research Laboratories.
Goldbrandson, F. L. and Writa, R. W. (1981) Bull. Pros. Res.18:153.
Hale, S. A (1990) Pros. Orth. Int. 14: 125-135.
James, U. and Öberg, K (1973) Scand. J. Rehab. Med. 5:35.
Marshall, R. N. et al. (1985). J. Biomech. 18:359-367.
Mena, D. et al. (1981). J. Biomech. 14:823-832.
Menkveld, S. et al. (1981) Trans. 27th Ann. Meeting, Orthop. Res. Soc.5:51.
Mochon, S. and T. A. McMahon (1980). J. Biomech. 13:49-57.
Murray M. P. et al. (1980) Bull. Pros. Res. 17:35.
Murray M. P. et al. (1983) Arch. Phys. Med. Rehab. 64:339.
Skinner, H. B. and C. D. Mote (1989) Rehab. Res. Develop. Prog. Reports 26:32.
Tsai, C. S. and J. M. Mansour (1986). J. Biomech. Eng. 108:65-72.
Tashman, S. et al.(1985) Clin. Pros. Orth. 9:23.
Winter, D. A. (1979) Physio. Canada 30:183.
Winter, D. A. (1991). The Biomechanics and Motor Control of Human Gait. Waterloo, University of Waterloo Press.