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Initial Biomechanical Analysis and Modeling of Transfemoral Amputee Gait

C. Dundass, MSc
G. Z. Yao, PhD
C. K. Mechefske, PhD, P ENG

ABSTRACT The purpose of this study is to evaluate the effects of hydraulic knee controller deterioration on the gait of a single transfemoral amputee subject. As such, this should be considered a preliminary study. A set of gait experiments was developed and conducted to achieve this purpose. Although the subject did feel the difference between the deteriorated hydraulic controllers, no substantial deterioration trends were isolated in the kinematic or kinetic data collected at various stages of knee controller deterioration. A large variability was observed in the baseline gait trials that were recorded on different days. To eliminate the variability, a dynamic model of transfemoral amputee gait was developed based on the experimental data. The model predictions of ground reaction forces showed good agreement with experimental data. The effectiveness of the model was validated.

Keywords: Above-knee prosthesis, ground reaction force, kinematics, knee controller deterioration, simulation

Research on human gait has a long history, and numerous factors involved in the gait cycle have been investigated. Researchers examined the effects of different prosthetic designs in search of optimum prosthetic performance and evaluated the kinematics of the knee joint in response to various prosthetic design conditions. Stein and Flowers¹ investigated the effects of knee controller performance on amputee gait during stance phase. Van Der Linden et al.² studied the effect of various prosthetic feet on the biomechanics of transfemoral amputee gait. Blumentritt et al.³ performed a biomechanical study on seven transfemoral amputees who utilized rotary hydraulic prosthetic knees.

Kinetic gait analysis focuses on the internal and external forces that cause the motion. Previous transfemoral amputee kinetic gait research has investigated the impact of different prosthetic designs on the ground reaction force (GRF) profile. Van Der Linden et al.² used three force plates to capture the GRFs and moments of one complete stride and observed that the vertical GRF profile of the prosthetic limb never attained full body weight during stance phase. Gitter et al.⁴ evaluated kinetic gait information of eight transfemoral amputees using a single force plate to capture GRFs of the prosthetic limb. Sutherland et al.⁵ performed kinetic evaluation of two different prosthetic knee joints.

Models have been developed to represent and simulate conditions that occur in reality. Modeling human gait is an extremely difficult task because many factors and unknowns play significant roles in the behavior and control of the limbs. To minimize the complexity, researchers often model a specific event of gait rather than the entire process. Several models of the lower limbs have been developed to increase understanding of gait. However, very few amputee gait models have been created and validated. To date, the majority of transfemoral amputee modeling has focused on the swing phase of gait. Mohan et al.⁶ developed a mathematical model of the transfemoral prosthesis during swing phase to determine the optimal location for the center of gravity of the prosthesis. Bach et al.^7,8 also investigated the swing phase of the transfemoral amputee gait with the use of computer simulations. The study developed a ballistic model of swing phase to determine the optimal inertial loading for a transfemoral prosthesis.

The majority of previous research on transfemoral amputee gait has been almost exclusively dedicated to evaluating new prosthetic components and concepts to improve gait. While this is extremely valuable and necessary for enhancements in component technology, the long term performance and, specifically, the reliability of current and older prosthetics still being used by amputees have received little attention. No previous study has been conducted that attempts to evaluate the relationship between component deterioration and gait. This apparent gap is the motivation for conducting the knee controller deterioration experiments in this paper. Computational models developed for able-bodied subjects show the usefulness for the simulation of gait kinematics and kinetics. The motivation for the development of a dynamic model that appropriately models transfemoral amputee gait is clear from the absence of such a model in the literature.

One male unilateral transfemoral amputee participated in the study. The subject was 24 years of age and considered to be in excellent physical condition. He had a body mass of approximately 76 kg at the time of the experiments. His left leg was amputated at approximately 30 cm distal to the greater trochanter. Prior to testing, the subject signed an informed consent conforming to the policies of the University of Western Ontario Ethics Review Committee.

The kinematic and kinetic data were collected at the Occupational Therapy Gait Laboratory at The University of Western Ontario. The facility consisted of an elevated walking platform approximately seven meters in length. The walking platform contained two force plates (see Figure 1 ) that were aligned perpendicular to a kinematic camera unit. The first force plate (Advanced Mechanical Technology Inc., AMTI model #OR6-5-1000, Watertown, MA) recorded the GRF of the prosthetic limb. The second force plate (Kistler model #9261A, Amherst, NY) measured the GRF of the sound limb. The output from the AMTI force plate was fed through an AMTI Strain Gage Amplifier System. The output from the Kistler force plate was fed into a Kistler 9261A electronic unit. The kinematic data were collected using an Optotrack 3010 System made by Northern Digital Inc. (Waterloo, Ontario, Canada). The system uses three optical sensors capable of recording infrared light that is actively emitted from IRED markers attached to the limb. The 3D kinematic data and force plate data were simultaneously collected with the Optotrak Data Acquisition unit (Northern Digital, Inc.). The data files were recorded and stored on line with a 486 IBM computer (White Plains, NY).

During the set of experiments on knee controller deterioration, the subject wore a quadrilateral socket with an Ohio Willow Wood Model 90 Knee (Mt. Sterling, OH) controlled by a Catech hydraulic knee controller (Catech Systems, Toronto, Canada). The Catech controller consists of a piston and cylinder configuration accompanied by a compression spring. The level of viscous damping can be manually adjusted, enabling the user to set different resistance levels for knee flexion and extension. A Greissenger multi-axle prosthetic foot was attached to the shank (Otto Bock, Duderstadt, Germany). The geometric and physical properties of the Ohio Willow Wood limb were measured for the purposes of modeling. The approximate location of the center of mass of the foot and shank was determined by balancing them on a straight edge. The inertia of each segment was calculated using the pendulum technique as described by Chandler et al.⁹

The knee controller deterioration experiments were designed to investigate the effects of hydraulic knee deterioration on gait. The study involved interchanging the subject's Catech knee controller unit with artificially deteriorated Catech knee controllers. The gait laboratory knee controller experiments were performed in conjunction with a series of mechanical life cycle tests that were performed on the Catech knee controller units.¹⁰ The research involved cycling five knee controllers at 1 Hz in a life cycle test machine to simulate wear that would occur under normal use. The manufacturer of the knee controller estimates that the useful life of the unit is approximately 2,000,000 cycles (typically 2 years for an average transfemoral amputee). In this study, 2,000,000 cycles corresponded to 100% deterioration.

During laboratory testing of gait, the five knee controllers ranged in condition from 0% to 100% deterioration at constant intervals of 25%. The study involved five separate days of testing so that each knee controller was tested at every level of deterioration from 0% to 100%. Each day of gait testing, the subject performed a baseline test consisting of three walking trials at a self-selected comfortable speed with his own knee controller unit. Subsequent tests (also consisting of three walking trials at a self-selected speed) were performed with each deteriorated knee controller. The knee controller units were interchanged without removal of the prosthesis. The subject was given the opportunity to familiarize himself with each new controller. The gait data were recorded once the subject reported that he was comfortable with the prosthesis. The subject walked in a straight line, completing 1.5 strides before contacting the two force plates with the respective feet. Only trials in which the subject contacted both force plates with the respective feet were retained. The kinematics of the prosthesis was also recorded during the experiments. Three markers were attached to each segment of the prosthesis. Five seconds of kinematics and kinetics data were recorded at 100 Hz sampling rate for each trial.

The kinematic and kinetic data were processed and analyzed with Matlab for Windows. The force plate data were zeroed for each trial by averaging the first five sample points of each trial (the subject had not initiated contact with force plate yet) and subtracting the calculated average from remaining data points of each trial. The subject was considered to be in contact with the force plate any time the vertical force was found to be greater than or equal to five Newtons. The kinematic data were analyzed for periods when the sensors were in view. The periods before and after the subject was in view were eliminated. Any data points that were missing while the subject was in range were calculated by linear interpolation. The kinematic data were filtered with a recursive second order Butterworth digital filter with a cut-off frequency of 6 Hz as described in Winter et al.¹¹ The limb segment angles were calculated based on the conventions outlined by Winter.¹²

EXPERIMENTAL RESULTS AND DISCUSSION

To successfully sample all possible deterioration trends, the testing was carried out over 5 separate days. This allowed deterioration trends to be evaluated through two approaches; deterioration trends within an individual knee controller (over different days) and trends within a single day (between different controllers).

Figure 2 illustrates the average of three trials for the vertical GRF profile of the 0%, 50%, and 100% knee controller deterioration levels recorded on the fourth day of testing (25% and 75% deterioration conditions were omitted for clarity). Similarly, Figure 3 displays the anterior/posterior (A/P) GRF profile for the 0%, 50%, and 100% knee controller deterioration levels. The first set of GRF profiles (0-50 normalized time) in Figures 2 and 3 relates to the prosthetic side and the second set of curves (40-100 normalized time) represents the sound limb.

Figure 2 shows that the overall profiles for the vertical GRF were not greatly influenced by the change in deterioration of the knee controller units. The only area that illustrated a considerable difference was the magnitude and location of the first relative maximum on the prosthetic side. Further analysis of all five deterioration conditions revealed no substantial trend (R2=0.16) for the first relative peak of the prosthetic vertical GRF (see Figure 4 ).

It was hypothesized that high variability in the subject's gait in the area of the first local maximum of the GRF profile could have masked the emergence of any trends. Zahedi et al.¹³ used standard deviation as a method to measure step-to-step variation of a transfemoral amputee. A plot of standard deviation revealed that, in fact, the variation was greatest in the first peak region of the vertical GRF. Figure 5 shows a standard deviation envelope of the three trials representing the baseline testing performed at the beginning. The other knee deterioration conditions also revealed that the greatest variation occurred in the region of the first local maximum vertical GRF.

There was little difference among knee controller deterioration in the A/P GRF profiles (Figure 3 ). Several other distinguishable gait parameters of the GRF profile, such as loading rate, maximum braking and propulsion, zero shear point, symmetry ratio, braking impulse, propulsion impulse, and stance time were also investigated for any evidence of deterioration trends. All GRF parameters investigated displayed only weak associations with knee controller deterioration.

A final search for deterioration trends was conducted on the kinematic data. Figures 6 and 7 show the average of three trials for the knee and ankle angle of the prosthetic limb for the 0%, 50%, and 100% deterioration conditions, where HS denotes heel strike and TO denotes toe off. The analysis yielded similar results. No significant deterioration trends were isolated, presumably because of the large variation within the trials. The deterioration of the knee controller had no effect on the walking speed, which was self-selected by the subject.

Before performing a detailed analysis of the GRFs and kinematics of the 5 days testing results, a variability study was conducted and compared with the single day variability. A variability analysis within the 5 days of baseline testing illustrated higher variation than the variability within baseline testing on the same day. This result implied that the subject's gait varied from 1 test day to another more than typical variation between trials on the same day. Figure 8 shows the average vertical GRF profile (average of three baseline trials) of the prosthetic limb for each day of testing. It clearly shows variability in the baseline testing from 1 day to another.

A standard deviation analysis of the 5 days baseline data was also conducted and compared with the standard deviation from a single day baseline data. Figure 9 confirms that, in fact, the 5 days baseline tests did reflect larger standard deviations than baseline testing from a single day. The highest levels of variability in the 5 days data occurred in the region of the first and second maximum peaks (approximately 68 N and 56 N, respectively). The highest standard deviation in the single day data (42 N) was also recorded near the first maximum peak of stance phase. Zahedi et al.¹³ reported that the largest standard deviation within the vertical GRF profile of a transfemoral amputee occurred at the first maximum peak followed by the second maximum peak. Winter¹⁴ performed repeatability studies in able-bodied subjects and reported that the largest standard deviation of stance in the vertical GRF occurred at the first and second peaks. Winter also compared repeatability of gait between trials on the same day with trials on different days for able-bodied subjects. He reported that the vertical GRF coefficient of variation remained constant (10%) for the two conditions. This result contradicts the results from this study, which shows the variability in different days increased from the same day variability. It is not possible to speculate whether this trend holds for the general transfemoral amputee population without further testing of several amputee subjects to satisfy the requirements of a statistically significant study. However, Zahedi et al.¹³ did report that the amount of step-to-step variation among trials on the same day increased for amputees compared with healthy subjects.

The results show a large amount of variation in gait during different days of testing. This variability makes it difficult to isolate any significant deterioration trends within any given knee controller. It was hypothesized that the changes caused by the knee controller deterioration fall within or near the standard deviation envelope and, as such, are difficult to isolate and distinguish from typical variation in gait. However, the gait deterioration experiments were not without merit because much information and insight were gained about the gait strategies used by a transfemoral amputee. Specifically, variation among different days was found to be substantially higher than variation within the same day. This observation should be carefully considered for future amputee gait research that requires testing on different days.

Based on the experimental results of the amputee gait study, a clear conclusion about the effect of knee joint controller deterioration on various gait parameters could not be reached. However, the subject did report that he could feel the change in resistance in the lower limb motion caused by the deterioration of the knee joint controller. To precisely capture the effect of knee joint controller deterioration on gait, a mathematical model was developed to predict the behavior of transfemoral amputee gait. The model developed here could be used to study a full deterioration on transfemoral amputee gait.

Modeling human gait is an extremely difficult task, because many variables are simultaneously affecting the performance of the system. The GRF component is perhaps the most complex component of the gait cycle to model. In this model, the GRF component is a combination of the two models developed by Kaplan and Heegaard¹⁵ and Gilchrist and Winter.¹⁶ The foot was modeled as a single rigid body connected to the shank through the ankle joint. The shank and thigh were also modeled as rigid bodies. The knee controller was modeled as a spring with two dashpots. Only one dashpot was active at any given time depending on whether the knee joint was flexing or extending. To appropriately model the knee controller unit, a series of compression tests was carried out on an Instron tensile testing machine (Canton, MA) to evaluate the effective spring stiffness. The damping coefficients of the dashpots were selected through trial and error. Figure 10 shows the complete model with the main inputs and outputs indicated.

The model was constructed in Working Model 2D, version 4.0.1 for Windows. The software uses numerical integration to solve for the motion and forces of the system. Working Model uses a variable time step that is adjusted for each animation frame if the numerical error exceeds the allowable integration tolerance.

Simulation of gait was performed with the experimental thigh data used as an input to the model. For verification purposes, the GRFs were compared with experimentally obtained data. Figure 11 illustrates the comparison between the simulated and experimental results for the vertical GRF. The comparison shows that the overall profile of the predicted results closely track the shape of the experimental data. The predicted magnitudes of the first and second maximum peak and the relative minimum agree well with the experimental data (less than 25 N difference or 4% of max GRF). The temporal location of the relative minimum and second peak tracked the experimental data. The predicted first maximum peak occurred slightly earlier (0.04 seconds or 5% of stance) in stance phase than the measured data. The region that showed the greatest abnormality occurred in the unloading phase during late stance. It is unclear which aspect of the model caused this deviation. Perhaps it was related to the non-rigid toe component of the prosthetic foot, which was modeled as rigid. Regardless of this deviation, the stance time is still accurately predicted.

The purpose of the modeling in this article was to develop a model that accurately represented the behavior of the core components of a typical transfemoral limb. It is shown through direct evidence that the model results strongly correlate with the experimental results. Although this type of model has proved its merit and future potential, this model has been evaluated only with the characteristics of a single subject transfemoral amputee. Only more testing of other transfemoral amputees can provide a solid evaluation of the comprehensiveness of the model.

CONCLUSIONS

From a series of gait experiments, the kinematics and kinetics of an above-knee prosthetic limb were analyzed for any substantial knee controller deterioration trends. All gait parameters investigated showed only weak association with knee controller deterioration. A variability study was conducted to evaluate the variation of the subject's gait within baseline testing on the same day and over 5 days. Variability in the subject's GRF profile over 5 days was significantly larger than variation within the same day. The prosthetic limb first peak in the vertical GRF illustrated the largest variation for both the single day and 5 days data. It was concluded that the variability was sufficiently large to mask any trends of knee controller deterioration.

The predicted results of the dynamic model were consistent with the experimental data. The validation of the effectiveness of this model in predicting the behavior of transfemoral amputee gait will facilitate further development for this model to predict the behavior of full deterioration transfemoral prostheses.

The authors thank Dr. S. Spaulding of the Occupational Therapy Gait Laboratory at The University of Western Ontario for her assistance in collecting the experimental data. This research was sponsored by the National Sciences and Engineering Research Council of Canada.

C. DUNDASS is affiliated with Forensic Dynamics Inc., Kamloops, British Columbia, Canada.

G. Z. YAO is affiliated with the Department of Mechanical Engineering, Queen's University, Kingston, Ontario, Canada.

C. K. MECHEFSKE is affiliated with the Department of Mechanical Engineering, Queen's University, Kingston, Ontario, Canada. Prof. Chris Mechefske, Department of Mechanical Engineering, Queen's University, McLaughlin Hall, Kingston, Ontario, Canada K7L 3N6; 1-613-5333148; fax: 1-613-5336489. E-mail: chrism@me.queensu.ca

References:

1. Stein JL, Flowers WC. Stance phase control of above-knee prostheses: knee control versus sach foot design. J Biomech 1987;20:19-28.
2. Van Der Linden ML, Solomonidis SE, Spence WD, Li Ning, Paul JP. A methodology for studying the effects of various types of prosthetic feet on the biomechanics of transfemoral amputee gait. J Biomech 1999;32:877-889.
3. Blumentritt S, Werner Scherer H, Michael JW, Schmalz T. Transfemoral amputees walking on a rotary hydraulic prosthetic knee mechanism: a preliminary report. J Prosthet Orthot 1998;10:61-70.
4. Gitter A, Czerniecki J, Meinders M. Effect of prosthetic mass on swing phase work during above-knee amputee ambulation. Am J Phys Med Rehab 1997;76:114-121.
5. Sutherland JL, Sutherland DH, Kaufman KR, Teel M. Case study forum: gait comparison of two prosthetic knee units. J Prosthet Orthot 1997;9:168-173.
6. Mohan D, Sethi PK, Ravi R. Mathematical modeling and field trials of an inexpensive endoskeletal above-knee prosthesis. Prosthet Orthot Int 1992;16:118-123.
7. Bach TM, Barnes LJ, Evans OM, Robinson IG. Optimization of inertia characteristics of transfemoral limb prosthesis using a computer simulation of human walking. Proceedings of the Canadian Society for Biomechanics Eighth Biennial Conference, Calgary, Canada, 1994;212-213.
8. Bach TM, Barnes LJ, Evans OM, Robinson IG. Optimization of inertia characteristics of transfemoral limb prostheses: tests of predictions of a computer simulation. Proceedings of the Canadian Society for Biomechanics Eighth Biennial Conference, Calgary, Canada 1994;124-125.
9. Chandler RF, Clauser CE, McConville JT, Reynolds HM, and Young JW. Investigation of inertial properties of the human body. Aerospace Medical Research Laboratories, Wright-Patterson Air Force Base, Ohio, 1975; AMRL-TR-74-137, AD-A016-485. DOT-HS-801-430.
10. Mechefske CK, Yang Y. Failure diagnosis of a type of hydraulic knee joint controller. Prosthet Orthot Int 2001;25:148-153.
11. Winter DA, Sidwall HG, Hobson DA. Measurement and reduction of noise in kinematics of locomotion. J Biomech 1974;7:157-159.
12. Winter DA. Biomechanics and motor control of human movement. 2nd Ed. Hoboken, NJ: Wiley, 1990.
13. Zahedi MS, Spence WD, Solomonidis SE, Paul JP. Repeatabiliy of kinetic and kinematic measurements in gait studies of the lower limb amputee. Prosthet Orthot Int 1997;11:55-64.
14. Winter DA. The biomechanics and motor control of human gait. Waterloo, Ontario: University of Waterloo Press, 1987.
15. Kaplan ML, Heegaard JH. Energy-conserving impact algorithm for the heel-strike phase of gait. J Biomech 2000;33:771-775.
16. Gilchrist LA, Winter DA. A two-part, viscoelastic foot model for use in gait simulations. J Biomech 1996;29:795-798.