Scientific Methods to Determine Functional Performance of Prosthetic Ankle-Foot Systems

Andrew H. Hansen, PhD

Not too long ago there were only a few kinds of prosthetic ankle-foot systems in widespread clinical use. However, today there are many prosthetic ankle-foot mechanisms that are commercially available and being used clinically. With the influx of these new mechanisms, a flurry of investigations ensued in an attempt to understand their function, specifically in comparison with the older standard ankle-foot components. Research studies of these devices had the clear and well-intentioned goal of understanding and identifying the specific products that could most benefit persons with amputations, depending on their health and functional level, so that the most appropriate components could be prescribed. Although many insights have been gained through research, it seems that the search for answers to questions regarding the function of prosthetic ankle-foot systems is ongoing. This article describes two methodological approaches used to determine differences and similarities in function between prosthetic ankle-foot types, lists the most consistent results of both approaches, and discusses a new method of analyzing the function of these devices that may tie contradictory results together.

METHODS TO DETERMINE FUNCTIONAL PERFORMANCE

Two general categories can be used to describe the kinds of methods used to study the function of prosthetic ankle-foot mechanisms. The most common category is human subjects testing, i.e., measurements made of the devices in use by persons with amputations. The less common category is mechanical properties testing of prosthetic ankle-foot systems, i.e., measurements made of the devices without human interaction. Both approaches have advantages and disadvantages. A research approach that incorporates a combination of these methodological approaches used in conjunction with modeling of human movements may lead to a clearer understanding of prosthetic ankle-foot function.

HUMAN SUBJECTS TESTING

Many studies have measured movement characteristics of persons with amputations using different prosthetic anklefoot mechanisms. These data can take the form of subjective information acquired from questionnaires or quantitative information acquired from measurements of physiologic behavior. Questionnaires are frequently administered to obtain information directly from the user about perceived benefits or drawbacks of a device in comparison with another.^1-9 Questions are often related to perceptions users have during specific movements with the device, but questions can also be asked regarding the cosmetic appearance of the device and other factors not related to movement. Users generally answer multiple-choice questions or rate the extent to which they agree or disagree with a particular statement regarding a device. This type of scaling is called a Likert scale if five or more levels are available for selection.¹⁰ Some questionnaires are set up to have a user mark a line between opposite extreme answers to a statement (e.g., between "strongly agree" and "strongly disagree"). The researcher can then measure the distance along the line to have a continuous scale between the extremes. This type of response is named a visual analogue scale¹⁰ and is used in the Prosthesis Evaluation Questionnaire developed by Prosthetics Research Study.¹¹ Qualitative data from questionnaires are important for understanding user preference for devices and can be used to form hypotheses regarding quantitative measurement results.

Many methods have been used in an attempt to quantify differences in walking performance when using various prosthetic ankle-foot systems. Nearly all studies on prosthetic ankle-foot systems involve some analysis of human movement with the devices. The most common form of movement assessment is gait analysis on level ground,^2,4-6,12-36 although gait of persons has also been studied on stairs²⁵ and on upward and downward sloping ramps.^2,13,23 Frequently, the user is asked to walk at a variety of speeds to see if differences between components will be more apparent at higher or lower speeds. This is done not only to see how users perform with the components at different walking speeds, but also to help distinguish components that will be more appropriate for persons with different levels of walking ability.

Perhaps the most frequently measured factors of gait are walking speeds that persons self-select (sometimes normal, slow, and fast speeds), step lengths or stride lengths, and cadence (steps/minute). Another common focus of gait analysis research is the measurement of angles between body segments, particularly in the sagittal plane. Hip, knee, and ankle flexion and extension angles are most frequently examined and can be measured in a variety of ways on a human subject including frame-by-frame analysis of video, collection of data from electrogoniometers (electrical devices for angular measurement), and automatic capture of motion from commercially available motion analysis systems. It is common to use existing rigid link models intended for ablebodied persons toward the study of persons with amputations. This approach models the prosthetic ankle-foot system as a device with an articulation (joint), even though not all systems have joints. The movement measured at the "ankle" joint in these feet is highly dependent on the material properties of the ankle-foot system and on the placement of the heel, ankle, and forefoot markers on the ankle-foot system. The "pseudo-dorsiflexion"³⁶ measured should be analyzed and interpreted with caution.

Ground reaction forces (GRFs) can be measured during walking using special platforms embedded in the floor. Three components of these forces in a laboratory-based coordinate system are frequently examined: vertical GRFs, anterior-posterior GRFs, and medial-lateral GRFs. Because most of the motion in walking is in the sagittal plane, attention is usually focused on the vertical and anterior-posterior components of the ground reaction force. The center of pressure of the GRF can also be found using force and moment data from the platform and from other platform specific data. If GRFs and their centers of pressure are measured simultaneously with motion data, they can be combined to find joint moments. If using a link-segment model, some assumptions must be made including the mass of the various segments, the location of each segment's center of gravity, and the rotational inertia of the segments. The link segment model uses a combination of dynamic equations developed from free body diagrams of each of the segments to find moments at the joints between segments. The system of equations is normally solved within specialized software packages. Joint moments can also be found by multiplying the GRF by the perpendicular distance from the joint to the GRF. This approach is acceptable at the ankle, but problematic at the knee and hip joints according to a comparison of these moments with those found by solving the link segment model equations.³⁷ Multiplying the moments at the joints by their rotational velocities is sometimes used to create joint power estimates. The rotational velocities are most often found by a numerical differentiation of joint angular motion data, which at the "ankle" can be problematic for some prosthetic ankle-foot systems. The area under ankle power versus time curves have been measured as estimates of energy storage and return in prosthetic mechanisms. Errors associated with the assumption of a true ankle articulation propagate and affect these measurements.

Human gait is periodic and is commonly sectioned into gait cycles. Researchers frequently compare movements of the person's body when using various prosthetic ankle-foot mechanisms at similar times in the gait cycle. Maximum or minimum values may be compared during the whole or part of a gait cycle as well as ranges of movements. The timings of various events within a gait cycle have also been studied to try to determine differences among various ankle-foot components.

Measures intended to reflect a person's energy expenditure during walking have been used to examine manufacturers' claims of energy storage and release of some types of feet. The rate of oxygen consumption has been measured and compared when persons use different types of prosthetic anklefoot mechanisms. The oxygen cost is found by dividing the oxygen consumption rate by the walking speed to estimate the amount of oxygen needed to move per unit distance. Other factors that have been measured (rarely) during walking include muscle activity (electromyography), percent of maximum theoretical heart rate, frequency components of acceleration at various body segments, velocity of body segment rotations, pressure measurements on the residual limb, pulse plethysmography, and transcutaneous oxygen tension in residual limb tissue.

Human subjects testing is necessary for evaluation of hypotheses related to ankle-foot prosthetic components because it yields results that are most relevant to the actual use of the devices. However, the extremely adaptive nature of the human can make it difficult to distinguish differences among prosthetic ankle-foot systems during their use. Other factors that exist in human subjects studies such as alignment, socket type, and the shoes that are used can also make results difficult to interpret.

MECHANICAL PROPERTIES TESTING

The testing of prosthetic feet outside of the human-device system is important for understanding the mechanical differences among prosthetic feet. Although mechanical properties testing can illustrate clear differences among feet without concern for some of the external factors associated with human subjects testing, it must be performed with care to most closely match conditions that would be experienced in clinical use.

A frequent test of material properties is to load a device or material in incremental steps and simultaneously monitor the displacement of the device or material under the load. This type of testing has been performed with prosthetic feet at a variety of loading angles that correspond to shank angles during walking.^21,22,38 If the loading is done in a static or quasi-static (slow) manner, the force versus deflection curve can give an indication of the stiffness of the foot at that given loading angle. These types of tests have been used to see which feet are "stiffer" and which feet are more "compliant" in the heel region, for example. More dynamic loading tests (faster loading) can be used to obtain combined effects of the stiffness and damping of the prosthetic ankle-foot system. When used in combination with quasi-static testing and assuming a particular mechanical model of stiffness and damping for the foot, the damping ratio and damping coefficient can be estimated. Specific types of loading are generally used such as a step load or unload of the system. These kinds of loading inputs are used because the transient responses of particular spring-damper systems to them have been widely characterized in physics and engineering textbooks.

The loading and unloading portions of the force versus deflection curve are often not the same and form what is called a hysteresis loop. For passive systems, the area within the hysteresis loop can be used as an estimate of energy that is lost in the system during a loading and unloading cycle. Hysteresis has been studied in prosthetic ankle-foot systems in an attempt to measure energy losses in their materials.^29,39 Postema et al.²⁹ compared energy storage and return measured in a mechanical testing device with that found using the area under an ankle power versus time curve and noted differences. In the mechanical apparatus, they measured the area under a force versus displacement curve during heel-totoe loading similar to that seen during walking. This approach may be more accurate because it does not assume an ankle joint within the system.

The natural frequency of a system is the frequency at which it will oscillate during a transient response to a step input. For example, if a spring-mass system is pushed away from its resting equilibrium point and let go, the mass will oscillate at the natural frequency of the system. Natural frequencies of prosthetic ankle-foot systems when connected with mass levels similar to that of the human have been investigated to estimate the degree of dynamic reaction prosthetic ankle-foot systems may have in walking and running.^21,22,38

MOST CONSISTENT RESULTS OF PROSTHETIC ANKLE-FOOT TESTING

Perhaps the most consistent result of human subjects testing is the lack of significant differences that have been found in gait characteristics when persons walk with various kinds of prosthetic feet. The significant results are covered in recent review articles.^40-47

Various studies have shown an increased "ankle" range of motion and increased dorsiflexion in late stance phase when using the Flex-Foot compared with other kinds of prosthetic feet. Another rather consistent finding is a reduced first peak of the vertical ground reaction force on the sound limb and a longer step length on the sound limb when the Flex-Foot was used compared with other systems. These findings have sometimes occurred in the same studies and have led authors to hypothesize the causal relationship that increased late stance dorsiflexion will reduce limb loading on the sound side and may allow a prosthesis user to take a longer step on that side. This type of relationship may be problematic when taken to extremes. Hypothetically, a soft rubber or foam foot with no keel would yield large amounts of measured "dorsiflexion" at late stance but the step length would likely be reduced on the sound limb and a drop-off effect could result. This dropoff effect could actually increase the loading on the sound limb in early stance.

The most consistent result of mechanical properties testing is that prosthetic ankle-foot systems have widely different properties when tested outside the human-device system. The stiffness properties of prosthetic ankle-foot systems cover a broad spectrum, and the location of the net loading force is highly variable between foot types. The natural frequencies of prosthetic ankle-foot systems reacting with body mass have been found to be much higher than usage frequencies in walking and even running. These results indicate that design changes would be needed to make feet resonate with the body's mass during walking or running gaits. However, the changes required to make feet resonate with body masses may not be desirable for walking.²¹ Damping values for prosthetic ankle-foot systems have also been found to be quite low. The main consequence of natural frequency and damping test results is that prosthetic ankle-foot systems can be modeled fairly accurately with quasi-static methods, greatly simplifying the analysis of these systems.³⁸

The results of both types of tests, human subjects and mechanical properties testing, seem contradictory. Although human subjects tests show very few differences among prosthetic ankle-foot systems, mechanical properties testing has shown large differences in mechanical characteristics among the various feet. A new methodology for analyzing prosthetic ankle-foot function may lend some insight into these differences and help to explain results of both types of tests.

A NEW METHOD OF ANALYZING PROSTHETIC ANKLE-FOOT FUNCTION

A new method has been developed for analyzing the function of prosthetic ankle-foot mechanisms. The method involves the measurement of the center of pressure (COP) of the net force on a prosthetic ankle-foot system during walking or under loads that simulate walking within a coordinate system that is fixed to a rigid part of the device, namely at its attachment point with a pylon or socket (Fig. 1 ). The development of this approach was influenced by the results of many researchers studying able-bodied and disabled persons' gait,⁴⁸ theoretical and computer modeling of walking,^48-53 and the creation and study of passive dynamic walking machines.^52,54 The common approach to the preceding research was the modeling of the foot and ankle as a rocker or as rocker mechanisms for the task of walking.

The path of the COP of the net force in the prosthetic ankle-foot system's local coordinates indicates an effective rocker shape, or roll-over shape, taken by the foot during the period between heel contact and opposite heel contact.⁵⁵ The path of the COP from opposite heel contact to toe-off may also be of interest in studies of energy return from the foot during unloading although this has not been examined extensively to date.

A strength of the roll-over shape approach is that prosthetic ankle-foot systems can be directly compared regardless of the level of complexity within their designs. For example, the roll-over shape of a prosthetic ankle-foot system with 20 joints can be compared with a prosthetic ankle-foot system that functions on material deformation alone. Roll-over shapes of prosthetic ankle-foot systems can be found using mechanical testing devices or directly from gait analysis data. The resulting shapes from both measurement techniques are similar.⁵⁵ Also, the roll-over shape of able-bodied systems can be measured for comparison by tracking the COP in a shankbased coordinate system.⁵⁶ Studies of the able-bodied anklefoot roll-over shape have shown that persons adapt to various conditions including changes in walking speed, wearing shoes of different heel heights, and carrying added weights to maintain a similar curvature and orientation of the roll-over shape.^56-58 It appears that the maintenance of the roll-over shape may be a goal of the physiologic system. This idea has been strengthened by findings suggesting that prosthetic ankle-foot systems with widely different roll-over shapes (a product of different mechanical properties) are aligned by experienced prosthetists in such a way that their roll-over shapes take the same general orientation on the limb.⁵⁹

Roll-over shape concepts seem to explain the contradictory results of mechanical properties and human subjects testing. Prosthetic ankle-foot systems have widely different mechanical properties, which gives them different roll-over shapes. The goal of alignment in the sagittal plane appears to be the approximate matching of the prosthetic ankle-foot system's roll-over shape with some "ideal" shape for the user (perhaps the roll-over shape of an able-bodied ankle-foot system). This theory suggests that dynamic alignment by an experienced prosthetist minimizes the differences that may be expected in a user's gait when using different kinds of prosthetic ankle-foot systems. Slight imperfections in this matching can also be masked by user adaptation. However, changes that are still seen in human subjects testing could be related to specific differences among the roll-over shapes of the prosthetic ankle-foot systems used in the study. For example, a Flex-Foot has a roll-over shape that is longer than the SACH foot's roll-over shape and that more closely matches the roll-over shape of the able-bodied ankle-foot system. For this reason, it may be impossible to perfectly match the SACH foot's roll-over shape with the "ideal" shape. Lehmann et al.'s²¹ measurements showed that the Flex Foot had the longest ankle moment arms in late stance phase, likely due to the Flex-Foot's longer roll-over shape compared with the other feet in their study. It is possible that the reduced moment arms in late stance of other feet, such as the SACH foot, could have led to a drop-off effect, creating an increased initial loading on the sound limb and a shorter step by that limb.^60,61 To examine this idea, an experimental foot was modified to reduce the length of its effective rocker (roll-over shape) in the forefoot area. With shorter effective rocker lengths, the external ankle dorsiflexion moment was decreased, limb loading on the sound limb increased, and the step length on the sound side was reduced for some persons with transtibial amputations.⁶²

Roll-over shape is focused on an important phase of gait but does not have all of the answers regarding prosthetic ankle-foot function. More study is necessary to determine effects of roll-over shape radius and the general stiffness used to attain the radius. Also, further studies are necessary to understand the importance of energy storage and return both during heel loading and during release of energy stored in a prosthetic system's keel and/or ankle joint during transfer of load to the contralateral limb.

OTHER NOVEL TECHNIQUES FOR EVALUATION OF THE PROSTHETIC FOOT/ANKLE

There are reports in literature from investigators using innovative methods and technologies to evaluate prosthetic devices and amputee gait and to study movement pathologies from other subject populations. For example, improved biomechanical models are being developed including multisegment foot models.^63-67 Investigators have applied artificial intelligence techniques such as neural networks and fuzzy logic to identify gait patterns and classify deviations.^68-72 Measurements are being made outside of the laboratory environment, such as plantar pressure measurements,⁷³ total daily energy expenditure,⁷⁴ and markerless motion capture.⁷⁵ Further development of some of these technologies may lead to improved evaluation of prosthetic componentry.

CONCLUSIONS

Regardless of the methods used, a stronger interaction among mechanical testing, human subjects testing, and modeling of movements is necessary to achieve a stronger scientific understanding of prosthetic ankle-foot systems. Future research should attempt to more clearly define hypotheses that can be tested using appropriate measurements and statistics. Suggestions of causal relationships that are found during exploratory research should be further examined with follow-up studies on experimental feet that can be adapted to address the specific hypotheses when possible. Most importantly, mechanical testing methods and modeling of devices should be seen as tools for understanding the results of human subjects testing and clinical use of prosthetic anklefoot systems.

ACKNOWLEDGMENTS

The author is partially funded by the National Institute on Disability and Rehabilitation Research (NIDRR) of the US Department of Education under grant No. H133E030030. The opinions contained in this publication are those of the grantee and do not necessarily reflect those of the Department of Education. The author thanks Dr. Steven Gard, Dr. Dudley Childress, Mr. Brian Ruhe, and Mr. Steven Steer for reviewing the initial draft of this article and for their helpful suggestions in its initial revision.

Correspondence to: Andrew H. Hansen, PhD, Department of Physical Medicine and Rehabilitation, Northwestern University Feinberg School of Medicine, 345 E. Superior Street, Room 1441, Chicago, IL 60611; e-mail: .

ANDREW H. HANSEN is affiliated with the Department of Physical Medicine and Rehabilitation, Northwestern University Feinberg School of Medicine, Chicago, Illinois.

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