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Energy Loss and Stiffness Properties of Dynamic Elastic Response Prosthetic Feet

Geil, Mark D. PhD

JPO Journal of Prosthetics and Orthotics: September 2001 - Volume 13 - Issue 3 - p 70-73
Prosthetic And Orthotic Science
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Dynamic elastic response prosthetic feet are designed to store and return energy during the gait cycle to assist the amputee with limb advancement. In so doing, the structural ability of the feet to store and return energy is significant, as is foot stiffness and the amount of input energy dissipated by the foot before it unloads. Manufacturers do not generally make subjective measures of stiffness and hysteresis available; instead, feet are classified according to manufacturer-specific stiffness categories. This investigation attempted to provide an independent measure of stiffness and hysteresis for eleven prosthetic feet. The feet were tested in constant strain rate and in cyclic tests on an Instron material-testing machine. Each foot demonstrated a stiffness value in one of only four categories, with multiple models of feet and even feet from multiple manufacturers showing essentially the same stiffness. Energy loss showed a broad range of feet in the middle of all values, with the greatest amount of loss occurring in the College Park feet and the least amount occurring in the Flex-Foot. Although structural property values do not fully explain a foot’s function in gait, data suggest the need for an independent classification scheme for stiffness and hysteresis among all manufacturers. Such a scheme would aid clinicians’ ability to appropriately prescribe and fit prosthetic feet.

MARK D. GEIL, PhD, is an assistant professor with the Department of Health and Performance Sciences at the Georgia Institute of Technology, Atlanta, GA.

Mark D. Geil, PhD, Department of Health and Performance Sciences, Georgia Institute of Technology, Atlanta, GA 30332-0356. Phone: (404) 894-9993; Fax: (404) 894-9982; E-mail: mark.geil@hps.gatech.edu

This work was supported by a grant from the Atlanta Veterans Administration Medical Center Rehabilitation Research and Development Center.

Dynamic elastic response (DER) prosthetic feet are designed to store and return energy during the gait cycle to assist the amputee with limb advancement. The material components of DER feet have properties and geometry specifically intended to dissipate, absorb, or return energy. All DER feet use a deformable forefoot keel designed to store energy as a leaf spring. Most DER feet use a foam heel to dissipate energy at heelstrike, borrowing from the design of the standard solid ankle cushioned heel (SACH) foot and replacing the function of controlled anatomic ankle plantarflexion. Others use an additional leaf spring in the heel designed to store energy sooner in the gait cycle. Most research and development in DER feet has concentrated on the leaf spring deformation plate, which is the key site for storage and return. The foam cover surrounding the deformation plate incorporates the cushioned heel (when present) and provides cosmesis. Although foam cover materials have been mentioned in the literature, 1 little research has addressed the important role of the foam in whole-foot energy dissipation throughout the gait cycle. Indeed, most DER research has focused not on material properties but on functional dynamic gait analysis. Although both foci have advantages, material testing provides an assessment of foot properties apart from intersubject variability. The material tests that have occurred have addressed hysteresis, strength, and fatigue. Postema et al. 2 measured hysteresis for three Otto Bock feet and a Quantum foot using a device from VanJaarsveld et al. 3 Toh et al. 4 designed a fatigue testing machine that applied cyclic vertical loads to the heel and forefoot of DER feet and measured fatigue properties for four feet over 500,000 cycles. The International Society of Prosthetics and Orthotics has defined standards regarding material and fatigue properties of lower limb prostheses. Lehmann et al. 5 combined objective structural testing with functional motion analysis in a study that tested the natural frequency of the oscillation of prosthetic feet at various loads.

The proliferation of DER feet in the market presents a challenge to the physicians and prosthetists charged with determining the most appropriate technology for each patient. When feet are accompanied by technical specifications, data supplied by manufacturers are not standardized, making it difficult to objectively differentiate between the properties of different manufacturers’ products. Even properties as fundamental as stiffness are noted in loosely defined categories that vary from brand to brand. Independent publication of data for properties such as stiffness and hysteresis, coupled with results of functional gait analysis, will allow clinicians to make better-informed decisions regarding patient prescription.

This investigation provides an independent measurement of material and structural properties for a broad sample of DER prosthetic feet. Tests were conducted on a servohydraulic material testing system using a custom-designed testing fixture. Data regarding energy loss and stiffness are presented to enable comparison of the feet.

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METHODS

Eleven prosthetic feet were tested to determine material and structural properties. The feet tested included multiple samples and models from a variety of manufacturers, including College Park (Fraser, MI), Flex-Foot (Aliso Viejo, CA), Kingsley (Costa Mesa, CA), Ohio Willow Wood (Mount Sterling, OH), Otto Bock (Duderstadt, Germany), and Seattle Limb Systems (Poulsbo, WA) (Table 1). Nine of the feet were 27 or 28 cm in length, with one 26-cm foot and one 22-cm foot. The feet were requested with a stiffness based on an average male active adult amputee. Specific stiffness characteristics varied from manufacturer to manufacturer. The Vari-Flex foot (from Flex-Foot) was tested without a cover. Unlike the other feet tested, the Vari-Flex uses a removable foot shell cover and not a molded and filled foam cover. In high performance settings such as athletic events, the foot is typically used without the cover. Consequently, it was tested without a cover to help explain the implications of the foam cover in energy dissipation.

Table 1

Table 1

Material tests were performed at the Georgia Institute of Technology Center for Human Movement Studies using an Instron 8521 Biaxial Servohydraulic Material Testing System (Canton, MA). The tests were controlled and the data collected using the Instron Series IX software package. A custom fixture was designed and machined to couple the Instron actuator to a standard female inverted pyramid adapter. Each foot was then attached to the adapter and aligned in maximum plantarflexion, at approximately 12°. The actuator provided compressive loading onto the table fixed to the load cell. Two Teflon sheets (DuPont, Wilmington, DE) were placed between the table and the foot to minimize friction during foot loading and deformation.

Two modes of material testing were used to determine the energy and stiffness characteristics of each foot. In load-deformation testing, the plantarflexed foot was compressed vertically at a constant strain rate of 1 mm/sec to a maximum load of 800 N. This maximum load figure was based on recommendations for fatigue testing by Toh et al. 4 and results for vertical propulsive force in Arya et al. 6 Stiffness was measured as the slope of the load-deformation curve. In cyclic testing, the plantarflexed foot was deformed based on a sinusoidal forcing function oscillating between 100 N and 800 N at a frequency of 1 Hz. Cyclic testing revealed energy lost during loading and unloading. Hysteresis was measured as the amount of energy absorbed in loading minus the amount of energy released in unloading (the area of the hysteresis loop), and also expressed as a percentage of the input or loading energy.

If multiple samples of the same foot were available, results for these samples were compared to determine repeatability. Additionally, if multiple models from the same manufacturer were available, results for these models were compared to determine similarity. Otherwise, results were analyzed as pairwise comparisons. The energy and hysteresis data that were compared included the absolute amount of loading and unloading energy and the amount of hysteresis, ie, the percentage of input energy lost in cyclic loading.

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RESULTS

Stiffness results for the eleven feet tested revealed that the each foot fell into one of four general levels of stiffness (Figure 1). Load-deformation curves were linear in the nondestructive tests, and three of the four general stiffness categories included feet from multiple manufacturers. Categories were spaced as follows:

Figure 1

Figure 1

  • Most Stiff (average, 0.0760 N/m): Kingsley Steplite Flattie, Kingsley Steplite Strider, and Seattle LightFoot II (22 cm, G6)
  • More Stiff (average, 0.0606 N/m): Seattle LightFoot II (27 cm, H6), Seattle Voyager (J7), and Ohio Willow Wood Carbon Copy High Performance
  • Less Stiff (average, 0.0384 N/m): Otto Bock Dynamic Plus (two samples), and Flex-Foot Vari-Flex (category 6, without cover)
  • Least Stiff (average, 0.0277 N/m): College Park TruStep (two samples)

The Most Stiff and the More Stiff categories showed a similar slope in the linear region of the curve (Fig. 1), and therefore a stiffness that was more similar than the other categories.

Each foot exhibited energy loss in a hysteresis loop during sinusoidal loading and unloading (Figure 2). Results for energy (Figure 3) and hysteresis (Figure 4) were similar, but did not always follow the same grouping as the stiffness data. The College Park feet, which represented the Least Stiff category, revealed the greatest amounts of loading (mean, 8.08 J) and unloading (mean, 7.10 J) energy and the highest hysteresis (31.27% energy loss). The least energy in loading (2.11 J) and unloading (1.62 J) was found in the Flex-Foot, which was tested without a foam cover. The Flex-Foot also showed the least actual energy loss, although its percentage of energy loss was near the overall mean (Fig. 4). Conversely, feet from Kingsley and Otto Bock showed the least percentage of energy loss.

Figure 2

Figure 2

Figure 3

Figure 3

Figure 4

Figure 4

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DISCUSSION

Stiffness and hysteresis are important properties to consider in a prosthetic foot prescription. Modern DER feet store and return energy to varying degrees to assist the amputee with limb advancement into the swing phase of gait. Manufacturers publish limited objective material property data, and each manufacturer has adopted a different scale with which to classify the stiffness of their feet. As such, independent assessment of stiffness and hysteresis will allow informed insight in the determination of which foot is appropriate for which amputee.

In this study, an initial analysis supported the hypothesis that multiple samples of the same foot model show repeatable results. This finding seems to confirm consistency in manufacturing. An unexpected result suggests that different models from the same manufacturer show very repeatable results. Stiffness and hysteresis data (Figures 1 and 3) for the Seattle Light Foot II and the Seattle Voyager were very similar, as were data for the Kingsley Steplite Strider and Kingsley Steplite Flattie. Differences in these models must therefore be reflected in some other functional gait parameter.

Surprisingly, stiffness data “self-classified”; that is, different models from the same manufacturer and models from different manufacturers revealed remarkable similarity. In fact, of 11 feet tested, only four discernibly different stiffness values emerged (Figure 1). One category, the Least Stiff, contained two samples of the College Park TruStep. The other three categories contained feet from different manufacturers. These data suggest that an independent, industry-wide stiffness classification system might be relatively easy to implement, because it seems it might already exist.

Hysteresis data give insight into both the function of the feet and the theoretical concept of energy storage and return. The single most important parameter in the design of a foot to store and return energy is the actual amount of energy that is returned to the amputee in the late stance phase. This value is rarely reported in the literature because investigators often prefer to report efficiency, ie, energy return divided by energy stored, expressed as a percentage. Although efficiency (as defined here) is a functional parameter, it reflects the material property of hysteresis. The College Park samples that were tested showed the largest actual amount of unloading energy (5.77 J) (Figure 3). However, these samples also required substantially more loading energy to reach 800 N than any other feet. Therefore, it seems that there is a cost involved in attaining this high amount of unloading energy, and, indeed, College Park feet are less efficient in achieving unloading energy, showing the largest hysteresis (31.27%) (Figure 4). As the least stiff foot studied, it should be noted that the TruStep will reach a given level of deformation at a lower force than the other feet (Figure 1). Consequently, if the amputee desires only a certain degree of ankle range of motion during normal walking and not a certain amount of energy return, the foot might require less input energy, while still returning energy with the least efficiency. On the other hand, the Flex-Foot, which was tested without a foam cover, required the least amount of energy to deform to 800 N force and showed the least actual energy loss, although it also showed the least actual amount of unloading energy (1.62 J). In between the extremes, it is difficult to distinguish energy properties of the feet from Otto Bock, Seattle Limb, and Ohio Willow Wood (Figure 3). Just as the feet “self-classified” for stiffness, there seems to be a broad middle ground for hysteresis results with similar input energy and unloading energy.

Although several different feet showed very similar structural properties, it is clear that designs such as Otto Bock’s complex curved-plate geometry or Ohio Willow Wood’s three separate deformation plates should provide different results for the same amputee. Naturally, material testing does not fully describe the function of a prosthesis. As such, although it is more important to assess foot function in dynamic use (as in an instrumented gait analysis), it is more difficult to achieve objective comparison data when considering intersubject and intrasubject variability and difficulties with biomechanical foot models. Consequently, it can be concluded that independent material testing should be pursued for a broad range of feet and that an independent classification scheme for stiffness and hysteresis data could aid in prosthetic prescription.

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ACKNOWLEDGMENTS

The author acknowledges both the donation to this study of the prosthetic feet by their respective manufacturers and the valuable assistance of research assistant Nicholas Kelling.

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REFERENCES

1. Michael J. Energy-storing feet: a clinical comparison. Clin Prosthet Orthot. 1987; 11: 154–168.
2. Postema K, Hermens HJ, DeVries J, Koopman HFJM, Eisma WH. Energy storage and release of prosthetic feet. Part 1: biomechanical analysis related to user benefits. Prosthet Orthot Int. 1997; 21: 17–27.
3. VanJaarsveld HWL, Grootenboer HJ, DeVries J, Koopman H. Stiffness and hysteresis properties of some prosthetic feet. Prosthet Orthot Int. 1990; 14: 117–125.
4. Toh SL, Goh JC, Tan P, Tay TE. Fatigue testing of energy-storing prosthetic feet. Prosthet Orthot Int. 1993; 17: 180–188.
5. Lehmann JF, Price R, Boswell-Bessette S, Dralle A, Questad K. Comprehensive analysis of dynamic elastic response prosthetic feet: Seattle Ankle/Lite Foot versus SACH Foot. Arch Phys Med Rehabil. 1993; 74: 853–861.
6. Arya AP, Lees A, Nirula HC, Klenerman L. A biomechanical comparison of the SACH, Seattle and Jaipur feet using ground reaction forces. Prosthet Orthot Int. 1995; 19: 37–45.
Keywords:

Dynamic elastic response prosthetic feet; energy loss; stiffness; hysteresis

© 2001 Lippincott Williams & Wilkins, Inc.