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The Effective Foot Length Ratio: A Potential Tool for Characterization and Evaluation of Prosthetic Feet

Hansen, Andrew H. PhD; Sam, Michel MS; Childress, Dudley S. PhD

JPO Journal of Prosthetics and Orthotics: April 2004 - Volume 16 - Issue 2 - p 41-45
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The purpose of this technical note is to introduce the effective foot length ratio (EFLR) as a possible measurement tool for evaluation of prosthetic feet. The EFLR multiplied by 100 provides the percentage of a foot that is effectively used during a walking step and may have clinical implications for step length and limb loading on the contralateral side. Prosthetic feet were manually rolled over a force platform while maintaining a constant level of force representative of a user’s weight. Effective foot lengths were measured by finding the distance from the heel of each prosthetic foot to the center of pressure in foot-based coordinates at a loading angle that represented the approximate shank angle at opposite heel contact during walking. The effective foot lengths were then normalized by overall foot length to determine the EFLR. EFLRs from 15 prosthetic feet used clinically during the 1990s are presented along with an estimate of the EFLR of the physiologic ankle–foot system. All prosthetic feet had EFLRs lower than the corresponding physiologic system, although some had ratios close to the physiologic system. The EFLRs for the prosthetic feet were between 0.63 and 0.81, whereas the EFLR estimated for the physiologic system was 0.83.

The authors discuss the effective foot length ratio (EFLR) as a possible measurement tool for evaluation of prosthetic feet. The authors conclude that although the EFLR may be helpful for evaluation and design of prosthetic feet, it does not give a complete picture of a prosthetic foot’s performance.

ANDREW H. HANSEN, PhD, is a Research Assistant Professor, Northwestern University Feinberg School of Medicine, Department of Physical Medicine and Rehabilitation, Chicago, Illinois.

MICHEL SAM, MS, is affiliated with the University of California Berkeley–University of California San Francisco Joint Medical Program, Berkeley-San Francisco, California.

DUDLEY S. CHILDRESS, PhD, is a Senior Research Health Scientist, VA Chicago Health Care System, Lakeside Division, Chicago; Professor, Department of Biomedical Engineering, Northwestern University, Evanston; and Professor, Northwestern University Fein-berg School of Medicine, Department of Physical Medicine and Rehabilitation, Chicago, Illinois.

This work was funded by the National Institute on Disability and Rehabilitation Research (NIDRR) of the U.S. Department of Education under grant No. H133E980023.

Copyright ©2004 American Academy of Orthotists and Prosthetists.

The opinions contained in this publication are those of the grantee and do not necessarily reflect those of the Department of Education.

Correspondence to: Andrew H. Hansen, PhD, Prosthetics Research Laboratory and Rehabilitation Engineering Research Program, Northwestern University, 345 East Superior Street, Room 1441, Chicago, IL 60611; e-mail:a-hansen@northwestern.edu

Several investigators have demonstrated that persons with gastrocnemius and soleus paralysis induced by nerve blocks or surgical excision tend to walk with shorter step lengths on the sound limb and/or with increased loading to the sound limb. 1–4 The disabled plantar flexors in these cases lead to a decreased excursion of the center of pressure under the foot in the direction of forward progression. 3

Other studies have examined walking with various types of prosthetic feet and have found increased sound limb loading and/or reduced step lengths on the sound side when using many kinds of prosthetic feet. 5–13 However, reduced sound limb loading was demonstrated when using a Flex-Foot® (Flex-Foot Inc., Aliso Viejo, CA) prosthetic foot in many of these studies. Our examinations have shown that the Flex-Walk™ (Flex-Foot Inc.), a foot that is similar to the Flex-Foot, has a long effective foot length and a roll-over shape that closely approximates that of the physiologic foot/ankle complex. 14

Ankle–foot roll-over shapes are the effective rocker shapes that ankle–foot systems conform to between heel contact and opposite heel contact. 14–15 These effective rockers (cams) are calculated by determining the center of pressure of the ground reaction force with respect to the lower leg (i.e., in a shank-based coordinate system). The center of pressure of the ground reaction force is the point at which the net force can be thought to act. The distance that the center of pressure moves forward in shank coordinates (from heel contact to opposite heel contact) indicates the forward rolling component of the step. Thus, roll-over shapes can be used to determine the effective foot lengths of feet, which may affect step lengths on the contralateral side.

The purpose of this article is to introduce the effective foot length ratio (EFLR) and to determine this ratio for 15 prosthetic feet that were mechanically tested in our laboratory. The feet spanned the range of mechanical properties of prosthetic feet available on the market during the 1990s. The EFLRs of the prosthetic feet tested are also compared with the EFLR of the physiologic ankle–foot system.

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MATERIALS AND METHODS

Fifteen prosthetic feet were characterized in this study: Carbon Copy 2 (Ohio Willow Wood, Mount Sterling, OH), Carbon Copy 3 (Ohio Willow Wood), College Park (College Park Industries, Fraser, MI), C-Walk (Otto Bock Health Care, Min-neapolis, MN), two Endolite feet (Blatchford Endolite, Hamp-shire, United Kingdom), Flex-Walk® (Flex-Foot Inc.), IPOS Cinetic (ipos North America, Niagara Falls, NY), IPOS CTV (ipos North America), Masterstep (Ossur Total Solutions, Reykjavik, Iceland), Quantum (Hosmer, Chattanooga, TN), SACH (Kingsley Mfg. Co., Costa Mesa, CA), Seattle (Seattle Limb Systems, Poulsbo, WA), Single-Axis (Otto Bock), and USMC E2 (USMC, Pasadena, CA). Some of the feet are no longer produced, and others are now produced with revised designs or by different manufacturers.

Most of the feet were size 27 centimeters, and some were size 26 or 28 centimeters. The two Endolite feet that were tested were designs before and after a design change was made to lengthen the keel of the foot. They are referred to in this article as Endolite DRF1 and Endolite DRF2. DRF stands for “dynamic response foot” and DRF2 is the more recent design with the extended keel. The prosthetic feet used in the study represent a wide variety of feet available for clinical use during the 1990s.

Roll-over shapes were measured using a modified quasi-static method described by Hansen et al. 14 Each prosthetic foot was attached in neutral alignment to a weight using a standard endoskeletal pylon (Figure 1). The loading apparatus (weight, pylon, and foot) was rolled across a force platform. Additional force was applied to the apparatus by a technician until the force between the foot and the force platform matched the weight of a person who would use the foot. The vertical force from the force platform was displayed to the technician in real time using a LabVIEW (National Instruments, Austin, TX) program. This instrumentation allowed the technician to adjust the applied force to the apparatus to attain the appropriate foot loading during the roll-over. A flat plate was placed between the attachment surface of the foot and the pyramid. Spherical light-reflective markers were attached to the plate and were used to indicate a line parallel to the attachment surface during the roll-over test. The trajectories of the markers were measured using an eight-camera motion analysis system (Motion Analysis Corporation, Santa Rosa, CA). The forces and moments applied to the rolling surface were measured using the force platform (Advanced Mechanical Technology, Inc., Watertown, MA) and were synchronized in time with the marker data. The center of pressure of the force applied to the foot was found using data specific to the force platform and equations similar to those of Barnes and Berme. 16 The center of pressure was collected at pylon angles ranging between 15° on the heel to 25° on the forefoot, where both angles are with respect to a vertical line (Figure 1). The quasistatic method described here has been found to yield roll-over shapes for prosthetic feet that are similar to the shapes found when they are subjected to walking loads. 14

Figure 1.

Figure 1.

Photographs were taken of each prosthetic foot, and overall length (foot length) was measured with a ruler. A custom imaging program was used to import the photograph, remove rotation of the image to make the attachment surface horizontal, digitize an outline of the foot (unloaded), scale the image based on the foot length, and identify the origin of the foot-based coordinate system. The origin of the foot-based coordinate system was chosen to be on the foot’s attachment surface and at the center of the hole for the attachment bolt. After retrieval, proper scaling, and orientation of the foot’s outline, the roll-over shape was computed as described earlier 14 and was plotted on the foot’s outline as shown in Figure 2.

Figure 2.

Figure 2.

From the foot outline/roll-over shape plot, the effective foot length was measured. This length starts at the heel and ends at the anterior end of the roll-over shape. The anterior end of the roll-over shape corresponds to the location of the center of pressure of the ground reaction force on the foot at a pylon angle corresponding to the approximate shank angle at opposite heel contact during walking. The effective foot length is defined as in Figure 2 because the force moves forward from the heel of the foot to the anterior end of the roll-over shape during a step. At the time of opposite heel contact during walking, the focus of attention can be shifted to the next foot and the analysis can be repeated, creating a continuous flow without overlap. The EFLR was computed as: EFLR = Effective Foot Length/Foot Length for each prosthetic foot. The EFLR multiplied by 100 is the percentage of the foot actually used during a walking step.

Only one foot was tested from each type. Because the effective foot length depends primarily on the structural aspects of the foot (keel) that essentially do not change with age or wear, and because the feet are likely fabricated to length tolerances of a millimeter or less, we do not believe there is much difference in EFLR for different production runs. It should be remembered that some feet have the same keel length for different foot lengths. For example, a specific type of foot may use the same keel for sizes 26 to 28 centimeters.

The EFLR of the physiologic foot was estimated from a height-normalized average roll-over shape from 24 able-bodied persons walking at speeds between 1.2 and 1.6 m/second. 15 This roll-over shape was converted into a foot length-normalized shape by assuming the foot length to be approximately 15.2% of the height. 17,18 The distance from the ankle to the anterior end of the physiologic roll-over shape was found to be 0.57 times the foot length. This was added to the distance from the heel to the ankle (0.26 times the foot length according to Dreyfuss 18) to obtain the effective foot length of the physiologic foot. The EFLR for the physiologic foot was determined based on this information and the equation.

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RESULTS

The EFLRs of the 15 prosthetic feet tested range from 0.63 to 0.81 (Figure 3). The estimated EFLR for the physiologic foot was found to be 0.83 and is also shown in Figure 3. A footprint is shown behind the graph in Figure 3 to illustrate the approximate forward location to which the force extended on each foot at the time of opposite heel contact. In the physiologic foot, the force extends to a location near the first metatarsal–phalangeal joint. Some prosthetic feet come close to mimicking the forward movement of the center of pressure on the physiologic foot (e.g., Flex-Walk), whereas others do not (e.g., Quantum and SACH).

Figure 3.

Figure 3.

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DISCUSSION

A walking step takes place between the heel contact of one foot and the heel contact of the contralateral foot. The length of a step is related to two factors: the distance the stance foot rolls forward and the distance the other leg swings forward. These factors probably are not independent. Rolling out farther on the foot contributes to a longer step but may also allow the swing leg to traverse a longer distance before contacting the walking surface. Rolling only a short distance on a foot and then pivoting about its effective endpoint can be referred to as a “drop-off” effect. This drop-off effect may lead to a shorter step length of the opposite foot and to more forceful loading of the contralateral foot. 14

The effective foot length begins at the heel end of the foot, which initially contacts the walking surface. The heel end of the foot is used instead of the beginning of the roll-over shape (posterior end of the roll-over shape) because roll-over shapes determined with the quasistatic method miss the movement of the center of pressure of the ground reaction force that occurs shortly after initial contact. This problem is also present when examining roll-over shapes directly from walking data because center-of-pressure measurements are noisy when forces are low (e.g., during a short period after initial contact). 14

The EFLR is presented as a possible tool for characterization or evaluation of prosthetic feet. The EFLR gives the fraction of the overall foot length that is effectively used during a walking step. For prosthetic feet, the effective length is dependent on the geometry and mechanical characteristics of the foot. For example, prosthetic feet with short or extremely soft keels will not be able to support the net force as far out on the toe as feet with longer and stiffer keels. The feet with shorter keels will in turn have shorter roll-over shapes and also smaller EFLRs. Direct evidence of this contention is seen in the results of the Endolite feet tested in the study. The EFLR of the Endolite DRF1 was 0.67. The Endolite DRF2, a newer design with a longer keel, had an EFLR of 0.78.

Although the EFLR may be helpful for evaluation and design of prosthetic feet, it does not give a complete picture of a prosthetic foot’s performance. Other factors, such as compliance of the foot, the radius of curvature of the foot’s roll-over shape, and the alignment of the roll-over shape with respect to the rest of the limb, are important to a user’s walking characteristics. We believe alignment of the roll-over shape with respect to the limb is what the prosthetist does during the fitting process. Experimental results suggest that experienced prosthetists position and orient prosthetic feet on the prosthesis such that their roll-over shapes match an ideal roll-over shape. 19 This alignment process may inherently neutralize the effects of quite different prosthetic feet by aligning their shapes with one another. However, this accommodation may be difficult for prosthetic feet with short effective lengths. Additional factors important to the process of prosthetic foot selection include weight, cosmesis, and cost.

One of the weaknesses of this study is a lack of consideration of activity levels and bumper durometers for the feet tested. Future examinations of prosthetic foot roll-over shapes should include variations of each foot type to determine the effects of each variable on the EFLR.

Additional research is needed to determine the importance of effective foot length for walking. The EFLR provides a quantitative measure of effective lengths for use in future studies. The range of EFLRs of the prosthetic feet tested in this study also provide a range of values clinically relevant for future prosthetics research.

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ACKNOWLEDGMENTS

The authors acknowledge the use of the VA Chicago Motion Analysis Research Laboratory of the VA Chicago Health Care System, Lakeside Division, Chicago, Illinois. The authors thank Mr. Brian Ruhe for his assistance with this project.

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Keywords:

rockers; roll-over shapes; walking

© 2004 American Academy of Orthotists & Prosthetists