Prescription of a prosthetic foot for a lower limb amputee is a key part of prosthetics rehabilitation. Despite the variety of foot-ankle systems that are now available, surveys of certified practitioners revealed most prosthetists, therapists, and physicians still only use a relatively small number of the numerous types and models of the foot-ankle mechanisms that are available. If prosthetists expand their working stock of prosthetic feet, it is done almost exclusively on an empirical basis.^{1–4} To address this issue, the US Health Care Finance Administration has published the Common Procedure Coding System,^{5} using code modifiers (K0, K1, K2, K3, and K4), as a five-level functional classification system (MFCL) to describe the functional abilities of lower limb amputees. To more explicitly target amputees' functional capabilities and assess their ability to perform various activities of daily living, and vocational and avocational tasks, Gailey et al.^{6} developed the Amputee Mobility Predictor (AMP). Both the K scale and the AMP metric are broad measures of amputees' general functional capabilities. They do not focus on amputees' gait characteristics and thus do not contain enough information on the characteristics and mechanical properties of the foot-ankle mechanisms that are most suited for given amputees. Czerniecki^{2} has stated that what is needed is (are) some simple instrumented test(s) that all manufacturers could be required to perform on their prosthetic feet before bringing them to market, the results of which could be compiled in a centralized database that clinicians can easily access. Without advancement of knowledge of quantitatively measured gait characteristics of a person, prosthetics clinical practice will remain much the same as it has for the past half century.

Human gaits have been studied by collecting instrumental measurements during gait trials. These measurements cover a broad range, including spatiotemporal (e.g., speed, stride length, step length, and cadence), kinematics (e.g., range of motion of hip, knee, and ankle angles), and kinetics (e.g., the moments of hip, knee, and ankle joints). These measurements can be used to measure human gait performance for nonamputees and the performance of prostheses for lower limb amputees.^{7–10} However, no measurement has been used to identify human gait characteristics and to choose optimal feet with mechanical properties that are appropriate for amputees' gait characteristics.

The purpose of this article is to create and introduce new metrics, gait characteristic indices, which can quantitatively measure the gait characteristics of a person. The authors' work may potentially lead to the development of a method and a device which quantitatively characterizes the gait of lower limb amputees' so that an optimal prosthetic foot with mechanical properties that closely match the amputee's gait characteristics can readily be identified from a generally available database of commercially available prosthetic feet that have undergone standardized instrumented testing.

METHOD
The investigators developed the “Gait Characteristic Indices” (GCI or the indices) to quantitatively characterize human gait. The indices are based on measures of a subject foot's vertical force, F _{z} (t ), when walking along a 10-m smooth, level, unobstructed walkway at the subject-selected normal speed. Figure 1 shows a typical plot of F _{z} (t ) during the stance phase of a gait cycle for a healthy, nonamputee subject. Two GCI, i.e., Heel Gait Characteristic Index (H _{i} ) and Forefoot Gait Characteristic Index (F _{i} ), are used. The detailed definitions of the GCI are included in Appendix .

Figure 1.:
Vertical force versus time of one gait cycle of a nonamputee subject, one side. Horizontal lines indicate 90% and 5% of subject body weight (BW). Time values are intersections at those BW levels for heel contact (HC) and push off (PO) sections. Force and time values are also found for the maximums of these sections and the minimum of the mid-stance (MS).

For 48 adult nonamputee subjects whose informed consents were obtained, the vertical forces were recorded using a Tekscan F-Scan Pressure Measurement System by integrating pressures measured by all cells. To expand the initial study, three unilateral transtibial adult amputee volunteers were recruited and their informed consents obtained. Each subject tested seven different prosthetic feet for a total of 21 cases. The amputee subjects' medical conditions and states of health were examined to validate their ability to safely participate in the gait studies. When acceptable fit, comfort, and function of the subjects' current prostheses were verified, experimental, endoskeletal prostheses (one for each amputee subject) were fabricated by duplicating their current sockets, suspension systems, and socket-foot alignments. The prosthetic feet selected for testing were installed by a VA NY/NJ Veterans Healthcare Network prosthetist. The same prosthetist performed the static and dynamic alignment for all the test subjects to minimize the variation because of different prosthetists' techniques. The feet chosen for the study are those prosthetic feet prescribed for US veterans, according to the record of prosthetic services at VA NY Harbor Healthcare System. The feet include Axition, Cwalk, Elite, Proprio, Sach, Trustep, and Variflex. The subjects have about 1 week to adapt to a new foot before the gait trails. All amputee subjects were asked to perform a sequence of gait trials four to six times each, walking along a 10-m smooth, level, unobstructed walkway at the subject-selected normal speed. The amputees performed three or more practice trials before measurements were recorded to control for the effects of “experimental learning.”^{11–13} The vertical forces, F _{z} (t ), under the amputees' prosthetic feet and nonamputated feet were measured with a Kistler Model 9284 force plate. The H _{i} and F _{i} were subsequently calculated using the measured F _{z} (t ) and averaged over four to six gait cycles.

The ability of the gait characteristic indices to identify individual gait characteristics can be estimated. The t -statistic is used to estimate the threshold difference to separate two different gaits with the GCI.

where Xa and S _{Xa} are the mean and standard deviation of sample A calculated over Na gait steps, and Xb and S _{Xb} are the mean and standard deviation of sample B calculated over Nb gait steps. The value of t is then used to test the null hypothesis that the mean value of the parameter for sample A does not differ significantly from the mean for sample B. For a level of significance α = 0.05, the null hypothesis H _{0} is accepted as true if t < 2.78 (for N = 5) and rejected as false if t ≥ 2.78. Although the deviation varies from sample to sample, in this analysis, the deviations for both samples A and B are assumed to be equal to the averaged value, S. For simplicity, the sample sizes (both Na and Nb ) are assumed to be equal to N. Thus, the threshold difference of the means between two samples could be calculated using the following formula:

RESULTS
Figure 2 shows four typical “modes of walking”: i) vigorous walkers with a Bactrian (double hump)-shaped vertical loading curve; (ii) heel walkers with asymmetric single-peaked vertical loading curves; iii) toe walkers with single-peaked (or single peak dominated), asymmetric vertical loading curves; and iv) shufflers with dromedary-shaped vertical loading curves. The curves represent four single gait cycles of four nonamputee subjects walking at subject-selected normal speeds.

Figure 2.:
The four typical “mode of walking” for level walk: i) vigorous walkers (H _{i} = 1.78, F _{i} = 1.69); ii) heel walkers (1.01, 0.52); iii) toe walkers (0.07, 1.30); and iv ) shufflers (0.42, 0.58). The vertical force is normalized by the subject's body weight, and the time is normalized by the time of stance phase defined by 5% body weight threshold.

Figure 3 shows the plot of the heel versus forefoot gait activity indices for the 48 nonamputees' both left and right feet tested in level walking at normal speed. The data points near lower-left corner represent shufflers ; the points toward upper-right corner represent vigorous walkers ; the points near left side excluding the shufflers represent toe walkers ; and the points near the bottom excluding the shufflers represent heel walkers .

Figure 3.:
A plot of heel gait characteristic index H _{i} versus forefoot gait characteristic index F _{i} for the 48 nonamputee subjects tested in level walking at normal speed. The data points near lower-left corner represent shufflers ; the points toward upper-right corner represent vigorous walkers ; the points near left side excluding those near the lower-left corner represent toe walkers ; and the points near the bottom excluding those near the lower-left corner represent heel walkers .

Figure 4 shows a plot of the heel versus forefoot gait characteristic indices measured from the prosthetic feet for each of the three amputees wearing the seven different prosthetic feet tested in level walking at normal speed. The data points from nonamputated foot of subject 3 are also plotted. The plot shows the mechanical properties of the prosthetic feet affect the amputees' gaits, which are measured by the gait characteristic indices.

Figure 4.:
A plot of heel gait characteristic index H i versus forefoot gait characteristic index F i for the three amputee subjects in tests of seven prosthetic feet in level walking at normal speed, as well as data from the nonamputated foot of the subject 3.

Figure 5 is a graph of the GCI deviations for the 48 nonamputees and 3 amputees. For amputee subjects, the data presented are based on the averaged values for each amputee wearing the seven different prosthetic feet measured from their prosthetic feet. Left-right differences for amputee are the averaged values of the absolute differences of subject 3's GCI of left and right feet.

Figure 5.:
The GCI deviations for the 48 nonamputees and 3 amputees tested in level walking at normal speed. For nonamputees, intersubject deviations are the standard deviations of GCI of the test subjects, and intrasubject deviations are the averaged values of the standard deviations of each subject's trial-to-trial GCI. Left-right differences are the averaged values of the absolute differences of each subject's GCI of left and right feet. For the three amputee subjects, intersubject deviations are the standard deviations of GCI of the three subjects, and intrasubject deviations are the averaged values of the standard deviations of each subject's trial-to-trial GCI measured from their prosthetic feet. Left-right differences* are the averaged values of the absolute differences of subject 3's GCI of left and right feet.

In this study, the average intrasubject standard deviations for both left and right feet of all nonamputee subjects are 0.12 and 0.10 for heel and forefoot gait characteristic indices, respectively. Let the number of gait steps be 5, which is the median of four to six gait steps used in the study, the threshold difference of H _{i} is 0.21 for S = 0.12. The threshold difference of F _{i} is 0.18 for S = 0.10. The threshold differences indicate that if the difference of mean H _{i} between two test subjects is greater than 0.21 or the difference of mean F _{i} between the two test subjects is greater than 0.18, the gait characteristics of the two subjects are significantly different. For the three amputees wearing seven prosthetic feet, the average intrasubject standard deviations for the amputated side are 0.09 and 0.05 for heel and forefoot gait characteristic indices, respectively.

DISCUSSION
The GCI was developed to quantitatively characterize human gait. The GCI were calculated using the vertical force of subjects' level walking. The results show that both nonamputee and amputee subjects have identifiable patterns of walking. Four typical “modes of walking” (Figure 2 ) are observed: i) vigorous walkers with a Bactrian-shaped vertical loading curve having high loading peaks at foot contact and at forefoot push off; ii) heel walkers with asymmetric single-peaked (or single peak dominated) vertical loading curves evidencing large forces at heel contact; iii) toe walkers with single-peaked, (or single peak dominated), asymmetric vertical loading curves evidencing great forces during push off; and iv) shufflers with dromedary-shaped vertical loading curves, evidencing gradual acceptance of body weight by one limb following foot contact, peak loading during mid-stance, and gradual transfer of body weight back to the other limb following heel rise without a prominent push off. Generally speaking, a vigorous walker is associated with both high heel gait characteristic index (H _{i} ) and forefoot gait characteristic index (F _{i} ). For the examples shown in Figure 2 , the “vigorous walker” has H _{i} and F _{i} values of 1.78 and 1.69, respectively; a “heel walker” has a relatively higher H _{i} and lower F _{i} ; a “toe walker” has a relative lower H _{i} and higher F _{i} ; and a “shuffler” has lower H _{i} and F _{i} .

Both force plate and F-Scan were used in this study. For the 48 nonamputees, the data reported were collected with F-Scan. The pressure measured using F-Scan was validated by Luo et al.^{14} Their study indicated that the transducer is adequate for determination of pressure distribution under contact conditions with soft materials. The transducer responded linearly up to 1.7 MPa with good homogeneity throughout the transducer's cells. In this study, the F-Scan was used to measure the foot vertical force by integrating the pressure over all cells during gait trials. The integration reduces the noise associated with each cell and makes the vertical force more accurate than the pressure measured by each individual cell. For each subject, each transducer (left and right feet) was calibrated using subject's body weight before gait trials to ensure the accuracy of the measurements. The estimated error of the GCI measured by the F-Scan is under 5%. The statistical analysis showed that the measured GCI were able to identify subject gait patterns. The advantage of using F-Scan system is that only a walkway is needed instead of a gait laboratory. However, the F-Scan system was not able to accurately collect vertical force of prosthetic feet for amputee subjects. Because some prosthetic feet have relative small contact areas, especially in heel segment, the cells of F-Scan transducers in these areas were saturated when loaded. Thus, the reported data for amputees were collected with a force plate in a gait laboratory.

The gait characteristic indices were distributed over a range from 0 to 2.5 for H _{i} and 0 to 2.0 for F _{i} for the nonamputee subjects (Figure 3 ). For the nonamputee subjects, the intersubject standard deviations are much bigger than both the intrasubject standard deviations and the left-right side differences (Figure 5 ). The intersubject standard deviation of heel gait characteristic index is approximately 4.5 times the intrasubject standard deviation and 3.5 times the left-right side difference. In other words, the difference in the gait characteristics from subject to subject is much bigger than that in trial-to-trial deviations for each subject and the difference between the subjects' left and right feet. For amputee subject 3 with a left prosthetic foot , the average heel/forefoot gait characteristic indices were 1.33/1.07 and interprosthetic foot standard deviation 0.21/0.07 for the amputated side; the average heel/forefoot gait characteristic indices for the right nonamputated side were 1.24/1.16, and interprosthetic foot standard deviation was 0.12/0.04. This subject's data showed that the mechanical properties of the seven prosthetic feet have a much more significant effect on the gait characteristics of the associated subjects' amputated limb than on the nonamputated side as the standard deviation of gait characteristic indices on the nonamputated side for the seven prosthetic feet is less than 60% of the prosthetic side. The average left-right absolute differences of gait characteristic indices for this amputee subject are much bigger than that of nonamputee subjects (Figure 5 ). This phenomenon can also be observed in Figure 4 . The left-right differences of gait characteristic indices for this amputee subject are highly dependent on the prosthetic feet that the subject wore during the tests. Because the points representing the data measured from the prosthetic foot of subject 3 are scattered over a larger area than the data from the nonamputated foot, it is possible that the gait characteristic indices measured on the nonamputated side more closely reflected the amputee's natural gait characteristics.

On the basis of the discussion above, the following observations can be made for level walking at normal speed by the 48 nonamputee subjects: a) the indices are sensitive to the gait characteristics and are able to identify patterns of walking; b) for each subject, the indices' standard deviations from step to step are small, compared with the intersubject standard deviations; and c) the differences between left and right feet for each subject were small. For the three amputee subjects, observations (a) and (b) described above were also observed to be true. There is an additional observation: d) the mechanical properties of prosthetic feet have a significant effect on the gait of the amputated side with prosthetic foot and affect the amputees' nonamputated side to a much smaller degree.

The ability of the indices to identify individuals gait is estimated using the t -test. According to the analysis, if the difference of mean H _{i} between two samples is greater than 0.21 or the difference of mean F _{i} between two samples is greater than 0.18, the gait characteristics of the two samples are significantly different. As Figure 3 shows, the range of H _{i} is approximately 0 to 2.5, and the range of F _{i} is approximately 0 to 2.0. Dividing the range of H _{i} by the threshold difference of H _{i} results in approximately 12 divisions, and dividing the range of F _{i} by the threshold difference of F _{i} results in approximately 11 divisions. Thus, the total area shown in Figure 3 can be divided into approximately 132 subregions. Because of the fact that the data points in Figure 3 are distributed around the diagonal, many of the subregions may not have any data points even as the number of test subjects increases. Therefore, the actual number of subregions may be less. On the other hand, increasing the number of gait cycles for calculating the average indices will likely reduce the threshold differences, and thus increase the sensitivity of the indices to identify an individual's gait pattern.

In conclusion, this study has introduced a new set of GCI that is able to quantitatively characterize gait in amputee and nonamputee subjects. Because of small sample size of amputee subjects, a further study with more amputee subjects will be needed to obtain the distribution of gait characteristic indices for amputees. This work may lead to development of a method for quantitatively characterizing the gait of lower limb amputees' so that optimal feet with mechanical properties that closely match the amputee's gait characteristics can readily be identified from a generally available database of commercially available prosthetic feet-ankle mechanisms. An ideal prosthetic foot prescription system may work like this: “For the patient with the measured gait characteristic indices, the system recommends the following three feet: Foot-O, Foot-H, and Foot-T.” A potential prosthetic foot testing system for manufacturers may work like this: “For this foot with tested mechanical properties, it is recommended for amputees with gait characteristic indices in a range from C to D.” For this purpose, further studies including collecting additional data of lower limb amputees' gaits with different prosthetic feet are needed to create the link between the amputees' gait characteristic indices and the optimal mechanical properties of prosthetic feet.

APPENDIX: GAIT CHARACTERISTIC INDICES
The vertical component of the ground reaction force generated in 10 m walking trials on a smooth, level, unobstructed surface by study subjects was measured. The vertical force, F _{z} (t ), was used to characterize the gait of the test subjects: a) for the heel segment of the foot during the weight acceptance phase of the gait cycle and b) for the forefoot segment of the foot during the weight transfer phase of the gait cycle.

Figure 1 shows a typical plot of the F _{z} (t ) during the stance phase of gait. A 5% threshold is used to facilitate an accurate and consistent definition of a starting time t _{s} for loading and an ending time t _{e} for unloading the foot during stance phase, whereas the 90% threshold is used to accurately and consistently define an end time for loading the foot, i.e., the time t _{r} − t _{s} required for the magnitude of the F _{z} (t ) to rise from 5% to 90% of the subject's body weight. Similarly, the time t _{e} − t _{d} required for the magnitude of the F _{z} (t ) to decline from 90% to 5% of the subject's body weight. The time t _{m} of the mid-stance phase equals (t _{s} + t _{e} )/2. The minimum stance force F _{ZminMS} is defined as the local minimum force between t _{r} and t _{d,} if a local minimum exists, otherwise it is set to F _{z} (t _{m} ). The heel contact peak force F _{ZmaxHC} is defined as the local maximum force between t _{r} and t _{m} , if a local maximum exists, otherwise is set to F _{ZminMS} . The push off peak force F _{ZmaxPO} is defined as the local maximum force between t _{m} and t _{d} , if a local maximum exists, otherwise it is set to F _{ZminMS} . Two gait characteristic indices are used in this study; they are the Heel Gait Characteristic Index (H _{i} ) and Forefoot Gait Characteristic Index (F _{i} ):

and

where ΔT _{rise} = t _{r} − t _{s} , ΔT _{fall} = t _{e} − t _{d} , T _{stance} = t _{e} − t _{s} , and BW is the body weight of the test subject. Please note that both H _{i} and F _{i} are nonnegative. In other words, if a calculated value of H _{i} or F _{i} is negative, it will be set to zero. The rationale to use the above formula is based on the following observations: a) there are large differences in the rising time and descending time between subjects. These times are important variables to distinguish the gait; b) the amplitudes of the heel contact peak and push off peak to mid-stance minimum force are also important variables to distinguish the gait.

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