Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency

Accepted Manuscript Short communication Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency Dovin Kiernan, Ross H. Miller, Brian S. Baum, Hyun Joon Kwon, Jae Kun Shim PII: DOI: Reference:

S0021-9290(17)30316-0 http://dx.doi.org/10.1016/j.jbiomech.2017.06.019 BM 8258

To appear in:

Journal of Biomechanics

Received Date: Revised Date: Accepted Date:

26 October 2016 28 April 2017 13 June 2017

Please cite this article as: D. Kiernan, R.H. Miller, B.S. Baum, H. Joon Kwon, J. Kun Shim, Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency, Journal of Biomechanics (2017), doi: http://dx.doi.org/10.1016/j.jbiomech.2017.06.019

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Amputee locomotion: frequency and filtration

Manuscript number: BM-D-16-01084 Revision number: 1 Designation: Original Amputee locomotion: Frequency content of prosthetic vs. intact limb vertical ground reaction forces during running and the effects of filter cut-off frequency Dovin Kiernan1,2, Ross H. Miller1, Brian S. Baum1,3, Hyun Joon Kwon1, & Jae Kun Shim1,4 1. Department of Kinesiology, University of Maryland College Park 4200 Valley Dr. College Park, MD 20742 2. Biomedical Engineering Graduate Group, University of California Davis 350 Howard Way Davis, CA 95616 3. School of Physical Therapy, Regis University 3333 Regis Blvd. Denver, CO 80221 4. Department of Mechanical Engineering, Kyung Hee University 1732, Deogyeong-daero, Giheung-gu Yongin-si, Gyeonggi-do 17104, Republic of Korea CORRESPONDING AUTHOR Jae Kun Shim Department of Kinesiology University of Maryland College Park 4200 Valley Drive College Park, MD 20742 (301) 405-2492 [email protected] MANUSCRIPT LENGTH (INTRO THROUGH DISCUSSION) 2141 words

1

RUNNING TITLE Amputee locomotion: frequency and filtration KEY WORDS Running; Impact peak; Ground reaction forces; Amputees; Filtering; Frequency content CONFLICT OF INTEREST STATEMENT None of the authors have potential conflicts of interest or will gain financially from the results of the study.

2

Amputee locomotion: frequency and filtration

ABSTRACT Compared to intact limbs, running-specific prostheses have high resonance non-biologic materials and lack active tissues to damp high frequencies. These differences may lead to ground reaction forces (GRFs) with high frequency content. If so, ubiquitously applying low-pass filters to prosthetic and intact limb GRFs may attenuate veridical high frequency content and mask important and ecologically valid data from prostheses. To explore differences in frequency content between prosthetic and intact limbs we divided signal power from transtibial unilateral amputees and controls running at 2.5, 3.0, and 3.5 m/s into Low (<10 Hz), High (10-25 Hz), and Non-biologic (>25 Hz) frequency bandwidths. Faster speeds tended to reduce the proportion of signal power in the Low bandwidth while increasing it in the High and Non-biologic bandwidths. Further, prostheses had lower proportions of signal power at the High frequency bandwidth but greater proportions at the Non-biologic bandwidth. To evaluate whether these differences in frequency content interact with filter cut-offs and alter results, we filtered GRFs with cut-offs from 1-100 Hz and calculated vertical impact peak (VIP). Changing cut-off had inconsistent effects on VIP across speeds and limbs: Faster speeds had significantly larger changes in VIP per change in cut-off while, compared to controls, prosthetic limbs had significantly smaller changes in VIP per change in cut-off. These findings reveal differences in GRF frequency content between prosthetic and intact limbs and suggest that a cut-off frequency that is appropriate for one limb or speed may be inappropriate for another.

3

INTRODUCTION High frequency content in ground reaction forces (GRFs) during running is often considered noise and is commonly attenuated using low-pass Butterworth filters. These filters model GRFs as sums of sine waves with various amplitudes and frequencies, attenuating frequencies above a certain cut-off and reconstructing the signal from the remaining content. Although critical in removing noise, filtering can also distort veridical signal as “real” and “noisy” bandwidths often overlap (Winter, 1990). Minimizing both distortion and noise requires careful selection of cut-off frequency as optimal cut-offs vary between datasets (Antonsonn & Mann, 1985; Yu et al., 1999). Selection of cut-off frequency may be particularly important when studying running-specific prostheses: they are composed of non-biologic, potentially highfrequency, materials (Lehmann et al., 1993; Major et al., 2012; Noroozi et al., 2012), novel motor strategies are used to run with them (Nolan, 2008), and they lack active tissue to damp high frequencies (Klute et al., 2001). Therefore, GRFs from runningspecific prostheses may have relatively high-frequency content that is not noise (see Wilson et al., 2009). Broadly applying the same cut-off frequency to prosthetic and intact limbs may therefore attenuate veridical frequency content and distort meaningful signal features. Indeed, research has demonstrated that cut-off frequency selection can alter waveforms to the extent that conclusions are affected (e.g., Bisseling & Hof, 2006; Kristianslund et al., 2012; Yu et al., 1999) yet no standards exist to guide cut-off selection for prosthetic GRFs. A wide variety of cut-off frequencies have been used with little justification and identical cut-offs are typically used across limbs and speeds (Table

4

Amputee locomotion: frequency and filtration

1). These practices may remove noise and distort signal differently across conditions, impacting study conclusions. To address these issues the present study aims to (1) evaluate whether the disparate characteristics of prostheses alter their frequency content, and (2) quantify the effects of changing filter cut-off on a common dependent variable. To evaluate whether prostheses have altered frequency content, we quantify frequency content of intact and prosthetic limbs across running speeds. As remarked in previous studies (Blackmore et al., 2016; Derrick et al., 1998; Gruber et al., 2014; Shorten & Winslow, 1992) intact limbs generate an ‘impact’ peak, composed of 10-25 Hz frequency content, followed by an ‘active’ peak, composed of content < 10Hz. In contrast, prostheses may not generate an impact peak (Baum et al., 2016) and may have high veridical frequency content. We hypothesize that, relative to intact limbs, prostheses will show reduced signal power in the 10-25 Hz frequency range but greater signal power >25 Hz, and that high frequency content will increase with running speed. To address our second aim and quantify the effects that changing filter cut-off can have on dependent variables, we use vertical GRF impact peak magnitude (VIP) due to its frequent use in amputee literature and its proposed relationship to injury (Hobara et al., 2013; 2014; Sagawa et al., 2011). We hypothesize that, in intact limbs, changes to cut-offs will not greatly attenuate signals and will have little effect on VIPs above a narrow range due to their predominantly low-frequency content. In contrast, the potentially higher-frequency content of prostheses will result in VIP attenuation across a range of higher frequencies. Thus, we expect changes in cut-off to affect VIP in prosthetic limbs to a greater degree than intact limbs. Similarly, since slower speeds tend

5

to have lower frequency content, we hypothesize that faster speed VIPs are more affected by changes in cut-off.

METHODS Data collection Eight participants with unilateral transtibial amputation wearing Cheetah or Flexrun prostheses (8 male, age = 32.0 ± 10.2 years, height = 1.80 ± 0.07 m, mass = 82.3 ± 13.0 kg; mean ± SD) and eight non-amputees (8 male, age = 29.0 ± 6.9 years, height = 1.84 ± 0.05 m, mass = 79.3 ± 7.9 kg) ran a 100 m track with 10-force plates embedded in series (1000 Hz, 9260AA6, Kistler, Amherst, NY) at prescribed speeds (2.5, 3.0, 3.5 m/s ± 0.2 m/s). Data were originally collected by Hobara et al. (2013) who describe further details. All participants gave written informed consent and procedures were approved by the University of Maryland, College Park Institutional Review Board. Stance was defined as the period between heel-strike and toe-off, which were identified using a 15 N threshold. Generalized Linear Models with General Estimating Equations were used to ensure frequency domain behaviour was statistically similar between left and right non-amputee limbs (ps ≥ 0.44); thus, for this study, six random stances were selected for each speed from the Prosthetic limbs of amputees and the right limbs of non-amputees (Control).

Frequency content of GRF signals To ensure periodicity vertical GRFs from each stance were zero-padded to 2048 points and MATLAB’s (R2016A, MathWorks, Natick, MA) fft function was used to calculate power spectral density at frequencies from 0-500 Hz in 1 Hz bins (Derrick et

6

Amputee locomotion: frequency and filtration

al., 1998; Gruber et al., 2014; Hamill et al., 1995). Power was integrated across three bandwidths: (1) A <10 Hz Low frequency bandwidth corresponding to the ‘active’ peak, (2) A 10-25 Hz High frequency bandwidth corresponding to the ‘impact’ peak, and (3) A >25 Hz Non-biologic frequency bandwidth, considered noise in intact limbs (e.g., Table 1). The proportion of power contributed by each bandwidth was calculated by dividing power in the bandwidth by total signal power. Each participant’s proportions were averaged across six stances for each Limb-Speed combination and entered into a 2 (Limb: Control, Prosthetic) x 3 (Speed: 2.5, 3.0, 3.5 m/s) mixed-measures ANOVA for each bandwidth. Statistical tests were conducted in SPSS (SPSS 20, IBM, Chicago, IL) with p < 0.05 significance. Bonferroni post-hoc comparisons were conducted on significant findings.

Effect of filter cut-off on impact peak To evaluate whether changes in filter cut-off differentially affect VIP across limb and speed, VIP timing was identified using the frequency content ≥10 Hz of vertical GRF (Blackmore et al., 2016). This method showed high agreement with visual identification and successfully identified peaks in all stances (peaks occurred at 13.3 ± 0.3% stance in Control limbs vs. 14.4 ± 0.4% with visual identification and at 7.7 ± 0.8% stance in Prosthetic limbs vs. 7.8 ± 0.7% with visual identification; mean ± 95%CI). Next, raw vertical GRF normalized to bodyweight from each stance was iteratively filtered with 4th order recursive low-pass Butterworth filters at each cut-off frequency from 1-100 Hz in 1 Hz increments. These parameters emulate current practices (e.g., Table 1) and encompass a broad range. For each filtered signal, VIP was calculated using the VIP timing described above. To quantify the effect of cut-off on VIP, VIP

7

values were plotted against cut-off frequency and fit with a logarithmic function (y = mln(x) + b). Larger slopes (m-values) indicate a greater sensitivity of VIP to cut-off frequency. Participant’s slopes were averaged over six stances for each Limb-Speed combination and entered into a 2 (Limb: Control, Prosthetic) x 3 (Speed: 2.5, 3.0, 3.5m/s) mixed-measures ANOVA.

RESULTS Frequency content of signals The ANOVA for bandwidth proportion revealed main effects of Speed on the proportion of signal power in the Low (F(2, 28) = 11.205, p < 0.001), High (F(2, 28) = 22.175, p < 0.001), and Non-biologic (F(2, 28) = 5.539, p = 0.022) bandwidths (Figure 2). Faster speeds tended to reduce the proportion of power in the Low bandwidth (Low2.5 > Low3.0, Low3.5; ps = 0.001) while increasing it in the High (High2.5 < High3.0 < High3.5; ps ≤ 0.001) and Non-biologic (Non-biologic2.5 < Non-biologic3.0, Non-biologic3.5; ps ≤ 0.01) bandwidths. A main effect of Limb also emerged at the High (F(1, 14) = 46.105, p < 0.001) and Non-biologic (F(1, 14) = 24.654, p < 0.001) bandwidths: Prostheses had smaller proportions of total signal power at the High frequency bandwidth but greater proportions at the Non-biologic bandwidth. No Speed by Limb interaction reached significance for any bandwidth (Fs ≤ 1.178, ps ≥ 0.323).

Effect of filter cut-off on impact peak The ANOVA for changes in VIP caused per change in filter cut-off (slope of the logarithmic line of fit) revealed a main effect of Speed (F(2, 28) = 20.457, p < 0.001; Figure 3). Faster speeds had significantly larger changes in VIP per change in cut-off

8

Amputee locomotion: frequency and filtration

(m2.5 < m3.0 < m3.5; ps ≤ 0.01). A main effect of Limb also revealed Control VIPs were more affected by changes to cut-off than Prosthetic VIPs (F(1, 14) = 32.259, p < 0.001). The Speed by Limb interaction did not achieve significance (F(2, 28) = 2.059, p = 0.146).

DISCUSSION This study measured frequency content of prosthetic and intact limbs across a range of running speeds and explored the interactions between limb, speed, and the cutoff frequency of a low-pass Butterworth filter. Consistent with previous literature (Shorten & Winslow, 1992), as speed increased the proportion of frequency content in the 0-10 Hz bandwidth decreased while proportions in the 10-25 and >25 Hz bandwidths increased. Relative to intact limbs, prostheses had lower proportions of frequency content in the 10-25 Hz bandwidth likely reflecting the lack/reduced magnitude of VIPs in prosthetic vertical GRF. A similar lack of pronounced VIPs is observed in runners using a ‘forefoot’ strike (Lieberman et al., 2010). Given their lack of VIP, forefoot runners may also evince reduced proportions of signal content in the 10-25 Hz bandwidth and thus, even between participants without amputation, data filtration has the potential to nonsystematically alter results. Evaluating this hypothesis is, however, beyond the scope of the current study given we did not screen for footstrike and our Control participants all exhibited GRF patterns consistent with a rearfoot strike. In contrast to their reduced 10-25 Hz content, prostheses had greater proportions of signal in the >25 Hz bandwidth. It is difficult to determine if this high frequency content in the vertical GRF is veridical. Force plates do, however, have a high natural frequency (natural oscillatory frequencies in the set-up used here >125 Hz). Thus, the high frequency content of prostheses likely reflects ecologically valid differences

9

between limbs, suggesting that researchers exercise caution when attenuating high frequencies from prostheses. This study also found that filter parameters affected results differently across limbs and running speeds. As speed increased, changes in cut-off frequency had greater effects on VIP. Changes in cut-off frequency also had greater effects on intact VIPs compared to prosthetic VIPs. This finding is in contrast to our hypothesis and is likely due to the variable selected: Prosthetic vertical GRF does not follow the stereotypical pattern observed in intact limbs during running. In our data, prosthetic VIPs either did not appear (36.1% had no visually identifiable impact peak) or were early, low magnitude, and short duration. These characteristics likely contribute to prosthetic VIPs being less affected by changes in cut-off because: (a) the shorter duration prosthetic VIP is composed of higher frequency content and its contribution to the time-domain signal is therefore attenuated across a larger range of low frequencies, and (b) the prosthetic VIP’s lower magnitude means that any attenuation to its frequency content will have a smaller effect on the time-domain signal. Thus, even though the prosthetic vertical GRF signal is composed of a greater proportion of frequency content >25 Hz and the overall signal is more attenuated by lower frequency cut-offs, that attenuation is not reflected by VIP values. It is likely that each variable has unique behaviour as a function of cut-off. Researchers should exercise caution when filtering data if their variables of interest consist of, or are calculated from, portions of the signal where high frequency content plays a dominant role. For example, due to its relation with the impact transient, the instantaneous rate of loading is extremely sensitive to changes in cut-off while, in contrast, maximum vertical GRF and vertical impulse are relatively insensitive (see Supplementary Material).

10

Amputee locomotion: frequency and filtration

Overall, our findings suggest that a cut-off frequency that is appropriate for one limb or speed may not be appropriate for another. Ubiquitous application of the same filter parameters to a variety of limb types and speeds may systematically alter results. Further, across studies, the use of different filter parameters for similar populations/conditions may make comparisons between studies difficult. Going forward, we recommend two possible approaches to mitigate these concerns: (1) given the high signal-to-noise ratio of GRFs, it may be desirable to leave data unfiltered when possible, or (2) researchers should use techniques such as Winter’s residual analysis (1990) that ‘objectively’ select a cut-off for each signal based on its properties (see Supplementary Material). Objectively compromising between signal distortion and noise removal should more accurately eliminate noise while maintaining veridical signal. Future work should adopt a standardized method of data treatment to avoid distorting veridical data and to facilitate comparisons between studies. This is of particular importance given the limited sample sizes available in ILEA research. Here we make recommendations for future work but the efficacy of these and other methods should be compared to find a ‘gold-standard’ that is agreeable to the biomechanics community.

ACKNOWLEDGEMENTS DK was supported by a scholarship from the Natural Sciences and Engineering Research Council of Canada. Supporting agencies had no involvement in the design, collection, or interpretation of this study.

11

Table 1: Sample of previous ILEA running research depicting variation in Butterworth filters used. NR = not reported. TTA = transtibial amputee. TFA = transfemoral amputee. RSP = running specific prosthesis. Within-study the same filter parameters tend to be used ubiquitously across limb type and gait speed. Between-study filter parameters for similar populations and gait speeds vary widely.

12

Amputee locomotion: frequency and filtration

Figure 1: Representative Control (intact) and Prosthetic limbs during 3.0m/s running showing: (A) unfiltered time domain, (B) the high (HiF) and low (LoF) frequency components separated using Blackmore et al. (2016)’s technique, and (C) and frequency domain from 1-50 Hz. In A, note the lack of a pronounced VIP in the Prosthetic vertical GRF. In spite of this lack, the HiF component in (B) shows a clear peak. The lack of VIP is, however, still reflected in C where the Prosthesis does not have a peak in spectral power in the 10-25 Hz range.

13

Figure 2: The proportion of total signal power explained by (A) Low (<10 Hz), (B) High (10-25 Hz), and (C) Non-biologic (>25 Hz) frequency bandwidths for Control (intact) and Prosthetic limbs across 3 different running speeds. *p < 0.05. Behaviour in the frequency domain varied by limb type and speed: As speed increased proportions tended to decrease in the Low bandwidth but increase in the High and Non-biologic bandwidths. Prostheses had lower proportions in the High bandwidth but greater proportions in the Non-biologic bandwidth.

14

Amputee locomotion: frequency and filtration

Figure 3: (A) Mean VIPs for each limb and speed combination calculated from signals filtered at each cut-off frequency from 1-100 Hz (lines) and from the raw signal (shapes). (B) Mean VIPs (gray lines) were well-described by logarithmic functions (y = mln(x) + b) whose slopes represent the change in VIP per change in cut-off frequency. Prosthetic limbs and slower speeds had smaller changes in VIP per change in cut-off frequency.

15

REFERENCES Antonsson, E.K., Mann, R.W., 1985. The frequency content of gait. J. Biomech. 18(1), 39-47. Baum, B.S., Hobara, H., Kim, Y.H., Shim, J.K., 2016. Amputee locomotion: Ground reaction forces during submaximal running with running-specific prostheses. J. Appl. Biomech. 32(3), 287-294. Bisseling, R.W., Hof, A.L., 2006. Handling of impact forces in inverse dynamics. J. Biomech. 39(13), 2438-2444. Blackmore, T., Willy, R.W., Creaby, M.W., 2016. The high frequency component of the vertical ground reaction force is a valid surrogate measure of the impact peak. J. Biomech. 49(3), 479-483. Brüggemann, G.P., Arampatzis, A., Emrich, F., Potthast, W., 2008. Biomechanics of double transtibial amputee sprinting using dedicated sprinting prostheses. Sport Tech. 1(4-5), 220-227. Buckley, J.G., 2000. Biomechanical adaptations of transtibial amputee sprinting in athletes using dedicated prostheses. Clin. Biomech. 15, 352-358. Czerniecki, J.M., Gitter, A., Munro, C., 1991. Joint moment and muscle power output characteristics of below knee amputees during running: The influence of energy storing prosthetic feet. J. Biomech. 24(1), 63-75. Derrick, T.R., Hamill, J., Caldwell, G.E., 1998. Energy absorption of impacts during running at various stride lengths. Med. Sci. Sport Exerc. 30(1), 128-135. Funken, J., Willwacher, S., Böcker, J., Müller, R., Heinrich, K., Potthast, W., 2014. Blade kinetics of a unilateral prosthetic athlete in curve sprinting. In proceedings of the 32nd International Conference of Biomechanics in Sports. Johnson City, TN.

16

Amputee locomotion: frequency and filtration

Gruber, A.H., Boyer, K.A., Derrick, T.R., Hamill, J., 2014. Impact shock frequency components and attenuation in rearfoot and forefoot running. J. Sport Health Sci. 3(2), 113-121. Hamill, J., Derrick, T.R., Holt, K.G., 1995. Shock attenuation and stride frequency during running. Hum. Movement Sci. 14, 45-60. Hobara, H., Baum, B.S., Kwon, H.J., Linberg, A., Wolf, E.J., Miller, R.H., Shim, J.K., 2014. Amputee locomotion: Lower extremity loading using running-specific prostheses. Gait Posture, 39(1), 386-390. Hobara, H., Baum, B.S., Kwon, H.J., Miller, R.H., Ogata, T., Kim, Y.H., Shim, J.K., 2013. Amputee locomotion: Spring-like leg behavior and stiffness regulation using running-specific prostheses. J. Biomech. 46(14), 2483-2489. Hobara, H., Baum, B.S., Kwon, H.J., Shim, J.K., 2013. Running mechanics in amputee runners using running-specific prostheses. Jpn. J. Biomech. Sport Exerc. 17, 53-61. Klute, G.K., Kallfelz, C.F., Czerniecki, J.M., 2001. Mechanical properties of prosthetic limbs: adapting to the patient. J. Rehabil. Res. Dev. 38(3), 299-307. Kristianslund, E., Krosshaug, T., van den Bogert, A.J., 2012. Effect of low pass filtering on joint moments from inverse dynamics: implications for injury prevention. J. Biomech. 45(4), 666-671. Lehmann, J.F., Price, R., Boswell-Bessette, S., Dralle, A., Questad, K., 1993. Comprehensive analysis of dynamic elastic response feet: Seattle Ankle/Lite Foot versus SACH foot. Arch. Phys. Med. Rehabil. 74(8), 853-861. Lieberman, D.E., Venkadesan, M., Werbel, W.A., Daoud, A.I., D’Andrea, S., Davis, I.S., Mang’Eni, R.O., Pitsiladis, Y., 2010. Foot strike patterns and collision forces in habitually barefoot versus shod runners. Nature 463(7280), 531-535.

17

Major, M.J., Kenney, L.P., Twiste, M., Howard, D., 2012. Stance phase mechanical characterization of transtibial prostheses distal to the socket: a review. J. Rehabil. Res. Dev. 49(6), 815-829. Nolan, L., 2008. Carbon fibre prostheses and running in amputees : A review, J Foot Ang Surg 14, 125-129. Noroozi, S., Sewell, P., Ghaffar, A., Rahman, A., Vinney, J., Chao, O.Z., Dyer, B., 2012. Performance enhancement of bi-lateral lower-limb amputees in the latter phases of running events : an initial investigation. J. Sport Eng. Tech. 227(2), 105-115. Oudenhoven, L.M., Boes, J.M., Hak, L., Faber, G.S., Houdijk, H., 2017. Regulation of step frequency in transtibial amputee endurance athletes using a running-specific prosthesis. J. Biomech. 51, 42-48. Sagawa, Y., Turcot, K., Armand, S., Thevenon, A., Vuillerme, N., Watelain, E., 2011. Biomechanics and physiological parameters during gait in lower-limb amputees: A systematic review. Gait Posture 33(4), 511-526. Sanderson, D.J., Martin, P.E., 1996. Joint kinetics in unilateral below-knee amputee patients during running. Arch. Phys. Med. Rehabil. 77, 1279-1285. Shorten, M.R., Winslow, D.S., 1992. Spectral analysis of impact shock during running. Int. J. Sport Biomech. 8, 288-304. Strike, S.C., Wickett, O., Schoeman, M., Diss, C.E., 2012. Mechanisms to absorb load in amputee running. Prosthet. Orthot. Int. 36(3), 318-323. Strutzenberger, G., Brazil, A., von Lieres und Wilkau, H., Davies, J.D., Funken, J., Muller, R., Exell, T., Willson, C., Willwacher, S., Potthast, W., Schwameder, H., lrwin, G., 2016. 1st and 2nd step characteristics proceeding the sprint start in amputee

18

Amputee locomotion: frequency and filtration

sprinting. In proceedings of the 34th International Conference of Biomechanics in Sports. Tsukuba, Japan. Taboga, P., Grabowski, A.M., Di Prampero, P.E., Kram, R., 2014. Optimal starting block configuration in sprint running: A comparison of biological and prosthetic legs. J. Appl. Biomech. 30(3), 381-389. Tominaga, S., Sakuraba, K., Fumio, U., 2015. The effects of changes in the sagittal plane alignment of running-specific transtibial prostheses on ground reaction forces. J. Phys. Ther. Sci. 27, 1347-1351. Waetjen, L., Parker, M., Wilken, J.M., (2012). The effects of altering initial ground contact in the running gait of an individual with transtibial amputation. Prosthet. Orthot. Int. 36(3), 356-360. Weyand, P.G., Bundle, M.W., McGowan, C.P., Grabowski, A., Brown, M.B., Kram, R., Herr, H., 2009. The fastest runner on artificial legs: different limbs, similar function? J. Appl. Physiol. 107(3), 903-911. Willwacher, S., Herrmann, V., Heinrich, K., Funken, J., Strutzenberger, G., Goldmann, J.P., Braunstein, B., Brazil, A., Irwin, G., Potthast, W., Brüggemann, G.P., 2016. Sprint start kinetics of amputee and non-amputee sprinters. PLoS ONE 11(11), 118. Wilson, J.R., Asfour, S., Abdelrahman, K.Z., Gailey, R., 2009. A new methodology to measure the running biomechanics of amputees. Prosthet. Orthot. Int., 33(3), 218229. Winter, D.A., 1990. Biomechanics and motor control of human movement. John Wiley & Sons, Inc., New York, pp. 1-384.

19

Yu, B., Gabriel, D., Noble, L., An, K.N., 1999. Estimate of the optimum cutoff frequency for the Butterworth low-pass digital filter. J. Appl. Biomech. 15, 318-329.

20

1A: Unfiltered Time Domain

2.5

2

2

1.5 1 0.5 0 -0.5

20

40

60

Time (% Stance)

80

100

1.5 1 0.5

0.5

0.4 0.3 0.2 0.1 0

0 0 -0.5

1C: Frequency Domain

0.6 Spectral Power (BW2/Hz)

2.5

0

1B: HiF and LoF Components

3

Vertical GRF (BW)

Vertical GRF (BW)

3

20

40

60

80

100

0

10

20

30

Frequency (Hz)

Time (% Stance)

Control

Control_HiF

Control_LoF

Control

Prosthetic

Prosthetic_HiF

Prosthetic_LoF

Prosthetic

40

50

*

0.85 0.80 0.75 0.70 2.5m/s

3.0m/s Running Speed

3.5m/s

0.20

2B: High Frequencies

*

0.15 0.10

*

0.05 0.00 2.5m/s

3.0m/s

3.5m/s

Running Speed Control

Proportion of Total Signal Power

2A: Low Frequencies

Proportion of Total Signal Power

Proportion of Total Signal Power

0.90

0.25

2C: Non-biologic Frequencies

*

0.20

0.15

*

0.10 0.05 2.5m/s

3.0m/s Running Speed

Prosthetic

3.5m/s

3A: Mean VIP as a Function of Filter Cut-off

3B: Logarithmic Line of Fit

2 Vertical Impact Peak (BW)

Vertical Impact Peak (BW)

2

1.5

1

0.5

1.5

1

0.5

0

0 01

10

20

30

40

50

60

70

80

90

100

Raw

1

10 Filter Cut-off Frequency (Hz)

Filter Cut-off Frequency (Hz) Control 2.5m/s

Control 3.0m/s

Control 3.5m/s

Prosthetic 2.5m/s

Prosthetic 3.0m/s

Prosthetic 3.5m/s

100

Amputee locomotion: frequency and filtration

Table 1 Study

Strike et al., 2012 Hobara et al., 2013 Taboga et al., 2014 Czerniecki et al., 1991 Buckley, 2000

Sample Frequency (Hz)

Filter Type

Order

Cut-off (Hz)

Gait Speed (m/s)

Sample

Prostheses

1080

None/NR

None/NR

None/NR

4.0

Unilateral TTA

RSP

1000

Butterworth

4th

30

2.5-3.5

Control and unilateral TTA

Variety of RSPs

1000

Butterworth

4th

30

2.78-3.09

Control and unilateral TTA

Variety of RSPs

60

None/NR

None/NR

None/NR

2.8

Control and unilateral TTA

Conventional and two RSPs

100

None/NR

None/NR

None/NR

6.81-7.05

Unilateral TTA

Two RSPs

Sanderson & Martin, 1996 Tominaga et al., 2015

480

None/NR

None/NR

None/NR

2.7-3.5

Control and unilateral TTA

RSP

1000

Butterworth

4th

30

5.46-6.18

Unilateral TTA

Variety of RSPs

Bruggemann et al., 2008

1250

None/NR

None/NR

None/NR

8.5-9.5

Control and bilateral TTA

RSP

1200

None/NR

None/NR

None/NR

2.8-3.0

Unilateral TTA

RSP

1000

Butterworth

4

100

7.7-8.6

Unilateral TTA

RSP

1000

Butterworth

NR

30

3.0-10.0

Control and bilateral TTA

RSP

10000

Butterworth

4th

120

2.93-3.21

Control, unilateral TTA and TFA, and bilateral TTA

Variety of RSPs

200

Butterworth

2nd

25

1.9-2.8

Unilateral TTA

RSP

1000

Butterworth

4th

25

2.7-4.6

Control and unilateral TTA

Variety of RSPs

Waetjen et al., 2012 Funken et al., 2012 Weyand et al., 2009 Willwacher et al., 2016 Oudenhoven et al., 2016 Strutzenberger et al., 2016

th

21