Prosthetic model, but not stiffness or height, affects maximum running velocity in athletes with unilateral transtibial amputations

The running-specific prosthetic (RSP) configuration used by athletes with transtibial amputations (TTAs) likely affects performance. Athletes with unilateral TTAs are prescribed C- or J-shaped RSPs with a manufacturer-recommended stiffness category based on body mass and activity level, and height based on unaffected leg and residual limb length. We determined how 15 different RSP model, stiffness, and height configurations affect maximum running velocity (vmax) and the underlying biomechanics. Ten athletes with unilateral TTAs ran at 3 m/s to vmax on a force-measuring treadmill. vmax was 3.8–10.7% faster when athletes used J-shaped versus C-shaped RSP models (p < 0.05), but was not affected by stiffness category, actual stiffness (kN/m), or height (p = 0.72, p = 0.37, and p = 0.11, respectively). vmax differences were explained by vertical ground reaction forces (vGRFs), stride kinematics, leg stiffness, and symmetry. While controlling for velocity, use of J-shaped versus C-shaped RSPs resulted in greater stance average vGRFs, slower step frequencies, and longer step lengths (p < 0.05). Stance average vGRFs were less asymmetric using J-shaped versus C-shaped RSPs (p < 0.05). Contact time and leg stiffness were more asymmetric using the RSP model that elicited the fastest vmax (p < 0.05). Thus, RSP geometry (J-shape versus C-shape), but not stiffness or height, affects vmax in athletes with unilateral TTAs.

Methods participants. Ten athletes with a unilateral TTA (Table 1) gave written informed consent prior to participation. The protocol was approved by the Colorado Multiple Institutional Review Board and the United States Army Medical Research and Materiel Command Human Research Protection Office. All research was performed in accordance with relevant guidelines and regulations. Participants reported no cardiovascular, pulmonary, musculoskeletal, or neurological disease or disorder beyond a TTA.
Each participant first completed an alignment and accommodation session lasting about 4 hours. A certified prosthetist aligned each participant with three different prosthetic models: Freedom Innovations Catapult FX6 (FDM; Irvine, CA), Ottobock 1E90 Sprinter (OBK; Duderstadt, Germany), and Össur Cheetah Xtend (OSR; Reykjavik, Iceland). We chose these models because we have previously established the mechanical properties for each model 4 . FDM is C-shaped, while OBK and OSR are J-shaped (Fig. 1). Each participant was aligned with the manufacturer's recommended stiffness category (based on body mass) and ±1 stiffness category, and at the manufacturer's recommended height and ±2 cm. We adjusted the height of FDM (C-shaped RSP) by changing the height of the pylon connecting the socket to the RSP, and we adjusted the height of OBK and OSR (J-shaped RSPs) using custom aluminum brackets (Fig. 1). Some athletes used two different sockets: one socket for the C-shaped RSP (FDM) and a different socket for the J-shaped RSPs (OBK, OSR). During the accommodation session, participants ran using each RSP configuration on a treadmill at self-selected speeds and the prosthetist made adjustments until both the participant and prosthetist were satisfied. Biomechanical measurements. Each athlete performed sets of running trials consisting of at least 8 strides per trial at constant velocities on a 3D force measuring treadmill (Treadmetrix, Park City, UT). Each series of trials began at 3 m/s, rest was provided between trials, and after each successive trial we incremented treadmill velocity by 1 m/s until the athlete approached their v max , where we used smaller velocity increments until athletes reached their v max . Athletes usually lowered themselves from the handrails onto the moving treadmill belt to initiate each trial; however, some athletes stood on the treadmill belt and accelerated at 1.0 m/s 2 (treadmill default acceleration that was constant for all athletes) with the treadmill belt until it reached the desired velocity and the trial began. All of the athletes were experienced with treadmill running. v max was defined as the velocity where athletes took at least 8 strides on the treadmill while maintaining their fore-aft position 9 . If an athlete could not maintain the velocity for 8 strides, we allowed them to repeat the trial, after ad-libitum rest. For each series of trials, athletes used one of 15 different combinations of RSP model, stiffness, and height. Prosthetic models were FDM, OBK, and OSR. Prosthetic stiffness conditions were the manufacturer recommended stiffness category (based on body mass and high activity level) and ±1 stiffness categories. Prosthetic height conditions were manufacturer recommended height and ±2 cm. We randomized the trial order of RSP model and stiffness category (3 RSP models × 3 stiffness categories = 9 trials). Then for each RSP model, height was only adjusted for the stiffness category that enabled the fastest v max . We randomly inserted the different height trials into the trial order (3 RSP models × 2 RSP heights = 6 trials). Participants completed a maximum of 3 series of trials per day to minimize any potential effects of fatigue; thus, the entire protocol required at least 5 days. Depending on the feedback of each participant, additional rest days were taken to further minimize fatigue, and the average duration to complete the protocol was 10 days.
Throughout each trial, we measured 3D GRFs at 1000 Hz and filtered them using a 4 th order low-pass Butterworth filter with a 30 Hz cutoff. We used these filtered data and a 30 N vertical GRF threshold to detect ground contact and calculate GRF parameters, step kinematics, and leg stiffness for each leg (AL and UL) during each step using a custom MATLAB script (MathWorks, Natick, MA). We determined step time for each leg as www.nature.com/scientificreports www.nature.com/scientificreports/ the sum of the ground contact time and subsequent aerial time. We calculated contact length as the product of ground contact time and the treadmill velocity. For each variable (step frequency, stance average vertical GRF, contact length, contact time, aerial time, and leg stiffness), we calculated the average of both legs. Participants ran with reflective markers attached to the distal end of their RSP and the fifth metatarsal head of their UL. We tracked the position of these markers at 200 Hz (Vicon Nexus, Oxford, UK), filtered marker position data using a 4 th order low-pass Butterworth filter with a 7 Hz cutoff, and used a custom MATLAB script to confirm treadmill belt velocity during each foot-or RSP-ground contact.
We used the mean AL peak resultant GRFs measured in the current study and the reported RSP stiffness values from each device reported by Beck et al. 4 (Supplementary Tables 1, 3 and 4) (k RSP ) to calculate RSP displacement (ΔRSP): (1)

RSP
We calculated leg stiffness (k leg ) in kN/m as the ratio between peak vertical GRF and maximum leg displacement (ΔL) during each stance phase for the respective limb: To determine ΔL, we calculated the angle of the leg (relative to vertical) at initial ground contact (contact angle, θ) using running velocity (v), ground contact time (t c ), and initial leg length (L 0 ) for each leg: We measured initial UL length (L 0 ) as the distance from the greater trochanter to the floor during standing, and AL length (L 0 ) as the distance from the greater trochanter to the distal end of the unloaded RSP 6,7,21 . We calculated maximum vertical displacement of the CoM (Δy) by twice integrating the vertical acceleration of the CoM with respect to time 22 . Then, we used Δy, L 0 , and θ to calculate ΔL according to McMahon and Cheng 12 : We also calculated the symmetry index (SI) for all biomechanical variables of the AL and UL as a ratio between legs, according to Robinson et al. 23 : AL UL

AL UL
A positive SI means that the value for the AL is greater than the value for the UL, while a negative SI means that the value for the AL is lower than the value for the UL. An SI of zero indicates perfect symmetry between the AL and UL.

Statistical analysis.
We used a linear mixed model to analyze the influence of RSP model, stiffness category, and height on v max . We used a second linear mixed model to analyze the influence of RSP model, actual stiffness (in kN/m), and height on v max . We used additional linear mixed models to analyze the influence of significant RSP configurations (model, stiffness, and/or height) on both legs' average and SI of biomechanical variables (step frequency, stance average vertical GRF, contact length, contact time, aerial time, and leg stiffness) while accounting for differences in v max . We report the fixed effect (β) from each statistically significant association (dependent variable = β independent variable + intercept). We selected linear mixed models, as opposed to simple linear regression analyses, to control for subject variability. Each subject was classified as a random effect, while the independent variables were classified as fixed-effect variables. Linear mixed models are particularly useful in a repeated measures design because they take into account the lack of independence between observations within the same athlete using different RSP configurations 24 . For all linear mixed models, RSP model was classified as a categorical variable, while the stiffness category, actual stiffness, height and all biomechanical variables were classified as continuous variables. We also used one-sample t-tests to compare SI values to perfect symmetry between legs (SI = 0). We used a significance level of p < 0.05. When applicable, we implemented Bonferroni corrections to account for multiple comparisons. We performed all statistical tests using RStudio (RStudio Inc., Boston, MA).
We found that step frequency SI was less than zero when using all three RSPs (all p < 0.05; Table 3); on average, step frequency was 6.4% slower for the AL compared to UL. However, there were no differences in step frequency SI between RSP models (OBK 1 vs. OSR 2 : p = 0.31; OBK 1 vs. FDM 3 : p = 0.72; OSR 2 vs. FDM 3 : p = 0.16). Stance average vertical GRF SI was less than zero across RSP conditions (all p < 0.05); on average stance average vertical GRFs were 6.2% lower for the AL compared to UL (Fig. 5, Table 3). However, use of OBK 1 and OSR 2 resulted in stance average vertical GRF SIs that were 0.078 and 0.105 more symmetric, respectively, compared to use of FDM 3 RSPs (both p < 0.05). There was no significant difference in stance average vertical GRF SI between use of OBK 1 and OSR 2 RSPs (p = 0.16). Contact length SI was greater than zero when using all three RSPs (all p < 0.05); on average, contact lengths were 7.2% longer for the AL compared to UL. However, use of OSR 2 resulted in contact length SIs that were 0.045 and 0.022 more symmetric compared to use of OBK 1 and FDM 3 RSPs, respectively (both p < 0.05), and use of FDM 3 resulted in contact length SIs that were 0.023 more symmetric compared to use of OBK 1 (p < 0.05).
We found that contact time SI was greater than zero when using all three RSPs (all p < 0.05); on average, ground contact times were 5.3% longer for the AL compared to UL. Use of OBK 1 resulted in contact time SIs that were 0.047 and 0.031 more asymmetric than use of OSR 2 and FDM 3 RSPs, respectively (both p < 0.05). Further, www.nature.com/scientificreports www.nature.com/scientificreports/ use of OSR 2 resulted in contact time SIs that were 0.016 more symmetric than use of FDM 3 RSPs (p < 0.05). Aerial time SI was greater than zero when using all three RSPs (all p < 0.05); on average aerial times were 9.4% longer for the AL compared to UL. Use of OSR 2 resulted in aerial time SIs that were 0.061 and 0.062 more asymmetric than use of OBK 1 and FDM 3 RSPs, respectively (both p < 0.05). There was no significant difference in aerial time SI between use of OBK 1 and FDM 3 RSPs (p = 0.79). Finally, leg stiffness SI was less than zero when using all three RSPs (all p < 0.05); on average, leg stiffness was 15.7% lower for the AL compared to UL. Use of OBK 1 resulted in leg stiffness SIs that were 0.052 and 0.090 more asymmetric than use of OSR 2 and FDM 3 RSPs, respectively (both p < 0.05). There was no difference in leg stiffness SI between use of OSR 2 and FDM 3 RSPs (p = 0.18).

Discussion
We reject our initial hypothesis because RSP model, but not stiffness or height, affects maximum running velocity in athletes with unilateral TTAs. Therefore, we only considered RSP model as a factor in determining the optimal configuration. Specifically, use of OBK 1 resulted in the fastest v max , followed by use of OSR 2, and FDM 3 RSPs. These results are in agreement with a previous study of running at 2.5-3.0 m/s for athletes with unilateral TTAs,    www.nature.com/scientificreports www.nature.com/scientificreports/ which found that RSP model, but not stiffness or height, affects metabolic cost 20 . Thus, in addition to optimizing distance running performance (i.e. metabolic cost), results of the present study suggest that use of a J-shaped RSP model could also improve sprinting performance (i.e. v max ) for athletes with unilateral TTAs compared to use of a C-shaped RSP.
There were biomechanical similarities when athletes with a TTA used OBK 1 and OSR 2 that were not present when they used FDM 3 RSPs that may explain the differences in v max elicited by use of different RSP models. Due to the inherent relationships between velocity and the biomechanical variables we investigated, we controlled for differences in velocity and determined the biomechanics elicited by use of different RSP models. When controlling for v max , use of J-shaped RSPs (OBK 1 and OSR 2 ) resulted in greater stance average vertical GRF compared to the C-shaped RSP (FDM 3 ). Additionally, compared to use of FDM 3 , use of OBK 1 and OSR 2 RSPs resulted in slower step frequencies due to longer aerial times together with shorter (OBK 1 ) or similar (OSR 2 ) ground contact times. These biomechanical findings may be attributable to RSP shape; OBK 1 and OSR 2 are J-shaped RSPs while FDM 3 is C-shaped. Compared to C-shaped RSPs, J-shaped RSPs have about 1% lower hysteresis and are wider 4,20,21 . The lower hysteresis from J-shaped RSPs could result in greater vertical CoM velocity at the end of the stance phase, and a longer aerial time for a given contact time, which would decrease step frequency. The wider geometry of J-shaped RSPs could enhance stability during running. When balance is perturbed, individuals with TTAs increase step frequency and decrease step length during walking, presumably to minimize the risk of falling 25 . It is possible that use of the narrower C-shaped RSPs resulted in greater medio-lateral instability that required athletes to run with increased step frequency compared to use of wider J-shaped RSPs. It is also possible that the alignment of the J-shaped RSPs enables a more vertical leg position during the stance phase compared to the C-shaped RSP. This could allow the leg to be more closely aligned with the GRF vector, resulting in a better effective mechanical advantage 26 and greater stance average vertical GRFs. Further, non-amputees achieve faster running speeds by producing greater stance average vertical GRF 9 . Our results show that the ability to generate greater stance average vertical GRFs may also be important for athletes with a TTA to achieve faster running speeds, because use of J-shaped RSPs resulted in faster v max and higher stance average vertical GRFs compared to use of a C-shaped RSP.
We also found some biomechanical differences between use of the two different J-shaped RSPs (OBK 1 and OSR 2 ) that could explain differences in v max . Use of OBK 1 resulted in lower stance average vertical GRFs and longer contact lengths than use of OSR 2 RSPs when accounting for velocity. These differences were offset, and step lengths were similar when using OBK 1 and OSR 2 RSPs. Although step frequencies were similar when using OBK 1 and OSR 2 RSPs, contact times were longer (p < 0.05) and aerial times were numerically but not statistically shorter with use of OBK 1 compared to OSR 2 RSPs (p = 0.057). Additionally, use of OBK 1 resulted in lower leg stiffness than use of OSR 2 RSPs. These differences between RSP models could be due to variations in RSP geometry or alignment 4,20,21,27 or differences in curvature between OBK 1 and OSR 2 RSPs (Fig. 6). Similar to alignment's effect on stance average vertical GRF, perhaps the curvature of the OSR 2 RSP enables a more vertical leg position during the stance phase compared to the OBK 1 RSP. This could allow the leg to be better aligned with the GRF vector, resulting in greater stance average vertical GRF despite a shorter contact time. A more vertical leg position during initial ground contact would also lead to a smaller leg sweep angle, and thus shorter contact length and contact time. Additionally, a smaller leg sweep angle would decrease leg spring displacement during the stance phase (Eq. 4), which would increase leg stiffness, assuming peak vertical GRF is held constant. Therefore, differences in RSP geometry/curvature or alignment could explain why stance average vertical GRFs were lower, contact lengths and contact times were longer, and leg stiffness was lower with use of OBK 1 compared to OSR 2 . Thus, future studies that determine the effects of RSP geometry/curvature and alignment are warranted to better understand the underlying biomechanical determinants of v max .
Our results partially support the hypothesis that the optimal RSP configuration would elicit more symmetric biomechanics. While considering differences in v max , RSP model did not affect step frequency symmetry, suggesting that step frequency symmetry may not be important for attaining faster v max . In contrast, RSP model did affect stance average vertical GRF symmetry. AL stance average vertical GRFs were, on average, 6.2% lower than UL stance average vertical GRFs with use of all three RSP models at v max . This finding is similar to a previous study  Table 3. Average symmetry indices (SI) between the affected leg (AL) and unaffected leg (UL) for biomechanical variables when using Ottobock 1E90 Sprinter (OBK 1 ), Össur Cheetah Xtend (OSR 2 ), and Freedom Innovations Catapult (FDM 3 ) running-specific prosthetic models. A positive SI means that the value for the AL is greater than the value for the UL, a negative SI means that the value for the UL is greater than the value for the AL, and an SI of zero indicates perfect symmetry between AL and UL. All SIs are significantly different than zero (p < 0.05). www.nature.com/scientificreports www.nature.com/scientificreports/ that found AL stance average vertical GRFs were 7.7% lower than UL stance average vertical GRFs at v max 7 . In the present study, AL stance average vertical GRFs were 3.6%, 2.9%, and 12.2% lower than UL stance average vertical GRFs when using OBK 1 , OSR 2 , and FDM 3 RSPs, respectively. Use of OBK 1 and OSR 2 elicited faster v max than use of FDM 3 RSPs and stance average vertical GRFs were more symmetric with use of OBK 1 and OSR 2 compared to FDM 3 RSPs. This suggests that stance average vertical GRF symmetry may influence v max . RSP model also influenced contact length symmetry. AL contact lengths were, on average, 7.2% longer than UL contact lengths with use of all three RSP models at v max . This contrasts with a previous study that found no difference in contact length between the AL and UL when athletes with unilateral TTA ran at v max 7 . However, contact lengths were least symmetric with use of OBK 1 , suggesting that contact length symmetry may not influence v max . Use of the OBK 1 RSP resulted in the most asymmetric and lowest average leg stiffness. Because use of the OBK 1 RSP elicited the fastest v max , this suggests that lower average leg stiffness, but not leg stiffness symmetry, may influence v max in athletes with unilateral TTAs. It is possible that lower leg stiffness results in a greater amount of time to generate force on the ground, which leads to faster v max . A previous study found that AL leg stiffness was 27% lower than UL leg stiffness at a maximum velocity of 9.5 m/s 6 . Similarly, we found that AL leg stiffness was 13-22% lower than UL leg stiffness at v max across all configurations at an average v max of 8.32 m/s. Overall, our results suggest that RSP configurations that result in more symmetric stance average vertical GRFs have the strongest influence on v max .
In the present study, we determined the effects of using fifteen different RSP configurations on v max and the underlying biomechanics used to achieve these velocities. However, a potential limitation of this study is that some athletes used two different sockets to complete the protocol. Athletes used one socket for J-shaped RSPs (OBK 1 , OSR 2 ) and a different socket for the C-shaped RSP (FDM 3 ), which could have contributed to different amounts of residual limb movement within the socket, and potentially affected running biomechanics 21  www.nature.com/scientificreports www.nature.com/scientificreports/ affect leg swing time and step frequency. However, Grabowski et al. 7 found no difference in v max or in leg swing time of the AL when adding up to 300 g to the distal end of the RSP of athletes with unilateral TTAs compared to the same RSP with no added mass. We found that use of the FDM 3 RSP resulted in 3.4% faster step frequencies than OBK 1 and OSR 2 RSPs yet use of the FDM 3 RSP did not elicit the fastest v max .
Seven of the athletes involved this study typically use J-shaped RSPs for competition compared to three athletes who typically use C-shaped RSPs (Table 1). This familiarity could have affected our results. However, for nine athletes, irrespective of their usual RSP, J-shaped RSPs resulted in the fastest maximum velocity (Table 1). Only subject 2, who usually runs using a J-shaped RSP, had a faster v max using the C-shaped FDM 3 . For all 3 of the subjects who usually run using a C-shaped RSP, use of the J-shaped RSPs resulted in a faster v max .
The spring-mass model has been used to calculate leg stiffness at running speeds ranging from 3.8 m/s 13 to 8.7 m/s 28 and up to 12.3 m/s 29 . Clark et al. 30 found that the vertical GRF trace is not symmetric during ground contact for professional non-amputee sprinters, which suggests that the assumptions for calculating leg stiffness using the spring-mass model may be violated. We found that the vertical GRF trace for the UL is not symmetric during ground contact (Fig. 5), and thus the leg stiffness of the UL may not be accurately represented by the spring-mass model. These differences may limit our calculations of leg stiffness for the UL and the leg stiffness symmetry index comparing UL and AL leg stiffness. However, our findings are similar to those of McGowan et al. 5 , who calculated leg stiffness of the UL using the spring-mass model at speeds between 3.0 and 9.5 m/s. Some athletes lowered themselves from the handrails onto the moving treadmill belt to initiate each trial while others stood on the treadmill and accelerated with the treadmill belt until it reached the desired velocity. Use of these different strategies is unlikely to influence v max because the treadmill accelerates at 1.0 m/s 2 and athletes used the same strategy for each RSP configuration. Additionally, the systematic trial order of progressively increasing velocity with each RSP configuration may have induced fatigue. To reduce any potential effects of fatigue, we allowed athletes rest ad libitum, and limited each day of testing to three sets of trials. The initial accommodation session was approximately four hours, but a longer accommodation period (multiple days/weeks) may have allowed athletes to reach a faster v max for each RSP configuration. Future studies are needed to determine how athletes accommodate to RSPs, and how accommodation time relates to performance.
We found that RSP height did not significantly affect v max (p = 0.11), but it is possible that changes of ±2 cm were not enough to significantly affect v max . However, ±2 cm changes in RSP height were noticeable by each athlete, and greater RSP height changes could have resulted in injury. The average maximum running velocity for all configurations in the present study (8.32 m/s) is similar to those reported previously for athletes with unilateral TTAs running on a treadmill (8.82 m/s and 8.75 m/s) 6,7 . Future studies are needed to investigate the effects of using different RSP configurations on joint mechanics and muscle activation patterns. These parameters could help to further explain differences in v max among RSP configurations by revealing changes in effective mechanical advantage or ability to produce muscle force during the stance phase. Future studies should also investigate the effects of different RSP configurations on the start and acceleration phase of sprint races, to determine if the RSP configuration that allows for the fastest v max is also the configuration that allows for a better start and acceleration, i.e. for a better racing performance. www.nature.com/scientificreports www.nature.com/scientificreports/ conclusions Athletes with unilateral TTAs reach different maximum running velocities when using different RSP models. Specifically, use of the J-shaped OBK 1 resulted in the fastest v max , followed by use of the J-shaped OSR 2 , and C-shaped FDM 3 RSPs. RSP stiffness and height do not have a significant effect on v max in athletes with unilateral TTAs. While controlling for velocity, use of J-shaped versus C-shaped RSPs resulted in greater stance average vertical ground reaction forces, slower step frequencies, and longer step lengths. Stance average vertical ground reaction forces were less asymmetric, while contact time and leg stiffness were more asymmetric when using J-shaped versus C-shaped RSPs.

Data availability
All data generated and analyzed during the current study are presented in the main text, figures, and tables. An alternative data format is available from the corresponding author on reasonable request.