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Fast Running Does Not Contribute More to Cumulative Load than Slow Running


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Medicine & Science in Sports & Exercise: June 2019 - Volume 51 - Issue 6 - p 1178-1185
doi: 10.1249/MSS.0000000000001888


Training programs for general health and performance often prescribe varying proportions of exercise intensity depending on outcome goals (1–4). Although the volumes and proportions of high versus low intensity running or walking may vary based on fitness level and training goal, incorporating proportions of each may be beneficial for runners with a range of fitness and experience (1–5). Running injury incidence has been found to be between 16% and 31% (5,6). The etiology of most running-related injuries is still not well understood and injury development is often attributed in whole or in part to so-called “training errors,” such as too much volume, too much intensity, or progressing volume and or intensity too quickly (7,8), as well as to biomechanical factors such as impact forces and internal loading (9,10).

Previous studies on intensity of training have reported that interval training, typically performed at a relatively fast speed, is associated with a lower rate of injury in recreational runners (5,11), suggesting that running at different proportions of speeds in a set training volume may be beneficial for injury prevention. The peak values per stride of most load-related variables in running increase with increasing speed (12,13), whereas the rate of “cumulative loading,” typically computed as the ratio between a load-related variable and the stride length, appears to decrease with increasing speed (14,15). Assessments of cumulative loads in running have been popular recently in studies on running-related injuries (14–16) and running injuries in general can be theoretically modeled as mechanical fatigue phenomena, where the damage accumulated by a structure from mechanical loading over time outpaces the structure’s ability to repair/recover/remodel (17). However, it is currently unknown how different proportions of fast or slow running speed within a given volume of training affects the loads applied to and accumulated by the body. This gap in knowledge is important for clarifying the role of speed distributions during training on cumulative loads, which is a necessary precursor to a better mechanistic understanding of how cumulative load (or load in general) affects running injury.

Several retrospective and prospective studies have shown that ground reaction force (GRF) characteristics and the vertical loading rate in particular may be associated with running injuries in general, and with tibial stress fracture specifically (6,18–22). The vertical GRF makes a relatively small contribution to tibial loading during running, whereas force applied to the tibia via the Achilles tendon accounts for up to 80% of the peak compressive tibial load in running (23) which can reach 13 times body weight at fast running speeds (23–25). The relationship between peak load and cycles to failure in bone is highly nonlinear (26,27) so even small differences in peak tibial loads such as those sustained during different speed combinations used in training may also affect likelihood of tibial stress fracture injury. Along with vertical loading rate and tibial loads, there is also evidence that external torsional loading contributes to the development of stress fractures. Specifically, the free moment of the GRF was greater in runners with a history of tibial stress fracture compared with controls, and predictive of membership in the tibial stress fracture group (19,28). Loading rates, muscle forces, and free moments increase concomitantly with speed (13), and exposure to higher peak values of these load-related variables may be associated with injury (20,28). However, it is currently unknown if or how running speed affects the accumulation of variables associated with stress fracture when different combinations of speed are used within a given volume of training.

Therefore, the purpose of this study was to compare the vertical average loading rate (VALR), peak free moment, and peak axial tibial load between two different proportions of running speed over an equal distance: (i) all distance at a “normal” self-selected speed, and (ii) the same distance split between self-selected “slow” and “fast” speeds such that the average speed equaled “normal.” Per-step magnitudes of each load variable and step length were expected to increase concomitantly with speed. It is unclear if load peaks or step lengths are more sensitive to speed, therefore we hypothesized that running all distance at normal speed and running the same distance at the same average speed using a combination of slow and fast speed would have similar estimated cumulative VALR, free moment, and tibial load, and that the slow and fast speed would contribute similarly to the total cumulative load of the slow and fast combination.



Previous studies on free moment and VALR in injured and uninjured runners have used sample sizes of 40 to 50 to achieve desired error rates of α = 0.05, β = 0.20, and reported effect sizes of 0.56 to 0.99 (20,28). Recreational runners from the local community were recruited to participate via contact with local running and endurance sports clubs. Inclusion criteria were (i) age between 18 and 50 yr; (ii) run at least three times per week on average and train for at least one race per year; and (iii) have had no lower limb surgeries in the past year and no major health issues in the past year that have affected their ability to walk, run, or exercise for more than a week consecutively. Protocol approval was obtained from the University of Maryland Institutional Review Board. A total of 43 participants (29 female and 14 male, 24 ± 6 yr, 1.68 ± 0.10 m, 63.12 ± 9.61 kg) completed this study. Participants represented a wide range of skill with an average weekly mileage of 25 miles (range, 6–70 miles), and all were habitually shod runners. Each participant gave written informed consent and completed a questionnaire on their exercise and injury history. The minimum detectable effect size with α = 0.05, β = 0.20, was 0.43 in a paired Student’s t test.

Experimental Setup

Participants wore their own running shoes and form-fitting spandex shorts. Participants wore 33 reflective markers on the pelvis (iliac crests, anterior superior iliac spines, posterior superior iliac spines, sacrum), lower extremity of the dominant leg, defined as the leg used to kick a soccer ball (greater trochanter, four-marker thigh cluster, lateral and medial epicondyles, fibula, shank, lateral and medial malleoli), and both feet (great toe, first and fifth metatarsal, calcaneus) (29). Marker positions were captured using a 13-camera motion capture system (VICON, Centennial, CO) sampling at 200 Hz. Eight embedded force plates (Kistler, Amherst, NY) measured GRF at 1000 Hz. The motion capture space is defined by the consecutive placement of the force plates on a 12-m straight stretch of the track. Participants first performed a static calibration trial by standing still with their feet shoulder-width apart and shoulders abducted to ~90° for 10 s.

For movement trials, calibration markers were removed and participants ran around a 50-m indoor track for three laps each at three speeds (nine laps total): self-selected “slow,” “normal,” and “fast” speeds. Specifically, participants were instructed to run at a recovery/conversation pace for slow speed, a moderate pace for normal speed, and a tempo or 5-km race pace for fast speed and ran freely based on these instructions. The “fast” speed was therefore likely substantially slower than each runner’s “maximum” speed, that is, an all-out sprint. However, many interval training programs and workouts prescribe paces at or near the target race pace in long-distance running. Participants were cued to change speed upon completion of the third pass through the motion capture space at the previous speed, allowing for at least 30 meters to accommodate to the new speed.

Data Reduction

Data processing was performed using Visual3D software (C-Motion, Inc., Germantown, MD). Marker positions and GRF were smoothed using a forward-reverse fourth-order low-pass Butterworth filter with a frequency cutoff of 10 and 50 Hz, respectively, with seven frames reflected and a six-frame buffer. A six-degree freedom link segment model was constructed for each subject from the static trial, and iterative Newton–Euler inverse dynamics was used to calculate forces and moments (29). A 20‐N threshold of the vertical GRF identified initial foot contact and toe off. Previous studies on running suggest three to four “trials” (strides) of data per subject per condition are minimally needed for stable and reliable results in running biomechanics (30,31). Data from at least three trials were processed for each speed of each subject, with an average of five trials per speed per subject. Velocity was determined using the stride length and the stride time between successive heel strikes.

Raw data from a representative subject that was used to calculate the VALR, peak free moment, and peak tibial load used to calculate the cumulative outcome variables are shown in Fig. 1. VALR was calculated as the average slope of the vertical GRF versus time between 20% and 80% of the time from initial contact to impact peak and scaled by body weight (BW) (20). When no impact peak was present, 13% of stance was used as a surrogate point to calculate loading rate (32). Free moment was scaled by bodyweight and height, and the peak absolute value during stance was determined (28). Tibial load was calculated by first estimating Achilles tendon moment arm length as 20% of foot length, with foot length defined as the distance between the calcaneus and great toe markers along the long axis of the foot (33), then dividing the plantarflexion ankle moment during stance by the moment arm estimate to calculate Achilles tendon force, and lastly by adding the Achilles tendon force to the axial component of the resultant inverse dynamics ankle force, with the tibial load also expressed on the long axis of the tibia. These calculations were performed for each measured stride, and the VALR, peak absolute free moment, and peak tibial load were averaged over strides to determine the ensemble averages used as outcome variables in all further calculations.

Time series data for a representative subject for vertical GRF (top row), absolute free moment (middle row), and axial tibial load (bottom row). Each plot shows the mean and standard deviation of the representative subject (blue) and the global standard deviation (all subjects and all speeds, gray).

Cumulative load of the VALR, absolute free moment, and tibial load was calculated per-kilometer for two hypothetical conditions of running an arbitrary distance/mileage in training and expressed as the load accumulated per kilometer of running. Condition 1 was calculated assuming that all distance was performed at the normal speed vnormal. The number of steps required to cover 1 km was determined by dividing this distance by the step length of vnormal. For each outcome variable, the number of steps was multiplied by the variable’s per-step magnitude to calculate the cumulative load. Condition 2 was calculated assuming that some distance was run at the slow speed vslow and some at the fast speed vfast, such that the average speed equaled vnormal. Specifically, the fraction of each kilometer run at the slow speed (dslow) and the fast speed (dfast) were:

where dnormal = dslow + dfast = 1 km and T is the time spent running per kilometer (see Document, Supplemental Digital Content 1, Derivation of equation 2b, Cumulative load of the three outcome variables in the combined slow and fast running condition was then calculated by: i) dividing the distance proportion determined from equations 2a–c by the step length at the corresponding speed to obtain the number of steps at each speed, ii) multiplying the step number by the per-step magnitude of each variable, and iii) summing the slow and fast contributions of each load variable. Thus, both conditions had the same total distance, the same total time T spent running, and the same average speed, and differed only in the specific speed(s) used.

Statistical Analysis

Statistical analysis was done using a customized script in R (R Core Team, 2016). To check for differences in outcome variables between the subjects’ self-selected speeds, within-subjects repeated measures ANOVA compared speed, step length, VALR, free moment, and peak tibial load between self-selected slow, normal, and fast speeds. When the assumption of sphericity was violated, Greenhouse–Geisser corrections were reported for departures from sphericity (denoted by epsilon) of less than 0.75 (VALR, free moment) (34). For variables with a significant main effect of speed, post hoc analysis was done using Tukey Honestly Significant Difference with a Bonferroni correction for multiple comparisons, resulting in a critical α of 0.01 to achieve significant differences between speeds.

For each of the three outcome variables, the cumulative loads for both speed conditions were tested for assumptions of normality and homoscedasticity. When the assumptions were met a paired t test was performed (VALR, tibial load), and for variables that violated these assumptions a Wilcoxon signed-rank test was used (free moment). Finally, a comparison of the contribution of slow and fast speeds to cumulative loads in Condition 2 was done using the appropriate t test (VALR, tibial load) or Wilcoxon signed-rank test (free moment). Significance was determined by α = 0.05 for comparisons of cumulative load. Cohen’s d effect sizes were calculated for all normal comparisons, where the numerator was the difference in means between the load-related variables for the two conditions, and the denominator was the pooled within sample standard deviation of the two conditions (35). Wilcoxon signed-rank test correlation coefficient r was calculated by dividing the test statistic Z by the square root of the total number of observations.


All subjects demonstrated a systematic increase in velocity as the self-selected speeds increased and were included in the analysis. The slow, normal, and fast self-selected running speeds averaged 2.70, 3.27, and 4.08 m·s−1, respectively. Speed, step length, VALR, peak absolute free moment, and peak tibial load were all greater at normal speed versus slow speed and at fast speed versus normal speed. Differences in magnitudes between speeds are shown in Figure 2, and the statistical significance and effect sizes are detailed in Table 1. There was a main effect of self-selected speed on running speed, step length, VALR, free moment, and tibial load (free moment: P = 0.002, all others: P ≤ 0.001). Post hoc Tukey Honestly Significant Difference tests revealed that speed, step length, VALR, and tibial load values were significantly different between normal and fast speeds, slow and fast speeds, and slow and normal speeds (d = 0.40–3.18), with these variables increasing with increasing speed (Table 1). Per-step free moment values differed only in normal compared with fast speeds and slow compared with fast speeds, and did not differ significantly in slow compared with normal speeds (Table 1).

A boxplot of the kinematics and per-step kinetics at slow, normal, and fast speeds. The mean and median are represented by the red circle and horizontal line within each box, respectively. The whiskers extend to the range of each variable. All variables significantly increased at faster self-selected speeds except free moment, which was significantly different between normal and fast, and slow and fast, but similar between slow and normal.
Comparisons of running kinematics and kinetics between speeds (difference, and below it, P value and Cohen’s d ES).

The proportions of slow and fast running required to equal normal speed over a hypothetical 1-km distance was 0.50 ± 0.15 km of slow running and 0.50 ± 0.15 km of fast running. Estimated cumulative VALR was significantly lower when running all distance at normal speed than at the combination of fast and slow running speeds (55,043 ± 15,481 vs 60,023 ± 16,667 BW·s−1, P < 0.001, d = 0.31). Estimated cumulative free moment was not significantly different between the two running speed distributions (7787% ± 3653% vs 8572% ± 4072% BW·Ht, P = 0.10, r = 0.18), nor was estimated cumulative tibial load (5792 ± 854 vs 5772 ± 827 BW, P = 0.58, d = 0.02) (Fig. 3). For the combination of fast and slow speeds, the contribution of the slow speed to estimated cumulative tibial load was significantly greater than the contribution of the fast speed (Table 2, Figure 4). The contribution of slow and fast speeds to estimated cumulative load did not differ for VALR or free moment (Table 2, Fig. 4).

Cumulative (A) VALR, (B) free moment, and (C) tibial load by conditions and self-selected speed. C1 represents all mileage at a “normal” self-selected speed, and C2 represents a combination of “slow” and “fast” speeds such that the average speed is equal to the “normal” speed. *Significant difference from C2.
The combined cumulative load of each variable, and individual contributions of slow and fast running to the combined condition (combined mean ± SD, mean ± SD by speed, significance, and ES between speeds)
A boxplot of the contribution of fast and slow speeds to cumulative VALR, absolute free moment, and tibial load. The mean and median are represented by the red circle and horizontal line within each box, respectively. The whiskers extend to the range of each variable. *Significantly lower than the cumulative load of slow running (p = 0.004).


The purpose of this study was to compare estimated cumulative values of three running biomechanics variables related to tibial stress fracture (VALR, peak free moment, and peak axial tibial load) between two different proportions of running speed over an equal distance: (i) all distance run at a “normal” self-selected speed, and (ii) the same distance split between self-selected “slow” and “fast” speeds such that the average speed equaled the “normal” speed. As expected, running speeds were significantly different between runners’ self-selected slow, normal, and fast speeds, and these differences were associated with concomitant increases in step length, peak VALR, peak free moment, and peak tibial load (Fig. 2, Table 1). The effects of running speed on peak load magnitudes are similar to previous investigations, where faster running speed led to higher magnitude per-step loads (12–15).

Our first hypothesis was that the estimated cumulative loads of running all mileage at self-selected normal speed compared with a combination of self-selected slow and fast speeds would be similar over the same distance and at the same average pace. This hypothesis was partially supported: estimated cumulative free moment and tibial load were similar between the two speed distributions; however, estimated cumulative VALR was significantly lower when all mileage was run at normal compared with the combination of slow and fast speed (Fig. 3). In other words, a combination of slow and fast running speeds increased the estimated VALR accumulated per kilometer of distance compared with running at a single moderate speed, even when the average pace was equal. The present results have implications for how training load is quantified in running, and for the inclusion of fast running in training programs. Training errors, such as too much volume, too much intensity, or progressing volume or intensity too quickly, are often cited as the primary cause of injury in runners (7,8). Volume is typically quantified with weekly mileage. Intensity can be quantified in a variety of ways and is not necessarily synonymous with speed, but the average speed is a common metric (18). Reports on how volume, intensity, and progression affect injury risk do not show a clear association between these factors and injury (5,8,18,36). Hreljac et al. (18) found no difference in mileage or average pace between injured and uninjured runners, i.e. there was no difference in volume or intensity between groups. In addition, equivalent increases in either volume or intensity caused no difference in running-related injury incidence after 24 wk of training (8). Tibial stress fracture injury rate decreased with running distance progression up to 30% (36). Our results indicate that average running pace alone may not provide sufficient information on a runner’s training to infer cumulative load since estimated cumulative VALR was different between conditions even though mileage and average running pace were the same. How or if cumulative load as we defined it here affects injury risk remains to be seen.

Our second hypothesis was that the slow and fast speeds would contribute similarly to the total cumulative load of the combined slow and fast condition. This hypothesis was also partially supported: slow and fast speeds contributed similarly to estimated cumulative VALR and free moment, but slow running had a significantly greater contribution to estimated cumulative tibial load than fast running (Fig. 4, Table 2). These results suggest that adding more fast running in a training program without also changing other aspects of training, for example, the amount of slow running will not necessarily increase cumulative load directly. Details of the entire training program including specific proportions of slow/easy and moderate pace runs need to also be considered. Future investigations into runners’ training habits should include more detailed descriptions and histories of training programs beyond average running speed and total volume to avoid filtering out relevant program characteristics that may contribute to cumulative load.

There are currently no known relationships between high (or low) values of any particular cumulative biomechanical load and the risk for any particular running injuries. Studies on running biomechanics and retrospective or prospective injuries to date have focused on more tradition “peak” or “per-step” variables. However, cumulative load has a compelling theoretical basis for playing a causal role in tissue damage and failure (9,10,16,17,37). If we assume high cumulative loads or an abrupt increase in cumulative loads are a risk factor for injury, the present results may partially explain why fast running in the form of interval training has not been associated with injury (5): it appears that the cumulative load from reasonable volumes of fast running is not particularly high. However, the present analyses are limited in that we did not model the relationship(s) between cumulative load, cumulative tissue damage, and positive or negative tissue adaptation. Such analyses could be informative of theoretical injury risk but would require much more sophisticated models.

Peak tibial load values were somewhat lower in the present than previous studies which reported ranges of 7.7 to 13 BW (23–25,33,38). It is likely that the differences in our estimates are due to differences in average speeds, ankle moment arm estimates, and calculation method. Our slow and normal average speeds were much lower (2.70 and 3.27 m·s−1, respectively) than those used in previous studies, where speeds ranged from 3.5 to 5.3 m·s−1. If we consider trials across all self-selected speeds where running velocity equals this range, per-step tibial load ranges from 5.1 to 12.2 BW (n = 58), which matches the velocity range and more closely matches previously reported peak tibial load values of 7.7 to 10.4 BW (n = 5) (25). We used a subject specific estimate based on percentage of foot length that averaged 0.053 m (33), whereas others used a standard length of 0.05 m for all subjects (38), or calculated a changing moment arm based on ankle range of motion throughout stance (23). Post hoc calculation of the tibial load using a standard 0.05 m ankle moment arm resulted in an average of 7.6 BW (range: 5.55–11.26 BW) for subjects running at 3.5 to 5.3 m·s−1, similar to the 7.7 to 10.8 BW range reported by Scott and Winter (25). Additional analysis showed that the average ankle dorsiflexion angle at the point of peak tibial load was 24.7°, 25.5°, and 25.8° at slow, normal, and fast speeds. The largest and smallest within subject between-speed differences were 8.5° and 2.8°, respectively. Previous research shows the sagittal plane Achilles tendon moment arm may decrease up to 2 cm from 20° to 35° of plantarflexion to 20° to 25° of dorsiflexion (39), so it is possible that a more detailed model of the Achilles tendon moment arm may affect the results. We also used a simplified method of estimating Achilles tendon force that assumed no contribution of any muscles other than the triceps surae to the ankle plantarflexion moment. The tibialis anterior has been shown to activate during the first 20% of ground contact (23,25), the peroneus longus activates in a similar pattern as the triceps surae muscles (25), and the peroneals and other plantarflexor muscles contribute less than 1 BW to Achilles tendon force (25). Because the contribution of these and other muscles to the ankle moment is small, and because we were most concerned with how the peak loads changed with step length across speeds, we used a simpler Achilles tendon force estimate. The tibial loads here could be interpreted as the minimum theoretical loads, assuming factors like antagonistic cocontraction and agonistic force-sharing are negligible at the range of speeds studies in these runners.

There are several other limitations to this study. First of these is the statistical strength of this study. Investigations into cumulative loads are relatively novel, therefore, we do not have a large number of previous studies to guide the selection of statistical power and effect sizes for these specific variables. Per-step magnitudes of VALR, free moment, and tibial load have been studied in-depth on the basis of their association with tibial stress fracture injury history (20,28). Because we are most interested in how the accumulation of these variables may also be associated with tibial stress fracture injury risk, we chose statistical power and effect sizes based on these stress fracture injury studies rather than investigations into the effect of running speed on cumulative load (15).

Additionally, our results do not account for potential within-run or between-run changes in running mechanics, muscle/tendon mechanics, structure-specific capacity, or metabolic factors that may cause changes in cumulative load experienced by runners within a run or as they perform runs over time. Most studies on cumulative load, including the present, have defined the “load per unit distance” using loads and stride lengths from fairly short distances of actual running in the laboratory (14,15,17) as opposed to measuring all steps within a distance that runners typically run (e.g., several miles), where factors such as fatigue and fluctuations in footstrike, speed, etc. may affect the actual load accumulated. Future investigations into how cumulative load is affected by related factors such as fatigue-related changes in running mechanics or changes in footstrike pattern with speed may further our understanding of how modifiable gait mechanics affect cumulative load in running.

A final limitation to both the present work and recent cumulative load research in general is that the causal relationship between injury and cumulative loading from any particular mechanical variable is unknown and is largely theoretical to date (9,10,14,17). Our results show that although faster running speed does not necessarily increase the cumulative loading of tibial stress fracture-related variables, it does increase the peak values of these variables and it is these peak values that have been more closely associated with actual injuries (18–21,28). Which “form” of these variables (e.g. peak, cumulative) is the best predictor of injury and has the most direct causal role in injury mechanisms is in need of further investigation. Prospective studies from different labs have shown inconsistent results between studies concerning which peak loads per step are associated with injury (21,22,40). Assessments of cumulative loads would not necessarily show more consistent results, but this possibility seems worthwhile of investigation.

In conclusion, when average running pace and distance are equal, a combination of slow and fast speeds leads to greater estimated cumulative VALR and similar magnitudes of estimated cumulative free moment and tibial load when compared with running at all normal speed. However, the greater cumulative VALR resulted from greater loading during slow running compared with fast running. These results suggest volume and average pace are not sufficient metrics for tracking cumulative load when speed fluctuated substantially over the course of a training volume or even within a single run.

This study was supported by a grant from Maryland Technology Enterprises Institute.

The authors have no conflicts of interest. The results of this study do not constitute endorsement by the ACSM. The results of this study are presented clearly and honestly without fabrication, falsification, or inappropriate data manipulation.


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