Per‐step and cumulative load at three common running injury locations: The effect of speed, surface gradient, and cadence

Understanding how loading and damage on common running injury locations changes across speeds, surface gradients, and step frequencies may inform training programs and help guide progression/rehabilitation after injuries. However, research investigating tissue loading and damage in running is limited and fragmented across different studies, thereby impairing comparison between conditions and injury locations. This study examined per‐step peak load and impulse, cumulative impulse, and cumulative weighted impulse (hereafter referred to as cumulative damage) on three common injury locations (patellofemoral joint, tibia, and Achilles tendon) across different speeds, surface gradients, and cadences. We also explored how cumulative damage in the different tissues changed across conditions relative to each other. Nineteen runners ran at five speeds (2.78, 3.0, 3.33, 4.0, 5.0 m s−1), and four gradients (−6, −3, +3, +6°), and three cadences (preferred, ±10 steps min−1) each at one speed. Patellofemoral, tibial, and Achilles tendon loading and damage were estimated from kinematic and kinetic data and compared between conditions using a linear mixed model. Increases in running speed increased patellofemoral cumulative damage, with nonsignificant increases for the tibia and Achilles tendon. Increases in cadence reduced damage to all tissues. Uphill running increased tibial and Achilles tendon, but decreased patellofemoral damage, while downhill running showed the reverse pattern. Per‐step and cumulative loading, and cumulative loading and cumulative damage indices diverged across conditions. Moreover, changes in running speed, surface gradient, and step frequency lead to disproportional changes in relative cumulative damage on different structures. Methodological and practical implications for researchers and practitioners are discussed.


| INTRODUCTION
2][3] While the etiology of these injuries is multifactorial and influenced by both biological and mechanical factors, there is a general consensus that repetitive cyclical loading coupled with inadequate recovery plays a significant role in their development. 4Specifically, submaximal repetitive loading imparts microdamage to the tissues, [5][6][7] and when insufficient time for remodeling and adaptation is provided, this microdamage can accumulate and eventually manifest as macroscopic damage (i.e., a running-related injury).
Understanding how loading on common running injury locations changes across different running speeds, surface gradients, and step frequencies may inform training programs and help guide progression and rehabilitation after injuries.Although several studies have investigated patellofemoral, [8][9][10][11] tibial, [12][13][14][15] and Achilles tendon 8,16 loading with changes in speed, 8,[11][12][13][14]16 surface gradient, 13,15 or different running styles (e.g., higher and lower step frequency), 9,10 the different methodologies such as the biomechanical modeling approach, and expressions of tissue load per-step or as cumulative load, makes direct comparisons of the tissue loads between studies and thus conditions difficult. Ths in turn also impairs the ability to use these findings to provide training recommendations. Previus studies for instance often investigated the effects of speed or surface gradient on per-step indices of loading.[13][14][15]17,18 However, the number of steps taken to run a given distance can change with alterations in speed and surface gradient, thereby potentially leading to a discordance between per-step loading and total loading to complete a given distance (i.e., cumulative load).Indeed, while the peak knee extensor moment (averaged over each individual step) increases with faster running speeds, the cumulative angular impulse (i.e., area under the forcetime moment × number of steps) decreases, primarily due to a smaller number of steps (and thus loading cycles) to complete a given distance.19 Such findings highlight the importance of accounting for cumulative measures of loading to accurately infer loading across different running conditions.
Moreover, most studies that investigated patellofemoral, 9,10 tibial, [12][13][14][15] and Achilles tendon load did not consider the non-linear relationship between load and damage. 4However, ex vivo studies show that the fatigue life of bone and tendinous tissue follows an inverse powerlaw relationship, [20][21][22][23] whereby higher loading magnitudes shorten the time to tissue failure substantially more than a higher number of loading cycles.For example, Wren and colleagues 21 found the human Achilles tendon to fail on average after 1400 cycles when stretched to 6% strain while stretching to half the strain magnitude (i.e., 3%) increased fatigue life by 6600% (i.e., failure occurred after 93 000 cycles).This nonlinear relationship between load and damage can be modeled by applying a weighting factor (b) to a given load (e.g., stress or strain value), with this weighting factor reflecting the slope of the power function between fatigue life and the tissue-specific stress or strain. 4,16,24For example, weighting factors of 7 and 9.3 have been derived for bone and tendon tissue, respectively. 4,16,21,23Research conducted by Firminger and colleagues 16 underscores the importance of this nonlinear relationship when examining the impact of speed on the risk of Achilles tendon injuries, as the cumulative impulse decreased with higher speeds, while the cumulative weighted impulse (i.e., a proxy of damage; often referred to as cumulative damage in the literature) and the probability of injury increased.The increase in probability of injury with higher speeds is in line with the higher risk of Achilles tendon injuries with higher running speed. 25As such, previous studies that did not consider this nonlinear relationship may have yielded findings that adversely impact training recommendations by suggesting strategies that reduce cumulative load but increase damage and the risk of injury.For example, Doyle and co-workers 11 found a decrease in cumulative patellofemoral joint stress with increases in running speed and suggested that small increases in running speed could therefore be beneficial to reduce pain or injury risk.However, they also found increases in the peak stress per step, and cumulative damage may therefore increase rather than decrease with increases in speed.
Given the importance of load and the resulting damage in the development of running injuries, and the limitations of previous studies exploring these associations across different conditions, this study investigates the per-step peak load and impulse, cumulative impulse, and cumulative weighted impulse on three common injury locations across different speeds, surface gradients, and with changes in step frequency.Further, although modifications in surface gradient, running technique, or speed may reduce the cumulative damage on one tissue, they may lead to (disproportional) increases in the damage on other tissues.Additionally, changes in selected conditions may also have larger effects on reducing damage in one tissue than another tissue.To investigate these hypotheses, we also explored how the cumulative weighted impulse in the different tissues changed across conditions relative to each other.Collectively, these findings may aid coaches, researchers and clinicians in prescribing training programs that optimally load the tissue of interest, hereby potentially preventing injuries and optimizing rehab.
2][3] Specifically, patellofemoral injuries are characterized by the presence of diffuse pain or discomfort between the patella and femur during activities that impose a load on the knee joint, such as running. 26The compressive stress experienced between the patella and femur during the stance phase of running is believed to be the primary cause of this injury, 27 although no studies have prospectively linked mechanical stress to the development of patellofemoral injuries thus far.Nevertheless, partial support for this hypothesis is evident in studies where individuals with patellofemoral pain exhibit higher levels of compressive and shear joint stress compared to control individuals. 28Although the specific tissue affected in patellofemoral pain remains equivocal, several findings indicate the potential involvement of richly innervated subchondral patellar bone. 27,29An estimation of compressive patellofemoral contact stress with subsequent estimation of bone damage by using an empirically derived fatigue-life exponent for bone on the computed stress could therefore be useful to inform on patellofemoral injury risk.Tibial medial stress fractures often occur along the distal third of the posteromedial border of the tibia, 6 which is also the location with peak compressive stresses. 24,30Ex vivo studies show that stress and in particular the resulting strain show strong associations with cortical bone fatigue-life. 23Information regarding the peak compressive stress and resulting damage at this location could therefore be useful to inform on tibial injury risk.Finally, Achilles tendinopathy is characterized by pain occurring 2-6 cm proximal to the tendon insertion 31 and is believed to primarily result from repetitive longitudinal tendon strain. 32Indeed, ex vivo studies have shown that the initial longitudinal peak strain magnitude best explains the fatigue life of tendons. 21,22The estimation of longitudinal tendon strain and resulting weighted strain using an empirically derived fatigue-life exponent for tendon (damage proxy) during running may therefore be useful to inform on Achilles tendon injury risk.

| Participants
All data were collected as part of a larger project aiming to validate wearable pressure sensors. 33In this project, 19 participants (10 males, 9 females, mean ± SD age 23.6 ± 3.7 years, body height 174.9 ± 9.2 m; body mass 67.2 ± 10.4 kg) that were free of any moderate (for previous 3 months) or minor (for previous 1 month) musculoskeletal injuries, were comfortable with treadmill running, had a body mass index (BMI) of <26, and were aged 18-45 volunteered to participate.The study was approved by the local ethics committee (no.2019-1138) and was conducted according to the declaration of Helsinki, and all participants signed an informed consent form prior to the measurements.

| General design of the study
All participants completed a single test session and were instructed to avoid strenuous activity for 36 h, alcohol for 24 h, caffeine for 6 h, and a heavy meal 1 h before the session.When entering the lab, anthropometric measurements were taken using standardized procedures and the participants were then equipped with retroreflective markers.After subject calibration and a familiarization period, the participants completed short (1 min) runs while ground reaction forces and lower body and trunk kinematics were collected.

| Instruments
The computer-assisted rehabilitation environment (CAREN, Motek, The Netherlands) system combines an instrumented split-belt treadmill (belt length and width 2.15 × 0.5 m, 6.28 kW motor per belt, 60 Hz belt speed update frequency, and 0-5 m s −1 speed range) with a 12-camera three-dimensional motion capture system (VICON NEXUS v2.1, Oxford Metrics Group, Oxford, UK, 100 Hz) and was used to measure kinetic and kinematic outcomes.Each participant ran in their own shoes rather than standardized shoes to maximize the applicability of the findings to in-field conditions.

| Data collection
After calibration of the systems, 26 retroreflective skin markers with a diameter of 14 mm were attached to the skin with double-sided tape using a modified lower-limb and trunk marker (Human Body Model v2). 34rior to data collection, the participants were instructed to run for 8 min at a fixed-paced speed of 2.78 m s −1 to familiarize themselves with treadmill running. 35This was followed by 4 min of running at 3.33 m s −1 .The participants then completed a series of 1-min runs at different fixed-paced speeds and treadmill slopes (Table 1), with the order of conditions being randomized by an online research randomizer (https:// www.rando mizer.org/ ).These speeds and slopes were selected to reflect conditions that recreational runners could encounter when running infield.We considered the 3.33 m s −1 condition a typical running speed for recreational runners.Therefore, step frequency manipulations were done at this speed (see below).Pilot experiments however showed that the steepest uphill slope was too fatiguing for some runners at this speed, and we therefore decided to perform all sloped running at 2.78 m s −1 .After the speed and sloped conditions, the participants ran at 3.33 m s −1 with a higher and lower step frequency (± 10 steps min −1 ) compared with their self-selected step frequency during the 4-min trial at 3.33 m s −1 .A target of ±10 steps min −1 (corresponding to 6% of the preferred frequency at the same speed) was used as this has been shown to be sufficient to alter running biomechanics associated with injury risk. 36Step frequency was manipulated using a metronome and participants were instructed to synchronize their step frequency with the beat frequency of the metronome.The order of the step frequency conditions was also randomized.The participants were allowed to take rest periods between trials when required and were instructed to run as if they were running outside and focus on the simulated virtual environment.

| Musculoskeletal modeling
Raw marker data were labeled in Vicon Nexus, and gaps were filled with a combination of cyclic, spline, and rigid body fills and smoothed with a Woltring quintic spline filter. 37The processed kinematic and kinetic data were then exported to musculoskeletal simulation software (OpenSim SimTK 3.3, Stanford, USA) 38 using custom-made Matlab scripts.Ground reaction forces and kinematics were filtered using a zero-lag fourth-order Butterworth with a low pass of 20 Hz.A 20 Hz cutoff was chosen because most treadmill noise is above 20 Hz, 39 and this cutoff avoids removing the physiologically relevant impact peaks, while at the same time, minimizing artificial variations in joint moments when the same cutoff is used for kinematics. 40Footstrike and toe-off were identified when vertical ground reaction force exceeded and dropped below 20 N. [41][42][43] Musculoskeletal simulation was performed using a modified full-body musculoskeletal model (22 rigid body segments, 37 degrees of freedom, and 80 muscles) that was designed to produce more realistic moment arms during tasks involving large hip and knee flexions. 44The generic model was modified by removing the arms and hands with their masses added to the trunk and therefore included six degrees of freedom between the pelvis and the ground, three rotational degrees of freedom between the pelvis and torso, three rotational degrees of freedom at the hip, one rotational degree of freedom at the knee that parametrized the remaining rotational and translational degrees of freedom of the tibiofemoral and patellofemoral joints, and one rotational degree of freedom at the ankle and subtalar joints.The metatarsal-phalangeal joint was "locked".The model's geometry and mass were subsequently scaled to the participant's individual segment length and total body mass.Tendon slack length and optimal fiber length were scaled using the approach by Modenese et al. 45 A weighted least squares minimization of markers on segments and joints was then used to match the virtual markers on the scaled model to the experimental markers in each frame using the "Inverse kinematics" option, while net joint moments for each degree of freedom were computed using the "Inverse dynamics" option.A dynamic optimization criterion that used a cost function that minimized the sum of the squared muscle activations was used to determine the muscle forces required to reproduce the joint moments. 46The optimization was solved for the following degrees of freedom: ankle, knee and hip flexion/extension, and hip ab/adduction.Hip internal rotation was not used in the optimization as pilot analysis showed this introduced inaccuracies in the estimated muscle forces, likely due to soft tissue artifacts.Ideal moment generators (i.e., reserve actuators) were included for each degree of freedom in the model to generate an extra moment if the muscles could not generate the measured moments.The maximum shortening velocity of muscle fibers was set to 20 fiber lengths/s. 30Further, the maximum isometric muscle forces were also doubled and the compliance of the triceps surae and quadriceps muscles was set to 12 and 15, respectively.The root-meansquare contribution of each reserve actuator was verified to be <5% of the net moment calculated via inverse dynamics. 47Muscle forces and joint contact forces (see Section 2.5.2) were determined for both legs over a period of 50 s of steady-state running.This duration was chosen All conditions were performed for 1 min, but some (untrained) participants could not always complete 1 min, and shorter periods were therefore used in these situations.
to ensure the sufficient number of steps (i.e., >25 48,49 ) to achieve stable biomechanical data.
2.5.2 | Determination of load and damage at common injury locations The "Joint Reaction analysis" tool 50 was used to calculate patellofemoral and ankle contact forces by vector summing the joint reaction/intersegmental forces from inverse dynamics and muscle forces from dynamic optimization (Figure 1).All contact forces were expressed in the local coordinate system of the proximal (i.e., tibia and femur) segment.
Patellofemoral contact stress was estimated by dividing the compressive component of the joint contact force by the angle-specific contact area.The contact area was determined based on sex-specific data from Besier and colleagues 51 who estimated patellofemoral contact areas as a function of the knee flexion angle during squats using magnetic resonance imaging.
Stress fractures often occur at the distal third of the tibia, which is also the location with peak compressive stresses. 24,30Modeling studies have shown that 72%-83% of the peak normal tibia stress during level running is caused by the bending moment (i.e., the moment around the mediolateral axis), with the remaining stress being caused by axial compressive forces. 15,30We, therefore, estimated the combined tibial stress due to the bending moment and axial force as follows: First, ankle contact force was multiplied by 0.9 to estimate tibial bone force since ankle contact force is estimated to be borne for 90% by the tibia, and 10% by the fibula. 24,52The axial force at a cross-section located at the distal third of the tibia can then be calculated by ( 1) adding or subtracting forces from muscles that insert below or above the cross-section, respectively and (2) the gravitational force of the tibia mass distal to the cross-section. 15Since no other muscles attach proximal to the distal third of the tibia, and because the distal third of the tibia has only a small mass, we used ankle force * 0.9 as a proxy of the tibial force at third of the tibia.Internal bending moments were determined as the sum of the moment produced by the ankle joint contact force and moment due to gravity. 15Normal stress at the posterior medial periphery was calculated as the axial compressive force F I G U R E 1 Schematic models of the approach used to model load and weighted load (damage proxy) at three common running injury locations.(Left) Patellofemoral joint where the compression stress between the femur and patella depends on the force produced by all quadriceps muscles (F Q ), and the knee flexion angle (Ɵ knee ), which alters both the angle of pull between the quadriceps and patella tendon and the contact area.F PT depicts the force vector of the patella tendon, and F PFJ depicts the contact force between the femur and patella.(Middle) Ankle contact force vector and bending moment on the distal third of the tibia.F G represents the gravitational force acting on the tibia center of mass, and F ACF the ankle contact force vector, which results from both the gravitational force and forces caused by muscle contraction (i.e., medial and, lateral gastrocnemius, soleus, tibialis posterior, flexor digitorum longus, flexor hallucis longus, tibialis anterior, peroneus brevis, longus, and tertius, extensor digitorum longus, and extensor hallucis longus).The vector of the ankle/tibia contact force will bend the tibia posteriorly, which will create compressive stress at the posterior side of the tibia (green arrows in the box), which is further increased by the gravitational force.(Right) Achilles tendon force vector (blue arrow) resulting from the sum of all individual triceps surae muscles (i.e., soleus and gastrocnemius lateralis and medialis as depicted by the green arrows).
plus the compressive forces caused by the bending moment divided by the tibial contact area.The tibia contact area was determined from a hollow ellipse model, as peak stresses with this model have been shown to correlate well with peak stresses from an inhomogeneous model of bone (r = 0.89-0.96). 30chilles tendon force was calculated by summing the forces from the medial and lateral gastrocnemius and soleus (Figure 1).Achilles tendon length change was estimated by dividing the Achilles tendon force by tendon stiffness, with tendon stiffness being derived from ultrasound experiments (420 N mm −1 ; Table S1).The length change was subsequently expressed as a percentage of resting length (i.e., strain), with resting length being set to 250 mm based on previous studies (Table S1).

| Per-step and cumulative load and damage
The amount of damage that tissues experience depends on the duration, magnitude, and frequency of loading. 4or each structure, we therefore determined the per-step peak stress or strain value as the loading proxy that reflects the magnitude of the load.To account for both the magnitude and duration of loading, we additionally determined the impulse by integrating the stress or strain over a gait cycle (Figure S1).To further account for the nonlinear relationship between load and damage, 4 we calculated a weighted impulse were stress or strain was raised to the power of an empirically derived exponent before impulse calculation 16,53 (Figure S1).The exponent used was 7 for patellofemoral and tibial bone damage, and 9.3 for Achilles tendon damage. 4,16,21,23This, therefore, provided one stress or strain impulse and one weighted impulse (damage) value per stride for each tissue.Finally, to also account for the frequency of loading, we calculated the cumulative weighted impulse by multiplying the stress and strain impulse by the number of strides/ km, 16,54,55 with the number of strides taken/km being determined from the stride frequency of each individual at each speed.The result of this multiplication was subsequently raised to the power of 1/b to reduce the magnitude, 16 where b reflects the exponent used.To aid in data interpretation, we also exported spatiotemporal running metrics, the peak axial tibial stress, bending stress, patellofemoral compressive force, and knee and trunk angles.

| Model validation
To validate our simulations, we qualitatively compared simulated activations to surface electromyographic linear envelopes.Moreover, modeled Achilles tendon strain was compared to in vivo measures of Achilles tendon strain, and estimated fiber behavior for the vastus lateralis was compared to fascicle behavior measured with ultrasound (see Appendix S1 for more details and results).

| Statistical analysis
Statistical analyses were conducted using SPSS (version 25, IBM Corporation, Chicago, IL).Linear mixed models were used to examine the relationships between the dependent variables of per-step peak stress/strain, or (weighted) (cumulative) stress/strain impulse, and the independent variables of running speed, surface gradient, and step frequency.Models included speed, surface gradient, and step frequency as continuous covariates (fixed effects) and a random intercept and slope per participant with an unstructured co-variate type.If the model did not converge, we modeled only a random intercept per participant.Separate models were used for uphill and downhill conditions.Secondary outcomes were investigated using the same statistical approach.Assumptions of each model were assessed by visually inspecting the level 1 (repeated measures across speeds/ slopes/step frequencies) and level 2 (participants) residuals on histograms, Q-Q plots, and boxplots to verify that the residuals were approximately normally distributed.For outcomes with a skewed distribution, we removed outliers (>1.5 times the interquartile range) as these were typically the cause of the skewed distribution.As this did not change the interpretation of the models, the original models were retained.Model fit was quantified by computing the root mean squared error between the predicted and actual data.We did not perform pairwise comparisons between all conditions (e.g., running speed 1 vs 2, 1 vs 3, etc.) since this would require 13 × (13-1)/2 = 39 t-tests per outcome, per tissue, thus drastically increasing the potential for type I errors.Instead, the p-value for the slope obtained from the mixed model regression was used to interpret whether the dependent variable significantly changed with changes in the independent variable.Statistical significance was set at 0.05.Descriptive statistics were presented as group means with standard deviations.
Finally, to compare the relative change in the cumulative weighted impulse between different structures, all cumulative weighted impulse values were first normalized by expressing them as a percentage relative to the cumulative weighted impulse in the level running condition at 2.78 m s −1 , or for cadence manipulations, relative to the 3.33 m s −1 condition (as all cadence manipulations were done at this speed).The percentage differences in the normalized cumulative weighted impulse between the structures were then computed and a linear mixed model was used to assess if the slope of this difference significantly differed from zero with changes in the independent variables.

| Model validation
The modeled muscle activation showed good temporal agreement with the experimentally measured activation across different muscles and conditions (Figure S2).Further, Achilles tendon strain closely matched ultrasound measures of Achilles tendon strain across all speeds (Figure S3) and modeled vastus lateralis fiber behavior closely agreed with vastus lateralis behavior measured using ultrasound (Figure S4).

| Spatiotemporal metrics
All outcomes for spatiotemporal metrics are reported in Table S3.Most importantly, step frequency was successfully manipulated in the lower and higher step frequency conditions for all but two subjects who showed <3 steps min −1 difference between the preferred and low step frequency condition and were therefore excluded partially from the step frequency analysis (but included in all other analyses) as we considered this change to be too small.Moreover, it was also clearly smaller than achieved by the other participants.

| Per-step peak load and impulse across conditions for each structure
Table S4 reports the per-step peak stress and strain values, as well as stress and strain impulses, while Figure 2 visualizes these per-step load estimates.The intercept, slope, and p-value for the effect of speed, slope, and step frequency changes from the mixed model are also provided in Table S4.The intercept and slope can be used to predict the change in the dependent variable with every unit increase in the independent variable.For example, the peak patellofemoral stress is predicted to be 7.44 MPa when running level at 2.78 m s −1 , and increases by 0.57 MPa with every degree increase in downhill gradient at 2.78 m s −1 .
The mixed model showed that both patellofemoral and tibial peak stress, as well as peak Achilles tendon strain significantly increased with increases in running speed (Figure 2).In contrast, the impulse did not significantly change with increases in running speed for the patellofemoral joint, while there was a significant decrease for the tibia and Achilles tendon (Figure 2).
Increases in treadmill inclination (i.e., steeper uphill gradients) significantly decreased patellofemoral peak stress and impulse, but increased both tibial and Achilles tendon peak stress, strain, and impulse, respectively (Figure 2).Conversely, increases in treadmill declination (i.e., steeper downhill gradients) significantly increased patellofemoral and tibial peak stress, and stress impulses, but decreased Achilles tendon peak strain and strain impulse.
Increases in step frequency were associated with significant decreases in peak stress, strain, or impulse for all structures (Figure 2).

| Cumulative impulse and weighted impulse across conditions within each structure
Table 2 reports the mean ± standard deviation cumulative impulse and cumulative weighted impulse across the different conditions for the three different structures as well as the intercept, slope, and p-value from the mixed model.Figure 3 visualizes these load and damage estimates.
The mixed model showed that both patellofemoral and tibial cumulative stress impulse as well as cumulative Achilles tendon strain impulse significantly decreased with increases in running speed (Figure 3).In contrast, the cumulative weighted impulse significantly increased with increases in running speed only for the patellofemoral joint, whereas the increase did not reach the conventional threshold for significance for the tibia and Achilles tendon (Figure 3).
Increases in treadmill inclination (i.e., steeper uphill gradients) significantly decreased the patellofemoral cumulative stress impulse and weighted impulse, but increased both the tibial and Achilles tendon cumulative stress and strain impulses, and weighted impulses, respectively.Conversely, increases in treadmill declination (i.e., steeper downhill gradients) significantly increased patellofemoral and tibial cumulative stress impulses and weighted impulses but decreased the Achilles tendon cumulative strain impulse and weighted impulse.
Increases in step frequency were associated with significant decreases in the cumulative stress and strain impulse or weighted impulse for all structures, except for the tibial cumulative stress impulse, where there was no significant effect of step frequency (Figure 3).

| Comparison of changes in the normalized cumulative weighted impulse across conditions between structures
Figure 4 shows the change in the normalized cumulative weighted impulse for the patellofemoral joint, tibia, and Achilles tendon with changes in speed (panel A), as a function of surface gradient (panel B), and with changes in step frequency (panel C).Table S6 provides the statistical results for the comparison of the normalized slopes.Briefly, increases in speed lead to larger increases in the normalized cumulative weighted impulse for the Achilles tendon and patellofemoral joint compared to the tibia (as indicated by significantly steeper slopes with increases in speed, Figure 4; Table S6).There were no significant differences in the change in the normalized cumulative weighted impulse between the Achilles tendon and the patellofemoral joint.
Incline running leads to larger increases in the normalized cumulative weighted impulse for the Achilles tendon compared with the tibia.The absolute decrease in the normalized patellofemoral joint cumulative weighted impulse did not differ significantly from the increase in the normalized tibial cumulative weighted impulse, but the normalized Achilles tendon cumulative weighted impulse increased more than the normalized patellofemoral cumulative weighted impulse decreased with increases in inclination.
F I G U R E 2 Per-step peak stress or strain (left columns) and stress or strain impulse (right columns) for the patellofemoral joint (top), tibia (middle), and Achilles tendon (bottom) across a range of running conditions.Box and whiskers depict the median, interquartile range, and Tukey whiskers, with dots representing outliers (>1.5 times the interquartile range).p-values reflect the main effect of speed, downhill gradient, uphill gradient, or step frequency obtained with the linear mixed model.Note that the 0° gradient is the 2.78 m s −1 condition.Similarly, the preferred step frequency is the 3.33 m s −1 condition.These conditions are, however, depicted in duplicate to ease comparisons.

T A B L E 2 Mean
± standard deviation patellofemoral joint, tibial, and Achilles tendon cumulative impulse and weighted impulse for each running condition.

Note:
Note that the 0° slope corresponds to the 2.78 m s −1 condition, while the preferred cadence corresponds to the 3.33 m s −1 condtion.These conditions are provided in duplicate to ease comparison.
Abbreviation: RMSE, root mean squared error between the predicted value and actual value; in the same units as the original value.
a Mean ± SD cadence for the −10, preferred, and −10 steps min −1 condition can be found in Table S3.
Decline running leads to larger increases in the normalized weighted impulse damage for the patellofemoral joint compared with the tibia.Further, the absolute normalized Achilles tendon cumulative weighted impulse decreased more than the normalized tibial weighted impulse increased with steeper downhill gradients.The absolute normalized Achilles tendon cumulative weighted impulse decreased less than the normalized patellofemoral cumulative weighted impulse increased with steeper downhill gradients.
There were no significant differences between the decrease in the normalized patellofemoral and tibial cumulative weighted impulse, or Achilles tendon and patellofemoral cumulative weighted impulse with increases in step frequency.The normalized Achilles tendon cumulative weighted impulse however decreased significantly more with increases in step frequency than the normalized tibial cumulative weighted impulse.

| DISCUSSION
The primary aim of this study was to investigate the perstep peak load and impulse, cumulative impulse, and cumulative weighted impulse (i.e., a proxy of damage) on three common injury locations across different running speeds, surface gradients, and step frequencies.Overall, our findings highlight the divergence between per-step and cumulative loading indices and between cumulative impulse and cumulative weighted impulse indices across F I G U R E 3 Cumulative load (left columns) and weighted impulse (damage) (right columns) indices for the patellofemoral joint (top), tibia (middle), and Achilles tendon (bottom) across a range of running conditions.Box and whiskers depict the median, interquartile range, Tukey whiskers, with dots representing outliers (>1.5 times the interquartile range).p-values reflect the main effect of speed, downhill slope, uphill slope, or step frequency obtained with the linear mixed model.Note that 0° gradient is the 2.78 m s −1 condition as all gradients were performed at a speed of 2.78 m s −1 .Similarly, the preferred step frequency is the 3.33 m s −1 condition.These conditions are, however, depicted in duplicate to ease comparisons.different running conditions.Moreover, we also show that changes in running speed, treadmill gradient, and step frequency lead to inconsistent changes in the normalized cumulative weighted impulse on different tissues.

| Effect of running speed, gradient, and cadence on per-step loading indices
Most studies traditionally compute the peak load or impulse (area under a waveform curve) on a specific structure and subsequently average this over multiple steps (e.g., 5-10 steps 9,10,18 ) to compare loading indices between running conditions.Using this approach, we observed that increases in running speed were associated with increases in peak patellofemoral and tibial stress as well as peak Achilles tendon strain (Figure 2).Because the peak load has a large contribution to the weighted impulse (see Figure S1), the following paragraphs will detail the biomechanical mechanisms that may explain the changes in peak loading and thus weighted impulse across conditions. 4.1.1| Effect of running speed, gradient, and cadence on patellofemoral per-step loading indices For the patellofemoral joint, peak compressive force significantly increased with increases in running speed, while the patellofemoral contact area did not significantly change (Table S5), thereby leading to a net increase in peak stress.The increase in peak patellofemoral joint stress with higher running speeds is consistent with previous findings, 8,9 thus collectively demonstrating a robust effect of running speed on peak patellofemoral loading.The patellofemoral stress impulse did not significantly change with running speed (Figure 2).This indicates that the increase in impulse due to higher peak stress was offset by the decrease in impulse due to a shorter contact time that accompanied increases in running speed (Table S3), resulting in no net change in the patellofemoral stress impulse.In contrast to our findings, Doyle and colleagues 11 reported a significant increase in the patellofemoral stress impulse with increases in running speed.It could be argued that this discrepancy may partially be explained by the inclusion of the flight phase in the impulse calculation in our study, whereas Doyle and colleagues 11 computed the impulse over the stance phase.However, a sensitivity analysis with patellofemoral impulse computed over the stance-only phase showed a significant decrease rather than increase in the impulse with increases in running speed.These differences may therefore rather be related to different modeling approaches to estimate the patellofemoral stress (e.g., estimation of individual muscle forces in the present study versus the use of a net moment with assumption about co-contraction in 11 ).
Increases in inclination (i.e., steeper uphill running) led to decreases in patellofemoral peak stress and stress impulse but increases in tibial peak stress and stress impulse as well as Achilles tendon peak strain and strain impulse.As contact time remained approximately constant with steeper uphill inclinations (Table S3), the increase in impulse was directionally consistent with the changes in peak values.For the patellofemoral joint, the decrease in peak stress with incline running resulted primarily from a decrease in patellofemoral compressive force (by 36% at 6°) with contact area increasing only slightly and nonsignificantly (~1.5%) (Table S5).The decreased compressive force may in turn result from a more forward trunk lean (Table S5) that in turn reduces the knee extension moment and thus compressive muscle forces.A previous study did not show a significant reduction in patellofemoral peak stress or stress impulse with a similar 6° inclination, although they also showed a more forward trunk lean compared to level running. 56The authors however also found a 10% increase in knee flexion angle during incline running, whereas knee flexion angle increased by only 3.4% in our study (Table S5).The larger increase in knee angle in their study may have resulted in a larger component of the quadriceps muscle force contributing to compression (as opposed to shear forces), thus offsetting the greater trunk lean.This suggests that differences in running technique (e.g., due to differences in surface stiffness or training experience) may impact the effects of surface gradient on tissue loading and implies that not all runners may show uniform effects in response to acute interventions that aim to alter tissue loading.
Increases in declination (i.e., steeper downhill running) showed a reversed pattern to uphill running, with increases in the patellofemoral peak stress and stress impulse.Contact time decreased in downhill conditions compared with level running (Table S3), but the change was too small to produce directionally diverging effects in the peak and impulse values.Mechanistically, the increase in patellofemoral stress with decline running resulted from a larger increase in peak compressive force than the increase in patellofemoral joint contact area at peak compressive force, thus resulting in a net increase in peak compressive stress.The patellofemoral force in turn increased because participants adopted a more upright trunk position as compared to level running (Table S5), consistent with previous findings. 56ncreases in step frequency led to decreases in the patellofemoral peak stress and stress impulse.Mechanistically, the decrease in patellofemoral peak stress with increases in step frequency primarily resulted from a smaller peak knee flexion angle (Table S5) that in turn reduced the knee extension moment and compressive component of muscle forces, with both these changes outweighing the decreases in contact area with smaller knee flexion.The decrease in peak patellofemoral stress with higher step frequencies is consistent with a reduced patellofemoral peak force and stress impulse reported previously. 9,104.1.2| Effect of running speed, gradient, and cadence on tibial per-step loading indices For the tibia, both the peak axial stress and bending stress increased with an approximate similar relative magnitude with increases in speed (12.4% and 11.8% at 5.0 m s −1 relative to 2.78 m s −1 , respectively), thus increasing overall tibial stress with increases in speed.This is in line with previous studies reporting increases in peak tibial force indices with increases in running speed, [12][13][14] thus also demonstrating a robust effect of increases in running speed on peak tibial loading.The tibial stress impulse however significantly decreased with increases in speed, indicating that the increase in tibial peak stress was not large enough to offset the decrease in contact time (Table S3).In contrast, Meardon and colleagues 14 reported no consistent effect of running speed on different tibia impulse indices.Differences in the estimated tibial impulse indices may explain these different observations.
The higher peak tibial stress with steeper inclines resulted from an increase in both the axial stress (28% increase at 6° relative to 0°) and bending stress (11%).This is in contrast to previous findings where the anterior-posterior ankle contact force and moment around the mediolateral axis did not significantly change, and the axial force decreased with increases in surface inclination. 15It could be argued that this discrepancy may in part be related to the different gradients used (up to 10° in 15 vs 6° in the present study).Specifically, there was a trend toward an increased moment around the mediolateral axis at 5°, but not 10° inclination in. 15This is consistent with the increase in the moment around the mediolateral axis and bending stress in our study at both 3° and 6° and could suggest that bending stress may decrease only at inclines beyond 6° whereas it increases at smaller inclinations.However, Rice and colleagues 13 did report continuous increases in the bending stress up to 15° in line with our findings, suggesting other factors such as differences in the modeling approach or running technique adopted by participants may also contribute to the conflicting findings.
The increased tibial stress in the steepest downhill condition resulted from increased bending stress (20%) as the axial stress actually decreased (up to 43%) relative to level running.Because the bending stress has a larger magnitude than the axial stress (Table S5), the smaller relative percentage increase in bending stress outweighed the larger relative percentage decrease in axial stress.Indeed, in line with previous studies, 13,15,30 we show that the bending stress has a larger contribution to total tibial stress than the axial force, with the bending stress being 64%-84% larger than the axial stress (Table S5).During level running conditions, the difference ranged from 70.0% to 70.8%, while the difference decreased to 63.8% during uphill running and increased up to 83.6% during downhill running.This therefore indicates that it is important to account for the stress caused by bending to make more accurate inferences on the changes in tibial stress across different running conditions.This is particularly important in graded running as the decrease in tibial axial stress with downhill running would incorrectly suggest that tibial load is lower in downhill running.Mechanistically, the decrease in tibial axial stress with decline running may have resulted from a more posteriorly placed center of pressure that in turn reduced the ankle joint moment and thereby compressive force by the triceps surae (which in turn also explained the lower Achilles tendon strain).Conversely, the increase in the bending moment may reflect changes in the ground reaction force vector, and muscle orientation with respect to the tibia that both result in a more posterior direction of the tibial force vector, thus increasing bending stress.For example, downhill running is characterized by a more extended lower limb posture at footstrike. 57A more extended knee increases the moment arm of the gastrocnemii muscles at the knee, 58 which in turn creates a more posteriorly directed angle of pull, thus increasing the bending moment and bending stress.Baggaley and co-workers 15 also reported a decrease in tibial axial force with downhill running, but in contrast to our findings, both Baggaley and co-workers 15 and Rice et al. 13 also reported a decrease rather than increase in the moment around the mediolateral axis.This discrepancy may be related to differences in running technique adopted by the participants, as seen previously with the knee angle in the patellofemoral stress comparison.
.1.3| Effect of running speed, gradient, and cadence on Achilles tendon per-step loading indices We assumed a fixed Achilles tendon stiffness regardless of force or loading rate (as discussed below in Table S1), and the increased peak strain with increases in speed therefore directly reflected higher peak muscle forces.The larger peak muscle forces at higher running speeds may in turn be required to increase propulsion and vertical displacement, and thereby stride length (as evidenced by a significant increase in flight time with faster speeds, Table S3).Although we did not quantify footstrike patterns, previous studies show that running speed has relatively small effects on the footstrike pattern up to speeds of 4.3-5.0m s −1 , with more substantial effects at higher speeds. 59,60This suggests that changes toward a mid or front footstrike may have contributed minimally to the higher peak Achilles tendon strain at the lowest speeds, but more prominently during the highest speed.The increase in peak Achilles tendon strain with faster speeds is also in line with previous modeling studies 8,18 and ultrasound experiments (Figure S3), thus again demonstrating a robust effect of speed on peak loading indices.While there was a significant overall decrease in the Achilles tendon impulse with increases in running speed (Figure 2 and Table S4), this effect was most pronounced at the highest speed (5.0 m s −1 ), with minor differences between the other speeds.The decrease in contact time therefore outweighed the increase in peak Achilles tendon strain at the highest speed, resulting in a net decrease in the Achilles tendon strain impulse.
The increased Achilles tendon peak strain and thus triceps surae force with steeper inclination may be a result of a more anteriorly placed center of pressure (i.e., mid or front footstrike) and thus larger ankle joint moment.Conversely, the decreased peak strain with steeper declinations may have resulted from a more posteriorly placed center of pressure.
Finally, the reduction in peak Achilles tendon strain and strain impulse with increases in step frequency may result from a lower vertical oscillation, 61,62 which in turn reduces the force production by the triceps surae and thereby Achilles tendon strain.When combining these latter findings with the speed effects they suggest that the increase in peak loads with increases in speed result from higher force production requirements to increase stride length as opposed to a higher step frequency at higher speeds.

| Effect of running speed on cumulative load and damage
The number of steps taken to run a given distance can differ depending on factors such as running speed and surface gradient (Table S3).Per-step loading indices may therefore not accurately reflect total tissue load to complete a given distance (i.e., cumulative load).Indeed, we found a discrepancy between per-step and cumulative load indices.While the per-step stress impulse for instance remained constant with increases in running speed for the patellofemoral joint (Figure 2), cumulative stress decreased for all tissues with increases in speed (Figure 3).This observation is in line with two studies showing decreases in cumulative loading indices with increases in running speed for the patellofemoral joint 11 and Achilles tendon. 16As the impulse did not always show a similar decrease with faster speeds (Figure 2), the decrease in cumulative load primarily reflects the smaller number of steps taken to cover a given distance at higher speeds rather than shorter contact times.For example, at a speed of 2.78 m s −1 , the mean step length was 1.03 m, thus requiring 977 steps to run 1 km, whereas step length increased to 1.56 m at 5 m s −1 , thus reducing the number of steps required to run 1 km to 644 (Table S3).The decrease in cumulative load with increases in speed could lead to the conclusion that the increased step/stride length beneficially offsets the higher loading magnitudes associated with faster running, thus reducing injury risk.Indeed, some authors have suggested that increases in running speed may reduce loading on certain tissues, reducing injury risk. 11,191][22] When we accounted for this nonlinear relationship by exponentially weighting the stress or strain values, the cumulative weighted impulse (i.e., a proxy of damage) generally increased rather than decreased with faster running speeds (Figure 3) due to the higher per-step peak loads (Figure 2).This is consistent with other studies reporting increases in Achilles tendon, 8,16 patellofemoral, 8 and tibial 24 weighted indices with increases in speed, although the increase in tibial cumulative weighted impulse in our study was marginal and nonsignificant.In fact, due to the exponential relationship between an applied load and the resulting damage, per-step peak load generally better reflected the change in cumulative damage across conditions than cumulative loading.Indeed, the repeatedmeasures correlation between the peak tissue load and weighted impulse was 0.76, 0.72, and 0.45, for the patellofemoral joint, tibia, and Achilles tendon, respectively.This suggests that measures of cumulative load should be used with caution to infer injury risk, although further research is required to establish the best (cumulative) loading measure to assess injury risk.

| Comparison of changes in normalized damage across conditions between structures
Although modifications in surface gradient, running technique, or speed may reduce the cumulative damage on one tissue, they may lead to (disproportional) increases in the damage on other tissues.Further, changes in selected conditions may also have larger effects on reducing damage in one tissue than in another tissue.To investigate these hypotheses, we compared the relative changes in the cumulative weighted impulse with changes in speed, surface gradient, and step frequency across conditions between the three different structures.
Our findings support both hypotheses as the changes in surface slope lead to greater reductions in the cumulative weighted impulse of one tissue than the increase it caused in another tissue.As an example, increases in surface gradient lead to smaller reductions in patellofemoral joint cumulative damage compared with the increase it caused in Achilles tendon cumulative damage (Figure 4, Table S6).Similarly, the magnitude of increase of decrease in the cumulative weighted impulse between conditions differed between the tissues.When increasing running speed, both normalized Achilles tendon and patellofemoral cumulative damage for example increased to a similar extend, with both structures increasing with a larger magnitude than tibial cumulative damage (Figure 4, Table S6).The implications of these findings are briefly discussed in Section 4.5.Reanalysis of results published by Starbuck and colleagues, 8 however, hints at a larger increase in the normalized cumulative damage for the patellofemoral joint than the Achilles tendon with increases in running speed.For example, cumulative patellofemoral and Achilles tendon damage increased by 5%-6% in our study up to the highest speed (Figure 4), while increasing by 13% and 5%, respectively, in the study by Starbuck and co-workers.These differences may partly reflect differences in the modeling approach (e.g., determination of patellofemoral stress from muscles forces obtained with optimization in the present study vs determination of patellofemoral force from net joint moments with assumption about co-contractions), differences in the exact speed range investigated (2.78-5 m s −1 vs 3.33-5.6m s −1 ), and the sample (wide range in performance levels in present study vs well-trained runners only).

| Limitations
There are several strengths but also limitations to this study.Major strengths include the examination of load and damage on different structures across multiple conditions in the same study, and the use of a mixed-sex and mixed-experienced cohort of runners, which increases generalizability to a broader running population.While the use of a state-of-the-art three-dimensional musculoskeletal model with dynamic optimization to determine tissue load can be regarded as another strength, musculoskeletal modeling relies on many assumptions (e.g., maximum muscle force, optimization function) that can impact the estimated loading values.Despite these assumptions, the comparison of our modeled peak Achilles tendon strain and experimentally measured peak Achilles tendon strain obtained from prior studies showed close agreement (Figure S3), thus suggesting the model provided an accurate estimation of Achilles tendon loading across conditions.Similarly, our peak axial tibial contact force agreed well with previous reports (e.g., 10.73 ± 1.03 BW in Edwards et al. 24 at 2.5 m s −1 vs 10.5 ± 1.5 BW at 2.78 m s −1 in our data) that in turn showed their tibial strain estimates from finite element modeling to yield reasonable agreement with tibial strains that were previously obtained using strain gage rosettes. 63,64To the authors' knowledge, there is no in vivo reference data available to validate our modeled patellofemoral joint outcomes.For instance, although some studies have measured the tibiofemoral contact force with instrumented knee plants during low-speed running (1.67 m s −1 ), 65 this speed is considerably slower than our slowest running speed (2.78 m s −1 ), thus not allowing us to use this data as a valid reference.Similarly, femoral strains have been measured in vivo but also at a slow speed of 1.8 m s −1 , thus not allowing comparison with our data. 66As an alternative way to "validate" our patellofemoral load estimates, we, therefore, compared the modeled vastus lateralis fiber length changes to experimentally measured fascicle behavior and showed this to exhibit close agreement (Figure S4).This suggests that the model closely replicated quadriceps muscle length and velocity and thereby possibly force production (as force potential is determined by the force-length-velocity relationship along with muscle activation) at more proximal structures such as the patellofemoral joint.We did however use a higher tendon compliance for the quadriceps muscles than the default value to achieve this agreement, which suggests future studies may also need to increase tendon compliance to increase agreement with in vivo data.Nevertheless, despite the agreement with experimental data, the absolute load and damage may differ from in vivo load and damage.However, as the same approach was used for all conditions, the relative change in load across conditions does likely reasonably reflect changes seen in vivo.
A second limitation relates to the use of relatively short and standardized running bouts to infer loading and damage in our study.In-field, fluctuations in surface gradient, speed, running technique, and fatigue may all impact the actual load and damage.For example, while we used a fixed speed to isolate the effect of changes in surface gradient from changes in speed, runners may slow down while running uphill, while speeding up while running downhill. 67Recent developments in wearable technology to estimate tissue loading may overcome this limitation and allow load and damage estimation in-field. 68,69 third limitation is that our relatively small sample size did not allow us to explore sex-specific effects that may occur due to biomechanical differences between males and females. 14,70Nevertheless, we attempted to account for sex effects, for example by including a sexspecific patellofemoral contact area.Further, we do expect such differences to primarily affect the absolute load and damage within each condition, but to have a smaller effect on the change in load across conditions.
A final consideration is that injuries are multifactorial, with both biological and mechanical factors contributing to injury development.For example, while our modeling approach would predict the same injury risk for two individuals running at the same absolute speed, running above the first ventilatory threshold results in more glycogen depletion, 71 prolonged cardiac parasympathetic recovery, 72 and higher overall central and muscular fatigue. 73This suggests that injury risk may differ between individuals at a given speed, slope, or step frequency depending on biological factors such as the relative exercise intensity.

| Perspective
The findings of this study have several implications for athletes, coaches, clinicians, and researchers.A first (methodological) implication relates to the method used to quantify load in running.Our data show a clear discrepancy between cumulative loading and cumulative weighted loading outcomes.Cumulative loading outcomes (i.e., the load accumulated to run a given distance), for example, showed a decrease with increases in running speed for all tissues, whereas the cumulative weighted impulse generally increased (Figure 3).This indicates that cumulative loading indices should be interpreted with caution in relation to injury risk.Similarly, per-step metrics such as the impulse may also lead to misleading inferences in some situations.Specifically, the decrease in contact time with increases in speed and increases in cadence may influence the (cumulative) impulse such that it could incorrectly suggest injury risk does not increase with increases in running speed (e.g., for the patellofemoral impulse in Figure 2), or that injury risk does not decrease with increases in cadence.Therefore, we also urge caution with the use of per-step impulse measures to infer injury risk.Although the outcome used to quantify load in running depends on the research question or application, our findings may suggest that the cumulative weighted impulse (i.e.proxy of damage) represents the most informative outcome in relation to mechanical load and injury risk.Nevertheless, prospective studies are required to substantiate this notion.
A second implication relates to the effects of running speed on injury risk.Specifically, our findings show that faster running speeds generally increase the cumulative weighted impulse on all investigated tissues, although the change was marginal and non-significant for the tibia (Figure 3, Table 2).This suggests that runners may reduce the risk of running injuries by running slower if total distance is kept constant.In support of this, previous studies have associated "speed training" (i.e., running at a relatively fast running speed) with a higher risk of overall running injuries. 74Moreover, training at higher running speeds has also been associated with an increased incidence of Achilles tendon injuries. 25he quantitatively higher cumulative Achilles tendon weighted impulse at faster speeds can also explain the higher prevalence of Achilles tendinopathy in elite distance runners (53%-83%) 75 as compared to recreational runners (~5%). 76Specifically, from mechanical fatigue perspective, the larger damage accumulated at running speeds may over time outpace the tendon's ability to repair and remodel, thus increasing injury risk.Importantly, the agreement between these experimental findings and our cumulative weighted impulse lends some support to our suggestion that the use of the cumulative weighted impulse may better reflect injury risk than cumulative load (which decreased with higher running speeds).
Our findings also have implications for running on graded surfaces and injury risk.Specifically, downhill running has been shown to exhibit lower peak vertical ground reaction forces 77 and ankle joint moments compared to level running. 57Based on these findings, one could conclude that downhill running may be useful to run with reduced lower limb loading for example during rehab.While our findings indicate that the Achilles tendon cumulative weighted impulse was indeed lower during decline running, the tibial cumulative weighted impulse increased (although most prominently at the steepest decline gradient, Figure 3).Similarly, the patellofemoral cumulative weighted impulse increased with steeper decline gradients.Conversely, uphill running increased both tibial and Achilles tendon cumulative weighted impulses, while decreasing the patellofemoral cumulative weighted impulse.While modifications in gradient may therefore be used to reduce load on a certain tissue, clinicians should also realize that it increases load on other tissues.Moreover, the increase in load on other tissues may be disproportionate to the reduction in load on a given tissue.For example, increases in inclination lead to larger relative increases in the Achilles tendon cumulative weighted impulse than decreases in the patellofemoral cumulative weighted impulse (Figure 4; Table S6), suggesting this would likely not be a primary loading modification strategy to reduce patellofemoral loading.
Conversely, increases in step frequency reduced the cumulative weighted impulse for all investigated tissues (Figure 3; Table 2).This could therefore present the more feasible way to reduce cumulative damage without substantially increasing damage on other structures.Importantly, increases in step frequency led to a larger relative reduction in the Achilles tendon cumulative weighted impulse than the tibial cumulative weighted impulse (Figure 4; Table S6).This suggests that larger increases in step frequency are required to achieve a given relative reduction in cumulative damage for the tibia relative to the Achilles tendon.Within this context, it is also important to note that manipulations in step frequency to reduce loading may have larger effects at slower speeds. 9n summary, our findings suggest that coaches and clinicians wishing to minimize patellofemoral cumulative damage may consider increasing step frequency, and avoid large volumes of downhill running.Individuals aiming to reduce Achilles tendon cumulative damage should primarily consider reductions in running speed, for example by reducing the speed or volume of high-speed interval training.Additionally, they may consider increasing step frequency and avoiding large volumes of uphill running.Finally, coaches and clinicians targeting reductions in tibial cumulative damage may primarily consider increases in step frequency and to a lesser extent reductions in running speed.Our findings suggest that downhill, and in particular, uphill running volume may also be reduced to lower tibial cumulative damage.

| CONCLUSION
We found a divergence between per-step peak and impulse indices and cumulative impulse indices and between cumulative impulse and cumulative weighted impulse (i.e., proxy of damage) indices across different running conditions.Moreover, we also show that changes in running speed, treadmill gradient, and step frequency lead to disproportional changes in relative cumulative damage on different structures.Overall, we show that increases in running speed increase the cumulative weighted impulse for the patellofemoral joint, and Achilles tendon (but not tibia), while increases in cadence reduce the cumulative weighted impulse on all three tissues.Finally, uphill running increased the tibia and Achilles tendon cumulative weighted impulse, but decreased the patellofemoral weighted impulse.Conversely, downhill running increased the patellofemoral cumulative weighted impulse while decreasing the tibia and Achilles tendon weighted impulse.

F I G U R E 4
Relative changes in the normalized cumulative weighted impulse (damage) across different speeds (A), surface gradients (B), and cadences (C) for the patellofemoral joint (blue lines), tibia (red lines), and Achilles tendon (green lines).Dots represent the mean normalized cumulative damage predicted by the linear mixed model.For speeds and surface gradients, all cumulative damage values are expressed (i.e., normalized) as a percentage relative to the cumulative damage during level running at 2.78 m s −1 .For cadence manipulations, all damage values are expressed relative to the cumulative damage during level running at 3.33 m s −1 as lower and higher cadence were performed at a speed of 3.33 m s −1 .