Running is cited as a common form of recreational activity (30). Numerous forms of overuse injury remain largely unchanged (9,33) despite different interventions (5,7,12,16,24,26,38). Patellofemoral pain (PFP) is one of the most commonly reported forms of pain among runners, especially in females (33). Yet, its specific pathoanatomical etiology and interventions used for treatment remain largely uncertain.
A prevailing theory underlying the etiology of PFP is that an increase in patellofemoral (PF) joint stress occurs (4,15), leading to pain from the subchondral tissues of the patella or femur (13,17). The primary factors that determine PF joint stress are PF joint reaction force and PF contact area. These may be affected by quadriceps force (22,29), knee angle (8), hip internal or external rotation angle (31,32), knee rotation (31), or foot pronation (23).
Current interventions for PFP in runners attempt to reduce knee loading by altering step length or step rate to allow continued participation in running without exacerbating symptoms (12,16,22,38). More specifically, Willson et al. (38) showed that a reduction in step length of at least 10% resulted in an average decrease of 16.3% in PF joint stress. Even small increases in step rate have been shown to reduce energy absorption at the knee (17). A more recent investigation found that a 10% increase from preferred step rate resulted in a 14% decrease in PF joint reaction force (22). PF loading rate and impulse were also reduced by 11% and 20%, respectively, with increased step rate (22). These results demonstrate that changes in running mechanics can lead to reductions in joint specific forces and stresses which may allow athletes to continue running without aggravating PFP symptoms.
However, increased step rate seems to be associated with a decreased foot inclination angle at initial contact (16), suggesting a more anterior foot strike pattern (2). Increasing step rate under controlled running speed conditions necessitates a shorter stride length (22), and decreasing step length results in increased shock attenuation at the ankle (12). This increased shock attenuation was attributed to a greater horizontal distance of the ground reaction force vector from the ankle joint center. A more anterior location of the ground reaction force vector is indicative of a more anterior foot strike pattern based on the foot strike index proposed by Cavanagh and LaFortune (6). Thus, whether decreased stress at the knee is a result of shorter step length, increased step rate, or a more anterior foot strike pattern is difficult to ascertain from these studies.
Further, Roos et al. (29) reported that knee extensor moment predicted 93% of the variance in PF joint reaction forces during forward and backward running. They also stated that a center of pressure closer to the heel was a primary predictor of increased knee extensor moments. This suggests that an intervention targeted toward training to run with a forefoot strike pattern may lead to even greater reductions in PF joint reaction force and PF joint stress.
Forefoot strike running patterns have gained much interest with regards to running injury and treatment in recent years (1,7,9,21,24,36,37). More anterior foot strike patterns, or less foot inclination at initial contact, have been reported to reduce overall loading of the lower extremity during running as well as to decrease the stress on the knee joint (24,37). Cheung and Davis (7) reported in a case series that there was an improvement in symptoms in three runners with PFP when using a landing pattern modification program. They attributed these improved symptoms to decreased ground reaction forces measured after training. However, whether a corresponding decrease in PF joint stress occurred with the change in foot strike pattern could not be determined because they did not collect data specifically with regard to PF joint stress. A more recent study did investigate the differences in PF joint stress between forefoot strike and rearfoot strike patterns and found PF joint stress to be 15% less in those with a forefoot strike pattern (20). However, this difference occurred between groups rather than as a result of runners simply changing foot strike pattern.
Although increased PF joint stress remains a prevailing theory with regard to the etiology of PFP (15,17), differences in PF joint stress between runners with and without PFP have only been suggested (39). However, these values of PF joint stress were calculated from the net knee moments using inverse dynamics to obtain the magnitude of quadriceps force, and thus, any coactivation of muscles surrounding the knee may lead to an underestimate of the actual quadriceps force produced (20,39).
Therefore, the primary aim of this study was to determine whether a simple alteration of one’s foot strike pattern changes the PF joint stress calculated by a static optimization technique estimating muscle forces of the lower extremity. Both peak PF joint stress and the PF joint stress–time integral will be investigated to garner an understanding of the maximal stress and the accumulated stress to the PF joint during stance. Secondary objectives included investigating whether differences were present in other variables contributing to PF joint stress such as stride length, peak vertical ground reaction force, peak quadriceps force, knee flexion angle at initial contact, and peak knee flexion angle between rearfoot strike and forefoot strike running conditions. We hypothesized that the forefoot strike condition would result in decreased PF joint stress, peak vertical ground reaction force, and peak quadriceps force; increased knee flexion angle at initial contact and peak knee flexion angle; and no change in step length. A post hoc analysis was completed to facilitate accurate interpretation of results and included investigation of such variables as the average hamstring force, average gastrocnemius force, average soleus force, and the lower extremity position at initial contact.
Seventeen healthy females 18–35 yr were included in this study (age = 22.8 ± 3.17 yr, height = 169 ± 5.8 cm, mass = 63.7 ± 5.4 kg, weekly running distance = 33.2 ± 14.7 km). Inclusion criteria consisted of a self-reported running routine of >10 miles per week, self-reported rearfoot strike pattern (first contact with the ground made with the heel) while running, score of 5 or greater on the Tegner activity scale (a measure of regular participation with recreational sports which require running and jumping), and no reported knee symptoms similar to PFP, which limited regular participation in running in the past 12 months. Exclusion criteria consisted of pregnancy, reported cardiovascular pathology, surgery on either lower extremity in the last 12 months, and traumatic injury to either knee in the past 6 months. All subjects gave their informed consent to the testing protocol as approved by the institutional review board at the university.
After completion of a minimum of three practice running trials, participants ran down a 20-m runway under two conditions: using 1) their typical rearfoot strike pattern and 2) an adapted forefoot strike pattern after simple instruction to “contact the ground on the ball of the foot.” The order of these conditions was randomized. All participants were fitted with the same model of footwear (Model 629; New Balance, Boston, MA). Speed was restricted to a range of 3.52–3.89 m·s−1 using photoelectric timers. Running pattern was observed carefully, and any trials where targeting of the force plate occurred were repeated. Foot strike pattern was verified after each trial via the use of in-sole pressure sensors (Novel GmbH, Munich, Germany). Rearfoot strike was defined as the subjects’ center of pressure occurring in the rear most third of the overall foot length at initial contact as previously defined by Cavanagh and LaFortune (6). For the purpose of this study, we combined the midfoot strike and forefoot strike categories of the foot strike index such that a forefoot strike was any pattern such that the center of pressure was located anterior to the 33% of foot length at initial contact. If a strike pattern was not the correct pattern, that trial was repeated. A total of 10 trials were completed under each condition. Foot strike pattern was then verified again during postprocessing by calculating the location of the center of pressure on the foot using force plate data as previously described (2).
Before all running trials participants were prepped for three-dimensional motion analysis using the Human Body Model (Motek Medical, Amsterdam, Netherlands). Reflective markers were placed on the right, left, top, and front of the head. Trunk markers were placed on C7 and T10 spinous processes, the navel, the xiphoid process, the sternal notch, and the right scapula. Bilateral upper extremity markers were placed at the acromion process, near the deltoid insertion, the medial and lateral humeral epicondyles, the forearm, the ulnar and radial styloid processes, and the second metacarpophalangeal joint. Markers defining the pelvis were placed at bilateral anterior superior and posterior superior iliac spines along with one marker being placed at the apex of the sacrum. Lower extremity markers were placed bilaterally on the greater trochanter, anterior thigh, lateral femoral epicondyle, anterior tibia, and lateral malleolus. The foot segment consisted of three markers placed on the shoe at the heel, the great toe, and the fifth metatarsophalangeal joint. All markers were left in place during data collection. Motion capture was completed via the use of 13 motion analysis cameras (Motion Analysis Corporation, Santa Rosa, CA) mounted around the runway, with a capture rate of 180 Hz. Ground reaction forces were collected with the use of a force platform (Model 4080; Bertec Corporation, Columbus, OH) mounted flush with the runway. Analog data were sampled at 1800 Hz. Both analog data from force platforms and kinematic data were filtered at 15 Hz.
The Human Body Model (Motek Medical) was used to calculate muscle forces based on a 44-degree of freedom (DOF) musculoskeletal model with 16 rigid segments (34). The head was modeled as a single segment with 3-DOF relative to the pelvis. The trunk was modeled as three segments with 3-DOF, upper arms with 6-DOF, elbow with 2-DOF, and wrist with 2-DOF. The pelvis segment had 6-DOF and was able to rotate and translate in all three dimensions with respect to the ground. The hip joint was modeled as a ball-in-socket joint with three rotational DOF using the method by Bell et al. (3). The knee joint was modeled as a single DOF hinge joint where any tibiofemoral translations and nonsagittal rotations were constrained as a function of knee flexion. The subtalar joint was modeled with 1-DOF, and the ankle joint was modeled with 2-DOF. The inertial characteristics of the segments used in the model were based on participants’ total body mass and segment lengths (10). Three hundred muscle tendon units were represented in the model: 86 in the legs, 204 in the arms, and 10 in the trunk. Muscle parameters such as muscle insertion points and wrapping points were determined by Delp et al. (11).
A kinematic solver within the Human Body Model used global optimization (25) to determine skeletal model kinematics using the Levenberg-Marquardt algorithm (28). Joint moments were then obtained from equations of motion. Residual loads, three force, and three moments on the pelvis were minimized in the inverse dynamics processing within the Human Body Model. Muscle forces were estimated from the joint moments by minimizing a static cost function where the sum of squared muscle activations is related to maximum muscle strengths (11,14) at each time step of the model. A recurrent neural network was used to solve the static optimization problem (40).
The muscle forces from the Human Body Model were then used to quantify the total quadriceps force by summing the muscle forces of the rectus femoris, vastus medialis, vastus lateralis, and vastus intermedius. To determine the PF joint reaction force, a k constant was calculated using the following equation derived by Brechter and Powers (4):
where x is the knee joint angle in the sagittal plane. The constant k represents the portion of the quadriceps force that is directly imposed on the PF joint as determined by the angle of the knee joint and the orientation of the quadriceps muscle as described by van Eijden et al. (35). Hence,
PF joint contact area was calculated as a function of knee angle using the data reported by Connolly et al. (8) to formulate a predictive equation as used previously (37):
PF joint stress was then determined by dividing PF joint reaction force by the contact area:
Step length was calculated as the horizontal difference of the heel markers of the left foot and right foot between successive foot falls.
Average hamstring force was calculated by summing the muscle forces of the semimembranosus, semitendinosus, and long and short heads of the biceps femoris muscles. The medial and lateral heads of the gastrocnemius were both included in calculating average gastrocnemius force. Reach was calculated as the horizontal distance between the locations of the greater trochanter and heel markers of the right lower extremity in the anteroposterior direction at initial contact.
Sample size was calculated a priori using β = 0.2 and α = 0.05. A minimum sample size of 14 was determined by the difference in PF joint stress of 1.9 MPa, with an SD of 2.9 between forefoot strike versus a rearfoot strike, as estimated from Kulmala et al. (20). A multivariate analysis of variance with repeated measures (foot strike pattern: forefoot strike and rearfoot strike) using an α = 0.05 was used to examine differences. Follow-up univariate tests were then completed to detect differences between foot strike conditions for each variable. Statistical calculations were completed in SPSS 21 (IBM, Aramonk, NY) software.
Of the 17 participants, 16 were included in final analysis (age = 22.2 ± 1.8 yr, height = 169 ± 6 cm, mass = 64.2 ± 5.1 kg, weekly running distance = 32.3 ± 14.7 km). One participant’s data were not analyzed because post hoc calculations of the foot strike index indicated that she did not land with a rearfoot strike pattern consistently as defined earlier during completion of rearfoot strike trials. Average foot strike indices across participants were 23.8% ± 15.2% for the rearfoot strike condition and 69.3% ± 13.8% for the forefoot strike condition. Multivariate analysis generated a Wilk’s λ of 0.015 (P = 0.001), indicating that the variables of interest could be investigated independently. Follow-up univariate tests revealed differences in all variables investigated except for peak knee flexion angle and step length (Table 1).
Peak PF joint stress decreased by 27% and the PF joint stress–time integral decreased by 12% when changing from rearfoot strike to forefoot strike (Fig. 1). The FFS condition resulted in a 6.6% increase in peak vertical ground reaction force and 27% decrease in peak quadriceps force. Kinematic changes occurring at the knee included an increased knee flexion angle at initial contact and decreased total knee excursion during the forefoot strike condition. Peak knee flexion angle did not change between conditions. Step length did not change between conditions. Despite a uniform decrease in peak PF joint stress when running with a forefoot strike, step length changes varied across participants (Fig. 2).
A post hoc analysis was completed to investigate the following variables: average hamstring force, average gastrocnemius force, average soleus force, and the lower extremity position of the leading leg at initial contact (reach; Table 1). Average hamstring force decreased by 27% in the FFS condition, whereas average gastrocnemius force and average soleus force increased by 12% and 29%, respectively. Reach distance was reduced by 19% (Table 1).
The primary purpose of this investigation was to determine how simple instruction to alter one’s foot strike pattern during running may affect PF joint stress. The study findings support our hypotheses in that running with a forefoot strike pattern leads to reductions in peak PF joint stress regardless of how step length changed (Fig. 2). This reduction in peak PF joint stress was also present despite an increase in peak vertical ground reaction force with a forefoot strike pattern.
The specific values of PF joint stress observed in this study are 13%–82% greater than those reported in previous investigations (20,38,39). However, these studies solely used the net knee moments obtained from inverse dynamics without the use of static optimization to estimate the quadriceps force in calculating PF joint stress. Results from our laboratory suggest that estimates of muscle force estimates using static optimization techniques after inverse dynamics calculations result in systematically larger estimates of PF joint stress in comparison to previous works (20,38,39).
The reduction in peak PF joint stress occurred despite an increase in peak vertical ground reaction force. Kulmala et al. (20) reported an 8% increase in peak vertical ground reaction force in forefoot strike runners, although they reported no statistical differences. Because the participants in our study all ran habitually with a rearfoot strike pattern, it is possible that the novelty of running with forefoot strike pattern may explain the difference in peak vertical ground reaction force presented here because differences in peak vertical ground reaction force have been reported between converted forefoot strike runners and habitual forefoot strike runners (36).
The reduction in peak PF joint stress is most likely attributed to the reduction in peak quadriceps force observed in the forefoot strike condition. A reduction in peak quadriceps force was made possible in the presence of increased peak vertical ground reaction force by greater force output from the soleus. Derrick et al. (12) attributed decreases in knee energy absorption after a reduction in step length due to increased power absorption at the ankle. The increased power absorption at the ankle was explained by a larger horizontal distance of the ground reaction force vector from the ankle joint center along with a decreased distance of the ground reaction force vector from the knee joint center. Williams et al. (37) also reported increased power absorption across the ankle with a forefoot strike pattern while power absorption at the knee was reduced. Because running with a forefoot strike pattern moves the center of pressure more anterior on the foot, the distance between the ankle joint center and the ground reaction force line of action may also increase, resulting in a larger moment and requiring greater force production by the ankle plantarflexors. Using musculoskeletal model–based estimates of muscle force, Almonroeder et al. (1) showed that Achilles tendon loading when using a forefoot strike pattern increased the Achilles tendon loading impulse by 11% with each step compared to rearfoot strike running. The increased energy absorbed about the ankle and greater force from the plantarflexors during forefoot strike running may allow for the impact forces experienced during running to be dissipated to a greater extent across an additional joint because rearfoot strike running seems to reduce the ability of the plantarflexors to absorb impact. Increased force production of the ankle plantarflexors may reduce the knee energy absorption and thereby reduce the amount of PF joint stress observed in our investigation.
The present investigation also revealed differences in knee angle at initial contact and total knee excursion between conditions. This is in disagreement with previous work where no differences in knee angle between rearfoot strike and forefoot strike conditions during running were observed (27,37). The reason for these differences is largely unknown but may be due to the individual techniques used to run with a forefoot strike pattern.
Although knee flexion angle at initial contact was increased in the forefoot strike condition, peak PF joint stress occurred near midstance near peak knee flexion. Because peak knee flexion was similar between foot strike patterns, and because knee angle was the sole input variable used to determine PF contact area, the differences observed in knee flexion angle at initial contact and knee flexion excursion likely do not contribute meaningfully to the reduction in peak PF joint stress. However, these differences do help to explain the reduced PF joint stress–time integral observed in the forefoot strike condition. Because PF contact area is increased with greater knee flexion, the more extended knee position used with the rearfoot strike condition may explain the greater slope in the PF joint stress curve during early stance (Fig. 1). This brief period of elevated stress may have contributed to the total stress implicated to the PF joint over the course of stance contributing to the greater PF joint stress–time integral seen in the rearfoot strike condition.
Perhaps the most interesting finding of this study is that large reductions in peak PF joint stress were observed across participants, whereas their average step length was unchanged. This reduction in peak PF joint stress was present despite some subjects increasing their step length (Fig. 2). However, the rearfoot strike condition did show a greater reach at initial contact (Table 1). This finding supports previous ideas that lower extremity position may play a vital role in impact attenuation during running (26). Thus, the reaching component of one’s overall step length occurring at impact may be of greater importance in determining PF joint stress than step length alone. Because knee flexion angle at initial contact and foot strike pattern are determinants of lower extremity position, instruction to run with a forefoot strike pattern may be a simple way to alter lower extremity posture and reduce PF joint stress during running. Thus, interventions aimed at transitioning toward a forefoot strike pattern during running may be beneficial to patients with PFP.
Further, a foot strike alteration program has shown to reduce PFP symptoms in three runners (7). However, this program consisted of eight formalized training sessions over the course of 2 wk, making use of a force sensor placed under the patient’s heel to elicit an audible noise to indicate if a heel strike occurred. This program may be difficult to impose in a clinical setting because most patients will likely not be able to commit to such a large number of treatment sessions in this short a period and not all settings have the means of providing audible feedback described by these authors. Our results suggest that healthy runners are able to alter their foot strike pattern with only simple instruction. Similar results were reported by Williams et al. (36) in that rearfoot strike runners were able to show similar kinematic patterns to habitual forefoot strike runners, with only simple instruction to “run on their toes.” This may offer a more independent method for selected patients to pursue for lessening the symptoms of PFP.
Finally, our findings do not indicate that a forefoot strike pattern is superior to a rearfoot strike pattern. Only the muscle forces produced and the stresses implicated to the PF joint seem different. Running imposes very large impact forces to the body that must be absorbed and adapted to to avoid surpassing an injury threshold (18). Therefore, when considering altering the running pattern of any participant, it is suggested that a period of transition be observed to avoid implicating other tissues to injury risk, especially because the injury profiles of forefoot and rearfoot strike runners differ (9). Specifically, increased Achilles tendon loading (1) and greater plantar loads in the forefoot region (19) have been described during forefoot strike running, which may pose a new type of injury risk. Nevertheless, runners prone to PFP may benefit from a transitioning program to alter their foot strike pattern because using a forefoot strike seems to reduce PF joint stress. However, how these foot strike alterations specifically affect the PFP, symptoms, and the best approaches for transitioning to a forefoot strike pattern have yet to be explored.
The findings of this study must be tempered with several limitations. First, our PF joint model was generalized from magnetic resonance imaging measures from previous research. Because joint geometries vary between individuals, the specific values of PF joint stress here will likely differ for each of the individual participants. Further, our model was a two-dimensional representation of the PF joint. Thus, any medial–lateral displacement of the PF joint reaction force vector cannot be accounted for in our methods. Also, the contribution of hip rotation that may contribute to PF contact area is not within the capabilities of this current model to detect and may change PF joint stress estimates. Further, the use of static optimization remains only a means to estimate muscle forces, and in the absence of in vivo measures of muscle force, it is difficult to ascertain the absolute accuracy of such methods. Thus, because our estimates of PF joint stress are largely determined by the quadriceps force estimates, this introduces another possible source of error in our PF joint model. Also, our subjects were all habitual rearfoot strike runners, thus the findings of this study cannot be used to characterize a reduced PF joint stress in habitual forefoot strike runners, although previous work does suggest this (20). Finally, we defined forefoot strike as any foot strike pattern where the center of pressure was located in the anterior two-thirds of the foot, which combines the classification of midfoot strike and forefoot strike as proposed by Cavanagh and Lafortune (6). This may explain some of the variability in our measures for the forefoot strike condition but also requires a word of caution if applying these results to a foot strike alteration program in terms of up to what extent one must land on the forefoot to see reductions in PF joint stress.
In conclusion, altering one’s foot strike pattern from that of a rearfoot strike to a forefoot strike with only simple instruction results in consistent reductions in PF joint stress independent of changes in step length. Thus, using programs that promote the use of a forefoot strike running pattern may be warranted in the treatment of PFP.
The authors would like to thank Di-An Hong, Ph.D., for his overall contributions to the project and manuscript review.
This work has not received any external funding.
The authors have no conflicts of interest to disclose.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
1. Almonroeder T, Willson JD, Kernozek TW. The effect of foot strike pattern on Achilles tendon load during running. Ann Biomed Eng
. 2013; 41: 1758–66.
2. Altman AR, Davis IS. A kinematic method for footstrike pattern detection in barefoot and shod runners. Gait Posture
. 2012; 35: 398–300.
3. Bell AL, Pedersen DR, Brand RA. A comparison of the accuracy of several hip center location prediction methods. J Biomech
. 1990; 23(6): 617–21.
4. Brechter JH, Powers CM. Patellofemoral stress during walking in persons with and without patellofemoral pain. Med Sci Sports Exerc
. 2002; 34(10): 1582–93.
5. Bredeweg SW, Zijlstra S, Bessem B, Buist I. The effectiveness of a preconditioning programme on preventing running-related injuries in novice runners: a randomized control trial. Br J Sports Med
. 2012; 46: 865–70.
6. Cavanagh PR, Lafortune MA. Ground reaction forces in distance running. J Biomech
. 1980; 13: 397–406.
7. Cheung RT, Davis IS. Landing pattern modification to improve patellofemoral pain in runners: a case series. J Orthop Sports Phys Ther
. 2011; 41: 914–9.
8. Connolly KD, Ronsky Jl, Westover LM, Kupper JC, Frayne R. Differences in patellofemoral contact mechanics associated with patellofemoral pain syndrome. J Biomech
. 2009; 42: 2802–7.
9. Daoud AI, Geissler GJ, Wang F, Saretsky J, Daoud YA, Lieberman DE. Foot strike and injury rates in endurance runners: a retrospective study. Med Sci Sports Exerc
. 2012; 44(7): 1325–34.
10. de Leva P. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J Biomech
. 1996; 29: 1223–30.
11. Delp SL, Loan JP, Hoy MG, Zajac FE, Topp EL, Rosen JM. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans Biomed Eng
. 1990; 37: 757–67.
12. Derrick TR, Hamill J, Caldwell GE. Energy absorption of impacts during running at various stride lengths. Med Sci Sports Exerc
. 1998; 30(1): 128–35.
13. Draper CE, Fredericson M, Gold GE, et al. Patients with patellofemoral pain exhibit elevated bone metabolic activity at the patellofemoral joint. J Orthop Res
. 2012; 30: 209–13.
14. Erdemir A, McLean S, Herzog W, van den Bogert AJ. Model-based estimation of muscle forces exerted druing movements. Clin Biomech
. 2007; 22: 131–54.
15. Farrokhi S, Keyak JH, Powers CM. Individuals with patellofemoral pain exhibit greater patellofemoral joint stress: a fine element analysis study. Osteoarthritis Cartilage
. 2011; 19: 287–94.
16. Heiderscheit BC, Chumanov ES, Michalski MP, Wille CM, Ryan MB. Effects of step rate manipulation on joint mechanics during running. Med Sci Sports Exerc
. 2011; 43(2): 296–302.
17. Ho KY, Keyak JH, Powers CM. Comparison of patella bone strain between females with and without patellofemoral pain: a finite element analysis study. J Biomech
. 2014; 47: 230–6.
18. Hreljac A. Impact and overuse injuries in runners. Med Sci Sports Exerc
. 2004; 36(5): 845–9.
19. Kernozek TW, Meardon S, Vannatta CN. In-shoe loading in rearfoot and non-rearfoot strikers during running using minimalist footwear. Int J Sports Med
. 2014; 35: 1112–7.
20. Kulmala JP, Avela J, Pasanen K, Parkkari J. Forefoot strikers exhibit lower running-induced knee loading than rearfoot strikers. Med Sci Sports Exerc
. 2013; 45(12): 2306–13.
21. Larson P, Higgins E, Kaminski J, et al. Foot strike patterns of recreational and sub-elite runners in a long-distance road race. J Sports Sci
. 2011; 29(15): 1665–73.
22. Lenhart RL, Thelen DG, Wille CM, Chumanov ES, Heiderscheit BC. Increasing running step rate reduces patellofemoral joint forces. Med Sci Sports Exerc
. 2014; 46(3): 557–64.
23. Levinger P, Gilleard W. The heel strike transient during walking in subjects with patellofemoral pain syndrome. Phys Ther Sport
. 2005; 6: 83–8.
24. Lieberman DE, Venkadesan M, Werbel WA, et al. Foot strike patterns and collision forces in habitually barefoot versus shod runners. Nature
. 2010; 463: 531–5.
25. Lu TW, O’Connor JJ. Bone position estimation from skin markers co-ordinates using global optimisation with joint constraints. J Biomech
. 1999; 32(2): 129–34.
26. Mercer JA, Devita P, Derrick TR, Bates BT. Individaul effects of stride length and frequency on shock attenuation during running. Med Sci Sports Exerc
. 2003; 35(2): 307–13.
27. Paquette MR, Zhang S, Dahl L. Acute effects of barefoot, minimal shoes and running shoes on lower limb mechanics in rear and forefoot strike runners. Footwear Science
. 2013; 5(1): 9–18.
28. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes. The Art of Scientific Computing
. 3rd ed. Cambridge (UK): Cambridge University Press; 2007. pp. 799–806.
29. Roos PE, Barton N, van Deursen RWM. Patellofemoral joint compression forces in backward and forward running. J Biomech
. 2012; 45: 1656–60.
30. Running USA. 2012 State of the Sport - Part III: U.S. Road Race Trends. 2012. Available from: http://www.runningusa.org/State-of-Sport-Road-Race-Trends
31. Salsich GB, Perman WH. Patellofemoral joint contact area is influenced by tibiofemoral rotation alignment in individuals who have patellofemoral pain. J Orthop Sports Phys Ther
. 2007; 37(9): 521–8.
32. Souza RB, Draper CE, Fredericson M, Powers CM. Femur rotation and patellofemoral joint kinematics: a weight-bearing magnetic resonance imaging analysis. J Ortho Sports Phys Ther
. 2010; 40(5): 277–85.
33. Taunton JE, Ryan MB, Clement DB, McKenzie DC, Lloyd-Smith DR, Zumbo BD. A retrospective case–control analysis of 2002 running injuries. Br J Sports Med
. 2002; 36: 95–101.
34. van den Bogert AJ, Geijtenbeek T, Even-Zohar O, Steenbrink F, Hardin EC. A real-time system for biomechanical analysis of human movement and muscle function. Med Biol Eng Comput
. 2013; 51: 1069–77.
35. van Eijden TMGJ, de Boer W, Weijs WA. The orientation of the distal part of the quadriceps femoris muscle as a function of the knee flexion–extension angle. J Biomech
. 1985; 18: 803–9.
36. Williams DS III, McClay IS, Manal KT. Lower extremity mechanics in runners with a converted forefoot strike pattern. J Appl Biomech
. 2000; 16: 210–8.
37. Williams DSB III, Green DH, Wurzinger B. Changes in lower extremity movement and power absorption during forefoot striking and barefoot running. Int J Sports Phys Ther
. 2012; 7(5): 525–32.
38. Willson JD, Sharpee R, Meadon SA, Kernozek TW. Effects of step length on patellofemoral joint stress in female runners with and without patellofemoral pain. Clin Biomech
. 2014; 29(3): 243–7.
39. Wirtz AD, Willson JD, Kernozek TW, Hong DA. Patellofemoral joint stress during running in females with and without patellofemoral pain. Knee
. 2012; 9: 703–8.
40. Xia Y, Feng G. An improved neural network for convex quadratic optimization with application to real-time beamforming. Neurocomputing
. 2005; 64: 359–74.