Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

Artur Struzik; Kiros Karamanidis; Anna Lorimer; Justin W. L. Keogh; Jan Gajewski

doi:10.1155/2021/9914278

Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

Struzik, Artur;Karamanidis, Kiros;Lorimer, Anna;Keogh, Justin W. L.;Gajewski, Jan 2021-10-21 00:00:00 Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 9914278, 25 pages https://doi.org/10.1155/2021/9914278 Review Article Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview 1 2 3,4 3,4,5,6 Artur Struzik , Kiros Karamanidis , Anna Lorimer , Justin W. L. Keogh , and Jan Gajewski Department of Biomechanics, Wroclaw University of Health and Sport Sciences, Poland Sport and Exercise Science Research Centre, School of Applied Sciences, London South Bank University, UK Faculty of Health Sciences and Medicine, Bond University, Gold Coast, Australia Sports Performance Research Centre New Zealand, AUT University, Auckland, New Zealand Cluster for Health Improvement, Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Australia Kasturba Medical College, Mangalore, Manipal Academy of Higher Education, Manipal, Karnataka, India Human Biology, Józef Piłsudski University of Physical Education, Warsaw, Poland Correspondence should be addressed to Artur Struzik; artur.struzik@awf.wroc.pl Received 25 March 2021; Revised 8 September 2021; Accepted 17 September 2021; Published 21 October 2021 Academic Editor: Cristiano De Marchis Copyright © 2021 Artur Struzik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Stiﬀness, the resistance to deformation due to force, has been used to model the way in which the lower body responds to landing during cyclic motions such as running and jumping. Vertical, leg, and joint stiﬀness provide a useful model for investigating the store and release of potential elastic energy via the musculotendinous unit in the stretch-shortening cycle and may provide insight into sport performance. This review is aimed at assessing the eﬀect of vertical, leg, and joint stiﬀness on running performance as such an investigation may provide greater insight into performance during this common form of locomotion. PubMed and SPORTDiscus databases were searched resulting in 92 publications on vertical, leg, and joint stiﬀness and running performance. Vertical stiﬀness increases with running velocity and stride frequency. Higher vertical stiﬀness diﬀerentiated elite runners from lower-performing athletes and was also associated with a lower oxygen cost. In contrast, leg stiﬀness remains relatively constant with increasing velocity and is not strongly related to the aerobic demand and fatigue. Hip and knee joint stiﬀness are reported to increase with velocity, and a lower ankle and higher knee joint stiﬀness are linked to a lower oxygen cost of running; however, no relationship with performance has yet been investigated. Theoretically, there is a desired “leg-spring” stiﬀness value at which potential elastic energy return is maximised and this is speciﬁc to the individual. It appears that higher “leg-spring” stiﬀness is desirable for running performance; however, more research is needed to investigate the relationship of all three lower limb joint springs as the hip joint is often neglected. There is still no clear answer how training could aﬀect mechanical stiﬀness during running. Studies including muscle activation and separate analyses of local tissues (tendons) are needed to investigate mechanical stiﬀness as a global variable associated with sports performance. 1. Introduction able bodies under application of external forces. In the seventeenth century, the British physicist Robert Hook Stiﬀness is a quantitative measure of the elastic properties of stated a proportional relationship between the magnitude the body and determines the ability to accumulate potential of the deforming force (F) and the deformation (Δl) of the elastic energy. The concept of stiﬀness was developed in clas- body. Therefore, as a part of Hooke’s law, stiﬀness (K) was sical mechanics to describe the behaviour of elastic deform- deﬁned as a ratio of the amount of deforming force (or force 2 Applied Bionics and Biomechanics muscle. It can be concluded that the activity of the muscles change) to the unit of deformation (or as a ratio of the amount of deforming torque to the angle of deformation allows the potential elastic energy to be stored in the tendons for rotational motions) [1–3]. since at the same deformation of the entire spring complex, the greater part of energy goes to less stiﬀ element. Muscle Elastic deformable bodies have the ability to recover the previous shape and volume (i.e., they return to their initial tension is a factor regulating the stiﬀness of the support limb size) after mechanical forces that cause deformation are during locomotion and jumps. The coactivation of extensors removed. These deformations are fully reversible. Due to and ﬂexors in the moment preceding contact with the the inﬂuence of external deforming forces, the elastic bodies ground is aimed at regulating the “leg-spring” stiﬀness and preparing the limb to transfer the anticipated forces in the accumulate potential elastic energy, which they release back to the system when returning to the original length. The contact phase [14]. Muscle stiﬀness increases in eccentric work performed by the deforming forces equals the value phase, when the stretch reﬂex generates an extra activation. of the potential elastic energy accumulated in the spring A musculotendinous unit is capable of resisting higher compliance elements (assuming there are no energy losses passive tensile forces when it is in a lengthened position or when it is stretched. In an active muscle state, the shape of due to friction and resistance forces) [2, 3]. The ability to absorb and return potential elastic energy generated muscle force over the entire physiological range is also observed in the musculotendinous groups in the of movement is not the same for every muscle as muscles human body. The potential elastic energy stored by the pas- in vivo can operate at diﬀerent regions of the force-length sive structures (tendon and aponeurosis) during contractile relationship [15–17]. Moreover, body parts may change con- cycle of a muscle, e.g., during lengthening of the entire ﬁguration in relation to each other (displacement) and not muscle-tendon unit, can increase the energy supplied by be deformed at all (like a passive bodies). Change in muscle the compliant tissues during the proceeding shortening length (deformation) can be caused by the action of contrac- phase. Consequently, the substantial capacity of the tendon tile elements or external forces. Therefore, length of an active and aponeurosis to store elastic strain energy can enhance muscle or joint angle can change without a contribution of the total mechanical energy produced by the muscle- deforming forces. Consequently, it is possible to obtain the tendon unit during the concentric phase of muscle work or same magnitude of force at diﬀerent joint angles and diﬀer- reduce muscle ﬁbre work and metabolic energy expenditure. ent force values at a speciﬁc joint angle [2]. Therefore, using Potential elastic energy stored in muscle-tendon units the concept of stiﬀness in locomotion and performance reduces the metabolic energy spent by muscles responsible analyses for much more complex biological objects than for movement in speciﬁc joints and is associated with the simple passive bodies is associated with numerous concep- change in the kinetic energy of the body being moved tual diﬃculties. [3–7]. Therefore, stiﬀness, the quantitative measure of the Stiﬀness should be understood as the resistance does not resistance oﬀered by an elastic body to deformation, may depend on time, velocity, or acceleration, but only on the be an essential factor in the optimization of human locomo- displacement (for a passive elastic body with linear force- tion, because it is related to the maximal performance of deformation characteristics, the value of stiﬀness will be cyclic and single dynamic movements [1, 8, 9]. the same at a relatively low or high level of deformation). However, the strict concept of stiﬀness has been intro- The proper measurements of stiﬀness are performed during duced for relatively simple passive bodies (they maintain steady-state body deformation (from one equilibrium state constant shape if external deforming forces are absent or to another equilibrium state). If stiﬀness measurements are sustainable). A human muscle (as a whole) does not behave not performed during steady-state body deformation but like a passive body with linear force-deformation character- during transient states, the substantial value of dF/dl might istics [2]. The muscle-tendon complex consists of two contain components originating from inertial forces and elements of diﬀerent stiﬀness connected in series. A muscle damping. Therefore, the variable measured in the above case is made of force-producing active (contractile) components is not stiﬀness viewed in strict mechanical terms due to the and passive components (serial and parallel elastic elements) substantial contribution of other factors that aﬀect the consisting of tendons, fascia, and other connective tissues, FðΔlÞ relationship, especially during transient states. In each with diﬀerent biomechanical properties [10]. The mag- locomotion analyses when the body is in motion, certain nitude of the forces (and mechanical power) generated “varieties” of stiﬀness are used [2, 3]. depends on muscle activation, muscle length and its velocity, With respect to living bodies, the mechanical stiﬀness and on the use of elastic elements, which increase the can be divided into quasi-stiﬀness and joint stiﬀness. Latash eﬀectiveness (and eﬃciency) of contractile elements. Tendon and Zatsiorsky [18] deﬁned quasi-stiﬀness as the ability of stiﬀness increases with lengthening [11] (due to the toe the human body to oppose external displacements with region in tendons’ force-length relationship), and muscle disregard to displacement proﬁle over time. Leg and vertical stiﬀness increases with muscle lengthening or tension stiﬀness are the most frequently used types of quasi-stiﬀness (activation level) [12]. However, while tendon stiﬀness is in human and animal locomotion analysis to describe the relatively constant, muscle stiﬀness is greatly inﬂuenced by mechanical properties of a “spring” representing the lower the force developed [12]. The stiﬀness of a muscle increases limbs (according to the assumptions of body modelling as the more motor units of the muscle which are activated [13]. a spring-mass model, which contains a massless supporting Thus, the stiﬀness of the entire muscle-tendon complex var- “leg-spring”, a material point representing the total body ies and depends to the greatest extent on the stiﬀness of the mass, and a parallel source of force resulting from the active Applied Bionics and Biomechanics 3 vals during 100 m sprint performance and presented a action of the muscles involved in the take-oﬀ) [1, 19]. Leg quasi-stiﬀness is understood as the ratio of changes in the larger deceleration between the second and the third inter- ground reaction force to the respective changes in “spring vals (60–100 m). However, vertical stiﬀness was also deter- length” representing both lower limbs, whereas vertical mined based on the hopping test. It seems that these quasi-stiﬀness is understood as the ratio of changes in the ﬁndings would be much more valuable if the stiﬀness ground reaction force to the respective vertical displacement was also measured during running. Lorimer et al. [53] of the centre of mass (COM). Unfortunately, these two dis- reported that comparability of stiﬀness (leg, vertical, and tinct stiﬀness concepts are often confused and consequently joint) during hopping and running was at most moderate. used interchangeably or incorrectly [20]. Joint stiﬀness is It would be expected that a stiﬀer “leg-spring” may resistance to displacement within a given joint (e.g., hip, increase athletic performance by enhanced utilisation of knee, or ankle) and depends on the mechanical properties potential elastic energy. Therefore, the aim of this overview of the movements related to this joint and all structures is to examine the relationships between mechanical stiﬀness involved in this movement [2, 9, 21]. Research analysing (leg, vertical, and joint) and running performance, both in leg, vertical, and/or joint stiﬀness have typically been con- cross-sectional and training studies. Such a review is impor- ducted during cyclic (e.g., walking, running, or hopping) tant as many studies assessing stiﬀness in humans have and single (e.g., vertical jumps) locomotor movements. focused on jumping or hopping motions that are not com- The relationships between mechanical stiﬀness (leg, ver- monly performed in sporting events, with the majority of tical, and joint) and movement performance are areas of the studies being cross-sectional in design. This review interest to the sport and research communities. Several may provide additional insight regarding how diﬀerent authors have already tried to organise an understanding of stiﬀness values obtained from running tasks may be repre- stiﬀness in their review articles [1, 6, 9, 18, 21–30]. However, sentative of common sporting locomotor activities and the multiple deﬁnitions and equations used to deﬁne verti- how training-related changes in stiﬀness characteristics cal, leg, and joint stiﬀness along with advances in research may underpin improvements in running performance. into the topic leave the relationship between stiﬀness and movement performance are still not fully explored. The 2. Materials and Methods practice of sports training reveals some questions regarding the role of potential elastic energy and stiﬀness as a key fac- A search of the PubMed and SPORTDiscus (EBSCO) biblio- tor responsible for determining performance. The reason for graphic electronic databases was conducted in October 2020. this may be the lack of longitudinal studies that have inves- The search terms used included (“leg” OR “lower limb” OR tigated the eﬀects of strength or power training on mechan- “lower extremity” OR “vertical” OR “joint”) AND (“stiﬀ- ical stiﬀness and consequently the relative lack of concrete ness”) AND (“run∗” OR “sprint∗” OR “jog∗”) AND recommendations that would allow to improve the speed- (“sport”). Review and original empirical research articles strength abilities of an athlete and their competitive sport and other related literature were selected based on the title results. The speculations concerning a desirable value of and abstract. Additionally, Google Scholar, ResearchGate, “leg-spring” stiﬀness that is the most advantageous for the and the reference lists of articles found were also checked accumulation of potential elastic energy and most favours to ensure no relevant studies were omitted during searching reaching maximal sport performance have been partially process. The following criteria were considered: examined [1, 3, 22, 24–28, 31–35]. However, no studies have provided unequivocal evidence for the presence of a desired (i) Papers written in English only value of “leg-spring” stiﬀness. Moreover, the conceptual and methodological confusion surrounding stiﬀness makes it (ii) Studies with human samples diﬃcult to organise the knowledge and compare the results (iii) No duplicates (papers found from several sources) obtained in the past research. Some reports refer to changes in stiﬀness under the (iv) No publication time restriction inﬂuence of sports training (e.g., plyometric or isometric). However, they take into account the stiﬀness of local struc- Only studies which had measures of mechanical (leg, tures (e.g., tendon) [36–46]; the determination of which vertical, or joint) stiﬀness during running performance were may be more complicated than the discussed values of leg, included in further analysis. Studies describing other human vertical, and joint stiﬀness. Several reports analysed the rela- movements (e.g., hopping), studies analysing the type of tionships between mechanical (leg, vertical, or joint) stiﬀness footwear, studies which failed to determine stiﬀness during and movement performance (e.g., during biomechanical the running performance (e.g., using oscillation technique, types of jumps) before and after the applied training pro- ultrasonography, or dynamometers or during other types gram. However, they did not concern the sport-speciﬁc of movement), and modelling-based studies or those con- movements , such as running [42, 47–50]. Chelly and Denis cerning diﬀerent types of stiﬀness than mechanical have [51] reported on positive relationships between maximal been omitted. After a detailed review of the full texts, 92 running velocity during 40 m sprint and vertical stiﬀness meet all the criteria (Figure 1) with a publication date during hopping task. Bret et al. [52] found that athletes between 1980 and 2021 (the range of the year’s results from with greater vertical stiﬀness obtained higher acceleration the selection process conducted). There were a number of between the ﬁrst (0–30 m) and the second (30–60 m) inter- papers that measured more than one type of stiﬀness and 4 Applied Bionics and Biomechanics Identiﬁcation of studies via databases and registers Records removed before Records identiﬁcation from: screening: PubMed (n = 542) Duplicate records removed SPORTDiscus (n = 345) (n = 339) Records screened Records excluded (n = 548) (n = 348) Reports sought for retrievel Reports not retrieved (n = 0) (n = 0) Reports assessed for eligibility Reports excluded: (n = 200) No stiﬀness analysis during running performance (n = 82) Footwear analysis (n = 8) Modelling-based studies (n = 18) Studies included in review (n = 92) Reports of included studies (n = 92) Figure 1: Selection process of papers focused on mechanical stiﬀness during running [54]. were therefore discussed in several subsections. The number of papers described mechanical stiﬀness was 68 for leg stiﬀ- ness, 65 for vertical stiﬀness and 23 for joint stiﬀness. COM Δy COM 3. Results and Discussion 3.1. Quasi-Stiﬀness during Running Tasks. Running is a com- ΔL plex motion that engages the whole body and it occurs in various forms in track and ﬁeld competitions or team sports games. Depending on the running distance, it is necessary to either reach submaximal velocity and cover the distance in the shortest possible time or keep the desired velocity for a certain distance. The running distance is covered through cyclic lower limb movements based on continuous accelera- tion and deceleration phases. Therefore, human running performance is similar to the motion of a bouncing ball (the so-called “bouncing gait”) and can be considered in accordance with the assumptions of spring-mass model (in GRF GRF which the lower limbs perform the role of “springs” respon- sible for the COM movement). Leg and vertical stiﬀness are Figure 2: An example of a simple spring-mass model used to commonly used to describe the mechanical properties of a estimate leg and vertical stiﬀness during vertical body “leg-spring” representing the lower limbs during running displacements only, where COM denotes the centre of mass, ΔL task [3]. Figure 2 shows a simple spring-mass model that is the change in “spring length” representing both lower limbs, Δy can be used to determine quasi-stiﬀness (leg or vertical) is the displacement of COM, and GRF means the ground reaction during vertical displacements only. The modiﬁcation of the force (based on Blickhan [19]). spring-mass model presented in Figure 3 also includes hori- zontal displacements. Therefore, leg and vertical stiﬀness can Screening Identiﬁcation Included Applied Bionics and Biomechanics 5 COM movement velocity), then quasi-stiﬀness (leg and vertical) does not signiﬁcantly change during running [55–57]. Δy COM Therefore, one of the most well researched topics to improve understanding of how quasi-stiﬀness is controlled during running is alterations in quasi-stiﬀness and other running ΔL variables with running velocity changes. Paradisis et al. [58] stated that quasi-stiﬀness (leg and vertical) are key to generating a higher top running velocity during a short sprint. Tables 1 and 2 list the studies on vertical and leg stiﬀ- ness that meet the inclusion criteria. 3.1.1. Vertical Stiﬀness. Vertical stiﬀness increases with run- ning velocity and stride frequency [33, 55, 58–68] and body mass [69]. Vertical stiﬀness also increases with the level of maturity [70, 71]. However, Meyers et al. [72] reported a Figure 3: An example of a spring-mass model used to estimate leg decrease in vertical stiﬀness with the level of maturity during and vertical stiﬀness during running tasks, where COM denotes 35 m sprint task. Arampatzis et al. [62] reported vertical centre of mass, ΔL is change in “spring length” representing both stiﬀness values between 30:8± 8:1 and 93:0±29:7 kN/m at lower limbs, and Δy is displacement of COM (based on running velocities from 2:6±0:2 to 6:6±0:2 m/s. Paradisis McMahon and Cheng [20]). et al. [58] obtained vertical stiﬀness values between 73:8± 9:7 and 105:1±16:8 kN/m at running velocities from 7:7± be estimated for vertical and horizontal movements. How- 0:3 to 9:4±0:4 m/s, whereas Kuitunen et al. [59] noted ever, vertical stiﬀness only considers vertical body displace- values between 103 and 171 kN/m at running velocities from ments. Leg stiﬀness (K ) and vertical stiﬀness (K ) are leg vert 6.7 to 10.3 m/s. Therefore, higher values of vertical stiﬀness expressed by the following equations: would be expected to be reached during maximal sprinting than during slower running conditions. Paradisis et al. [58] K = , reported that faster sprinters are characterised by shorter leg ΔL ground contact time, longer stride length, higher stride fre- ð1Þ quency, and greater vertical stiﬀness than slower sprinters K = , vert Δy during a 35 m sprint task. García-Pinillos et al. [66] also reported that elite level runners are characterised by greater where F is the deforming force (the causes of the change in vertical stiﬀness than novice runners during treadmill run- deformation), ΔL denotes the change in “leg-spring” length ning at velocities from 6.2 to 11.2 m/s. Rumpf et al. [73] (deformation), and Δy is the displacement of COM (defor- noted positive relationships between relative vertical stiﬀness mation). However, if the relationship between the deforming and sprint velocity, vertical COM displacement, relative force and the deformation is nonlinear or deformation is vertical peak force, and maximal “leg-spring” displacement plastic, the derivative (d) from Equations (2) or (3) should during 30 m treadmill sprint. be used [2]: An important factor that aﬀects vertical stiﬀness and stride frequency is fatigue. Dalleau et al. [74] reported nega- dF tive relationships between vertical stiﬀness and energy cost ð2Þ K = , leg of running, as determined from the O consumption. Heise dL and Martin [75] concluded from the negative relationships between vertical stiﬀness and aerobic demand that less dF K = : ð3Þ vert economical runners possess a more compliant “leg-spring” dy running style during ground contact phase. These ﬁndings The work performed by the deforming forces F equals may support the role of the mechanical stiﬀness in the met- the value of the potential elastic energy accumulated in the abolic energy cost of running at a given velocity (velocities: spring compliance elements. Potential elastic energy is pro- 3.35 m/s has been applied by Heise and Martin [75] and portional to the square of deformation and can be given by 5 m/s has been applied by Dalleau et al. [74]). Dutto and the following equation: Smith [76] observed that runners decreased vertical stiﬀness and stride frequency during a moderate-intensity treadmill 2 run to exhaustion. Changes in vertical stiﬀness were primar- E = ∙K∙Δl , ð4Þ pe 2 ily associated with increases in vertical COM displacement, and not to changes in the peak vertical ground reaction where E is the potential elastic energy, K denotes the stiﬀ- force. The runners altered their running kinematics to allow pe ness (longitudinal), and Δl is the deformation (change in for longer stride lengths and decreased stride frequency to length, displacement). maintain a constant running velocity. Decreases in vertical If stride frequency is relatively constant or the accelera- stiﬀness were proportional to decreases in stride frequency tion of the runners COM is relatively low (relatively constant [76]. Hobara et al. [64] noted that vertical stiﬀness peaked 6 Applied Bionics and Biomechanics Table 1: List of the studies on leg stiﬀness during running. Authors Year Number of participants Sport background Motor skill Submaximal constant load running test on treadmill Ache-Dias et al. [128] 2018 18 (males + females) Recreational runners (6 min at 9 km/h) Arampatzis et al. [62] 1999 13 runners Not mentioned Running at 2.5, 3.5, 4.5, 5.5, and 6.5 m/s Avogadro et al. [138] 2004 13 runners Healthy trained runners 3 min running on treadmill at 12, 14, 16, and 18 km/h Trained + untrained runners Bitchell et al. [97] 2019 7+13 runners Incremental running on treadmill Brocherie et al. [81] 2015 8 males International football players RAST test (6 × 35 m sprint) Cavagna et al. [63] 2005 4 males + 1 female Not mentioned Running at diﬀerent velocities (from 5.2 to 20.5 km/h) Choukou et al. [106] 2012 8 males Sprinters competing at the regional level 100 m sprint Coleman et al. [141] 2012 19 males Well-trained middle-distance runners Running at diﬀerent velocities (from 2.5 to 6.5 m/s) Cronin and Rumpf [69] 2014 16 males Young athletes 30 m sprint on treadmill Dal Pupo et al. [107] 2017 21 males Futsal players 10 m sprint Running on treadmill to exhaustion at a velocity 11 males + 4 females Dutto and Smith [76] 2002 Well-trained runners corresponding to 80% of the VO 2max Running on treadmill at 2.5 m/s (while using a range Farley and González [33] 1996 4 males Experienced treadmill runners of stride frequencies from 26% below to 36% above the preferred stride frequency) Ferris et al. [88] 1999 6 females Healthy 17 m running at 3.0 m/s Ferris et al. [87] 1998 5 humans Not mentioned Running at 5 m/s Running on treadmill to exhaustion at a velocity Fourchet et al. [102] 2015 11 males Highly trained middle-distance runners corresponding to 95% of the VO 2max García-Pinillos et al. [103] 2020 22 males Endurance runners 60 min running on treadmill Incremental running on treadmill at 10, 12, 14, 16, García-Pinillos et al. [66] 2019 22 males Novice and elite endurance runners and 18 km/h Gill et al. [155] 2020 16 males + 12 females Runners 32 m running at 3.3, 3.9, 4.8, and 5.6 m/s 77 males + 14 females Gindre et al. [83] 2016 Healthy and active 50 m running at 3.3, 4.2, and 5.0 m/s Giovanelli et al. [95] 2016 18 males Ultraendurance runners “Supermaratona dell’Etna” Girard et al. [150] 2015 13 males Team and racket sport background 3× 5s sprints on treadmill Girard et al. [80] 2017 20 males Field hockey players 6 × 30 s running on treadmill at 115% of the VO 2max 3 × 5 s sprints on treadmill + running on treadmill at Girard et al. [57] 2017 14 males Recreationally intermittent sports 10 and 20 km/h Physical education students practicing a Girard et al. [56] 2016 11 males 100, 200, and 400 m sprint on treadmill ﬁeld sport Recreational team or racket sports 12 × 40 m sprints Girard et al. [79] 2011 16 males athletes Girard et al. [96] 2017 18 males Physical education students 800 m running Girard et al. [91] 2010 12 triathletes Highly and well-trained triathletes 5000 m running at self-selected velocity Applied Bionics and Biomechanics 7 Table 1: Continued. Authors Year Number of participants Sport background Motor skill Girard et al. [93] 2013 12 males National level triathletes 5000 m running at self-selected velocity Girard et al. [78] 2011 13 males Young soccer players 6 × 20 m sprints 8 males + 4 females Günther and Blickhan [122] 2002 Sports students and active sportsmen Running at convenience velocity (from 3.7 to 5.6 m/s) He et al. [61] 1991 4 males Healthy Running on treadmill at 2.0, 3.0, 4.0, 5.0, and 6.0 m/s Heise and Martin [75] 1998 16 males Recreational runners 15 m running at 3.35 m/s Hobara et al. [64] 2010 8 males Well-trained sprinters and runners 400 m sprint 11 males + 5 females Hunter and Smith [105] 2007 Recreational runners 1 h running on treadmill at constant velocity Joseph et al. [148] 2013 20 males Various sports 10 m running at 3.35 m/s Joseph et al. [121] 2014 20 males Various sports 10 m running at 3.35 m/s Running on treadmill to exhaustion at velocity Hayes and Caplan [101] 2014 6 runners Subelite middle-distance runners corresponding to VO 2max Li et al. [104] 2021 28 males Collegiate distance runners Running at 12, 14, and 16 km/h Liew et al. [143] 2017 20 females Recreational runners 20 m running at 5.0 m/s Liew et al. [110] 2021 10 males + 7 females Healthy 45 cut at 4 m/s approach velocity Lorimer et al. [53] 2018 12 males Well-trained triathletes 2 min running on treadmill at 3.0, 3.3, 3.7, and 4.2 m/s Lum et al. [129] 2019 14 males Moderately trained endurance runners 10 km running on treadmill at 10 km/h and 12 km/h Lussiana and Gindre [84] 2016 31 runners Well-trained runners 15 min running at self-selected velocity Lussiana et al. [85] 2017 58 males Recreational runners 5 min running on treadmill at 12 km/h Performance of each participant was examined during 43 males + 36 females Meur et al. [94] 2013 Elite triathletes the running section of the World Triathlon Grand Final Meyers et al. [67] 2019 375 boys Biweekly physical education classes 30 m sprint Meyers et al. [71] 2016 189 boys Biweekly physical education classes 30 m sprint Meyers et al. [72] 2017 344 boys Biweekly physical education classes 35 m sprint 80 m sprint with diﬀerent stride frequencies 20 males + 20 females Monte et al. [65] 2017 Elite and intermediate sprinters (preferred and +15%, +30%, −15%, and −30% of the self-selected) 6 min running on treadmill at theoretical half- Monte et al. [68] 2020 32 males Endurance runners marathon running velocity Running on treadmill at 3:33, 3:89, 4:44, 5:0, 5:56, 6:11 Physical education students + elite , and 6:67 m/s + 10 m running at 4:0, 5:0, 6:0, and 7:0 Morin et al. [139] 2005 8+10 males middle − distance runners m/s and maximal velocity Morin et al. [55] 2006 8 males Physical education students 100 m sprint Physically active physical education Morin et al. [92] 2012 11 males Running on treadmill at 10 and 20 km/h students Sprinter, 2 jumpers, 5 pole vaulters, and Nagahara and Zushi [127] 2017 9 males 60 m sprint a decathlete 8 Applied Bionics and Biomechanics Table 1: Continued. Authors Year Number of participants Sport background Motor skill Pappas et al. [147] 2014 22 males Healthy physical education students Running on treadmill at 4.44 m/s Paradisis et al. [58] 2019 50 males Subelite sprinters 35 m sprint Powell et al. [168] 2017 20 females Recreational athletes Running at self-selected velocity Running to exhaustion at constant velocity Rabita et al. [100] 2013 12 males Runners corresponding to VO 2max Running to exhaustion at a velocity corresponding to 6 males + 3 females Rabita et al. [99] 2011 Elite triathletes 95% of the VO 2max Rogers et al. [86] 2017 11 males Highly trained middle-distance runners 50 m sprint Physically active and trained a Rumpf et al. [73] 2015 32 children 30 m sprint on treadmill minimum of two times per week Rumpf et al. [70] 2013 74 boys Physically active 30 sprint on treadmill Shih et al. [114] 2019 20 males + 20 females Recreational runners 14 m running at 3.4 m/s 14 males + 14 females Sinclair et al. [145] 2015 Recreational runners Running at 4.0 m/s Staﬁlidis and Arampatzis [90] 2007 10 male Experienced sprinters 60 m sprint Weir et al. [98] 2020 13 males Recreational runners Prolonged running on treadmill (2 × 21 min) Williams III et al. [166] 2004 18 males + 22 females Healthy 25 m running at 3.35 m/s Yin et al. [109] 2020 78 males Healthy amateur runners 15 m running at 3.3 m/s Applied Bionics and Biomechanics 9 Table 2: List of the studies on vertical stiﬀness during running. Authors Year Number of participants Sport background Motor skill Submaximal constant load running test on treadmill Ache-Dias et al. [128] 2018 18 (males + females) Recreational runners (6 min at 9 km/h) Arampatzis et al. [62] 1999 13 runners Not mentioned Running at 2.5, 3.5, 4.5, 5.5, and 6.5 m/s Trained + untrained runners Bitchell et al. [97] 2019 7+13 runners Incremental running on treadmill Brocherie et al. [81] 2015 8 males International football players RAST test (6 × 35 m sprint) Running at a variety of diﬀerent constant velocities Cavagna et al. [60] 1988 10 males Untrained (range of very low velocities) 4 males + 1 female Cavagna et al. [63] 2005 Not mentioned Running at diﬀerent velocities (from 5.2 to 20.5 km/h) Cherif et al. [77] 2017 21 males Healthy and active 5× 5s sprints on treadmill Choukou et al. [106] 2012 8 males Sprinters competing at the regional level 100 m sprint Cronin and Rumpf [69] 2014 16 males Young athletes 30 m sprint on treadmill Dal Pupo et al. [107] 2017 21 males Futsal players 10 m sprint Running on treadmill (4 min at a velocity Dalleau et al. [74] 1998 8 males Healthy corresponding to 90% of the VO ) 2max Running on treadmill to exhaustion at a velocity 11 males + 4 females Dutto and Smith [76] 2002 Well-trained runners corresponding to 80% of the VO 2max Running on treadmill at 2.5 m/s (while using a range Farley and González [33] 1996 4 males Experienced treadmill runners of stride frequencies from 26% below to 36% above the preferred stride frequency) Ferris et al. [88] 1999 6 females Healthy 17 m running at 3.0 m/s Ferris et al. [87] 1998 5 humans Not mentioned Running at 5 m/s Running on treadmill to exhaustion at a velocity Fourchet et al. [102] 2015 11 males Highly trained middle-distance runners corresponding to 95% of the VO 2max García-Pinillos et al. [103] 2020 22 males Endurance runners 60 min running on treadmill Incremental running on treadmill at 10, 12, 14, 16, García-Pinillos et al. [66] 2019 22 males Novice and elite endurance runners and 18 km/h Gindre et al. [83] 2016 77 males + 14 females Healthy and active 50 m running at 3.3, 4.2, and 5.0 m/s Giovanelli et al. [172] 2017 12 males Ultraendurance runners 6 h running “6 ore Città di Buttrio” Giovanelli et al. [95] 2016 18 males Ultraendurance runners “Supermaratona dell’Etna” Girard et al. [150] 2015 13 males Team and racket sport background 3× 5s sprints on treadmill 6 × 30 s running on treadmill at 115% of the VO Girard et al. [80] 2017 20 males Field hockey players 2max 3 × 5 s sprints on treadmill + running on treadmill at Girard et al. [57] 2017 14 males Recreationally intermittent sports 10 and 20 km/h Physical education students practicing a Girard et al. [56] 2016 11 males 100, 200, and 400 m sprint on treadmill ﬁeld sport Girard et al. [79] 2011 16 males Recreational team or racket sports athletes 12 × 40 m sprints Girard et al. [96] 2017 18 males Physical education students 800 m running 10 Applied Bionics and Biomechanics Table 2: Continued. Authors Year Number of participants Sport background Motor skill Girard et al. [91] 2010 12 triathletes Highly and well-trained triathletes 5000 m running at self-selected velocity Girard et al. [93] 2013 12 males National level triathletes 5000 m running at self-selected velocity Girard et al. [78] 2011 13 males Young soccer players 6 × 20 m sprints Running on treadmill to exhaustion at velocity Hayes and Caplan [101] 2014 6 runners Subelite middle-distance runners corresponding to VO 2max He et al. [61] 1991 4 males Healthy Running on treadmill at 2.0, 3.0, 4.0, 5.0, and 6.0 m/s Heise and Martin [75] 1998 16 males Recreational runners 15 m running at 3.35 m/s Hobara et al. [64] 2010 8 males Well-trained sprinters and runners 400 m sprint Hunter [157] 2003 9 males + 7 females Not mentioned 10 min running on treadmill at self-selected velocity 11 males + 5 females Hunter and Smith [105] 2007 Recreational runners 1 h running on treadmill at constant velocity Joseph et al. [148] 2013 20 males Various sports 10 m running at 3.35 m/s Joseph et al. [121] 2014 20 males Various sports 10 m running at 3.35 m/s Kuitunen et al. [59] 2002 10 males Sprinters Sprint at 70%, 80%, 90%, and maximal velocity Lorimer et al. [53] 2018 12 males Well-trained triathletes 2 min running on treadmill at 3.0, 3.3, 3.7, and 4.2 m/s Lum et al. [129] 2019 14 males Moderately trained endurance runners 10 km running on treadmill at 10 km/h and 12 km/h Luhtanen and Komi [156] 1980 6 athletes Track and ﬁeld athletes Running at 40%, 60%, 80%, and maximal velocity Lussiana et al. [85] 2017 58 male Recreational runners 5 min running on treadmill at 12 km/h McMahon et al. [82] 1987 6 males Healthy 30 m constant velocity running Performance of each participant was examined during 43 males + 36 females Meur et al. [94] 2013 Elite triathletes the running section of the World Triathlon Grand Final Meyers et al. [67] 2019 375 boys Biweekly physical education classes 30 m sprint Meyers et al. [71] 2016 189 boys Biweekly physical education classes 30 m sprint Meyers et al. [72] 2017 344 boys Biweekly physical education classes 35 m sprint 80 m sprint with diﬀerent stride frequencies 20 males + 20 females Monte et al. [65] 2017 Elite and intermediate sprinters (preferred and +15%, +30%, −15%, and −30% of the self-selected) 6 min running on treadmill at theoretical half- Monte et al. [68] 2020 32 males Endurance runners marathon running velocity Running on treadmill at 3:33, 3:89, 4:44, 5:0, 5:56, 6:11 Physical education students + elite middle − Morin et al. [139] 2005 8 + 10 males , and 6:67 m/s + 10 m running at 4:0, 5:0, 6:0, and 7:0 distance runners m/s and maximal velocity Morin et al. [55] 2006 8 males Physical education students 100 m sprint Morin et al. [92] 2012 11 males Physically active physical education students Running on treadmill at 10 and 20 km/h Sprinter, 2 jumpers, 5 pole vaulters, and Nagahara and Zushi [127] 2017 9 males 60 m sprint a decathlete Pappas et al. [147] 2014 22 males Healthy physical education students Running on treadmill at 4.44 m/s Applied Bionics and Biomechanics 11 Table 2: Continued. Authors Year Number of participants Sport background Motor skill Paradisis et al. [58] 2019 50 males Subelite sprinters 35 m sprint Running to exhaustion at constant velocity Rabita et al. [100] 2013 12 males Runners corresponding to VO 2max Running to exhaustion at a velocity corresponding to 6 males + 3 females Rabita et al. [99] 2011 Elite triathletes 95% of the VO 2max Rogers et al. [86] 2017 11 males Highly trained middle-distance runners 50 m sprint Submaximal running tests on treadmill (10 min at Roschel et al. [130] 2015 15 humans Recreational runners 12 km/h and 90% ventilatory threshold intensity) Physically active and trained a minimum of Rumpf et al. [73] 2015 32 children 30 m sprint on treadmill two times per week Rumpf et al. [70] 2013 74 boys Physically active 30 sprint on treadmill Staﬁlidis and Arampatzis [90] 2007 10 males Experienced sprinters 60 m sprint 28 males + 26 females Vincent et al. [146] 2020 Recreational runners Running on treadmill at self-selected velocity Yin et al. [109] 2020 78 males Healthy amateur runners 15 m running at 3.3 m/s 12 Applied Bionics and Biomechanics ning velocity [33]. Therefore, humans can change the stiﬀ- at the 50-100 m interval and consistently decreased from the middle to the later part of the 400 m sprint. Morin et al. [55] ness of the “leg-spring” during running tasks, which can be reported that the decrease in 100 m sprint performance useful, for example, when running on a variety of surfaces (decreased maximal and mean velocity) in fatigue conditions with diﬀerent stiﬀness. Runners can adjust leg stiﬀness for induced by the four repetitions of this running task was also their ﬁrst step on a surface with diﬀerent compliances allow- accompanied by decreases in vertical stiﬀness and step fre- ing them to maintain similar running mechanics on diﬀerent quency and increased ground contact time [55]. Girard surfaces [87, 88]. By comparison with a hard surface, if the et al. [56] showed that a decrease in running velocity in surface is soft and compliant, more time is required to the last 50 m distance interval of a 100, 200, and 400 m sprint reverse the COM downward velocity and perform take-oﬀ performances was accompanied by a decrease in stride [89]. Staﬁlidis and Arampatzis [90] observed that surfaces length, stride frequency, and vertical stiﬀness and by an of diﬀerent compliances (stiﬀness from 550 to 5500 kN/m) increase in ground contact time. The magnitude of decre- did not have any clear eﬀect on 60 m sprint performance ment in vertical stiﬀness increased with sprint distance and on the leg and vertical stiﬀness values. However, as the [56]. Other studies have also discovered signiﬁcant relation- optimal track stiﬀness may be inﬂuenced by each of the run- ship between decrements in both stride frequency and verti- ners’ inherent stiﬀness characteristics, their shoes, and key cal stiﬀness and a progressive slowing in running velocity running spatiotemporal characteristics, the lack of any clear after two sets of ﬁve 5 s sprints [77], three sets of ﬁve 5 s association between track stiﬀness to running performance sprints [57], six 20 m sprints [78], twelve 40 m sprints [79], is not necessarily unsurprising [90]. six 30 s runs at 5.5 m/s [80], and during running anaerobic In contrast to vertical stiﬀness, leg stiﬀness is not sprint test (RAST test, 6 × 35 m) [81]. Therefore, it can be strongly related to the aerobic demand of running and concluded that fatigue causes decreased vertical stiﬀness fatigue [55–57, 76, 80, 81, 91–98]. The exceptions are the during running tasks, resulting in lower eﬃciencies of run to exhaustion at the velocity at VO [99–102] and 2max movement with a concomitant increase in metabolic cost. 60 min time trial run [103] during which leg stiﬀness Athletes characterised by enough high vertical stiﬀness dur- decreases and vertical stiﬀness remains relatively constant. ing running may execute running tasks more economically Dutto and Smith [76] reported that leg stiﬀness decreased (with less vertical COM displacements) and with higher per- initially from the beginning to 25% duration time in formance through gaining a greater potential elastic energy moderate-intensity treadmill run to exhaustion and then return from musculotendinous structures. remained relatively constant. Decrease in leg stiﬀness was It is also possible to change (decrease) leg and vertical stiﬀ- associated with increased changes in “leg-spring” length ness by running with diﬀerent (increased) knee ﬂexion (the during ground contact phase and with decrease in the peak so-called “Groucho running”). This type of running technique vertical ground reaction force [76]. Li et al. [104] reported lowers ground reaction forces and reduces ﬂight time, but a negative relationship between running economy and leg requires increased metabolic power (oxygen consumption) stiﬀness. Hobara et al. [64] noted that leg stiﬀness peaked [82–85]. The above phenomenon should be taken into at ﬁrst 50 m interval and remained constant from next account in particular by team sport games coaches, where 50 m interval to ﬁnish during 400 m sprint. Morin et al. technique like “Groucho running” is often used. This running [55] found that leg stiﬀness and peak vertical ground reac- style is necessary to minimise ﬂight time and therefore to max- tion force remained relatively constant in fatigue conditions imise the potential to decelerate and change direction quickly. induced by four repetitions of 100 m sprints. Similar conclu- sions were obtained by Brocherie et al. [81] during RAST 3.1.2. Leg Stiﬀness. In contrast to vertical stiﬀness, leg stiﬀ- test with additional accompanying decrease in stride fre- ness (with increasing running velocity) remains relatively quency and increase in ground contact time. Leg stiﬀness constant or changes (increase) to a smaller extent during decreases during the last 50 m distance interval of a 100, running [33, 55, 56, 58, 61–63, 65–68, 81]. However, leg stiﬀ- 200, and 400 m sprint performances which were smaller ness increases with the level of maturity [70, 71]. Arampatzis than decreases in vertical stiﬀness and limited to 200 and et al. [62] reported leg stiﬀness values between 25:3±4:2 400 m tasks [56]. Other studies conﬁrm that decreases in and 35:2±4:3 kN/m at running velocities from 2:6±0:2 to leg stiﬀness due to fatigue-induced reduction in sprinting 6:6±0:2 m/s. Paradisis et al. [58] obtained leg stiﬀness velocity were much smaller than decreases in vertical stiﬀ- values between 12:7±2:3 and 15:5±2:7 kN/m at running ness [55, 57, 78, 79, 105–107]. velocities from 7:7±0:3 to 9:4± 0:4 m/s. Paradisis et al. At relatively low running velocity, runners predomi- [58] reported that faster sprinters are characterised by nantly hit the ground with the heel (heel strike), whereas greater leg stiﬀness than slower sprinters during 35 m sprint at higher running velocity (sprinting), the foot strike is usu- task. In contrast, García-Pinillos et al. [66] observed that leg ally performed with the forefoot [59, 108]. Rearfoot strike stiﬀness has similar values in elite and novice runners during pattern runners touching the ground with heel and using a treadmill running at velocities from 6.2 to 11.2 m/s. Rogers rolling foot strategy result in increased ground contact time. et al. [86] reported that leg stiﬀness has relationships with In contrast, forefoot runners immediately shift from energy running economy (negative) and maximal sprinting velocity absorption phase to the propulsion phase which will (positive). decrease ground contact times and hence increase the rate However, it is possible to change leg stiﬀness value more of the ground reaction force application [109]. Therefore, than twofold by increasing stride frequency at a given run- using the forefoot strike pattern may also be more beneﬁcial Applied Bionics and Biomechanics 13 to team sport players than rearfoot strike pattern. Forefoot strike pattern runners are characterised by greater leg stiﬀ- ness, greater peak vertical ground reaction force, shorter contact time, and smaller “leg-spring” change compared with rearfoot strike pattern runners [109]. hip Leg stiﬀness is also likely to inﬂuence the ability to eﬀec- tively execute change of direction tasks. Greater leg stiﬀness allows to less loss of velocity when changing direction [110]. knee An inability to preplan a side-step cutting manoeuvre may result in a greater decrease in velocity and reduce cut angle. Reduced preplanning time available for side-step cutting ankle increased leg stiﬀness. Moreover, unanticipated cutting sig- niﬁcantly increased leg stiﬀness compared to the anticipated cutting [110]. The diﬀerence in behaviour between vertical stiﬀness Figure 4: An example of torsional spring model used to estimate and leg stiﬀness during running tasks is potentially due ankle, knee, and hip joint stiﬀness during running tasks, where to the fact that leg stiﬀness is mainly determined through α denotes the ankle joint angle, α is the knee joint angle, ankle knee the mechanical properties and activation of lower limb and α is the hip joint angle (based on Farley et al. [111]). hip musculotendinous system with only small “leg-spring” stiﬀness variations depending on velocity. Vertical stiﬀ- or deformation is plastic, the derivative (d) from Equation ness is not only reliant on the properties and activation (6) should be used [2]: of the lower limb but also on the whole body [22]. More- over, COM displacement depends on the spatial position dM K = : ð6Þ of each body part, including the upper limbs. The total joint dα mass of the body (COM) is not concentrated at the upper end of the “leg-spring”. Therefore, the displace- The analysis of lower limb joint springs (hip, knee, and ment of the COM is not the same as the displacement ankle) oﬀers a diﬀerent view of “leg-spring” stiﬀness than of the upper end of the “leg-spring” [3]. Diﬀerences the quasi-stiﬀness. Table 3 lists the studies on joint stiﬀness between leg and vertical stiﬀness may also be due to that meet the inclusion criteria. Unfortunately, only a few the hip joint displacement. It has a much smaller eﬀect manuscripts consider all three lower limb joint springs or on vertical stiﬀness. even hip joint stiﬀness [53, 112–114]. Hip joint stiﬀness increases with running velocity [113]. Jin and Hahn [113] 3.2. Joint Stiﬀness during Running Tasks. Quasi-stiﬀness is a stated that hip joint has a crucial role during swing phase concept that considers the limb (leg stiﬀness) or body (verti- for work and power generation. cal stiﬀness) as a whole system rather than only the muscu- lotendinous system. Therefore, quasi-stiﬀness also depends 3.2.1. Knee and Ankle Joint Springs. Knee joint stiﬀness on the stiﬀness of other tissues, such as ligaments, blood ves- increased with running velocity [59, 62, 113, 115, 116]. sels, and bones. The elastic properties and the ability to accu- Arampatzis et al. [62] reported knee joint stiﬀness values mulate potential elastic energy are diﬀerent for each of these ° between 6:8±4:1 and 19:1±8:9 Nm/ at running velocities tissues [2]. However, the “leg-spring” model is dependent from 2:6±0:2 to 6:6±0:2 m/s. Kuitunen et al. [59] obtained also on hip, knee, and ankle kinematics. Therefore, the tor- knee joint stiﬀness values between 17 and 24 Nm/ at sional spring model oﬀers a diﬀerent view of “leg-spring” running velocities from 6.7 to 10.3 m/s. Knee joint stiﬀness stiﬀness than the spring-mass models. By using the torsional during initial ground contact increases also with running spring model, it is possible to estimate the joint stiﬀness velocity [116]. Tam et al. [115] reported that knee joint stiﬀ- values of the main joints of lower limb during vertical and ness has positive relationships with rectus femoris activation horizontal movements. Figure 4 shows an example of the and rectus femoris : biceps femoris coactivation ratio. Jin and torsional spring model that can be used in the determination Hahn [113] stated that knee joint has a crucial role during of ankle, knee, and hip joint stiﬀness during vertical and swing phase for energy absorption. horizontal displacements. In turn, ankle joint stiﬀness (with increasing running For rotational motions, joint stiﬀness (K ) is expressed joint velocity) remains relatively constant or changes (increase) by the following equation: to a smaller extent compared to knee joint stiﬀness [59, 62, 115, 117, 118]. Stefanyshyn and Nigg [117] and Kuitunen et al. [59] argued that ankle joint stiﬀness is depen- K = , ð5Þ joint dent on the task activity rather than on the individual. Δα Arampatzis et al. [62] reported ankle joint stiﬀness values between 16:4±5:5 and 20:5±8:2 Nm/ at running velocities where M denotes the deforming torque and Δα is the angle from 2:6± 0:2 to 6:6±0:2 m/s. Stefanyshyn and Nigg [117] of deformation. However, if the relationship between the reported ankle joint stiﬀness values of 5.7 Nm/ in running deforming torque and the angle of deformation is nonlinear at 4 m/s and 7.4 Nm/ in sprinting at velocities from 7.1 to 14 Applied Bionics and Biomechanics Table 3: List of the studies on joint stiﬀness during running. Authors Year Number of participants Sport background Motor skill Stiﬀness measure 7 males + 9 females and Adult well − trained sprinters + well − Aeles et al. [119] 2018 10 m sprint Ankle joint 11 males + 10 females trained young athletes Arampatzis et al. [62] 1999 13 runners Not mentioned Running at 2.5, 3.5, 4.5, 5.5, and 6.5 m/s Knee joint, ankle joint Running on treadmill (30 min at Chan et al. [126] 2020 20 males Recreational distance runners Knee joint, ankle joint self-reported velocity) Internationally competitive sprint Maximal sprint starts with 10 m Charalambous et al. [120] 2012 1 male Ankle joint hurdle athlete acceleration Running at convenience velocity Günther and Blickhan [122] 2002 8 males + 4 females Sports students and active sportsmen Knee joint, ankle joint (from 3.7 to 5.6 m/s) Hamill et al. [125] 2014 27 males + 13 females Runners 25 m running at 3.5 m/s Knee joint, ankle joint Hip joint, knee joint, Hamill et al. [112] 2009 33 runners Runners Running on treadmill at 3.8 m/s ankle joint Running on treadmill (from 1.8 to Hip joint, knee joint, 5 males + 5 females Jin and Hahn [113] 2018 Healthy 3.8 m/s) ankle joint Joseph et al. [148] 2013 20 males Various sports 10 m running at 3.35 m/s Knee joint, ankle joint Sprint at 70%, 80%, and 90% and Kuitunen et al. [59] 2002 10 males Sprinters Knee joint, ankle joint maximal velocity 2 min running on treadmill at 3.0, 3.3, Hip joint, knee joint, Lorimer et al. [53] 2018 12 males Well-trained triathletes 3.7, and 4.2 m/s ankle joint 11 males + 16 females Mager et al. [118] 2018 Healthy students Running at self-selected velocity Ankle joint Melcher et al. [124] 2017 13 males Well-trained runners 25 m running with a 15 m acceleration Knee joint, ankle joint Sprinter, 2 jumpers, 5 pole vaulters, Nagahara and Zushi [127] 2017 9 males 60 m sprint Knee joint, ankle joint and a decathlete Powell et al. [167] 2014 20 females Recreational athletes Running at self-selected velocity Ankle joint Hip joint, knee joint, Shih et al. [114] 2019 20 males + 20 females Recreational runners 14 m running at 3.4 m/s ankle joint Sinclair et al. [145] 2015 14 males + 14 females Recreational runners Running at 4.0 m/s Knee joint, ankle joint Running at 4 m/s and maximal Stefanyshyn and Nigg [117] 1998 10 males Distance runners and sprinters Ankle joint acceleration sprint Tam et al. [115] 2017 14 males Elite runners 60 m running at 12 and 20 km/h Knee joint, ankle joint Tam et al. [123] 2019 30 males Runners 60 m running at 3.3 m/s Knee joint, ankle joint 70 m running at 2.5, 3.5, 4.5, and 5.5 m/s Verheul et al. [116] 2017 26 (males + females) Runners Knee joint and maximal velocity Prolonged running on treadmill Weir et al. [98] 2020 13 males Recreational runners Knee joint, ankle joint (2 × 21 min) Williams III et al. [166] 2004 18 males + 22 females Healthy 25 m running at 3.35 m/s Knee joint Applied Bionics and Biomechanics 15 inﬂuence joint stiﬀness [124–126]. Change in foot strike pat- 8.4 m/s. Aeles et al. [119] did not obtain signiﬁcant diﬀer- ences in ankle joint stiﬀness between young and adult well- tern from rearfoot strike to midfoot strike may cause a trained sprinters during 10 m sprint (ﬁrst stance phase). decrease in ankle joint stiﬀness and increase in knee joint Charalambous et al. [120] noted a positive relationship stiﬀness [126]. Melcher et al. [124] noted that knee joint between ankle joint stiﬀness on the ascending limb and the range of motion, knee joint moment, and ankle joint stiﬀ- horizontal COM velocity at the end of the ﬁrst stance phase. ness were lower during imposed forefoot strike compared Kuitunen et al. [59] reported a negative relationship between with rearfoot strike pattern. ankle joint stiﬀness and ground contact time. Jin and Hahn [113] stated that ankle joint has a crucial role during stance 3.3. The Eﬀect of Training on Mechanical Stiﬀness. The phase for energy generation in running. Higher ankle joint assessment of training eﬀects in runners seems to be the stiﬀness results in more positive work performed and power most correct when it is carried out with the use of running generation [113]. tests. Therefore, the possible changes in mechanical stiﬀness Larger peak moment and mechanical power values at the can then be determined based on a measurement during ankle and knee joints are observed with increasing running running. Table 4 lists the longitudinal studies that meet this velocity [62]. Running velocity also inﬂuences the change criterion. Nagahara and Zushi [127] have examined well- in the angle at the ankle and knee joint [62]. With increasing trained male athletes during 60 m sprints before and after a running velocity, larger changes are observed in the knee 6-month winter training session (combining of plyometric, joint stiﬀness than in the ankle joint stiﬀness [59, 62]. There- sprint, weight, circuit, and individualised trainings). How- fore, the increase in “leg-spring” stiﬀness may be mainly ever, the participants specialized in diﬀerent events (includ- caused by the increase in knee joint stiﬀness. Joseph ing a sprinter, two jumpers, ﬁve pole vault jumpers, and a et al. [121] stated that knee joint mechanics may be decathlete) and followed their own training plans during altered to maintain consistent levels of leg and vertical stiﬀ- the winter training period. Nagahara and Zushi [127] ness. Arampatzis et al. [62] suggested that with increasing reported that the development of maximal velocity sprinting running velocity, the athletes alter the knee joint stiﬀness performance through longer step length was accompanied ﬁrst. In accordance with the assumptions of the torsional by increases in vertical and ankle joint stiﬀness, although spring model, “leg-spring” stiﬀness depends on the stiﬀness leg and knee joint stiﬀness remained constant. Ache-Dias of three joint springs (in the ankle, knee, and hip joint). et al. [128] reported that the addition of 4 weeks of jump The contribution to the overall “leg-spring” stiﬀness of each interval training into a continuous endurance treadmill training program induced an increase in the stiﬀness (leg joint spring is diﬀerent. According to Equation (7), the greatest contribution to the overall stiﬀness value of the and vertical) and stride frequency and a decrease in stride “leg-spring” will have the most compliant joint spring: length. However, these changes do not aﬀect running econ- omy. Lum et al. [129] noted that 6 weeks of intermittent sprint training and plyometric training led to improvement K = , ð7Þ leg‐spring in 10 km performance in moderately trained endurance 1/K +1/K +1/K ðÞ ðÞ ankle knee hip runners despite reduction in weekly training mileage. The improvement in running performance was accompanied by where K is the “leg-spring” stiﬀness, K denotes leg−spring ankle an increase in power, whereas leg and vertical stiﬀness the ankle joint stiﬀness, K is the knee joint stiﬀness, and remained relatively constant. Similarly, Roschel et al. [130] knee K is hip joint stiﬀness. did not report changes in vertical stiﬀness in recreational hip Therefore, depending on the running velocity, theoreti- runners after 6 weeks of resistance training or whole-body cally, knee joint stiﬀness or ankle joint stiﬀness will have vibration training. the most inﬂuence of overall “leg-spring” stiﬀness. Ankle In contrast, Rumpf et al. [73] observed decreases in 30 m joint spring should be more compliant than knee joint spring treadmill sprint time, relative leg stiﬀness, and relative verti- cal stiﬀness during substantial running velocity (sprinting). Günther and in youth after 6 weeks of resisted sled towing Blickhan [122] concluded that the knee joint is always stiﬀer training. Stride frequency, average power, peak horizontal and more extended than the ankle joint. However, this state- force, average relative vertical forces, and vertical displace- ment only seems true from a certain running velocity and ment increased. While this study reported decreased sprint may depend on the running technique [62]. times, the decrease in stiﬀness might be viewed as disadvan- Lower ankle joint stiﬀness and greater knee joint stiﬀness tageous in the long term as these reductions in stiﬀness may were associated with lower oxygen consumption during con- actually increase foot contact time and result in a reduction stant velocity running. More economical runners are charac- in stride frequency and ultimately running speed. terised also with short ground contact times and greater While McMahon et al. [26] and Brazier et al. [22] have stride frequencies [123]. Weir et al. [98] reported that knee recommended that in terms of training to increase “leg- joint stiﬀness increased and ankle joint stiﬀness decreased spring” stiﬀness, resistance training should be performed with running time during a prolonged treadmill run. More- with loads above 75% of 1 repetition maximum and should over, Melcher et al. [124] noted that oxygen consumption, precede high-intensity plyometric and power training, there ankle joint moment, and knee joint stiﬀness were greater is still no clear answer how training could aﬀect mechanical during imposed forefoot strike pattern compared with rear- stiﬀness during running due to a very small number of stud- foot strike pattern. Therefore, the foot strike angle can also ies on this topic. Papers that did not assess mechanical 16 Applied Bionics and Biomechanics Table 4: List of the longitudinal studies on training eﬀects on mechanical stiﬀness. Authors Year Number of participants Sport background Motor skill Stiﬀness measure Submaximal constant load running test Ache-Dias et al. [128] 2018 18 (males + females) Recreational runners Leg, vertical on treadmill (6 min at 9 km/h) 10 km running on treadmill at 10 km/h Lum et al. [129] 2019 14 males Moderately trained endurance runners Leg, vertical and 12 km/h Sprinter, 2 jumpers, 5 pole vaulters, Leg, vertical, knee Nagahara and Zushi [127] 2017 9 males 60 m sprint and a decathlete joint, ankle joint Submaximal running tests on treadmill Roschel et al. [130] 2015 15 humans Recreational runners (10 min at 12 km/h and 90% ventilatory Vertical threshold intensity) Physically active and trained a Rumpf et al. [73] 2015 32 children 30 m sprint on treadmill Leg, vertical minimum of two times per week Applied Bionics and Biomechanics 17 hits the ground, therefore reducing the amount of muscle stiﬀness changes (caused by training) during running task were omitted from this review. Perhaps due to the increase stretch during initial ground contact and absorption in rate of force development, some power (plyometric) train- (braking) phase [32]. However, to generate suﬃciently large ankle joint torques, the ankle plantar ﬂexor muscles shorten ing would result in an increase in mechanical stiﬀness. How- ever, it is not known how power training aﬀects leg, vertical, throughout the entire ground contact phase (or work in or joint stiﬀness during running, although it is presumably quasi-isometric conditions during the early part of the known how mechanical stiﬀness changes might aﬀect run- ground contact phase), despite the entire musculotendinous ning performance. Moreover, there is a lack of studies on units undergoing a SSC [134]. Most of the stretch can be taken up by the tendons, resulting in potential elastic energy training eﬀects in elite athletes. There is also the question of obtaining the possible desired “leg-spring” stiﬀness value storage in these spring elements [32]. The musculotendinous under the inﬂuence of training. system design of the ankle plantar ﬂexors supports the stor- age and utilization of tendon elastic strain energy over mus- 3.4. Desired “Leg-Spring” Stiﬀness. The total mechanical cular work [134, 135]. In muscle-tendon units with long energy involved in human body movement is the sum of compliant tendons (such as the Achilles tendon), the tendons kinetic and potential energy. With each running stride, the can store a high amount of potential elastic energy; therefore, kinetic energy change of horizontal motion (related to the during the push-oﬀ phase, less work needs to be performed braking action of the ground) and the gravitational potential by the muscles due the energy returned by the tendons. For energy change due to the (vertical) displacements of the run- example, the Achilles tendon, which is long and compliant, ners COM. Potential elastic energy is associated with the is able to contribute about 35% of the mechanical energy nec- change in the kinetic energy of the body being moved. Due essary for performing each running stride (obviously, the to braking and lowering of the runners COM in the initial entire “leg-spring” is formed also by other soft tissues with part (absorption) of the ground contact phase during run- elastic properties) [32]. The compliance of the serial elastic ning, the decrease in the kinetic energy and gravitational elements allows the muscle ﬁbres to contract at preferred potential energy is partially stored in the form of potential velocities for maximal power output and eﬃciency (accord- elastic energy by the stretched musculotendinous groups. ing to force-length curve) and allows to deactivating ﬁbres The ability of the musculotendinous groups to store and during shortening periods. Therefore, the muscle fascicles return potential elastic energy increases the mechanical shorten at a much slower velocity (often very diﬀerent from energy supplied by active contracting muscles used in the the velocity of the whole musculotendinous units) with high take-oﬀ phase. Consequently, the total mechanical energy velocity shortening during take-oﬀ in running achieved by supplied by the entire muscle-tendon unit during the pro- recoil of the serial elastic elements [134, 136, 137]. pulsion phase can obtain greater values and/or less work For a given human body modelled as a spring-mass needs to be performed by the muscles’ contractile elements system (with speciﬁc body mass, leg-spring length, the hori- [3, 6]. A certain amount of “leg-spring” stiﬀness is required zontal and vertical landing velocities, and leg-spring swept for eﬀective storage and utilization of potential elastic energy angle), some particular value of the “leg-spring” stiﬀness in the musculotendinous groups during “stretch-shortening may hypothetically be the most beneﬁcial for movement cycle” (SSC) movements, such as running [22]. Greater stiﬀ- performance. Greater or lower “leg-spring” stiﬀness com- ness of the “leg-spring” provides the capacity to store more pared to desired values can cause the lower limbs to partially potential elastic energy during the ground contact phase. lose elastic capacity, which will have a negative eﬀect on the Therefore, it would be expected that higher (or high enough) accumulation and utilization of elastic energy. If the “leg- values of mechanical stiﬀness (leg, vertical, and joint) may spring” is too stiﬀ, the body may take-oﬀ too soon reducing also increase running performance and/or execute running the capacity to improve ﬂight time through addition of mus- tasks with more mechanical economy. Cavagna et al. [131] cular force. If the “leg-spring” is too compliant, the body suggested that the role of potential elastic energy becomes may rise too late with considerable energy lost through more important in sprint tasks at running velocities greater relaxation of the elastic tissue, thereby reducing the advan- than 7 m/s, although its contribution to lower velocity run- tage for the musculotendinous system during the SSC [20]. ning is also of importance. “Leg-spring” stiﬀness is expected to be greater in athletes The total “leg-spring” involves many skeletal muscles than nonathletes during running tasks. With similar changes and tendons and other passive structures. These tissues can in the length of the “leg-spring”, athletes release greater force be stretched and recoil and consequently accumulate poten- than nonathletes. Therefore, increases in “leg-spring” stiﬀ- tial elastic energy during these actions [32]. During running ness make it theoretically possible for runners to absorb with relatively low velocity, ankle plantar ﬂexors contribute greater loads, as a higher level of deforming force (torque) the majority of the force necessary for vertical support and is required to perform joint movement. This phenomenon horizontal propulsion, whereas the quadriceps muscle group may be important in training, as it allows for working with is the largest contributor to horizontal braking of the run- higher loads. However, based on the analysis of vertical ners COM and vertical support during the early stage of jumps, it seems that the desired “leg-spring” stiﬀness value the ground contact phase [132]. The gluteus maximus, is relatively small in relation to the “maximum” [3]. quadriceps, and ankle plantar ﬂexors are the major contrib- Greater accumulation of potential elastic energy may utors to acceleration of the body COM during running occur by increasing stiﬀness and/or deformation. However, [132, 133]. The muscles are activated before the lower limb according to Equation (4), increases in deformation seem 18 Applied Bionics and Biomechanics eﬀort conditions. It should be remembered that the mea- more beneﬁcial because the value of potential elastic energy depends on the squared length change. Therefore, theoreti- surements performed on the treadmill give slightly diﬀerent cally smaller “leg-spring” stiﬀness allows “leg-spring” length values of kinematic and kinetic variables (including “leg- change by using a lower force and consequently greater spring” stiﬀness) compared to the analysis carried out under length change can be obtained, which should increase the ﬁeld conditions [144]. accumulated potential elastic energy. However, the “leg- Another important factor that seems necessary to take spring” length change cannot be too excessive (beyond the into account in stiﬀness estimation is body mass. A positive desired range of lower limb joint ﬂexion during ground con- relationship between stiﬀness and body mass can result from tact phase), as such changes would result in large increases maintaining the natural vibration frequency of the human in ground contact time and decreases in step frequency. body, which is dependent on internal elastic forces and iner- After reaching an “optimal” lower limb joints ﬂexion angle, tia [7]. Therefore, the relationships of mechanical stiﬀness further increases in the accumulated potential elastic energy with the variables describing the running tasks may be dif- are possible by increasing stiﬀness. “Leg-spring” stiﬀness will ferent if the value of stiﬀness related to body mass is taken increase with increased deforming force at “optimal” lower into account, not the absolute value [3, 65, 67, 145, 146]. limb joint ﬂexion angles during running tasks [3]. Mechanical stiﬀness is commonly assessed in both labo- Because athletes are able to generate a greater ground ratory and ﬁeld tests. Regardless of the test mode, any stiﬀ- reaction force than nonathletes, their maximum “leg- ness test must be valid and reliable if the data can be used spring” stiﬀness is greater. Therefore, a relatively low “leg- to inform training decisions. Pappas et al. [147] reported that leg and vertical stiﬀness, as well as related kinematic spring” stiﬀness will be greater for an athlete than for a non- athlete. The greater value of “leg-spring” stiﬀness in athletes parameters, obtained using the sine wave method during (in comparison to nonathletes) will be (on the condition that treadmill running at 4.4 m/s, were highly reliable, both the desired range of motion in the lower limb joints is within and across days. However, Joseph et al. [148] obtained) an additional factor that increases the accumu- reported that during 10 m overground running (at 3.8 m/s), lated potential elastic energy and, consequently, perfor- vertical stiﬀness has good reliability, leg stiﬀness has mance. Therefore, the desired “leg-spring” stiﬀness value moderate reliability, and knee and ankle stiﬀness has poor can be an individual variable property [3]. reliability. Leg stiﬀness [75] and knee joint stiﬀness [59] The speculations concerning a desirable value “leg- are characterised by substantial interindividual variations. spring” stiﬀness that is the most advantageous for the Therefore, researchers may need to better demonstrate the accumulation of potential elastic energy and most favours validity and reliability of their stiﬀness measures, with con- reaching maximal sport performance have already been sensus recommendations from experts warranted, perhaps addressed in many previous studies [1, 3, 22, 24–28, 31–35]. similar to the SENIAM approach for electromyography data However, no studies have provided unequivocal evidence for collection and analysis [149]. the presence of a desired “leg-spring” stiﬀness value. Because desired “leg-spring” stiﬀness can be inﬂuenced by task, and 3.5.2. Running Phases. There are several consecutive phases individual and environmental factors, the estimation of this during running distance: start, push-oﬀ, acceleration, max- imum velocity (or desired submaximal velocity for longer desired value and determination of how this value might be inﬂuenced by changes in stiﬀness at each joint spring may distances), and velocity maintenance [120]. All these run- prove to be extremely diﬃcult. ning phases are characterised by diﬀerent stride length- to-frequency ratios, technical and physiological demands that may require diﬀerent “leg-spring” stiﬀness values to 3.5. Limitations and Other Important Factors maximise performance and diﬀerent training programs 3.5.1. Computation Methods. The studies included in this [120, 150–152]. This may indicate that diﬀerent forms of review utilised several computational methods to estimate training may be required to improve the stiﬀness charac- mechanical stiﬀness, with such approaches not always necessar- teristics relevant to each running phase. ily yielding the same values [1, 21, 24, 53, 62, 122, 138–143]. Ground contact can be divided into absorption (braking) Therefore, it may be important to be aware of these and propulsion phases, which diﬀer in their characteristics between-study diﬀerences, meaning that analysing the pro- and purpose [153]. This suggests that the mechanical stiﬀ- ﬁle of the force-displacement (or torque-displacement) ness during braking and propulsion phases does not neces- curve and the values of deforming force (torque) and dis- sarily have to be the same. To understand the phenomena placement (change in length, deformation) may be useful. occurring during running tasks, it seems necessary to Estimation of the mechanical stiﬀness value does not always determine the mechanical stiﬀness for both these phases follow the force-displacement proﬁle, and the displacement separately [154, 155]. Such an approach has been used in (of COM or “leg-spring” compression) during ground a number of studies, although these approaches diﬀer. contact phase is deﬁned in various ways. High magnitudes Luhtanen and Komi [156] estimated vertical stiﬀness dur- of deforming force and displacement at one hand and low ing running and long jump with a division into eccentric magnitudes of deforming force and displacement on the and concentric phases. Butler et al. [1] proposed to calcu- other hand could both lead to similar stiﬀness values. More- late joint stiﬀness with division into two separate phases: over, mechanical stiﬀness during running tasks has been during the joint moment increase and during the joint evaluated during both treadmill and typical over ground moment decrease. Hunter [157] proposed separation of Applied Bionics and Biomechanics 19 mance. Moreover, only a few works concern the analysis of the heel strike part from the ground contact phase during running as a part with much greater stiﬀness compared to spring-mass model properties performed on top-level ath- rest of ground contact phase. However, these approaches letes and players or over an entire running distance in ﬁeld do not appear to be commonly used. conditions with typical acceleration-deceleration running velocity pattern [55, 64, 93, 94, 171, 172]. 3.5.3. Running Technique. The speciﬁc nature of each sport The number of factors inﬂuencing mechanical stiﬀness should also be considered in the analysis because running during running makes it diﬃcult to formulate clear and gen- technique used by team sports players (like a “Groucho run- eral conclusions about training recommendations. All three ning”)diﬀers signiﬁcantly from track athlete technique levels of constraint eﬀecting the individual, environment, [158]. It is important because running performance aﬀects or task constraints including age, gender, running technique, game performance indicators [159]. Team sport players (in sporting background, fatigue, running distance, and running soccer, rugby, football, basketball, handball, lacrosse, or ﬁeld surface should be taken into account. Until researchers hockey) run with a relatively lower height of the COM, less investigate how mechanical stiﬀness can be altered with knee ﬂexion during swing phase, and lower knee lift. This diﬀerent forms of training, the inﬂuence of “leg-spring” stiﬀ- technique helps team sport players to decelerate and change ness on running performance will remain somewhat unclear. direction faster [158, 160]. The acceleration phase for team It seems that studies focusing on the analysis of local tissues sport players is much shorter than that for track sprinters, (muscle, tendon) as well as more global phenomenon and the maximal running velocity is reached earlier [161]. including the interaction of the central nervous and periph- All of these factors may therefore alter the desired level of eral systems and how the plasticity of these systems aﬀects “leg-spring” stiﬀness for team sport players compared to their interplay with regard to “leg-spring” stiﬀness on run- track athletes. The type of footwear used by athletes and ning performance may allow for a better understanding of team sport players also may have some role in terms of alter- the running mechanics. ing the “leg-spring” stiﬀness and subsequent sporting per- formance [162–165]. The anatomical structure of the foot is another individual factor that can inﬂuence leg stiﬀness. Conflicts of Interest High-arched runners have increased leg stiﬀness, knee joint The authors declare that there is no conﬂict of interest stiﬀness, and ankle joint stiﬀness compared to low-arched regarding the publication of this paper. runners [166–169]. 4. Conclusions References Mechanical stiﬀness is a group of variables (leg, vertical, and [1] R. J. Butler, H. P. Crowell 3rd, and I. McClay Davis, “Lower joint stiﬀness) that seem to have an important role in run- extremity stiﬀness: implications for performance and injury,” ning performance. 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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2021 Artur Struzik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN: 1176-2322
eISSN: 1754-2103
DOI: 10.1155/2021/9914278
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Abstract

Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 9914278, 25 pages https://doi.org/10.1155/2021/9914278 Review Article Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview 1 2 3,4 3,4,5,6 Artur Struzik , Kiros Karamanidis , Anna Lorimer , Justin W. L. Keogh , and Jan Gajewski Department of Biomechanics, Wroclaw University of Health and Sport Sciences, Poland Sport and Exercise Science Research Centre, School of Applied Sciences, London South Bank University, UK Faculty of Health Sciences and Medicine, Bond University, Gold Coast, Australia Sports Performance Research Centre New Zealand, AUT University, Auckland, New Zealand Cluster for Health Improvement, Faculty of Science, Health, Education and Engineering, University of the Sunshine Coast, Australia Kasturba Medical College, Mangalore, Manipal Academy of Higher Education, Manipal, Karnataka, India Human Biology, Józef Piłsudski University of Physical Education, Warsaw, Poland Correspondence should be addressed to Artur Struzik; artur.struzik@awf.wroc.pl Received 25 March 2021; Revised 8 September 2021; Accepted 17 September 2021; Published 21 October 2021 Academic Editor: Cristiano De Marchis Copyright © 2021 Artur Struzik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Stiﬀness, the resistance to deformation due to force, has been used to model the way in which the lower body responds to landing during cyclic motions such as running and jumping. Vertical, leg, and joint stiﬀness provide a useful model for investigating the store and release of potential elastic energy via the musculotendinous unit in the stretch-shortening cycle and may provide insight into sport performance. This review is aimed at assessing the eﬀect of vertical, leg, and joint stiﬀness on running performance as such an investigation may provide greater insight into performance during this common form of locomotion. PubMed and SPORTDiscus databases were searched resulting in 92 publications on vertical, leg, and joint stiﬀness and running performance. Vertical stiﬀness increases with running velocity and stride frequency. Higher vertical stiﬀness diﬀerentiated elite runners from lower-performing athletes and was also associated with a lower oxygen cost. In contrast, leg stiﬀness remains relatively constant with increasing velocity and is not strongly related to the aerobic demand and fatigue. Hip and knee joint stiﬀness are reported to increase with velocity, and a lower ankle and higher knee joint stiﬀness are linked to a lower oxygen cost of running; however, no relationship with performance has yet been investigated. Theoretically, there is a desired “leg-spring” stiﬀness value at which potential elastic energy return is maximised and this is speciﬁc to the individual. It appears that higher “leg-spring” stiﬀness is desirable for running performance; however, more research is needed to investigate the relationship of all three lower limb joint springs as the hip joint is often neglected. There is still no clear answer how training could aﬀect mechanical stiﬀness during running. Studies including muscle activation and separate analyses of local tissues (tendons) are needed to investigate mechanical stiﬀness as a global variable associated with sports performance. 1. Introduction able bodies under application of external forces. In the seventeenth century, the British physicist Robert Hook Stiﬀness is a quantitative measure of the elastic properties of stated a proportional relationship between the magnitude the body and determines the ability to accumulate potential of the deforming force (F) and the deformation (Δl) of the elastic energy. The concept of stiﬀness was developed in clas- body. Therefore, as a part of Hooke’s law, stiﬀness (K) was sical mechanics to describe the behaviour of elastic deform- deﬁned as a ratio of the amount of deforming force (or force 2 Applied Bionics and Biomechanics muscle. It can be concluded that the activity of the muscles change) to the unit of deformation (or as a ratio of the amount of deforming torque to the angle of deformation allows the potential elastic energy to be stored in the tendons for rotational motions) [1–3]. since at the same deformation of the entire spring complex, the greater part of energy goes to less stiﬀ element. Muscle Elastic deformable bodies have the ability to recover the previous shape and volume (i.e., they return to their initial tension is a factor regulating the stiﬀness of the support limb size) after mechanical forces that cause deformation are during locomotion and jumps. The coactivation of extensors removed. These deformations are fully reversible. Due to and ﬂexors in the moment preceding contact with the the inﬂuence of external deforming forces, the elastic bodies ground is aimed at regulating the “leg-spring” stiﬀness and preparing the limb to transfer the anticipated forces in the accumulate potential elastic energy, which they release back to the system when returning to the original length. The contact phase [14]. Muscle stiﬀness increases in eccentric work performed by the deforming forces equals the value phase, when the stretch reﬂex generates an extra activation. of the potential elastic energy accumulated in the spring A musculotendinous unit is capable of resisting higher compliance elements (assuming there are no energy losses passive tensile forces when it is in a lengthened position or when it is stretched. In an active muscle state, the shape of due to friction and resistance forces) [2, 3]. The ability to absorb and return potential elastic energy generated muscle force over the entire physiological range is also observed in the musculotendinous groups in the of movement is not the same for every muscle as muscles human body. The potential elastic energy stored by the pas- in vivo can operate at diﬀerent regions of the force-length sive structures (tendon and aponeurosis) during contractile relationship [15–17]. Moreover, body parts may change con- cycle of a muscle, e.g., during lengthening of the entire ﬁguration in relation to each other (displacement) and not muscle-tendon unit, can increase the energy supplied by be deformed at all (like a passive bodies). Change in muscle the compliant tissues during the proceeding shortening length (deformation) can be caused by the action of contrac- phase. Consequently, the substantial capacity of the tendon tile elements or external forces. Therefore, length of an active and aponeurosis to store elastic strain energy can enhance muscle or joint angle can change without a contribution of the total mechanical energy produced by the muscle- deforming forces. Consequently, it is possible to obtain the tendon unit during the concentric phase of muscle work or same magnitude of force at diﬀerent joint angles and diﬀer- reduce muscle ﬁbre work and metabolic energy expenditure. ent force values at a speciﬁc joint angle [2]. Therefore, using Potential elastic energy stored in muscle-tendon units the concept of stiﬀness in locomotion and performance reduces the metabolic energy spent by muscles responsible analyses for much more complex biological objects than for movement in speciﬁc joints and is associated with the simple passive bodies is associated with numerous concep- change in the kinetic energy of the body being moved tual diﬃculties. [3–7]. Therefore, stiﬀness, the quantitative measure of the Stiﬀness should be understood as the resistance does not resistance oﬀered by an elastic body to deformation, may depend on time, velocity, or acceleration, but only on the be an essential factor in the optimization of human locomo- displacement (for a passive elastic body with linear force- tion, because it is related to the maximal performance of deformation characteristics, the value of stiﬀness will be cyclic and single dynamic movements [1, 8, 9]. the same at a relatively low or high level of deformation). However, the strict concept of stiﬀness has been intro- The proper measurements of stiﬀness are performed during duced for relatively simple passive bodies (they maintain steady-state body deformation (from one equilibrium state constant shape if external deforming forces are absent or to another equilibrium state). If stiﬀness measurements are sustainable). A human muscle (as a whole) does not behave not performed during steady-state body deformation but like a passive body with linear force-deformation character- during transient states, the substantial value of dF/dl might istics [2]. The muscle-tendon complex consists of two contain components originating from inertial forces and elements of diﬀerent stiﬀness connected in series. A muscle damping. Therefore, the variable measured in the above case is made of force-producing active (contractile) components is not stiﬀness viewed in strict mechanical terms due to the and passive components (serial and parallel elastic elements) substantial contribution of other factors that aﬀect the consisting of tendons, fascia, and other connective tissues, FðΔlÞ relationship, especially during transient states. In each with diﬀerent biomechanical properties [10]. The mag- locomotion analyses when the body is in motion, certain nitude of the forces (and mechanical power) generated “varieties” of stiﬀness are used [2, 3]. depends on muscle activation, muscle length and its velocity, With respect to living bodies, the mechanical stiﬀness and on the use of elastic elements, which increase the can be divided into quasi-stiﬀness and joint stiﬀness. Latash eﬀectiveness (and eﬃciency) of contractile elements. Tendon and Zatsiorsky [18] deﬁned quasi-stiﬀness as the ability of stiﬀness increases with lengthening [11] (due to the toe the human body to oppose external displacements with region in tendons’ force-length relationship), and muscle disregard to displacement proﬁle over time. Leg and vertical stiﬀness increases with muscle lengthening or tension stiﬀness are the most frequently used types of quasi-stiﬀness (activation level) [12]. However, while tendon stiﬀness is in human and animal locomotion analysis to describe the relatively constant, muscle stiﬀness is greatly inﬂuenced by mechanical properties of a “spring” representing the lower the force developed [12]. The stiﬀness of a muscle increases limbs (according to the assumptions of body modelling as the more motor units of the muscle which are activated [13]. a spring-mass model, which contains a massless supporting Thus, the stiﬀness of the entire muscle-tendon complex var- “leg-spring”, a material point representing the total body ies and depends to the greatest extent on the stiﬀness of the mass, and a parallel source of force resulting from the active Applied Bionics and Biomechanics 3 vals during 100 m sprint performance and presented a action of the muscles involved in the take-oﬀ) [1, 19]. Leg quasi-stiﬀness is understood as the ratio of changes in the larger deceleration between the second and the third inter- ground reaction force to the respective changes in “spring vals (60–100 m). However, vertical stiﬀness was also deter- length” representing both lower limbs, whereas vertical mined based on the hopping test. It seems that these quasi-stiﬀness is understood as the ratio of changes in the ﬁndings would be much more valuable if the stiﬀness ground reaction force to the respective vertical displacement was also measured during running. Lorimer et al. [53] of the centre of mass (COM). Unfortunately, these two dis- reported that comparability of stiﬀness (leg, vertical, and tinct stiﬀness concepts are often confused and consequently joint) during hopping and running was at most moderate. used interchangeably or incorrectly [20]. Joint stiﬀness is It would be expected that a stiﬀer “leg-spring” may resistance to displacement within a given joint (e.g., hip, increase athletic performance by enhanced utilisation of knee, or ankle) and depends on the mechanical properties potential elastic energy. Therefore, the aim of this overview of the movements related to this joint and all structures is to examine the relationships between mechanical stiﬀness involved in this movement [2, 9, 21]. Research analysing (leg, vertical, and joint) and running performance, both in leg, vertical, and/or joint stiﬀness have typically been con- cross-sectional and training studies. Such a review is impor- ducted during cyclic (e.g., walking, running, or hopping) tant as many studies assessing stiﬀness in humans have and single (e.g., vertical jumps) locomotor movements. focused on jumping or hopping motions that are not com- The relationships between mechanical stiﬀness (leg, ver- monly performed in sporting events, with the majority of tical, and joint) and movement performance are areas of the studies being cross-sectional in design. This review interest to the sport and research communities. Several may provide additional insight regarding how diﬀerent authors have already tried to organise an understanding of stiﬀness values obtained from running tasks may be repre- stiﬀness in their review articles [1, 6, 9, 18, 21–30]. However, sentative of common sporting locomotor activities and the multiple deﬁnitions and equations used to deﬁne verti- how training-related changes in stiﬀness characteristics cal, leg, and joint stiﬀness along with advances in research may underpin improvements in running performance. into the topic leave the relationship between stiﬀness and movement performance are still not fully explored. The 2. Materials and Methods practice of sports training reveals some questions regarding the role of potential elastic energy and stiﬀness as a key fac- A search of the PubMed and SPORTDiscus (EBSCO) biblio- tor responsible for determining performance. The reason for graphic electronic databases was conducted in October 2020. this may be the lack of longitudinal studies that have inves- The search terms used included (“leg” OR “lower limb” OR tigated the eﬀects of strength or power training on mechan- “lower extremity” OR “vertical” OR “joint”) AND (“stiﬀ- ical stiﬀness and consequently the relative lack of concrete ness”) AND (“run∗” OR “sprint∗” OR “jog∗”) AND recommendations that would allow to improve the speed- (“sport”). Review and original empirical research articles strength abilities of an athlete and their competitive sport and other related literature were selected based on the title results. The speculations concerning a desirable value of and abstract. Additionally, Google Scholar, ResearchGate, “leg-spring” stiﬀness that is the most advantageous for the and the reference lists of articles found were also checked accumulation of potential elastic energy and most favours to ensure no relevant studies were omitted during searching reaching maximal sport performance have been partially process. The following criteria were considered: examined [1, 3, 22, 24–28, 31–35]. However, no studies have provided unequivocal evidence for the presence of a desired (i) Papers written in English only value of “leg-spring” stiﬀness. Moreover, the conceptual and methodological confusion surrounding stiﬀness makes it (ii) Studies with human samples diﬃcult to organise the knowledge and compare the results (iii) No duplicates (papers found from several sources) obtained in the past research. Some reports refer to changes in stiﬀness under the (iv) No publication time restriction inﬂuence of sports training (e.g., plyometric or isometric). However, they take into account the stiﬀness of local struc- Only studies which had measures of mechanical (leg, tures (e.g., tendon) [36–46]; the determination of which vertical, or joint) stiﬀness during running performance were may be more complicated than the discussed values of leg, included in further analysis. Studies describing other human vertical, and joint stiﬀness. Several reports analysed the rela- movements (e.g., hopping), studies analysing the type of tionships between mechanical (leg, vertical, or joint) stiﬀness footwear, studies which failed to determine stiﬀness during and movement performance (e.g., during biomechanical the running performance (e.g., using oscillation technique, types of jumps) before and after the applied training pro- ultrasonography, or dynamometers or during other types gram. However, they did not concern the sport-speciﬁc of movement), and modelling-based studies or those con- movements , such as running [42, 47–50]. Chelly and Denis cerning diﬀerent types of stiﬀness than mechanical have [51] reported on positive relationships between maximal been omitted. After a detailed review of the full texts, 92 running velocity during 40 m sprint and vertical stiﬀness meet all the criteria (Figure 1) with a publication date during hopping task. Bret et al. [52] found that athletes between 1980 and 2021 (the range of the year’s results from with greater vertical stiﬀness obtained higher acceleration the selection process conducted). There were a number of between the ﬁrst (0–30 m) and the second (30–60 m) inter- papers that measured more than one type of stiﬀness and 4 Applied Bionics and Biomechanics Identiﬁcation of studies via databases and registers Records removed before Records identiﬁcation from: screening: PubMed (n = 542) Duplicate records removed SPORTDiscus (n = 345) (n = 339) Records screened Records excluded (n = 548) (n = 348) Reports sought for retrievel Reports not retrieved (n = 0) (n = 0) Reports assessed for eligibility Reports excluded: (n = 200) No stiﬀness analysis during running performance (n = 82) Footwear analysis (n = 8) Modelling-based studies (n = 18) Studies included in review (n = 92) Reports of included studies (n = 92) Figure 1: Selection process of papers focused on mechanical stiﬀness during running [54]. were therefore discussed in several subsections. The number of papers described mechanical stiﬀness was 68 for leg stiﬀ- ness, 65 for vertical stiﬀness and 23 for joint stiﬀness. COM Δy COM 3. Results and Discussion 3.1. Quasi-Stiﬀness during Running Tasks. Running is a com- ΔL plex motion that engages the whole body and it occurs in various forms in track and ﬁeld competitions or team sports games. Depending on the running distance, it is necessary to either reach submaximal velocity and cover the distance in the shortest possible time or keep the desired velocity for a certain distance. The running distance is covered through cyclic lower limb movements based on continuous accelera- tion and deceleration phases. Therefore, human running performance is similar to the motion of a bouncing ball (the so-called “bouncing gait”) and can be considered in accordance with the assumptions of spring-mass model (in GRF GRF which the lower limbs perform the role of “springs” respon- sible for the COM movement). Leg and vertical stiﬀness are Figure 2: An example of a simple spring-mass model used to commonly used to describe the mechanical properties of a estimate leg and vertical stiﬀness during vertical body “leg-spring” representing the lower limbs during running displacements only, where COM denotes the centre of mass, ΔL task [3]. Figure 2 shows a simple spring-mass model that is the change in “spring length” representing both lower limbs, Δy can be used to determine quasi-stiﬀness (leg or vertical) is the displacement of COM, and GRF means the ground reaction during vertical displacements only. The modiﬁcation of the force (based on Blickhan [19]). spring-mass model presented in Figure 3 also includes hori- zontal displacements. Therefore, leg and vertical stiﬀness can Screening Identiﬁcation Included Applied Bionics and Biomechanics 5 COM movement velocity), then quasi-stiﬀness (leg and vertical) does not signiﬁcantly change during running [55–57]. Δy COM Therefore, one of the most well researched topics to improve understanding of how quasi-stiﬀness is controlled during running is alterations in quasi-stiﬀness and other running ΔL variables with running velocity changes. Paradisis et al. [58] stated that quasi-stiﬀness (leg and vertical) are key to generating a higher top running velocity during a short sprint. Tables 1 and 2 list the studies on vertical and leg stiﬀ- ness that meet the inclusion criteria. 3.1.1. Vertical Stiﬀness. Vertical stiﬀness increases with run- ning velocity and stride frequency [33, 55, 58–68] and body mass [69]. Vertical stiﬀness also increases with the level of maturity [70, 71]. However, Meyers et al. [72] reported a Figure 3: An example of a spring-mass model used to estimate leg decrease in vertical stiﬀness with the level of maturity during and vertical stiﬀness during running tasks, where COM denotes 35 m sprint task. Arampatzis et al. [62] reported vertical centre of mass, ΔL is change in “spring length” representing both stiﬀness values between 30:8± 8:1 and 93:0±29:7 kN/m at lower limbs, and Δy is displacement of COM (based on running velocities from 2:6±0:2 to 6:6±0:2 m/s. Paradisis McMahon and Cheng [20]). et al. [58] obtained vertical stiﬀness values between 73:8± 9:7 and 105:1±16:8 kN/m at running velocities from 7:7± be estimated for vertical and horizontal movements. How- 0:3 to 9:4±0:4 m/s, whereas Kuitunen et al. [59] noted ever, vertical stiﬀness only considers vertical body displace- values between 103 and 171 kN/m at running velocities from ments. Leg stiﬀness (K ) and vertical stiﬀness (K ) are leg vert 6.7 to 10.3 m/s. Therefore, higher values of vertical stiﬀness expressed by the following equations: would be expected to be reached during maximal sprinting than during slower running conditions. Paradisis et al. [58] K = , reported that faster sprinters are characterised by shorter leg ΔL ground contact time, longer stride length, higher stride fre- ð1Þ quency, and greater vertical stiﬀness than slower sprinters K = , vert Δy during a 35 m sprint task. García-Pinillos et al. [66] also reported that elite level runners are characterised by greater where F is the deforming force (the causes of the change in vertical stiﬀness than novice runners during treadmill run- deformation), ΔL denotes the change in “leg-spring” length ning at velocities from 6.2 to 11.2 m/s. Rumpf et al. [73] (deformation), and Δy is the displacement of COM (defor- noted positive relationships between relative vertical stiﬀness mation). However, if the relationship between the deforming and sprint velocity, vertical COM displacement, relative force and the deformation is nonlinear or deformation is vertical peak force, and maximal “leg-spring” displacement plastic, the derivative (d) from Equations (2) or (3) should during 30 m treadmill sprint. be used [2]: An important factor that aﬀects vertical stiﬀness and stride frequency is fatigue. Dalleau et al. [74] reported nega- dF tive relationships between vertical stiﬀness and energy cost ð2Þ K = , leg of running, as determined from the O consumption. Heise dL and Martin [75] concluded from the negative relationships between vertical stiﬀness and aerobic demand that less dF K = : ð3Þ vert economical runners possess a more compliant “leg-spring” dy running style during ground contact phase. These ﬁndings The work performed by the deforming forces F equals may support the role of the mechanical stiﬀness in the met- the value of the potential elastic energy accumulated in the abolic energy cost of running at a given velocity (velocities: spring compliance elements. Potential elastic energy is pro- 3.35 m/s has been applied by Heise and Martin [75] and portional to the square of deformation and can be given by 5 m/s has been applied by Dalleau et al. [74]). Dutto and the following equation: Smith [76] observed that runners decreased vertical stiﬀness and stride frequency during a moderate-intensity treadmill 2 run to exhaustion. Changes in vertical stiﬀness were primar- E = ∙K∙Δl , ð4Þ pe 2 ily associated with increases in vertical COM displacement, and not to changes in the peak vertical ground reaction where E is the potential elastic energy, K denotes the stiﬀ- force. The runners altered their running kinematics to allow pe ness (longitudinal), and Δl is the deformation (change in for longer stride lengths and decreased stride frequency to length, displacement). maintain a constant running velocity. Decreases in vertical If stride frequency is relatively constant or the accelera- stiﬀness were proportional to decreases in stride frequency tion of the runners COM is relatively low (relatively constant [76]. Hobara et al. [64] noted that vertical stiﬀness peaked 6 Applied Bionics and Biomechanics Table 1: List of the studies on leg stiﬀness during running. Authors Year Number of participants Sport background Motor skill Submaximal constant load running test on treadmill Ache-Dias et al. [128] 2018 18 (males + females) Recreational runners (6 min at 9 km/h) Arampatzis et al. [62] 1999 13 runners Not mentioned Running at 2.5, 3.5, 4.5, 5.5, and 6.5 m/s Avogadro et al. [138] 2004 13 runners Healthy trained runners 3 min running on treadmill at 12, 14, 16, and 18 km/h Trained + untrained runners Bitchell et al. [97] 2019 7+13 runners Incremental running on treadmill Brocherie et al. [81] 2015 8 males International football players RAST test (6 × 35 m sprint) Cavagna et al. [63] 2005 4 males + 1 female Not mentioned Running at diﬀerent velocities (from 5.2 to 20.5 km/h) Choukou et al. [106] 2012 8 males Sprinters competing at the regional level 100 m sprint Coleman et al. [141] 2012 19 males Well-trained middle-distance runners Running at diﬀerent velocities (from 2.5 to 6.5 m/s) Cronin and Rumpf [69] 2014 16 males Young athletes 30 m sprint on treadmill Dal Pupo et al. [107] 2017 21 males Futsal players 10 m sprint Running on treadmill to exhaustion at a velocity 11 males + 4 females Dutto and Smith [76] 2002 Well-trained runners corresponding to 80% of the VO 2max Running on treadmill at 2.5 m/s (while using a range Farley and González [33] 1996 4 males Experienced treadmill runners of stride frequencies from 26% below to 36% above the preferred stride frequency) Ferris et al. [88] 1999 6 females Healthy 17 m running at 3.0 m/s Ferris et al. [87] 1998 5 humans Not mentioned Running at 5 m/s Running on treadmill to exhaustion at a velocity Fourchet et al. [102] 2015 11 males Highly trained middle-distance runners corresponding to 95% of the VO 2max García-Pinillos et al. [103] 2020 22 males Endurance runners 60 min running on treadmill Incremental running on treadmill at 10, 12, 14, 16, García-Pinillos et al. [66] 2019 22 males Novice and elite endurance runners and 18 km/h Gill et al. [155] 2020 16 males + 12 females Runners 32 m running at 3.3, 3.9, 4.8, and 5.6 m/s 77 males + 14 females Gindre et al. [83] 2016 Healthy and active 50 m running at 3.3, 4.2, and 5.0 m/s Giovanelli et al. [95] 2016 18 males Ultraendurance runners “Supermaratona dell’Etna” Girard et al. [150] 2015 13 males Team and racket sport background 3× 5s sprints on treadmill Girard et al. [80] 2017 20 males Field hockey players 6 × 30 s running on treadmill at 115% of the VO 2max 3 × 5 s sprints on treadmill + running on treadmill at Girard et al. [57] 2017 14 males Recreationally intermittent sports 10 and 20 km/h Physical education students practicing a Girard et al. [56] 2016 11 males 100, 200, and 400 m sprint on treadmill ﬁeld sport Recreational team or racket sports 12 × 40 m sprints Girard et al. [79] 2011 16 males athletes Girard et al. [96] 2017 18 males Physical education students 800 m running Girard et al. [91] 2010 12 triathletes Highly and well-trained triathletes 5000 m running at self-selected velocity Applied Bionics and Biomechanics 7 Table 1: Continued. Authors Year Number of participants Sport background Motor skill Girard et al. [93] 2013 12 males National level triathletes 5000 m running at self-selected velocity Girard et al. [78] 2011 13 males Young soccer players 6 × 20 m sprints 8 males + 4 females Günther and Blickhan [122] 2002 Sports students and active sportsmen Running at convenience velocity (from 3.7 to 5.6 m/s) He et al. [61] 1991 4 males Healthy Running on treadmill at 2.0, 3.0, 4.0, 5.0, and 6.0 m/s Heise and Martin [75] 1998 16 males Recreational runners 15 m running at 3.35 m/s Hobara et al. [64] 2010 8 males Well-trained sprinters and runners 400 m sprint 11 males + 5 females Hunter and Smith [105] 2007 Recreational runners 1 h running on treadmill at constant velocity Joseph et al. [148] 2013 20 males Various sports 10 m running at 3.35 m/s Joseph et al. [121] 2014 20 males Various sports 10 m running at 3.35 m/s Running on treadmill to exhaustion at velocity Hayes and Caplan [101] 2014 6 runners Subelite middle-distance runners corresponding to VO 2max Li et al. [104] 2021 28 males Collegiate distance runners Running at 12, 14, and 16 km/h Liew et al. [143] 2017 20 females Recreational runners 20 m running at 5.0 m/s Liew et al. [110] 2021 10 males + 7 females Healthy 45 cut at 4 m/s approach velocity Lorimer et al. [53] 2018 12 males Well-trained triathletes 2 min running on treadmill at 3.0, 3.3, 3.7, and 4.2 m/s Lum et al. [129] 2019 14 males Moderately trained endurance runners 10 km running on treadmill at 10 km/h and 12 km/h Lussiana and Gindre [84] 2016 31 runners Well-trained runners 15 min running at self-selected velocity Lussiana et al. [85] 2017 58 males Recreational runners 5 min running on treadmill at 12 km/h Performance of each participant was examined during 43 males + 36 females Meur et al. [94] 2013 Elite triathletes the running section of the World Triathlon Grand Final Meyers et al. [67] 2019 375 boys Biweekly physical education classes 30 m sprint Meyers et al. [71] 2016 189 boys Biweekly physical education classes 30 m sprint Meyers et al. [72] 2017 344 boys Biweekly physical education classes 35 m sprint 80 m sprint with diﬀerent stride frequencies 20 males + 20 females Monte et al. [65] 2017 Elite and intermediate sprinters (preferred and +15%, +30%, −15%, and −30% of the self-selected) 6 min running on treadmill at theoretical half- Monte et al. [68] 2020 32 males Endurance runners marathon running velocity Running on treadmill at 3:33, 3:89, 4:44, 5:0, 5:56, 6:11 Physical education students + elite , and 6:67 m/s + 10 m running at 4:0, 5:0, 6:0, and 7:0 Morin et al. [139] 2005 8+10 males middle − distance runners m/s and maximal velocity Morin et al. [55] 2006 8 males Physical education students 100 m sprint Physically active physical education Morin et al. [92] 2012 11 males Running on treadmill at 10 and 20 km/h students Sprinter, 2 jumpers, 5 pole vaulters, and Nagahara and Zushi [127] 2017 9 males 60 m sprint a decathlete 8 Applied Bionics and Biomechanics Table 1: Continued. Authors Year Number of participants Sport background Motor skill Pappas et al. [147] 2014 22 males Healthy physical education students Running on treadmill at 4.44 m/s Paradisis et al. [58] 2019 50 males Subelite sprinters 35 m sprint Powell et al. [168] 2017 20 females Recreational athletes Running at self-selected velocity Running to exhaustion at constant velocity Rabita et al. [100] 2013 12 males Runners corresponding to VO 2max Running to exhaustion at a velocity corresponding to 6 males + 3 females Rabita et al. [99] 2011 Elite triathletes 95% of the VO 2max Rogers et al. [86] 2017 11 males Highly trained middle-distance runners 50 m sprint Physically active and trained a Rumpf et al. [73] 2015 32 children 30 m sprint on treadmill minimum of two times per week Rumpf et al. [70] 2013 74 boys Physically active 30 sprint on treadmill Shih et al. [114] 2019 20 males + 20 females Recreational runners 14 m running at 3.4 m/s 14 males + 14 females Sinclair et al. [145] 2015 Recreational runners Running at 4.0 m/s Staﬁlidis and Arampatzis [90] 2007 10 male Experienced sprinters 60 m sprint Weir et al. [98] 2020 13 males Recreational runners Prolonged running on treadmill (2 × 21 min) Williams III et al. [166] 2004 18 males + 22 females Healthy 25 m running at 3.35 m/s Yin et al. [109] 2020 78 males Healthy amateur runners 15 m running at 3.3 m/s Applied Bionics and Biomechanics 9 Table 2: List of the studies on vertical stiﬀness during running. Authors Year Number of participants Sport background Motor skill Submaximal constant load running test on treadmill Ache-Dias et al. [128] 2018 18 (males + females) Recreational runners (6 min at 9 km/h) Arampatzis et al. [62] 1999 13 runners Not mentioned Running at 2.5, 3.5, 4.5, 5.5, and 6.5 m/s Trained + untrained runners Bitchell et al. [97] 2019 7+13 runners Incremental running on treadmill Brocherie et al. [81] 2015 8 males International football players RAST test (6 × 35 m sprint) Running at a variety of diﬀerent constant velocities Cavagna et al. [60] 1988 10 males Untrained (range of very low velocities) 4 males + 1 female Cavagna et al. [63] 2005 Not mentioned Running at diﬀerent velocities (from 5.2 to 20.5 km/h) Cherif et al. [77] 2017 21 males Healthy and active 5× 5s sprints on treadmill Choukou et al. [106] 2012 8 males Sprinters competing at the regional level 100 m sprint Cronin and Rumpf [69] 2014 16 males Young athletes 30 m sprint on treadmill Dal Pupo et al. [107] 2017 21 males Futsal players 10 m sprint Running on treadmill (4 min at a velocity Dalleau et al. [74] 1998 8 males Healthy corresponding to 90% of the VO ) 2max Running on treadmill to exhaustion at a velocity 11 males + 4 females Dutto and Smith [76] 2002 Well-trained runners corresponding to 80% of the VO 2max Running on treadmill at 2.5 m/s (while using a range Farley and González [33] 1996 4 males Experienced treadmill runners of stride frequencies from 26% below to 36% above the preferred stride frequency) Ferris et al. [88] 1999 6 females Healthy 17 m running at 3.0 m/s Ferris et al. [87] 1998 5 humans Not mentioned Running at 5 m/s Running on treadmill to exhaustion at a velocity Fourchet et al. [102] 2015 11 males Highly trained middle-distance runners corresponding to 95% of the VO 2max García-Pinillos et al. [103] 2020 22 males Endurance runners 60 min running on treadmill Incremental running on treadmill at 10, 12, 14, 16, García-Pinillos et al. [66] 2019 22 males Novice and elite endurance runners and 18 km/h Gindre et al. [83] 2016 77 males + 14 females Healthy and active 50 m running at 3.3, 4.2, and 5.0 m/s Giovanelli et al. [172] 2017 12 males Ultraendurance runners 6 h running “6 ore Città di Buttrio” Giovanelli et al. [95] 2016 18 males Ultraendurance runners “Supermaratona dell’Etna” Girard et al. [150] 2015 13 males Team and racket sport background 3× 5s sprints on treadmill 6 × 30 s running on treadmill at 115% of the VO Girard et al. [80] 2017 20 males Field hockey players 2max 3 × 5 s sprints on treadmill + running on treadmill at Girard et al. [57] 2017 14 males Recreationally intermittent sports 10 and 20 km/h Physical education students practicing a Girard et al. [56] 2016 11 males 100, 200, and 400 m sprint on treadmill ﬁeld sport Girard et al. [79] 2011 16 males Recreational team or racket sports athletes 12 × 40 m sprints Girard et al. [96] 2017 18 males Physical education students 800 m running 10 Applied Bionics and Biomechanics Table 2: Continued. Authors Year Number of participants Sport background Motor skill Girard et al. [91] 2010 12 triathletes Highly and well-trained triathletes 5000 m running at self-selected velocity Girard et al. [93] 2013 12 males National level triathletes 5000 m running at self-selected velocity Girard et al. [78] 2011 13 males Young soccer players 6 × 20 m sprints Running on treadmill to exhaustion at velocity Hayes and Caplan [101] 2014 6 runners Subelite middle-distance runners corresponding to VO 2max He et al. [61] 1991 4 males Healthy Running on treadmill at 2.0, 3.0, 4.0, 5.0, and 6.0 m/s Heise and Martin [75] 1998 16 males Recreational runners 15 m running at 3.35 m/s Hobara et al. [64] 2010 8 males Well-trained sprinters and runners 400 m sprint Hunter [157] 2003 9 males + 7 females Not mentioned 10 min running on treadmill at self-selected velocity 11 males + 5 females Hunter and Smith [105] 2007 Recreational runners 1 h running on treadmill at constant velocity Joseph et al. [148] 2013 20 males Various sports 10 m running at 3.35 m/s Joseph et al. [121] 2014 20 males Various sports 10 m running at 3.35 m/s Kuitunen et al. [59] 2002 10 males Sprinters Sprint at 70%, 80%, 90%, and maximal velocity Lorimer et al. [53] 2018 12 males Well-trained triathletes 2 min running on treadmill at 3.0, 3.3, 3.7, and 4.2 m/s Lum et al. [129] 2019 14 males Moderately trained endurance runners 10 km running on treadmill at 10 km/h and 12 km/h Luhtanen and Komi [156] 1980 6 athletes Track and ﬁeld athletes Running at 40%, 60%, 80%, and maximal velocity Lussiana et al. [85] 2017 58 male Recreational runners 5 min running on treadmill at 12 km/h McMahon et al. [82] 1987 6 males Healthy 30 m constant velocity running Performance of each participant was examined during 43 males + 36 females Meur et al. [94] 2013 Elite triathletes the running section of the World Triathlon Grand Final Meyers et al. [67] 2019 375 boys Biweekly physical education classes 30 m sprint Meyers et al. [71] 2016 189 boys Biweekly physical education classes 30 m sprint Meyers et al. [72] 2017 344 boys Biweekly physical education classes 35 m sprint 80 m sprint with diﬀerent stride frequencies 20 males + 20 females Monte et al. [65] 2017 Elite and intermediate sprinters (preferred and +15%, +30%, −15%, and −30% of the self-selected) 6 min running on treadmill at theoretical half- Monte et al. [68] 2020 32 males Endurance runners marathon running velocity Running on treadmill at 3:33, 3:89, 4:44, 5:0, 5:56, 6:11 Physical education students + elite middle − Morin et al. [139] 2005 8 + 10 males , and 6:67 m/s + 10 m running at 4:0, 5:0, 6:0, and 7:0 distance runners m/s and maximal velocity Morin et al. [55] 2006 8 males Physical education students 100 m sprint Morin et al. [92] 2012 11 males Physically active physical education students Running on treadmill at 10 and 20 km/h Sprinter, 2 jumpers, 5 pole vaulters, and Nagahara and Zushi [127] 2017 9 males 60 m sprint a decathlete Pappas et al. [147] 2014 22 males Healthy physical education students Running on treadmill at 4.44 m/s Applied Bionics and Biomechanics 11 Table 2: Continued. Authors Year Number of participants Sport background Motor skill Paradisis et al. [58] 2019 50 males Subelite sprinters 35 m sprint Running to exhaustion at constant velocity Rabita et al. [100] 2013 12 males Runners corresponding to VO 2max Running to exhaustion at a velocity corresponding to 6 males + 3 females Rabita et al. [99] 2011 Elite triathletes 95% of the VO 2max Rogers et al. [86] 2017 11 males Highly trained middle-distance runners 50 m sprint Submaximal running tests on treadmill (10 min at Roschel et al. [130] 2015 15 humans Recreational runners 12 km/h and 90% ventilatory threshold intensity) Physically active and trained a minimum of Rumpf et al. [73] 2015 32 children 30 m sprint on treadmill two times per week Rumpf et al. [70] 2013 74 boys Physically active 30 sprint on treadmill Staﬁlidis and Arampatzis [90] 2007 10 males Experienced sprinters 60 m sprint 28 males + 26 females Vincent et al. [146] 2020 Recreational runners Running on treadmill at self-selected velocity Yin et al. [109] 2020 78 males Healthy amateur runners 15 m running at 3.3 m/s 12 Applied Bionics and Biomechanics ning velocity [33]. Therefore, humans can change the stiﬀ- at the 50-100 m interval and consistently decreased from the middle to the later part of the 400 m sprint. Morin et al. [55] ness of the “leg-spring” during running tasks, which can be reported that the decrease in 100 m sprint performance useful, for example, when running on a variety of surfaces (decreased maximal and mean velocity) in fatigue conditions with diﬀerent stiﬀness. Runners can adjust leg stiﬀness for induced by the four repetitions of this running task was also their ﬁrst step on a surface with diﬀerent compliances allow- accompanied by decreases in vertical stiﬀness and step fre- ing them to maintain similar running mechanics on diﬀerent quency and increased ground contact time [55]. Girard surfaces [87, 88]. By comparison with a hard surface, if the et al. [56] showed that a decrease in running velocity in surface is soft and compliant, more time is required to the last 50 m distance interval of a 100, 200, and 400 m sprint reverse the COM downward velocity and perform take-oﬀ performances was accompanied by a decrease in stride [89]. Staﬁlidis and Arampatzis [90] observed that surfaces length, stride frequency, and vertical stiﬀness and by an of diﬀerent compliances (stiﬀness from 550 to 5500 kN/m) increase in ground contact time. The magnitude of decre- did not have any clear eﬀect on 60 m sprint performance ment in vertical stiﬀness increased with sprint distance and on the leg and vertical stiﬀness values. However, as the [56]. Other studies have also discovered signiﬁcant relation- optimal track stiﬀness may be inﬂuenced by each of the run- ship between decrements in both stride frequency and verti- ners’ inherent stiﬀness characteristics, their shoes, and key cal stiﬀness and a progressive slowing in running velocity running spatiotemporal characteristics, the lack of any clear after two sets of ﬁve 5 s sprints [77], three sets of ﬁve 5 s association between track stiﬀness to running performance sprints [57], six 20 m sprints [78], twelve 40 m sprints [79], is not necessarily unsurprising [90]. six 30 s runs at 5.5 m/s [80], and during running anaerobic In contrast to vertical stiﬀness, leg stiﬀness is not sprint test (RAST test, 6 × 35 m) [81]. Therefore, it can be strongly related to the aerobic demand of running and concluded that fatigue causes decreased vertical stiﬀness fatigue [55–57, 76, 80, 81, 91–98]. The exceptions are the during running tasks, resulting in lower eﬃciencies of run to exhaustion at the velocity at VO [99–102] and 2max movement with a concomitant increase in metabolic cost. 60 min time trial run [103] during which leg stiﬀness Athletes characterised by enough high vertical stiﬀness dur- decreases and vertical stiﬀness remains relatively constant. ing running may execute running tasks more economically Dutto and Smith [76] reported that leg stiﬀness decreased (with less vertical COM displacements) and with higher per- initially from the beginning to 25% duration time in formance through gaining a greater potential elastic energy moderate-intensity treadmill run to exhaustion and then return from musculotendinous structures. remained relatively constant. Decrease in leg stiﬀness was It is also possible to change (decrease) leg and vertical stiﬀ- associated with increased changes in “leg-spring” length ness by running with diﬀerent (increased) knee ﬂexion (the during ground contact phase and with decrease in the peak so-called “Groucho running”). This type of running technique vertical ground reaction force [76]. Li et al. [104] reported lowers ground reaction forces and reduces ﬂight time, but a negative relationship between running economy and leg requires increased metabolic power (oxygen consumption) stiﬀness. Hobara et al. [64] noted that leg stiﬀness peaked [82–85]. The above phenomenon should be taken into at ﬁrst 50 m interval and remained constant from next account in particular by team sport games coaches, where 50 m interval to ﬁnish during 400 m sprint. Morin et al. technique like “Groucho running” is often used. This running [55] found that leg stiﬀness and peak vertical ground reac- style is necessary to minimise ﬂight time and therefore to max- tion force remained relatively constant in fatigue conditions imise the potential to decelerate and change direction quickly. induced by four repetitions of 100 m sprints. Similar conclu- sions were obtained by Brocherie et al. [81] during RAST 3.1.2. Leg Stiﬀness. In contrast to vertical stiﬀness, leg stiﬀ- test with additional accompanying decrease in stride fre- ness (with increasing running velocity) remains relatively quency and increase in ground contact time. Leg stiﬀness constant or changes (increase) to a smaller extent during decreases during the last 50 m distance interval of a 100, running [33, 55, 56, 58, 61–63, 65–68, 81]. However, leg stiﬀ- 200, and 400 m sprint performances which were smaller ness increases with the level of maturity [70, 71]. Arampatzis than decreases in vertical stiﬀness and limited to 200 and et al. [62] reported leg stiﬀness values between 25:3±4:2 400 m tasks [56]. Other studies conﬁrm that decreases in and 35:2±4:3 kN/m at running velocities from 2:6±0:2 to leg stiﬀness due to fatigue-induced reduction in sprinting 6:6±0:2 m/s. Paradisis et al. [58] obtained leg stiﬀness velocity were much smaller than decreases in vertical stiﬀ- values between 12:7±2:3 and 15:5±2:7 kN/m at running ness [55, 57, 78, 79, 105–107]. velocities from 7:7±0:3 to 9:4± 0:4 m/s. Paradisis et al. At relatively low running velocity, runners predomi- [58] reported that faster sprinters are characterised by nantly hit the ground with the heel (heel strike), whereas greater leg stiﬀness than slower sprinters during 35 m sprint at higher running velocity (sprinting), the foot strike is usu- task. In contrast, García-Pinillos et al. [66] observed that leg ally performed with the forefoot [59, 108]. Rearfoot strike stiﬀness has similar values in elite and novice runners during pattern runners touching the ground with heel and using a treadmill running at velocities from 6.2 to 11.2 m/s. Rogers rolling foot strategy result in increased ground contact time. et al. [86] reported that leg stiﬀness has relationships with In contrast, forefoot runners immediately shift from energy running economy (negative) and maximal sprinting velocity absorption phase to the propulsion phase which will (positive). decrease ground contact times and hence increase the rate However, it is possible to change leg stiﬀness value more of the ground reaction force application [109]. Therefore, than twofold by increasing stride frequency at a given run- using the forefoot strike pattern may also be more beneﬁcial Applied Bionics and Biomechanics 13 to team sport players than rearfoot strike pattern. Forefoot strike pattern runners are characterised by greater leg stiﬀ- ness, greater peak vertical ground reaction force, shorter contact time, and smaller “leg-spring” change compared with rearfoot strike pattern runners [109]. hip Leg stiﬀness is also likely to inﬂuence the ability to eﬀec- tively execute change of direction tasks. Greater leg stiﬀness allows to less loss of velocity when changing direction [110]. knee An inability to preplan a side-step cutting manoeuvre may result in a greater decrease in velocity and reduce cut angle. Reduced preplanning time available for side-step cutting ankle increased leg stiﬀness. Moreover, unanticipated cutting sig- niﬁcantly increased leg stiﬀness compared to the anticipated cutting [110]. The diﬀerence in behaviour between vertical stiﬀness Figure 4: An example of torsional spring model used to estimate and leg stiﬀness during running tasks is potentially due ankle, knee, and hip joint stiﬀness during running tasks, where to the fact that leg stiﬀness is mainly determined through α denotes the ankle joint angle, α is the knee joint angle, ankle knee the mechanical properties and activation of lower limb and α is the hip joint angle (based on Farley et al. [111]). hip musculotendinous system with only small “leg-spring” stiﬀness variations depending on velocity. Vertical stiﬀ- or deformation is plastic, the derivative (d) from Equation ness is not only reliant on the properties and activation (6) should be used [2]: of the lower limb but also on the whole body [22]. More- over, COM displacement depends on the spatial position dM K = : ð6Þ of each body part, including the upper limbs. The total joint dα mass of the body (COM) is not concentrated at the upper end of the “leg-spring”. Therefore, the displace- The analysis of lower limb joint springs (hip, knee, and ment of the COM is not the same as the displacement ankle) oﬀers a diﬀerent view of “leg-spring” stiﬀness than of the upper end of the “leg-spring” [3]. Diﬀerences the quasi-stiﬀness. Table 3 lists the studies on joint stiﬀness between leg and vertical stiﬀness may also be due to that meet the inclusion criteria. Unfortunately, only a few the hip joint displacement. It has a much smaller eﬀect manuscripts consider all three lower limb joint springs or on vertical stiﬀness. even hip joint stiﬀness [53, 112–114]. Hip joint stiﬀness increases with running velocity [113]. Jin and Hahn [113] 3.2. Joint Stiﬀness during Running Tasks. Quasi-stiﬀness is a stated that hip joint has a crucial role during swing phase concept that considers the limb (leg stiﬀness) or body (verti- for work and power generation. cal stiﬀness) as a whole system rather than only the muscu- lotendinous system. Therefore, quasi-stiﬀness also depends 3.2.1. Knee and Ankle Joint Springs. Knee joint stiﬀness on the stiﬀness of other tissues, such as ligaments, blood ves- increased with running velocity [59, 62, 113, 115, 116]. sels, and bones. The elastic properties and the ability to accu- Arampatzis et al. [62] reported knee joint stiﬀness values mulate potential elastic energy are diﬀerent for each of these ° between 6:8±4:1 and 19:1±8:9 Nm/ at running velocities tissues [2]. However, the “leg-spring” model is dependent from 2:6±0:2 to 6:6±0:2 m/s. Kuitunen et al. [59] obtained also on hip, knee, and ankle kinematics. Therefore, the tor- knee joint stiﬀness values between 17 and 24 Nm/ at sional spring model oﬀers a diﬀerent view of “leg-spring” running velocities from 6.7 to 10.3 m/s. Knee joint stiﬀness stiﬀness than the spring-mass models. By using the torsional during initial ground contact increases also with running spring model, it is possible to estimate the joint stiﬀness velocity [116]. Tam et al. [115] reported that knee joint stiﬀ- values of the main joints of lower limb during vertical and ness has positive relationships with rectus femoris activation horizontal movements. Figure 4 shows an example of the and rectus femoris : biceps femoris coactivation ratio. Jin and torsional spring model that can be used in the determination Hahn [113] stated that knee joint has a crucial role during of ankle, knee, and hip joint stiﬀness during vertical and swing phase for energy absorption. horizontal displacements. In turn, ankle joint stiﬀness (with increasing running For rotational motions, joint stiﬀness (K ) is expressed joint velocity) remains relatively constant or changes (increase) by the following equation: to a smaller extent compared to knee joint stiﬀness [59, 62, 115, 117, 118]. Stefanyshyn and Nigg [117] and Kuitunen et al. [59] argued that ankle joint stiﬀness is depen- K = , ð5Þ joint dent on the task activity rather than on the individual. Δα Arampatzis et al. [62] reported ankle joint stiﬀness values between 16:4±5:5 and 20:5±8:2 Nm/ at running velocities where M denotes the deforming torque and Δα is the angle from 2:6± 0:2 to 6:6±0:2 m/s. Stefanyshyn and Nigg [117] of deformation. However, if the relationship between the reported ankle joint stiﬀness values of 5.7 Nm/ in running deforming torque and the angle of deformation is nonlinear at 4 m/s and 7.4 Nm/ in sprinting at velocities from 7.1 to 14 Applied Bionics and Biomechanics Table 3: List of the studies on joint stiﬀness during running. Authors Year Number of participants Sport background Motor skill Stiﬀness measure 7 males + 9 females and Adult well − trained sprinters + well − Aeles et al. [119] 2018 10 m sprint Ankle joint 11 males + 10 females trained young athletes Arampatzis et al. [62] 1999 13 runners Not mentioned Running at 2.5, 3.5, 4.5, 5.5, and 6.5 m/s Knee joint, ankle joint Running on treadmill (30 min at Chan et al. [126] 2020 20 males Recreational distance runners Knee joint, ankle joint self-reported velocity) Internationally competitive sprint Maximal sprint starts with 10 m Charalambous et al. [120] 2012 1 male Ankle joint hurdle athlete acceleration Running at convenience velocity Günther and Blickhan [122] 2002 8 males + 4 females Sports students and active sportsmen Knee joint, ankle joint (from 3.7 to 5.6 m/s) Hamill et al. [125] 2014 27 males + 13 females Runners 25 m running at 3.5 m/s Knee joint, ankle joint Hip joint, knee joint, Hamill et al. [112] 2009 33 runners Runners Running on treadmill at 3.8 m/s ankle joint Running on treadmill (from 1.8 to Hip joint, knee joint, 5 males + 5 females Jin and Hahn [113] 2018 Healthy 3.8 m/s) ankle joint Joseph et al. [148] 2013 20 males Various sports 10 m running at 3.35 m/s Knee joint, ankle joint Sprint at 70%, 80%, and 90% and Kuitunen et al. [59] 2002 10 males Sprinters Knee joint, ankle joint maximal velocity 2 min running on treadmill at 3.0, 3.3, Hip joint, knee joint, Lorimer et al. [53] 2018 12 males Well-trained triathletes 3.7, and 4.2 m/s ankle joint 11 males + 16 females Mager et al. [118] 2018 Healthy students Running at self-selected velocity Ankle joint Melcher et al. [124] 2017 13 males Well-trained runners 25 m running with a 15 m acceleration Knee joint, ankle joint Sprinter, 2 jumpers, 5 pole vaulters, Nagahara and Zushi [127] 2017 9 males 60 m sprint Knee joint, ankle joint and a decathlete Powell et al. [167] 2014 20 females Recreational athletes Running at self-selected velocity Ankle joint Hip joint, knee joint, Shih et al. [114] 2019 20 males + 20 females Recreational runners 14 m running at 3.4 m/s ankle joint Sinclair et al. [145] 2015 14 males + 14 females Recreational runners Running at 4.0 m/s Knee joint, ankle joint Running at 4 m/s and maximal Stefanyshyn and Nigg [117] 1998 10 males Distance runners and sprinters Ankle joint acceleration sprint Tam et al. [115] 2017 14 males Elite runners 60 m running at 12 and 20 km/h Knee joint, ankle joint Tam et al. [123] 2019 30 males Runners 60 m running at 3.3 m/s Knee joint, ankle joint 70 m running at 2.5, 3.5, 4.5, and 5.5 m/s Verheul et al. [116] 2017 26 (males + females) Runners Knee joint and maximal velocity Prolonged running on treadmill Weir et al. [98] 2020 13 males Recreational runners Knee joint, ankle joint (2 × 21 min) Williams III et al. [166] 2004 18 males + 22 females Healthy 25 m running at 3.35 m/s Knee joint Applied Bionics and Biomechanics 15 inﬂuence joint stiﬀness [124–126]. Change in foot strike pat- 8.4 m/s. Aeles et al. [119] did not obtain signiﬁcant diﬀer- ences in ankle joint stiﬀness between young and adult well- tern from rearfoot strike to midfoot strike may cause a trained sprinters during 10 m sprint (ﬁrst stance phase). decrease in ankle joint stiﬀness and increase in knee joint Charalambous et al. [120] noted a positive relationship stiﬀness [126]. Melcher et al. [124] noted that knee joint between ankle joint stiﬀness on the ascending limb and the range of motion, knee joint moment, and ankle joint stiﬀ- horizontal COM velocity at the end of the ﬁrst stance phase. ness were lower during imposed forefoot strike compared Kuitunen et al. [59] reported a negative relationship between with rearfoot strike pattern. ankle joint stiﬀness and ground contact time. Jin and Hahn [113] stated that ankle joint has a crucial role during stance 3.3. The Eﬀect of Training on Mechanical Stiﬀness. The phase for energy generation in running. Higher ankle joint assessment of training eﬀects in runners seems to be the stiﬀness results in more positive work performed and power most correct when it is carried out with the use of running generation [113]. tests. Therefore, the possible changes in mechanical stiﬀness Larger peak moment and mechanical power values at the can then be determined based on a measurement during ankle and knee joints are observed with increasing running running. Table 4 lists the longitudinal studies that meet this velocity [62]. Running velocity also inﬂuences the change criterion. Nagahara and Zushi [127] have examined well- in the angle at the ankle and knee joint [62]. With increasing trained male athletes during 60 m sprints before and after a running velocity, larger changes are observed in the knee 6-month winter training session (combining of plyometric, joint stiﬀness than in the ankle joint stiﬀness [59, 62]. There- sprint, weight, circuit, and individualised trainings). How- fore, the increase in “leg-spring” stiﬀness may be mainly ever, the participants specialized in diﬀerent events (includ- caused by the increase in knee joint stiﬀness. Joseph ing a sprinter, two jumpers, ﬁve pole vault jumpers, and a et al. [121] stated that knee joint mechanics may be decathlete) and followed their own training plans during altered to maintain consistent levels of leg and vertical stiﬀ- the winter training period. Nagahara and Zushi [127] ness. Arampatzis et al. [62] suggested that with increasing reported that the development of maximal velocity sprinting running velocity, the athletes alter the knee joint stiﬀness performance through longer step length was accompanied ﬁrst. In accordance with the assumptions of the torsional by increases in vertical and ankle joint stiﬀness, although spring model, “leg-spring” stiﬀness depends on the stiﬀness leg and knee joint stiﬀness remained constant. Ache-Dias of three joint springs (in the ankle, knee, and hip joint). et al. [128] reported that the addition of 4 weeks of jump The contribution to the overall “leg-spring” stiﬀness of each interval training into a continuous endurance treadmill training program induced an increase in the stiﬀness (leg joint spring is diﬀerent. According to Equation (7), the greatest contribution to the overall stiﬀness value of the and vertical) and stride frequency and a decrease in stride “leg-spring” will have the most compliant joint spring: length. However, these changes do not aﬀect running econ- omy. Lum et al. [129] noted that 6 weeks of intermittent sprint training and plyometric training led to improvement K = , ð7Þ leg‐spring in 10 km performance in moderately trained endurance 1/K +1/K +1/K ðÞ ðÞ ankle knee hip runners despite reduction in weekly training mileage. The improvement in running performance was accompanied by where K is the “leg-spring” stiﬀness, K denotes leg−spring ankle an increase in power, whereas leg and vertical stiﬀness the ankle joint stiﬀness, K is the knee joint stiﬀness, and remained relatively constant. Similarly, Roschel et al. [130] knee K is hip joint stiﬀness. did not report changes in vertical stiﬀness in recreational hip Therefore, depending on the running velocity, theoreti- runners after 6 weeks of resistance training or whole-body cally, knee joint stiﬀness or ankle joint stiﬀness will have vibration training. the most inﬂuence of overall “leg-spring” stiﬀness. Ankle In contrast, Rumpf et al. [73] observed decreases in 30 m joint spring should be more compliant than knee joint spring treadmill sprint time, relative leg stiﬀness, and relative verti- cal stiﬀness during substantial running velocity (sprinting). Günther and in youth after 6 weeks of resisted sled towing Blickhan [122] concluded that the knee joint is always stiﬀer training. Stride frequency, average power, peak horizontal and more extended than the ankle joint. However, this state- force, average relative vertical forces, and vertical displace- ment only seems true from a certain running velocity and ment increased. While this study reported decreased sprint may depend on the running technique [62]. times, the decrease in stiﬀness might be viewed as disadvan- Lower ankle joint stiﬀness and greater knee joint stiﬀness tageous in the long term as these reductions in stiﬀness may were associated with lower oxygen consumption during con- actually increase foot contact time and result in a reduction stant velocity running. More economical runners are charac- in stride frequency and ultimately running speed. terised also with short ground contact times and greater While McMahon et al. [26] and Brazier et al. [22] have stride frequencies [123]. Weir et al. [98] reported that knee recommended that in terms of training to increase “leg- joint stiﬀness increased and ankle joint stiﬀness decreased spring” stiﬀness, resistance training should be performed with running time during a prolonged treadmill run. More- with loads above 75% of 1 repetition maximum and should over, Melcher et al. [124] noted that oxygen consumption, precede high-intensity plyometric and power training, there ankle joint moment, and knee joint stiﬀness were greater is still no clear answer how training could aﬀect mechanical during imposed forefoot strike pattern compared with rear- stiﬀness during running due to a very small number of stud- foot strike pattern. Therefore, the foot strike angle can also ies on this topic. Papers that did not assess mechanical 16 Applied Bionics and Biomechanics Table 4: List of the longitudinal studies on training eﬀects on mechanical stiﬀness. Authors Year Number of participants Sport background Motor skill Stiﬀness measure Submaximal constant load running test Ache-Dias et al. [128] 2018 18 (males + females) Recreational runners Leg, vertical on treadmill (6 min at 9 km/h) 10 km running on treadmill at 10 km/h Lum et al. [129] 2019 14 males Moderately trained endurance runners Leg, vertical and 12 km/h Sprinter, 2 jumpers, 5 pole vaulters, Leg, vertical, knee Nagahara and Zushi [127] 2017 9 males 60 m sprint and a decathlete joint, ankle joint Submaximal running tests on treadmill Roschel et al. [130] 2015 15 humans Recreational runners (10 min at 12 km/h and 90% ventilatory Vertical threshold intensity) Physically active and trained a Rumpf et al. [73] 2015 32 children 30 m sprint on treadmill Leg, vertical minimum of two times per week Applied Bionics and Biomechanics 17 hits the ground, therefore reducing the amount of muscle stiﬀness changes (caused by training) during running task were omitted from this review. Perhaps due to the increase stretch during initial ground contact and absorption in rate of force development, some power (plyometric) train- (braking) phase [32]. However, to generate suﬃciently large ankle joint torques, the ankle plantar ﬂexor muscles shorten ing would result in an increase in mechanical stiﬀness. How- ever, it is not known how power training aﬀects leg, vertical, throughout the entire ground contact phase (or work in or joint stiﬀness during running, although it is presumably quasi-isometric conditions during the early part of the known how mechanical stiﬀness changes might aﬀect run- ground contact phase), despite the entire musculotendinous ning performance. Moreover, there is a lack of studies on units undergoing a SSC [134]. Most of the stretch can be taken up by the tendons, resulting in potential elastic energy training eﬀects in elite athletes. There is also the question of obtaining the possible desired “leg-spring” stiﬀness value storage in these spring elements [32]. The musculotendinous under the inﬂuence of training. system design of the ankle plantar ﬂexors supports the stor- age and utilization of tendon elastic strain energy over mus- 3.4. Desired “Leg-Spring” Stiﬀness. The total mechanical cular work [134, 135]. In muscle-tendon units with long energy involved in human body movement is the sum of compliant tendons (such as the Achilles tendon), the tendons kinetic and potential energy. With each running stride, the can store a high amount of potential elastic energy; therefore, kinetic energy change of horizontal motion (related to the during the push-oﬀ phase, less work needs to be performed braking action of the ground) and the gravitational potential by the muscles due the energy returned by the tendons. For energy change due to the (vertical) displacements of the run- example, the Achilles tendon, which is long and compliant, ners COM. Potential elastic energy is associated with the is able to contribute about 35% of the mechanical energy nec- change in the kinetic energy of the body being moved. Due essary for performing each running stride (obviously, the to braking and lowering of the runners COM in the initial entire “leg-spring” is formed also by other soft tissues with part (absorption) of the ground contact phase during run- elastic properties) [32]. The compliance of the serial elastic ning, the decrease in the kinetic energy and gravitational elements allows the muscle ﬁbres to contract at preferred potential energy is partially stored in the form of potential velocities for maximal power output and eﬃciency (accord- elastic energy by the stretched musculotendinous groups. ing to force-length curve) and allows to deactivating ﬁbres The ability of the musculotendinous groups to store and during shortening periods. Therefore, the muscle fascicles return potential elastic energy increases the mechanical shorten at a much slower velocity (often very diﬀerent from energy supplied by active contracting muscles used in the the velocity of the whole musculotendinous units) with high take-oﬀ phase. Consequently, the total mechanical energy velocity shortening during take-oﬀ in running achieved by supplied by the entire muscle-tendon unit during the pro- recoil of the serial elastic elements [134, 136, 137]. pulsion phase can obtain greater values and/or less work For a given human body modelled as a spring-mass needs to be performed by the muscles’ contractile elements system (with speciﬁc body mass, leg-spring length, the hori- [3, 6]. A certain amount of “leg-spring” stiﬀness is required zontal and vertical landing velocities, and leg-spring swept for eﬀective storage and utilization of potential elastic energy angle), some particular value of the “leg-spring” stiﬀness in the musculotendinous groups during “stretch-shortening may hypothetically be the most beneﬁcial for movement cycle” (SSC) movements, such as running [22]. Greater stiﬀ- performance. Greater or lower “leg-spring” stiﬀness com- ness of the “leg-spring” provides the capacity to store more pared to desired values can cause the lower limbs to partially potential elastic energy during the ground contact phase. lose elastic capacity, which will have a negative eﬀect on the Therefore, it would be expected that higher (or high enough) accumulation and utilization of elastic energy. If the “leg- values of mechanical stiﬀness (leg, vertical, and joint) may spring” is too stiﬀ, the body may take-oﬀ too soon reducing also increase running performance and/or execute running the capacity to improve ﬂight time through addition of mus- tasks with more mechanical economy. Cavagna et al. [131] cular force. If the “leg-spring” is too compliant, the body suggested that the role of potential elastic energy becomes may rise too late with considerable energy lost through more important in sprint tasks at running velocities greater relaxation of the elastic tissue, thereby reducing the advan- than 7 m/s, although its contribution to lower velocity run- tage for the musculotendinous system during the SSC [20]. ning is also of importance. “Leg-spring” stiﬀness is expected to be greater in athletes The total “leg-spring” involves many skeletal muscles than nonathletes during running tasks. With similar changes and tendons and other passive structures. These tissues can in the length of the “leg-spring”, athletes release greater force be stretched and recoil and consequently accumulate poten- than nonathletes. Therefore, increases in “leg-spring” stiﬀ- tial elastic energy during these actions [32]. During running ness make it theoretically possible for runners to absorb with relatively low velocity, ankle plantar ﬂexors contribute greater loads, as a higher level of deforming force (torque) the majority of the force necessary for vertical support and is required to perform joint movement. This phenomenon horizontal propulsion, whereas the quadriceps muscle group may be important in training, as it allows for working with is the largest contributor to horizontal braking of the run- higher loads. However, based on the analysis of vertical ners COM and vertical support during the early stage of jumps, it seems that the desired “leg-spring” stiﬀness value the ground contact phase [132]. The gluteus maximus, is relatively small in relation to the “maximum” [3]. quadriceps, and ankle plantar ﬂexors are the major contrib- Greater accumulation of potential elastic energy may utors to acceleration of the body COM during running occur by increasing stiﬀness and/or deformation. However, [132, 133]. The muscles are activated before the lower limb according to Equation (4), increases in deformation seem 18 Applied Bionics and Biomechanics eﬀort conditions. It should be remembered that the mea- more beneﬁcial because the value of potential elastic energy depends on the squared length change. Therefore, theoreti- surements performed on the treadmill give slightly diﬀerent cally smaller “leg-spring” stiﬀness allows “leg-spring” length values of kinematic and kinetic variables (including “leg- change by using a lower force and consequently greater spring” stiﬀness) compared to the analysis carried out under length change can be obtained, which should increase the ﬁeld conditions [144]. accumulated potential elastic energy. However, the “leg- Another important factor that seems necessary to take spring” length change cannot be too excessive (beyond the into account in stiﬀness estimation is body mass. A positive desired range of lower limb joint ﬂexion during ground con- relationship between stiﬀness and body mass can result from tact phase), as such changes would result in large increases maintaining the natural vibration frequency of the human in ground contact time and decreases in step frequency. body, which is dependent on internal elastic forces and iner- After reaching an “optimal” lower limb joints ﬂexion angle, tia [7]. Therefore, the relationships of mechanical stiﬀness further increases in the accumulated potential elastic energy with the variables describing the running tasks may be dif- are possible by increasing stiﬀness. “Leg-spring” stiﬀness will ferent if the value of stiﬀness related to body mass is taken increase with increased deforming force at “optimal” lower into account, not the absolute value [3, 65, 67, 145, 146]. limb joint ﬂexion angles during running tasks [3]. Mechanical stiﬀness is commonly assessed in both labo- Because athletes are able to generate a greater ground ratory and ﬁeld tests. Regardless of the test mode, any stiﬀ- reaction force than nonathletes, their maximum “leg- ness test must be valid and reliable if the data can be used spring” stiﬀness is greater. Therefore, a relatively low “leg- to inform training decisions. Pappas et al. [147] reported that leg and vertical stiﬀness, as well as related kinematic spring” stiﬀness will be greater for an athlete than for a non- athlete. The greater value of “leg-spring” stiﬀness in athletes parameters, obtained using the sine wave method during (in comparison to nonathletes) will be (on the condition that treadmill running at 4.4 m/s, were highly reliable, both the desired range of motion in the lower limb joints is within and across days. However, Joseph et al. [148] obtained) an additional factor that increases the accumu- reported that during 10 m overground running (at 3.8 m/s), lated potential elastic energy and, consequently, perfor- vertical stiﬀness has good reliability, leg stiﬀness has mance. Therefore, the desired “leg-spring” stiﬀness value moderate reliability, and knee and ankle stiﬀness has poor can be an individual variable property [3]. reliability. Leg stiﬀness [75] and knee joint stiﬀness [59] The speculations concerning a desirable value “leg- are characterised by substantial interindividual variations. spring” stiﬀness that is the most advantageous for the Therefore, researchers may need to better demonstrate the accumulation of potential elastic energy and most favours validity and reliability of their stiﬀness measures, with con- reaching maximal sport performance have already been sensus recommendations from experts warranted, perhaps addressed in many previous studies [1, 3, 22, 24–28, 31–35]. similar to the SENIAM approach for electromyography data However, no studies have provided unequivocal evidence for collection and analysis [149]. the presence of a desired “leg-spring” stiﬀness value. Because desired “leg-spring” stiﬀness can be inﬂuenced by task, and 3.5.2. Running Phases. There are several consecutive phases individual and environmental factors, the estimation of this during running distance: start, push-oﬀ, acceleration, max- imum velocity (or desired submaximal velocity for longer desired value and determination of how this value might be inﬂuenced by changes in stiﬀness at each joint spring may distances), and velocity maintenance [120]. All these run- prove to be extremely diﬃcult. ning phases are characterised by diﬀerent stride length- to-frequency ratios, technical and physiological demands that may require diﬀerent “leg-spring” stiﬀness values to 3.5. Limitations and Other Important Factors maximise performance and diﬀerent training programs 3.5.1. Computation Methods. The studies included in this [120, 150–152]. This may indicate that diﬀerent forms of review utilised several computational methods to estimate training may be required to improve the stiﬀness charac- mechanical stiﬀness, with such approaches not always necessar- teristics relevant to each running phase. ily yielding the same values [1, 21, 24, 53, 62, 122, 138–143]. Ground contact can be divided into absorption (braking) Therefore, it may be important to be aware of these and propulsion phases, which diﬀer in their characteristics between-study diﬀerences, meaning that analysing the pro- and purpose [153]. This suggests that the mechanical stiﬀ- ﬁle of the force-displacement (or torque-displacement) ness during braking and propulsion phases does not neces- curve and the values of deforming force (torque) and dis- sarily have to be the same. To understand the phenomena placement (change in length, deformation) may be useful. occurring during running tasks, it seems necessary to Estimation of the mechanical stiﬀness value does not always determine the mechanical stiﬀness for both these phases follow the force-displacement proﬁle, and the displacement separately [154, 155]. Such an approach has been used in (of COM or “leg-spring” compression) during ground a number of studies, although these approaches diﬀer. contact phase is deﬁned in various ways. High magnitudes Luhtanen and Komi [156] estimated vertical stiﬀness dur- of deforming force and displacement at one hand and low ing running and long jump with a division into eccentric magnitudes of deforming force and displacement on the and concentric phases. Butler et al. [1] proposed to calcu- other hand could both lead to similar stiﬀness values. More- late joint stiﬀness with division into two separate phases: over, mechanical stiﬀness during running tasks has been during the joint moment increase and during the joint evaluated during both treadmill and typical over ground moment decrease. Hunter [157] proposed separation of Applied Bionics and Biomechanics 19 mance. Moreover, only a few works concern the analysis of the heel strike part from the ground contact phase during running as a part with much greater stiﬀness compared to spring-mass model properties performed on top-level ath- rest of ground contact phase. However, these approaches letes and players or over an entire running distance in ﬁeld do not appear to be commonly used. conditions with typical acceleration-deceleration running velocity pattern [55, 64, 93, 94, 171, 172]. 3.5.3. Running Technique. The speciﬁc nature of each sport The number of factors inﬂuencing mechanical stiﬀness should also be considered in the analysis because running during running makes it diﬃcult to formulate clear and gen- technique used by team sports players (like a “Groucho run- eral conclusions about training recommendations. All three ning”)diﬀers signiﬁcantly from track athlete technique levels of constraint eﬀecting the individual, environment, [158]. It is important because running performance aﬀects or task constraints including age, gender, running technique, game performance indicators [159]. Team sport players (in sporting background, fatigue, running distance, and running soccer, rugby, football, basketball, handball, lacrosse, or ﬁeld surface should be taken into account. Until researchers hockey) run with a relatively lower height of the COM, less investigate how mechanical stiﬀness can be altered with knee ﬂexion during swing phase, and lower knee lift. This diﬀerent forms of training, the inﬂuence of “leg-spring” stiﬀ- technique helps team sport players to decelerate and change ness on running performance will remain somewhat unclear. direction faster [158, 160]. The acceleration phase for team It seems that studies focusing on the analysis of local tissues sport players is much shorter than that for track sprinters, (muscle, tendon) as well as more global phenomenon and the maximal running velocity is reached earlier [161]. including the interaction of the central nervous and periph- All of these factors may therefore alter the desired level of eral systems and how the plasticity of these systems aﬀects “leg-spring” stiﬀness for team sport players compared to their interplay with regard to “leg-spring” stiﬀness on run- track athletes. The type of footwear used by athletes and ning performance may allow for a better understanding of team sport players also may have some role in terms of alter- the running mechanics. ing the “leg-spring” stiﬀness and subsequent sporting per- formance [162–165]. The anatomical structure of the foot is another individual factor that can inﬂuence leg stiﬀness. Conflicts of Interest High-arched runners have increased leg stiﬀness, knee joint The authors declare that there is no conﬂict of interest stiﬀness, and ankle joint stiﬀness compared to low-arched regarding the publication of this paper. runners [166–169]. 4. Conclusions References Mechanical stiﬀness is a group of variables (leg, vertical, and [1] R. J. Butler, H. P. Crowell 3rd, and I. McClay Davis, “Lower joint stiﬀness) that seem to have an important role in run- extremity stiﬀness: implications for performance and injury,” ning performance. 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Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

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Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

Application of Leg, Vertical, and Joint Stiffness in Running Performance: A Literature Overview

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