Running economy (RE) is a gold standard measure of the oxygen cost to move the center of mass (COM) at a constant submaximal running speed. As an important predictor of distance running performance, RE is a particularly effective measure for differentiating distance runners at a given level of competition.1,2 The oxygen cost of running is in turn associated with the magnitude and rate of force actively produced by lower limb muscles during the stance phase of running. These forces are generated in a cyclical fashion in order to absorb mechanical energy from the COM during early stance and perform mechanical work on the COM during the propulsive phase, thus creating bouncing-like movements).3–5
The energy to do work on the COM is primarily delivered via 2 mechanisms—energy produced by contractile elements resulting from shortening of the lower limb muscles and elastic energy recovered from previously stretched tendons and ligaments in the legs and feet (eg, Achilles tendon and plantar fascia).6–8 The relative importance of these 2 mechanisms depends on many factors, including the biomechanical and physical characteristics of the runner and external variables such as running velocity, step frequency, running surface properties, and footwear. It has been estimated that the spring-like behavior of tendons may be responsible for over half of the mechanical work performed at higher running speeds because elastic and kinetic energy become more readily converted to potential energy during the stance phase,1,9,10 reducing the oxygen cost of running by up to 30% to 40%.2,11 Therefore, it stands to reason that changes in factors that affect elastic contributions to spring-mass mechanics may directly relate to changes in RE.
In recent years, footwear manufacturers have focused on developing advanced footwear technologies (AFTs) that reduce the energy cost of running.12–15 Although no formal definition exists, AFTs are characterized as “performance-enhancing footwear technologies that combine lightweight, resilient midsole foams with rigid moderators and pronounced rocker profiles in the sole”13,16 The rigid moderator is a plate, usually curved, often made from carbon fiber and is typically embedded in the midsole.
Assuming midsoles have the potential to act in series with the leg spring system, a change to their spring-like behavior is likely to be associated with a change in the spring-mass characteristics exhibited by the runner, such as a change in leg stiffness, vertical impulse, or ground contact time, which in turn influences RE.17–19 When selected footwear components that have the potential to affect the relationship between the leg spring and RE are then enhanced such as greater midsole thickness, higher energy return, reduced mass, and potentially greater longitudinal bending stiffness (LBS), a consistent and predictable change in spring-mass characteristics and RE is perhaps to be expected. This change would theoretically be associated with low variability among individuals. Decreased footwear mass in isolation has, for example, repeatedly been shown to lower the energy cost of running at the approximate rate of 1% per 100 g.20–22
However, AFTs, which have smaller mass, greater energy return, thicker midsoles, and greater LBS when compared with traditional footwear, show a highly variable RE response. The Nike Vaporfly 4% (NVF)—the first commercially available AFT—was named as such because a seminal study found that it was associated with a significant 4% average improvement in RE compared with the previous best competitive distance running shoes.15 While subsequent studies confirmed a positive and significant response, average effects were as low as 1.9%.23,24 Yet, what is more important at the individual level is that responses to the NVF were highly variable, ranging from a worse RE for some runners at specific speeds to a 6% benefit.15,23
The robust association between the NVF and improved RE at the group level occurring alongside a highly variable response at the individual level suggests the effect is not solely a direct mechanical effect, resulting from a change in footwear properties but may be biomechanically mediated. According to this hypothesis, a given footwear property will be associated with greater or smaller variability in RE. The magnitude of this variability will depend on the propensity of the effect to be interdependent with an individual’s biomechanics. Interdependence in this context is linked to the idea that there are no precisely delineated boundaries to discern natural processes.25 In this sense, the effects of footwear properties and individual biomechanics are difficult to isolate precisely because they are mutually constituted or integrated processes. In a similar way, previous studies have demonstrated how biomechanical and neurophysiological processes integrate to maintain functional equilibrium.26 Thus, the total effect of a change in footwear on RE may be greater or smaller than expected simply because footwear properties, physical constraints, and biomechanical constraints form an integrated, interdependent response. Nonetheless, it is established that biomechanical changes occur in response to a change in footwear, and in this way, it must be assumed that biomechanical adaptations mediate the effect of a change in footwear on RE.
The NVF is associated with several biomechanical changes including altered spring-mass behavior and changes in ankle and foot biomechanics. However, the traditional theoretical and statistical approach considers biomechanical variables separately, not as variables that mediate the relationship between footwear and RE.12,24,27 Accordingly, existing theoretical and statistical methods implicitly ignore biomechanical variables in the analysis and assume that changes in RE are directly and solely caused by the change in footwear.
Taken together the results of previous studies indicate that the total effect of footwear on RE may perhaps constitute the sum of 2 interdependent effects, which we posit as namely (1) a direct effect of footwear on spring-mass characteristics (eg, greater energy returned from the midsole) and (2) a mediated biomechanical effect of footwear on spring-mass characteristics (eg, the control strategy to deal with changed mechanical conditions at the foot and ankle). In this paradigm, both effects are important to understanding the total effect.
The highly individual response to wearing AFTs has led to increased calls for research into individualization of running footwear. Individualization is not merely about identifying footwear that improves RE; rather, it entails developing footwear or footwear components that maximize RE according to an individual’s physical, biomechanical, and environmental characteristics.16,28 Individualization therefore requires developing footwear that causes improvements in RE via the aforementioned mediated pathway. Thus, the direct effect is inherent to footwear properties, and the mediated pathway is integral to maximizing the full effect of an individual’s biomechanical characteristics. However, using existing paradigms, this is unfortunately problematic because there is no recognized framework for separately quantifying the direct and mediated pathways and their potential cooperation or interaction.
In this paper, we explore a theoretical framework for quantifying direct and mediated effects of footwear on RE as both are important, depending on the context. It is important to quantify the direct effect when the aim is to understand the effect inherent to footwear properties, whereas it is important to quantify the mediated effect when the aim is to individualize the biomechanical response. The aim of the framework is to describe a paradigm for understanding the direct and mediated effects and to consider ways to evaluate and improve the process of individualizing footwear.
The Framework
Figure 1 shows a directed acyclic graph illustrating the potential relationships among changes to footwear properties; spring-mass characteristics, including leg biomechanics and ankle and foot biomechanics; and RE for a given runner. Note that the framework assumes a given set of environmental conditions such as the same running surface, gradient, ambient temperature, and time of day. Each pathway (coefficients a–d) represents the transfer of causal information. Two pathways—represented by coefficient “a” (the direct effect) and coefficients “b” + “c” (the mediated effect)—are of particular importance to the total effect of footwear on the change in energy cost associated with spring-mass characteristics and RE. While these may not be the only pathways that impact on RE, the example provided offers a framework to understand how an individual might respond to different footwear in a way that causes a known response. Note that hereafter, we assume that changes in the energy cost associated with altered spring-mass characteristics are directly related to changes in RE when all other things are equal; therefore, we adopt “change in RE” as a latent representation of the change in energy cost associated with altered spring-mass characteristics.
—Directed acyclic graph showing the total causal effect of changing footwear properties on running economy for a given runner and a given set of environmental conditions (ie, same surface, gradient, ambient temperature, and time of day). The total effect is measured in laboratory studies. However, the total effect is the sum of 2 distinct pathways. Pathway “a” represents the direct effect of changing footwear properties on the change in energy cost resulting from the change in spring-mass characteristics. The change in energy cost resulting from changes in spring-mass characteristics are proportional and directly related to changes in running economy (pathway “d”). The mediated effect (via changes in ankle and foot biomechanics) is pathways b + c. The mediated effect comprises a direct effect of changing footwear properties on the changes in ankle and foot biomechanics (pathway “b”) and a direct effect of the changes in ankle and foot biomechanics on the changes in energy cost associated with spring-mass characteristics (pathway “c”).
Citation: Journal of Applied Biomechanics 41, 1; 10.1123/jab.2024-0109
Nevertheless, when only the total effect is known, optimizing footwear according to the principles of individualization is challenging because the mediated effect, which is perhaps of greater interest to individualization than the total effect, is not differentiated from the direct effect of the footwear’s mechanical properties. Specifically, the direct and mediated effects provide the necessary frames of reference to understand how an individual achieves a given change in RE in response to a given change in footwear.
Consider an example in which a runner shows a 5% improvement in RE (ie, a 5% total effect) in response to changing to a new footwear condition. The extent to which this improvement is caused directly by the change in mechanical properties of footwear and the extent to which the improvement is caused by altered mediated effects resulting from the change in footwear are wholly unknown. Indeed, there are several mechanisms that could potentially explain this improvement.
It is possible that the direct pathway is entirely responsible for the 5% total effect in this runner. In this scenario, the midsole materials and components in the new footwear would, in some way, have capacity for profoundly superior function compared with the materials and components of the previous footwear (discussed later). Theoretically, all runners using the new footwear in this scenario would have the potential to benefit to a similar degree because the direct effect of the footwear is mechanical. In the case of our hypothetical runner, in this scenario, the footwear imposes constraints on ankle and foot biomechanics, which is equal to that of the previous footwear; thus, there are no additional benefits (or losses) resulting from the mediated pathway.
The total effect might instead be attributable to the mediated pathway alone. In this case, the new and previous footwear materials and components would have a similar mechanical capacity to directly contribute to the total effect (ie due to similar midsole properties). The total effect would, in this instance, be solely due to the mediated pathway dictated by a reduction in constraints imposed by the footwear on the individual’s ankle and foot biomechanics that would improve outcomes such as the timing and magnitude of energy return or a more optimal gearing ratio at the ankle.29,30 This in turn influences spring-mass characteristics and ultimately reduces the cost associated with muscle force or work production. This scenario demonstrates a strong individualization effect because the new footwear has a strong positive mediated effect of 5%.
A third explanation for a 5% improvement in RE is that the total effect of the footwear is a summation of nonzero positive effects along both the direct and mediated pathways. For example, the footwear may have directly caused a 3% increase in RE and simultaneously caused a footwear-mediated 2% positive change in RE from biomechanical changes at the foot and ankle. This explanation also incorporates circumstances where the direct effect is greater than 5%, for example, in the case that footwear contributes a 7% direct effect. While the footwear structure and function may be deemed profoundly superior to the previous footwear, the mediated effect must in fact be negative to arrive at a total effect of 5%. This latter example is particularly instructive. The runner shows an overall 5% improvement in RE. But the negative mediated effect indicates the footwear constraints or interferes with ankle and foot biomechanics in such a way that the full mechanical effects of the performance-enhancing footwear are not realized. This, for example, could be due to suboptimal timing of footwear energy return such that it fails to coincide with positive ankle power.29 This outcome is entirely inimical to the concept of individualization despite an overall positive total effect on RE.
We contend it is important that, in the developing field of individualization, footwear selection is informed by how much of the total effect is attributable to the inherent effect of changing footwear (the direct pathway) and how much is attributable to the mediated pathway. When the total effect is regarded as 2 separate, interdependent, potentially interacting effects, it provides a framework that enables development of relevant footwear components that can maximize or optimize the effects of relevant footwear properties, which cause increased direct and mediated effects.
The Direct Effect
Definition
The notion that the direct effect will correspond to an average of the total effects in a sample of individuals (ie, because an average of the total effects is not biased by individual data) is tempting but inaccurate for several reasons.
The direct effect is defined as the effect of a change in the mechanical properties of footwear on the relative sensitivity of RE to change while the key mediating variables are held constant. The total effect, on the other hand, is a summation of the direct and mediated effects.
Because the direct and mediated effects are interdependent, they must be individual specific. Averaging the total effects across individuals is therefore not analogous to the direct effect, but it is analogous to summing the average individual-specific direct and mediated effects.
Footwear Mechanisms
Intuitively, it is the mechanical properties of footwear materials and components that directly affect spring-mass characteristics and RE. The rigid moderator is one such component that potentially contributes to the direct mechanical effect as it controls LBS, which influences metatarsophalangeal (MTP) and ankle joint biomechanics.30,31 It is also partially responsible for the “teeter-totter effect,” where the point of ground reaction force application is moved to a more anterior part of the foot during push off.32 Thus, there are several potential mechanisms of action relating to LBS. However, research shows high individual variability in response to a rigid moderator.33 This implies there exists an optimal LBS at the individual level, which increases the likelihood that it acts via a mediated pathway. More research is therefore needed to determine the extent to which the rigid moderator has a direct mechanical effect that is consistent across individuals and the extent to which it is associated with a biomechanically mediated effect via altered ankle and foot biomechanics.
Midsole properties such as mass, energy return, and thickness arguably have a relatively strong body of evidence linking them to a direct effect on spring-mass characteristics with relatively consistent effects on RE.34 Midsoles are made from various viscoelastic materials such as ethylene-vinyl acetate, thermoplastic polyurethane, and polyether block amide because, to varying extents, these materials exhibit spring-like qualities that have the capacity to absorb and then return mechanical energy via the stance leg.15,35 Midsoles demonstrating greater resilience are known to return a greater proportion of initially absorbed energy. Mechanical testing of midsoles indicates that polyether block amide foam used in the NVF returns 87% of the stored energy, compared with 65% and 76% of energy returned from ethylene-vinyl acetate- and thermoplastic polyurethane-based foams used in the best competitive footwear prior to 2016.15 These differences (along with greater stored energy) contribute to the polyether block amide-based midsole returning more than twice the absolute energy compared with the other foams.15 Over the course of a marathon race, this “footwear work” has the potential for substantial oxygen savings.36 Energy return has the potential to serve 2 purposes in relation to RE. More energy returned is likely associated with less positive work done by muscles and, therefore, smaller oxygen cost. It also denotes a smaller proportion of the energy stored in the midsole is lost to heat during the stance phase.
The capacity of the midsole to absorb and return energy is also dependent on other midsole material properties and dimensions. For a given running velocity, greater compliance and thicker midsole foam will enable greater energy absorption.35,37,38 The effect is greater energy stored in the “midsole spring” and smaller energy absorbed by the leg. This results in a reduction in the energy cost associated with cushioning the body and altered spring-mass characteristics such as increased vertical oscillation and impulse, albeit that some of this energy may be passively absorbed by other soft tissues such as the tendons and heel pad.15,21,24,35,39 Changing the mechanical properties of running surfaces is known to significantly alter both the leg stiffness and the resulting RE.40 For example, runners on a highly compliant surface will typically increase leg stiffness, with muscles acting more isometrically, and allow the surface to undergo the compression and extension while approximately maintaining stride characteristics (eg, step length, stride frequency, and contact time).40 This mechanism may also contribute to the effects of altered midsole thickness, mass, and compliance on RE.
There are further potential direct pathways that influence RE. For example, greater footwear mass requires larger inertial forces to decelerate and accelerate the leg, leading to greater energy cost of running.20 As previously indicated, a consistent finding is that each 100 g added to the feet increases the oxygen cost of running by approximately 1%.20–22 Therefore, although a thicker midsole can effectively improve RE through greater absorption and return of energy, the effect can be outweighed by the negative effect of greater mass associated with a thicker midsole. Lower density foams in the midsoles of AFTs such as the NVF are effective precisely because, compared with the previous best competitive footwear, they have greater capacity to absorb and return energy while costing relatively less energy due to a smaller mass.15
Thicker, more lightweight, more compliant, and resilient foams, especially when combined in the same midsole, have the potential to directly affect spring-mass characteristics of the leg and body and the energy demands of distance running. Research is encouraged to examine the theory that these properties along with LBS are associated with a direct effect on altered spring-mass characteristics and RE.
Quantifying the Direct Effect
The large interindividual variability in biomechanical and physical constraints makes it challenging to use observational data to isolate the direct effect from the mediated effect. However, with a sufficiently large sample or using machine learning algorithms, it may be possible to estimate the direct effect by holding the mediated pathway constant while changing footwear condition. A hypothetical experimental aim would be to constrain the relevant mediating variables, potentially ankle and foot biomechanics, and compare the effects of this intervention on spring-mass characteristics and RE across a range of footwear conditions. Assuming the relevant mediating variables were held constant, differences in observed RE among footwear conditions would now provide more informed data on the direct effect of a given shoe.
It may also be possible to develop a model that estimates the direct effect based on mechanical testing data from midsole foams, rigid moderators, and other footwear measurements. As the polymer foams used in midsole construction exhibit a range of mechanical properties, their response can be quantified through simple measurements of mass and through more involved benchtop testing procedures such as energy- or force-constrained protocols. These protocols provide repeatable, controlled, and reproducible ways of quantifying the passive mechanical energy storage and return capacities.28,41,42 Ostensibly, the foam absorbs energy during early stance and passively recoils to return energy in late stance. Similarly, the curvature of a rigid moderator and LBS can be quantified along with the effects.33 Thus, several of the isolated mechanisms—energy absorption, energy return, and the effect of the rigid moderator—can be tested mechanically and in isolation to avoid a confounding influence from the mediated pathway, which involves dynamic effects at the ankle and foot during running.15 As such, benchtop testing would yield an expected direct mechanical effect based on isolated mechanical responses of footwear components.
It is important to note that benchtop testing does not quantify the direct effect of footwear on RE during running and is therefore not assessing the integrated response. This is largely because under foot loading during running is characterized by variable midsole loading patterns, which are not captured by benchtop testing protocols.29 However, benchtop testing does add a degree of reliability and objectivity resulting in an expected direct mechanical effect, which is measured under highly standardized conditions.
The Mediated Effect
Definition
A working definition of the mediated effect is the observed change in RE when holding footwear constant while altering relevant ankle and foot characteristics to equivalent values that would be caused by a change in footwear. The difficulty in quantifying this effect is the potential interaction between the direct and mediated effects, namely, that footwear inherently constrains the ability to systematically change ankle and foot function.
Mediated Effect Mechanisms
Runners are known to adopt spring-like mechanics, including a self-selected stride frequency and contact time that, influenced by leg stiffness, minimizes energy consumption at a given speed.1,9,17,18,35,43 Although, according to Miller et al,44 these spring-mass characteristics are, to a degree, controllable through activation of muscles, it is likely that changes in the action of muscles and the resulting energy storage and return from elastic tendons within the arch of the foot and across the ankle contribute substantial explanatory power to the changes in energy cost associated with spring-mass characteristics of an individual running at a given speed.7,8,45
Given that footwear directly contributes to the spring-mass system (by effectively sitting in series with the leg spring system), we hypothesize that specific footwear properties contribute to the energetics of spring-mass dynamics via a mediated pathway, which is shaped by an individual’s foot and ankle biomechanical response to a given footwear condition. Research on AFTs has consistently shown that footwear alters COM biomechanics, including reduced step frequency and increased vertical oscillation, impulse, and ground reaction force, which are considered spring-mass characteristics.15,22 While some of this is attributable to the direct effect of footwear, modifications to foot and ankle biomechanics are likely to also impact these spring-mass characteristics. For example, although benchtop testing of an AFT midsole substantially underestimates the average mechanical energy returned to the runner underfoot, it may in part be due to better timing of returned energy corresponding to reduced mechanical demand at the ankle joint.29 Furthermore, several studies have shown the NVF is associated with reduced positive and negative work at the ankle and reduced negative work at the MTP joint. 46,47
One of the most well-researched footwear properties known to influence ankle and foot biomechanics during running is LBS. AFTs usually have high LBS due to an embedded rigid moderator, the inclusion of which is reported to reduce the metabolic cost of running by approximately 1%.33 The energy savings have been attributed to changes in MTP and ankle joint mechanics and are highly variable among individuals depending on physical characteristics such as body mass and running ability.33,48 Greater midsole LBS is associated with smaller dorsiflexion, smaller moments, less negative work around the MTP joint, a delay in the redistribution of joint work and slower shortening velocities of the main muscle-tendon units in the foot and shank.31,49,50 LBS is also linked to a gearing change at the foot and ankle; whereby, the ratio of internal moment arm to external lever arm of the GRF as it acts at the MTP and ankle joint is changed notably, once again, with high individual variability.30 Additionally, the changes associated with the higher LBS conditions found by Willwacher et al30 were a corollary to increased forward lean of the body at toe-off and longer stance times, indicating a causal sequence of effects that may link footwear properties to altered foot and ankle function and to changes in spring-mass characteristics.
Quantifying the Mediated Effect
If the premise of footwear individualization is to design and select shoes based on individual physical and biomechanical characteristics of the runner, it then requires quantifying the mediated effect. One method to estimate the mediated effect would be to simply rearrange Equation 1 by subtracting the direct effect from the total effect: ME = TE − DE. This method would, however, require estimating the direct mechanical effect, and it would assume minimal interactions between footwear properties and changes in ankle and foot biomechanics on the changes in spring-mass characteristics.
For there to be a mediating effect, variance in the independent variable (eg, footwear) should account for significant variance in the mediating variable (eg, ankle and foot biomechanics), and variance in the mediating variable should account for significant variance in the dependent variable (ie, RE).51 These relationships can be assessed potentially using observational data. However, a stronger design would be to use mediation analysis.52 A relevant hypothetical aim would be to hold footwear condition fixed and systematically changing foot and ankle biomechanics to values that would occur in comparison footwear. However, caution would be needed in designing such a study due to the potential for footwear and biomechanical interactions. Given this challenge to individualizing footwear, the development of methods that aim to quantify the mediated effect of footwear is strongly encouraged.
Summative or Interactive Effects
The proposed framework described in Figure 1 and Equation 1 indicates a summative effect whereby the direct mechanical effects of footwear on spring-mass characteristics are added to the direct mechanical effects of footwear on ankle and foot biomechanics and the consequent direct effects of changes in ankle and foot biomechanics on spring-mass characteristics and changes in RE. A possible alternative, but complimentary framework, would be that changes in spring-mass characteristics and RE are determined by an interactive relationship between footwear properties and ankle and foot biomechanics. In this scenario, there is an additional effect whereby the effect of a change in footwear properties on RE would depend on the change in ankle and foot biomechanics.
As in the summative model, changes in biomechanical effects can be both positive and negative. Methods to tease out individual effects in both models are near identical, and only the specific mathematical interpretation differs. Nevertheless, research is required to determine the extent to which effects are summative or interactive.
The Benefits From Quantifying the Direct and Mediated Effects
There are several benefits of using the proposed framework to quantify the direct, mediated, and total effects. These include the following.
- 1.A method for quantifying the mediated effect allows genuine individualization of footwear based on a given runner’s physical and biomechanical characteristics. Better individualization is characterized by a greater mediated effect relative to the direct effect of a footwear condition.
- 2.The proposed framework can be used by researchers to identify footwear properties and biomechanical variables that contribute to the mediated effect.
- 3.When 2 of the effects are known, it is possible to infer the third effect. For example, when the direct and total effects are known, it may be possible to infer the mediated effect, which is difficult to quantify experimentally.
- 4.A method that estimates the direct effect would permit manufacturers to design footwear based on the theoretical benefits from the midsole foam and rigid moderator, prior to development and testing on runners in laboratory conditions.
- 5.The robustness of footwear regulations in elite level competition could be further strengthened. Current World Athletics footwear regulations stipulate an upper limit to midsole thickness.53 The ability to quantify the direct effect would permit regulation of all footwear properties known to directly influence RE.
Conclusion
RE is a gold standard laboratory-based measure of the oxygen cost to run at a given velocity, and it is the primary outcome measure when comparing the total effects of footwear models. Here, we propose that footwear individualization—the process of developing footwear that improves RE according to an individual’s physical, biomechanical, and environmental characteristics—requires differentiating the direct and mediated effects. To date, methods for quantifying the direct and mediated effects of footwear on RE have not been developed.
The current article describes a framework that defines and contextualizes the direct and mediated effects to encourage development of methods to quantify them. It is proposed that the total effect is a sum of the direct and mediated effects. The direct effect of footwear is likely to be associated with footwear properties that have a theoretical relationship to spring-mass dynamics. We posit that the mediated effect is likely to be driven by ankle and foot biomechanics that have an association with spring-mass dynamics and RE via the biomechanical and physical constraints of the individual.
Research is needed to develop methods for quantifying the direct and mediated effects so that they can be incorporated in the design of future research studies that aim to understand the effects of footwear on RE. If the direct or mediated effects can be differentiated using mechanical testing, footwear measurements, or from observational data, then it may be possible to (1) develop processes for individualizing footwear according to biomechanical constraints, (2) identify footwear properties and biomechanical variables involved in the mediated effect, (3) infer the mediated effect from the direct and total effects, (4) optimize footwear properties using the direct effect, and (5) develop regulations that control for all footwear properties that contribute to the direct effect.
References
- 1.↑
Barnes KR, Kilding AE. Running economy: measurement, norms, and determining factors. Sports Med Open. 2015;1:8. doi:
- 2.↑
Saunders PU, Pyne DB, Telford RD, Hawley JA. Factors affecting running economy in trained distance runners. Sports Med. 2004;34(7):465–485. doi:
- 4.
Chang Y, Hunag HC, Hamerski CM, Kram R. The independent effects of gravity and inertia on running mechanics. J Exp Biol. 2000;203:229–238. doi:
- 5.↑
Kipp S, Grabowski AM, Kram R. What determines the metabolic cost of human running across a wide range of velocities? J Exp Biol. 2018;221(18):218. doi:
- 6.↑
Lichtwark GA, Wilson AM. Interactions between the human gastrocnemius muscle and the Achilles tendon during incline, level and decline locomotion. J Exp Biol. 2006;209:4379–4388. doi:
- 7.↑
Ker RF, Bennett MB, Bibby SR, Kester RC, Alexander RM. The spring in the arch of the human foot. Nature. 1987;325(7000):147–149. doi:
- 8.↑
Stearne SM, McDonald KA, Alderson JA, North I, Oxnard CE, Rubenson J. The foot’s arch and the energetics of human locomotion. Sci Rep. 2016;6:19403. doi:
- 10.↑
Cavagna GA, Kaneko M. Mechanical work and efficiency in level walking and running. J Physiol. 1977;268:467–481.
- 11.↑
Cavagna GA, Saibene FP, Margaria R. Mechanical work in running. J Appl Physiol. 1964;19(2):249–256.
- 12.↑
Burns G, Tam N. Is it the shoes? A simple proposal for regulating footwear in road running. Br J Sports Med. 2020;54(8):439–440. doi:
- 13.↑
Frederick EC. Let’s just call it advanced footwear technology (AFT). Footwear Sci. 2022;14(3):131. doi:
- 14.
Hebert-Losier K, Finlayson SJ, Driller MW, Dubois B, Esculier JF, Beaven CM. Metabolic and performance responses of male runners wearing 3 types of footwear: Nike Vaporfly 4%, Saucony Endorphin racing flats, and their own shoes. J Sport Health Sci. 2022;11:275–284. doi:
- 15.↑
Hoogkamer W, Kipp S, Frank JH, Farina EM, Luo G., Kram R. A comparison of the energetic cost of running in marathon racing shoes. Sports Med. 2018;48:1009–1019. doi:
- 16.↑
Hébert-Losier K, Pamment M. Advancements in running shoe technology and their effects on running economy and performance – a current concepts overview, Sports Biomechanics, 2023;22(3):335–350.
- 17.↑
Dalleau G, Belli A, Bourdin M, Lacour JR. The spring-mass model and the energy cost of treadmill running. Eur J Appl Physiol. 1998;77:257–263. doi:
- 18.↑
Moore IS. Is there an economical running technique? A review of modifiable biomechanical factors affecting running economy. Sports Med. 2016;46:793–807. doi:
- 19.↑
Kelly LA, Lichtwark GA, Farris DJ, Cresswell A. Shoes alter the spring-like function of the human foot during running. J R Soc Interface. 2016;13:174. doi:
- 20.↑
Franz JR, Wierzbinski CM, Kram R. Metabolic cost of running barefoot versus shod: is lighter better? Med Sci Sports Exerc. 2012;44(8):1519–1525. doi:
- 21.↑
Frederick EC, Clarke TE, Larsen JL, Cooper LB. The effect of shoe cushioning on the oxygen demands on running. In: Nigg BM, Kerr BA, eds. Biomechanical Aspects of Sports Shoes and Playing Surfaces. Calgary (Canada). University of Calgary; 1983:107–114.
- 22.↑
Frederick EC. Physiological and ergonomics factors in running shoe design. Appl Ergon. 1984;15(4):281–287. doi:
- 23.↑
Barnes KR, Kilding AE. A randomized crossover study investigating the running economy of highly-trained male and female distance runners in marathon racing shows versus track spikes. Sports Med. 2019;49:331–342. doi:
- 24.↑
Hunter I, McLeod A, Valentine D, Low T, Ward J, Hager R. Running economy, mechanics, and marathon racing shoes. J Sports Sci. 2019;37(20):2367–2373. doi:
- 26.↑
Sueki DG, Chaconas EJ. The effect of thoracic manipulation on shoulder pain: a regional interdependence model. Phys Ther Rev. 2011;16(5):399–408.
- 27.↑
Hoogkamer W, Kipp S, Kram R. The biomechanics of competitive male runners in three marathon racing shoes: a randomized crossover study. Sports Med. 2018;49:133–143.
- 28.↑
Willwacher S, Weir G. The future of footwear biomechanics research. Footwear Science, 2023;15(2):145–154.
- 29.↑
Matijevich ES, Honert EC, Yang F, Lam WK, Nigg BM. Greater foot and footwear mechanical work associated with less ankle joint work during running. Sports Biomech. 2024;10:916. doi:
- 30.↑
Willwacher S, Konig M, Braunstein B, Goldmann JP, Bruggemann GP. The gearing function of running shoe longitudinal bending stiffness. Gait Posture. 2014;40(3):386–390. doi:
- 31.↑
Willwacher S, König M, Potthast W, et al. Does specifc footwear facilitate energy storage and return at the metatarsophalangeal joint in running? J Appl Biomech. 2013;29:583–592. doi:
- 32.↑
Nigg BM, Cigoja S, Nigg SR. Teeter-totter effect: a new mechanism to understand shoe-related improvements in long-distance running. Br J Sports Med. 2021;55(9):462–467. doi:
- 33.↑
Roy JP, Stefanyshyn DJ. Shoe midsole longitudinal bending stiffness and running economy, joint energy, and EMG. Med Sci Sports Exerc. 2006;38(3):562–569. doi:
- 34.↑
Ortega JA, Healey LA, Swinnen W, Hoogkamer W. Energetics and biomechanics of running footwear with increased longitudinal bending stiffness: a narrative review. Sports Med. 2021;51:873–894. doi:
- 36.↑
Matijevich ES, Fletcher JR, Nigg BM. Footwear energy return is intuitively ‘good’, but should not be considered in isolation. Footwear Sci. 2023;15(2):71–76.
- 37.↑
Hardin EC, Van Den Bogert AJ, Hamill J. Kinematic adaptations during running: effects of footwear, surface, and duration. Med Sci Sports Exerc. 2004;36(5):838–844. doi:
- 38.↑
Tung KD, Franz JR, Kram R. A test of the metabolic cost of cushioning hypothesis during unshod and shod running. Med Sci Sports Exerc. 2014;46(2):324–329. doi:
- 39.↑
Silva RM, Rodrigues JL, Pinto VV, Ferreira MJ, Russo R, Pereira CM. Evaluation of shock absorption properties of rubber materials regarding footwear applications. Polym Test. 2009;28:642–647.
- 40.↑
Kerdok AE, Biewener AA, McMahon TA, Weyand PG, Herr H. Energetics and mechanics of human running on surfaces of different stiffnesses. J Appl Physiol. 2002;92:469–478. doi:
- 41.↑
Lippa NM, Collins PK, Bonacci J, Piland SG, Rawlins JW, Gould TE. Mechanical ageing performance of minimalist and traditional footwear foams. Footwear Sci. 2016;9(1):9–20.
- 42.↑
Schwanitz S, Moser S, Odenwald S. Comparison of test methods to quantify shock attenuating properties of athletic footwear. 8th Conference of the International Sports Engineering Association (ISEA). Procedia Engineering 2. 2010:2805–2810.
- 43.↑
Blickhan R. The spring-mass model for running and hopping. J Biomech. 1989;22(11–12):1217–1227. doi:
- 44.↑
Miller RH, Umberger BR, Hamill J, Caldwell GE. Evaluation of the minimum energy hypothesis and other potential optimality criteria for human running. Proceedings of the Royal Society B, 2012;279:1498–1505.
- 45.↑
Holowka NB, Richards A, Sibson BE, Lieberman DE. The human foot functions like a spring of adjustable stiffness during running. J Exp Biol. 2021;224(1):9667. doi:
- 47.↑
Martinez E 3rd, Hoogkamer W, Powell DW, Paquette MR. The influence of “super-shoes” and foot strike pattern on metabolic cost and joint mechanics in competitive female runners. Med Sci Sports Exerc. 2024;56(7):1337–1344. doi:
- 48.↑
Chollet M, Michelet S, Horvais N, Pavailler S, Giandolini M. Individual physiological responses to changes in shoe bending stiffness: a cluster analysis study on 96 runners. Eur J Appl Physiol. 2023;123:169–177. doi:
- 49.↑
Cigoja S, Asmussen MJ, Firminger CR, Fletcher JR, Edwards WB, Nigg BM. The effects of increased midsole bending stiffness of sport shoes on muscle-tendon unit shortening and shortening velocity: a randomised crossover trial in recreational male runners. Sports Med Open. 2020;6:241. doi:
- 50.↑
Cigoja S, Fletcher JR, Nigg BM. Can changes in midsole bending stiffness of shoes affect the onset of joint work redistribution during a prolonged run? J Sport Health Sci. 2022;11:293–302. doi:
- 51.↑
Barron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. J Pers Soc Psychol. 1986;51(6):1173–1182. doi:
- 53.↑
World Athletics. Book C: competition. C2.1A—athletics shoe regulations. 2022. Accessed 2023. https://www.worldathletics.org/about-iaaf/documents/book-of-rules