Integrating muscle energetics into biomechanical models to understand variance in the cost of movement

Legged animals move in vastly different ways to achieve a given movement goal, depending on factors such as their environmental constraints and conditions, interactions with other animals, and the goal itself. This creates a challenge in understanding the amount of energy that is required to move under these variable conditions. Whilst it is possible to directly estimate the rate of energy consumption under specific steady-state conditions (e.g. constant velocity) using methods such as indirect calorimetry (or respirometry), animals rarely move at a steady state and are often constrained by environmental factors, e.g. walking in groups, variable terrains, prescribed routes. As such, estimates of energy consumption based on steady-state parameters, similar to that undertaken by a smart watch for human movement, are often highly variable in relation to actual energy consumed and often do not predict the variability in metabolic rates that occur with subtle changes in an individual's movement patterns (Hall et al., 2004; Jeran et al., 2016; Pope et al., 2019).

In this Review, we consider how mechanical models of movement are used to predict energy consumption during terrestrial locomotion and the various advantages and disadvantages for modelling approaches of varying complexity. We then consider the main determinants of muscle energy use during contractions and how phenomenological models of muscle energy consumption can be applied to explicit musculoskeletal models (capturing both body and muscle dynamics) for determining energy consumption under different movement conditions. We highlight the limitations in our current knowledge and potential opportunities to rectify these limitations. Finally, we provide some insight into how muscle energetic models may be applied to more general conceptual models to improve estimates of absolute energy consumed during terrestrial locomotion under a variety of conditions. Being able to better predict how movement energetics of humans and animals change under different conditions has important implications for understanding movement adaptations in response to environmental changes, ageing and disease states and for understanding behaviour.

Over 100 years of research has been conducted to establish links between the mechanics of movement and the metabolic energy cost to perform movement. Several mechanical frameworks for explaining energy consumption based on locomotor mechanics have emerged to explain findings of how energetic rates change both across species of different sizes and also within a species when the locomotor requirements change (Fig. 1A). Each framework makes different assumptions about the role muscles play in generating movement depending on the complexity of the measurements of motion and or force.

The first approach is based on thermodynamics and accounts for work done and the related muscle efficiency to undertake this work (Peyré-Tartaruga et al., 2021) (Fig. 1B). When applied to work done on the centre of mass of legged animals, this approach is capable of predicting increases in metabolic rate with factors such as speed of locomotion; however, assumptions about muscle efficiencies do not hold across species size: increasing animal size results in an apparent increase in economy of locomotion (Fig. 1C) (Alexander, 2005; Heglund et al., 1982a,b). It has been presumed that the increased efficiency of positive work production is related to a greater capacity for elastic energy storage and return through elastic tissues, potentially reducing the work requirements of muscles (Alexander and Bennet-Clark, 1977; Heglund et al., 1982b).

The cost of force hypothesis suggests that the rate of energy consumption (metabolic power) is inversely proportional to the contact time of the limb, or directly proportional to the rate of force development (Kram and Taylor, 1990; Taylor et al., 1980). For running animals, the cost coefficients related to the rate of force development are relatively consistent across animals of different sizes and running at different speeds (Kram and Taylor, 1990). A further development of this approach has been to divide the costs into those related to activation and cross-bridge cycling in order to overlay the observation with some physiological mechanism (Pontzer, 2016). Although such approaches can predict scaling effects, they are limited in their ability to predict changes in metabolic rate within a species when movement parameters are constrained by external factors that are no longer optimal for minimising energy consumption. For example, if a person runs at a given speed with a slower stride frequency (or cadence), the rate of force development reduces, but the metabolic cost of transport increases (Swinnen et al., 2022); this is in direct opposition to the cost of transport prediction. Whilst additional energy consumption might be explained by other costs (e.g. swing phase costs; Cavagna et al., 1991; Umberger, 2010), it is unlikely that force alone can always predict variability in movement within a species, particularly when additional constraints are placed on the movement (e.g. stride length or frequency, stride width).

Another framework suggests that the cost of work to redirect the centre of mass during collisions of legs with the ground can generally explain required energy consumption during terrestrial locomotion (Donelan et al., 2002; Kuo et al., 2005). Work rates accounted in this way show strong positive relationships with metabolic power across different speed and gait conditions in select species tested (Lee et al., 2013). However, similar to other cost of work approaches, this approach relies on assumptions about muscle efficiency of generating work which may be variable under different modes of locomotion.

The above simple mechanical models of movement generally consider movement of the centre of mass and/or limbs of the animal without consideration of the work or forces required from individual muscles. An alternative approach has been to use more detailed biomechanical models to examine the mechanical role of individual joints and use similar approaches to those applied to the centre of mass to understand the relationship between mechanics and energetics. For example, human experiments that have measured both the body movement and ground reaction forces have been able to use inverse dynamics approaches to quantify the positive and negative mechanical work at joints during walking and running at different speeds (Farris and Sawicki, 2012b; Riddick and Kuo, 2022) and stride rates (Umberger and Martin, 2007), and with external assistive devices (Farris and Sawicki, 2012a). These studies typically demonstrate that the rate of metabolic energy consumption does not change linearly with the rate of mechanical work performed across joints; as such, the apparent efficiency of positive work varies under different conditions. Indeed, when comparing different species, such as ostriches and humans (Rubenson et al., 2011), there also seem to be differences in mechanical efficiency. It is presumed that these differences stem from variation in the contributions of elastic tissue to positive work and/or differences in mechanics, including soft tissue deformations (Riddick and Kuo, 2022), that may change muscle efficiency under different conditions.

The cost of force hypothesis has also been applied to examine joint-level mechanics, by using the moments produced at joints (which are indicative of the rotational force applied by muscles to generate the movements) to predict the muscle volume required to generate the ground reaction force (Biewener et al., 2004; Griffin et al., 2003; Kipp et al., 2018). When humans increase speed during walking or running, there is typically an increase in active muscle volume required to generate force that increases with the measured metabolic rate (Griffin et al., 2003; Kipp et al., 2018). Whilst authors often describe this relationship as near linear with changes in speed, with an associated cost co-efficient that is relatively resilient to changes in weight (Griffin et al., 2003), the reality is that the relationship is typically curvilinear and not well tested across a range of locomotor tasks. Furthermore, they accuracy of predictions using this method has not been thoroughly examined where there are subtle changes in an individual's movement patterns due to constraints, nor has this been tested thoroughly across different species.

An alternative approach is to use highly explicit biomechanical models that attempt to recreate the muscle forces required to generate terrestrial locomotion and make predictions of the costs associated with generating these forces and the resulting muscle work (Fig. 1). Such models typically account for the muscle and tendon dynamics and muscle activations to more explicitly assign an energetic rate to each muscle during locomotion. The potential impact of such approaches for understanding energetics of movement, as well as the current limitations, is outlined further below. However, for such models to provide useful estimates requires a detailed understanding of how muscle mechanics links to energetics.

Over 100 years of research has also been conducted to investigate how and why muscles consume energy to generate force and mechanical work (Barclay, 2023; Woledge et al., 1985). A recent review by Barclay and Curtin (2023) nicely outlines the primary determinants of muscle energy output during muscle contraction. These ideas are based on direct measurements of work and/or heat output from isolated muscle and are consistent with the extensive understanding of the biochemical changes underlying muscle contraction.

From a mechanical perspective, there are numerous key drivers of muscle energy use. When a muscle contracts isometrically, it consumes energy as a result of both cross-bridge cycling (maintaining tension) and muscle activation (primarily calcium transport costs) (Barclay and Curtin, 2023). The latter contributes approximately 30% of total energy use if the muscle is at an optimum length (Barclay et al., 2007). If a muscle is allowed to shorten while generating tension, then energy is liberated as both mechanical work and heat. Heat is liberated at a rate directly proportional to the velocity of shortening – commonly referred to as the Fenn effect (Barclay, 2023; Fenn, 1923). In contrast, if a muscle is actively lengthened, then the cross-bridge costs reduce to almost zero, with heat generated to activate the fibres (Barclay and Curtin, 2023; Linari et al., 2003). Additional heat is also (eventually) generated in direct proportion to the work done on the muscle (Linari et al., 2003). Other important factors, including the muscle length (dictating the relative number of potential bound cross-bridges within each active fibre) and the relative muscle activation (the fraction of active muscle fibres), also scale energetic rates. These basic, steady-state, phenomena can be summarised based on their individual components as a function of the muscle shortening velocity and scaled based on muscle length and activation (Fig. 2). Other factors such as muscle temperature and muscle fibre type (governed by the myosin heavy chain isoform composition in muscle) (Barclay, 1996; Barclay et al., 2010) alter the rate at which energy is liberated. Furthermore, other potential history-dependent effects (e.g. residual force enhancement, shortening deactivation) may also alter the time history of both force and energy consumption (Joumaa and Herzog, 2013; Lichtwark and Wilson, 2005b), although limited research has been conducted on these phenomena from an energetic perspective.

Given this general understanding of how muscles consume energy during contraction and the subsequent mechanical output, numerous models of muscle energy use during contraction have been developed and validated against experiments from different levels of organisational scale (muscle fibres to whole-body motion). A common approach has been to use phenomenological Hill-type muscle models that predict muscle force output based on the same muscle states that are known to influence energetic rates (length, velocity, activation), henceforth referred to as extended Hill-type muscle models.

There are numerous examples of where extended Hill-type muscle models have been used to predict energy output during cyclical contractions. For example, Lichtwark and Wilson (2005b) compared model outputs to experimental data from dogfish muscles that were undergoing contractions during imposed sinusoidal length changes (termed work loops) at different frequencies and with different timings of stimulation relative to the length change cycle (Curtin and Woledge, 1996). They showed that changes in total energy rate were generally predictable using a Hill-type muscle model with predictions of energy based on the instantaneous state of the muscle through the contraction and known rates of energy consumption based on length, velocity and activation of the muscle. The model was also cross-validated against data from a mammalian muscle preparation (mouse), which demonstrated the general applicability across muscle types (Barclay, 1994). Generally, variations on these models (Bhargava et al., 2004; Houdijk et al., 2006; Umberger et al., 2003) show similar relationships between changes in the mechanical state of the muscle and mechanical and energetic outputs; however, scaling such outputs correctly to generate the correct absolute amount of heat remains problematic (Umberger et al., 2003).

A remaining challenge in applying extended Hill-type muscle models to predict energy from cyclical contractions, steady or non-steady state, is dealing with the time course of energy consumption associated with glycolysis or oxidative recovery. Both processes regenerate phosphocreatine (PCr) required for muscle contraction, but this regeneration occurs over a longer time scale in comparison to initial reactions that provide rapid regeneration of adenosine triphosphate (ATP) (Fig. 3). The ‘recovery’ heat produced, which is directly associated with generation of PCr, can be as much as the initial heat required to generate force/work in the initial contraction; however, this occurs over a longer time period at a lower rate (Barclay et al., 1995; Curtin et al., 1997; Gibbs and Gibson, 1972). The magnitude of recovery heat that is produced depends on the duration of contraction, number of contractions, fibre type and other metabolic processes (Barclay et al., 1995; Crow and Kushmerick, 1982; Curtin et al., 2002). While it is possible to predict the time course of oxidative recovery based on the known reaction rates, to the authors’ knowledge, such models have yet to be incorporated within extended Hill-type models; therefore, this remains a challenge when using such phenomenological models to estimate muscle energy use over prolonged periods.

There are a number of current challenges that make it difficult to scale muscle models based on experimental data from isolated muscle fibre preparations to predict muscle energy consumption from larger legged animals, including humans. Firstly, there are limited data that directly measure both the mechanical and energetic properties of muscle fibres from larger animals. With the exception of some recent data on wildebeest and domestic cows (Curtin et al., 2018), the majority of enthalpy data come from smaller mammalian muscles, fish or amphibian muscle, as reviewed in Barclay and Curtin (2023). Data on ATPase activity during contractions from skinned fibres in large animals such as humans (He et al., 2000) are available, but it is difficult to directly use these data to estimate energy rates under a range of mechanical conditions. As such, estimates of rate constants that impact activation, maintenance and shortening heat are often questionable.

The structure of large animal muscles also complicates predictions of energy consumption. In the weight-supporting muscles of large animals, muscles often consist of short fibres relative to the length of the muscle–tendon unit, packed in at large pennation angles to increase the cross-sectional area and hence force-generating capacity of these muscles (Wilson and Lichtwark, 2011). During contraction, there can be complex shape changes to muscle, including changes in pennation angle and three-dimensional deformation that influence the dynamics (force, length, velocity) of the muscle, often referred to as gearing (Azizi et al., 2008). Moreover, these dynamics are shown to be adversely affected – from an energetic standpoint – by inertial resistance with larger muscle mass (Ross and Wakeling, 2021). Finite-element models have been developed that may predict these dynamics, demonstrating that some energy must go into deformation of a muscle when it contracts, thereby influencing the mechanical work generated at the whole-muscle level (Wakeling et al., 2020). However, the difficulty in predicting muscle gearing and mass-specific effects across species or within individuals with varying muscle characteristics (e.g. with ageing; Kelp et al., 2023) remains a challenge that impedes the prediction of, and links between, muscle dynamics and energy consumption.

Elastic tendinous tissue arguably plays a much more significant role in altering muscle dynamics during contraction because it can drastically influence predictions of energy consumption. Larger animals typically rely on tendinous tissue to absorb and return mechanical energy, which is considered to be a primary mechanism that enables the apparent mechanical efficiency of large terrestrial animal muscle to be higher than that of smaller terrestrial animals (Alexander, 2005; Wilson and Lichtwark, 2011).

Direct measure of large animal muscle fascicle length changes (e.g. horse, human, goat) during locomotor tasks clearly demonstrates that tendon recoil can account for the majority of the length change in anti-gravity muscles during stretch–shorten cycles, allowing muscle fascicles to remain near isometric (Biewener, 1998; Lichtwark et al., 2007; McGuigan et al., 2009). Whilst absorbing and then generating work (stretch–shorten cycle) does not always cost more energy than isometric contractions (Holt et al., 2014), sufficient compliance allows for large amplitude stretch of the muscle–tendon unit to absorb energy and then significantly reduce the required shortening to generate energy, which is instead achieved through elastic tendon recoil (Holt and Mayfield, 2023; Wilson and Lichtwark, 2011). Based on the knowledge of how muscles consume energy, and particularly that minimising muscle work will reduce the energy burden of that muscle, it is logical to assume that elastic tendons can reduce energy consumption during cyclical contractions. This assertion is supported by simulations using Hill-type muscle models (Lichtwark and Wilson, 2005a; 2007; Robertson and Sawicki, 2014).

Only one study has used enthalpy methods to directly address the hypothesis that elastic tendons can directly reduce energy consumption during cyclic, stretch–shorten contractions. Lichtwark and Barclay (2010) used mouse soleus muscle fibre bundle preparations (high proportion of slow fibres) and measured heat and work generation during imposed sinusoidal length changes, while varying the timing and duration of stimulation to the muscle. Artificial tendons (latex) of varying compliance were attached in series to the fibres, thereby acting to decouple fibre length changes from those of the muscle–tendon unit when muscle force was generated. More compliant tendons were able to work through a greater amplitude of the muscle–tendon unit stretch–shorten range without damage because the tendon underwent considerably more of stretch than the fibres themselves. Fig. 4 shows an example of how both power and efficiency were affected by the compliance condition, as well as the duration (duty cycle) and timing of stimulation (phase) relative to the muscle shortening. These experiments demonstrate that superior efficiency could be achieved across a broad range of activation conditions with more compliant tendons during contraction cycles designed to generate power (e.g. accelerative movements, moving uphill or working against constant resistance) and provide a clear demonstration of the role that compliant tendons can play in modifying the energetics of muscle contraction.

A further challenge when extrapolating energetic measures from isolated muscle fibres is that such experiments neglect the role and need for neural control of muscles to appropriately generate forces for acceleration of bodies. By varying both the firing frequency of individual motor units and the number of recruited motor units, force can be modulated to achieve the required system dynamics. Hill-type muscle models typically make assumptions about the relationships between recruitment and muscle activation (Hodson-Tole and Wakeling, 2009). Whilst these models generally try to account for activation dynamics that affect the relationship between stimulation of muscle and force generation (calcium transport and binding to troponin), simplified representation remains a limitation of such models and their ability to predict precise force outputs. Complexity, including additional consideration of fibre type relative to recruitment (size principle), has been added to such models to simulate the predicted effects on both mechanics and energetics (Biewener et al., 2014; Dick et al., 2017; Lai et al., 2018). However, with advancement in our ability to measure individual motor unit activity and the general principles of recruitment in different movement conditions, new models that incorporate how motor unit recruitment influences force output (Caillet et al., 2023) may be combined with energetic models to better predict energy consumption during cyclical tasks with constantly varying recruitment profiles.

The sensitivity of muscle dynamics to the parameters used in models (e.g. compliance of the in-series tendon, muscle fibre length, fibre-type distribution, muscle cross-sectional area) is likely to contribute to errors when muscle models are used to predict energy consumption during contractions or movement tasks. It is possible to directly measure some of these properties from individual muscles, including directly measuring the dynamics of muscle contraction (e.g. ultrasound or sonomicrometry; Roberts and Dick, 2023); however, the complexity of models will often dictate accuracy. Despite these limitations, there is a growing body of literature that uses extended Hill-type models, extrapolated from the limited data we have, to understand movement energetics (see explicit models section below). A major challenge remains how we validate the accuracy of such models across different scales and locomotor conditions.

The most accessible method for assessing metabolic rate in animals (including humans) under different locomotor conditions is to use indirect calorimetry (or respirometry). Beyond the assumptions that are required to convert gas analysis to metabolic rates (Mtaweh et al., 2018), these methods can be used to measure systemic energy consumption, which includes metabolic rate increases due not only to muscle contraction but also to other biological processes that require energy to support basal function. Some of these basal functions (e.g. blood circulation, breathing) likely depend on the task being undertaken (Burton et al., 2011). Therefore, when comparing changes in metabolic rate relative to changes in movement mechanics and predicted or measured muscle function, it is important to note that there are multiple sources of energy consumption. Even when isolating individual joints to perform isometric, concentric or eccentric contractions, the energy predictions based on muscle models often underpredict the whole-body energy consumption substantially (Lentz-Nielsen et al., 2023; Umberger et al., 2003). While it is tempting to assume this is a problem with the model, the methodological assumption that only the target muscles contribute to consumption of energy is also likely to be flawed. For example, the rates of energy consumption during isolated unilateral ankle contractions at relatively low contraction intensities have been reported to be as high as 20% of that during walking (Beck et al., 2020). It is likely that factors such as co-contraction of other muscles to maintain joint stability may contribute to the overall metabolic rate, making interpretation of total energetic rates during voluntary contraction tasks more challenging.

Innovative, direct methods to measure an individual muscle's energy expenditure are desperately needed. In isolated preparations, heat measurement is a gold standard; however, this method does not scale easily. Muscle preparations need to be sufficiently small to enable the heat to be transferred to the measuring device (typically a thermopile; Barclay, 2023) without significant delay, otherwise heat is absorbed by the muscle mass itself and takes time to be transferred to the environment. Extrapolating to whole muscle during in vivo contractions is even more complicated because heat is also removed as a result of blood flow. There have been a number of very valiant attempts to directly measure heat in vivo from contracting muscles in humans that have attempted to account for the heat removed by blood flow or other phenomena (González-Alonso et al., 2000; Krustrup et al., 2001; Saugen and Vollestad, 1995). The results from these experiments generally fit with the expected heat production from contractions; however, calibration for the absolute value remains difficult and the procedures are highly invasive. Well-calibrated thermodynamic models that account for temperature, measures or estimates of blood flow and other factors (e.g. adjacent tissue mass, ambient or skin temperature) are needed to open up new possibilities for direct measure of muscle energy fluctuations during contractions and/or movement. Alternatively, muscle models could be better tuned based on alternative measures of energy consumption during more isolated muscle contractions, including imaging methods (e.g. magnetic resonance spectroscopy) to directly measure PCr concentrations, as has previously been demonstrated in human calf muscles (Haeufle et al., 2020; Hogan et al., 1999; Ortega et al., 2015).

Musculoskeletal modelling of both human and animal locomotion has become ubiquitous for understanding neuromuscular function to generate movement. A general historical review (50 years) of the advancements of muscle models and integration into musculoskeletal simulations that aim to predict the required muscle forces for movement is outlined in Wakeling et al. (2023).

A main challenge of such simulations is the requirement to solve for the muscle redundancy problem: that there are many more muscles that actuate joints than the number of joints present. Forward or predictive approaches solve for muscle forces based on inputs of time-varying activation patterns to generate motions that meet similar movement objectives to those of the animal (Anderson and Pandy, 2001; Falisse et al., 2019). Conversely, inverse approaches start with the measured movement and forces and attempt to solve for the muscle activations that are required to generate this motion, requiring an optimisation to solve the problem of redundancy (Lloyd and Besier, 2003; Thelen et al., 2003). Such explicit musculoskeletal models require considerable assumptions about how muscles themselves are controlled by the nervous system (Song et al., 2008), as well as the general properties and geometry of individual muscles that are used in the simulations (Arnold et al., 2010). As such, the calculation of energy also requires considerable assumptions about how well these simulations can predict the force and work produced by each muscle, and the energetic costs that may be associated.

Despite the many assumptions required, explicit musculoskeletal models provide advantages over conceptual models in that both force and work are accounted for at the level of the muscle. Hence, changes in mechanical requirements can be explicitly accounted for in the model. As such, when an animal changes the way it moves by choice or necessity to achieve a given movement goal, explicit models can account for which muscles are likely to contribute and therefore make estimations of the changes in energy output.

There are numerous examples where estimates of energy consumption based on musculoskeletal simulations have been compared with direct measurements of energy consumption based on indirect calorimetry. For example, Anderson and Pandy (2001) first used a forward dynamics approach and showed that by minimising energy consumption predicted from Hill-type muscle actuators, and energetic models similar to those previously described, gait characteristics similar to those measured experimentally could be reproduced. Their model, however, overpredicted energy consumption for the single walking speed that they examined. Subsequently, Miller (2014), Koelewijn et al. (2019) and Luis et al. (2024) examined the effect of speed and slope on energy predictions using different methods that more closely tracked or prescribed kinematics and kinetics. These studies found that existing energetic models, based on similar phenomenological principles to those described earlier, generally show strong correlations with experimental measures of energetic rates. However, the absolute performance of the cost models (i.e. how closely they can predict the measured energetic rate) vary considerably as a result of either inaccuracies in the predicted muscle actions or issues with the implementation of energetic models.

We have recently employed an inverse solution to examine the performance of musculoskeletal models with energetic calculations during hopping, a similar spring-like movement to running. Hopping was selected because it enables a large space of different movement patterns to be explored by placing constraints on factors such as hopping frequency and height achieved (Gutmann and Bertram, 2017; Jessup et al., 2023a), which also creates great variability in the metabolic rate of achieving the movement (Fig. 5A). Our simulations employed an open-source musculoskeletal modelling approach (Dembia et al., 2020) and the energetic model described by Umberger et al. (2003). Our predicted muscle activations were similar to those measured with electromyography, and fibre length changes of lateral gastrocnemius, soleus and vastus lateralis muscles were similar to those measured with B-mode ultrasound. We found that, similar to previous studies, there is a strong correlation between predicted energy output and that measured with indirect calorimetry; however, the prediction accuracy of absolute energy varied across participants considerably, generally underestimating the energetic rate to perform hopping (Fig. 5B). This work, like previous work on walking and running, demonstrates that musculoskeletal models can be useful for understanding movement energetics in animals under variable gait conditions, although caution needs to be exercised in the attribution of total costs, which may be important in some situations (e.g. understanding the energy budget of an animal in a real-world setting).

One of the continuing challenges of musculoskeletal modelling approaches is the criterion for movement selection that guides the optimisations to solve for individual muscle forces to achieve the goal. Minimisation of muscle stress (Crowninshield and Brand, 1981), energy (Anderson and Pandy, 2001), activation (Dembia et al., 2020) and hybrid criteria (Falisse et al., 2019) have all been used to generate realistic simulations of movement. In many instances during terrestrial locomotion, it is likely that multiple criteria are close to their minimum under the same conditions. For example, humans typically choose to walk or run at stride frequencies or stride lengths that minimise both activation and energy (Russell and Apatoczky, 2016). However, in some special instances such as human cycling (MacIntosh et al., 2000) or when constraints are placed on how people walk (McDonald et al., 2022), humans tend to minimise muscle activation rather than energy. By exploring different constraints on movement and how these constraints impact chosen movement patterns, it is likely that we can gain a better understanding of what dictates the muscle activation patterns and therefore improve the performance of musculoskeletal models under variable gait conditions.

As outlined earlier, more simple models that account for costs based on work or force are often useful for understanding when energetic rates are likely to increase or decrease under different conditions. However, their ability to broadly predict the absolute rate of energy consumption across species or movement conditions remains a challenge. In contrast, while explicit biomechanical models are improving in their ability to predict absolute energy consumption rates, these methods require highly detailed measures of motion of the entire body and the resulting ground reaction forces. A future challenge is to find the middle ground, where simple measures of motion like those possible from a smart watch, can be converted into an accurate prediction of energy consumption across a period of movement time using our understanding of how muscles consume energy.

There have been a number of approaches that have attempted to combine simple mechanical models of movement with models of energy consumption inspired by muscle energetics knowledge that might be useful for further investigation. For example, Alexander (1992) presented a model of the leg as a telescopic actuator with an in-series compression spring that estimated the work required to generate force profiles for walking. The model was used to examine optimum gait patterns for different speeds of motion in bipedal gait. A similar approach was applied by Srinivasan and Ruina (2006) to predict specific gait patterns (pendular versus bouncing gait). Alexander's (1992) model was further elaborated on by Minetti and Alexander (1997), who modified the model and overlayed an energetic cost model based on the requirements of the actuator (in series with a spring) to absorb and generate work. The model was able to predict general changes in the costs of bipedal locomotion under different conditions, although the predictions of energy consumption were substantially higher than those measured experimentally.

We believe that there is promise in using such models to improve predictions of energy consumption related to generating force and mechanical work, although there a number of important steps that need to be considered. Firstly, estimates of the contributions of muscle, as opposed to spring-like tendinous tissue, need to be better understood across animals of different sizes and shapes (mass, leg length, etc.). Secondly, models need to be able to better predict ground forces for animals across different gait conditions (e.g. speed, acceleration, etc.) and different animal sizes. Although spring–mass models have proved to be generally useful under steady-state conditions in both running and walking gaits, new methods to accurately estimate forces acting on the limbs and the subsequent movement of the centre of mass will enable improved estimates of force and work, which ultimately impact the energy predictions using muscle models such as those presented in this Review. Finally, further understanding of how the energetics of muscle scales with animal size (as previously outlined) will also be a major consideration.

Further promising alternatives for estimating the variance in human movement energetics under different locomotor conditions have also emerged that may be practically applied. These will typically select different biomechanical features of movement that might contribute to the energetic costs of movement. For example, Faraji et al. (2018) selected a range of simple factors that contribute to energy consumption (collision costs, cost of supporting body weight, foot clearance costs) and tuned these within a model to reasonably estimate energy consumption across a range of constrained walking conditions. Other attempts have been made to use statistical models or neural networks to effectively isolate terms or physical measurements that most directly relate to energy cost (Gambietz et al., 2024; Slade et al., 2021) and use these to predict energy cost of movement under different movement conditions. These approaches may have practical application for developing specific wearable devices that improve energy cost predictions. However, they need to be tested in a greater range of conditions and may not be easily transferable to understanding locomotor energetics of other species.

It is an exciting time to research the links between the mechanics and energetics of terrestrial locomotion. New technologies [e.g. MEMS (micro-electromechanical systems) and quantum motion and heat sensors, computer vision, high-density electromyography, machine learning algorithms, etc.] are likely to enable researchers to better quantify movement and energy consumption in real-world conditions. With over 100 years of knowledge accumulation to build on, it is now time to address the limitations of current approaches and develop tools for accurate estimates of energy consumption during movement.

The authors acknowledge the anonymous reviewers for their constructive suggestions for improvement to the Review. We also acknowledge the important discussions enabled through participation in the Journal of Experimental Biology Symposium, 2024.