Arthur J. ‘Knoek’ van Soest

Accurate prediction of both mechanical and metabolic behavior of muscle remains an important challenge in biomechanics. The typically employed Hill-type muscle models have shown limited success in this regard. Therefore, Huxley-type models, in which mechanical and metabolic behavior is linked through cross-bridge cycling, have gained renewed attention. Previous studies fitted the cross-bridge cycling rate parameter values of such models on mechanical behavior only. It seems reasonable to assume that accurate predictions of mechanical behavior in a Huxley-type model will also result in accurate predictions of metabolic behavior as both depend on the cross-bridge dynamics. Here, we show that this assumption does not hold. We simulated previously collected mechanical and metabolic data from an experiment where participants performed either isometric or dynamic knee extensions in the gravitational field. We modeled this experiment with a musculoskeletal model consisting of two segments driven by one Huxley-type muscle model. We obtained 10 sets of cross-bridge rate parameter values by systematically varying the value of one of the rate parameters and optimizing the values of the remaining rate parameters with respect to the mechanical behavior. We then compared the predicted mechanical and metabolic behavior between the 10 sets. The predicted mechanical behavior was similar for all 10 sets. However, the accuracy of the predicted metabolic behavior differed substantially between the 10 sets. Our findings illustrate that different sets of cross-bridge rate parameter values may lead to similar mechanical behavior. We conclude that this should be exploited to obtain accurate predictions of mechanical and metabolic behavior simultaneously in Huxley-type muscle models.

We examined how knee joint movements influence the maximally attainable average mechanical power output (AMPO) of human quadriceps femoris under all-out (sprint) conditions. Experimental dynamometry measurements showed strong correlation with predictions from a Hill-type muscle-tendon-complex model. Further model exploration revealed that cycle frequency and joint excursion interact: increasing one requires reducing the other to maximize AMPO. Furthermore, to maximize AMPO, quadriceps should spend ∼80% of each cycle shortening, independent of cycle frequency and/or joint excursion.

The aim of this study was to advance muscle models that unify mechanical behaviour and metabolic energy expenditure. To that end, we compared predictions of force and metabolic energy expenditure of a Huxley-type muscle–tendon complex (MTC) model with previously obtained experimental data. In our published model, we extended the classic Huxley formulation by incorporating force–length dependency, series elasticity and activation dynamics. Metabolic energy expenditure was modelled as the weighted sum of cross-bridge cycling and calcium pumping costs. In the associated experiment, fibre bundles from nine mouse soleus muscles underwent sinusoidal contractions, while oxygen consumption and tendon force were measured. The bundles were stimulated during both shortening and lengthening, and measurements were taken before and after adding blebbistatin, which blocks cross-bridge cycling but leaves calcium handling unaffected. This enabled separate estimation of metabolic energy costs for each process. In the present study, we modelled these previously published data. Parameters governing model mechanical behaviour were calibrated using trials without oxygen measurements. We used these parameters in simulations of the oxygen measurement trials, and metabolic parameters were optimized to best match average metabolic power. We found that simulated and measured forces corresponded well (root-mean-square error, RMSE <10% of maximum force). Metabolic energy predictions showed higher error (mean RMSE 20.3%, s.d. 12.6% of measured value), with large inter-animal variability. In four animals, where repeated measures were consistent and data followed expected trends, predictions of metabolic energy expenditure were accurate (RMSE <15%). In the remaining five, greater variability or inconsistent data patterns led to poorer fits. Despite this, given the within-animal variability in oxygen measurements, the metabolic predictions are promising. Combined with previous findings, these results support the potential of Huxley-type models in predictive simulations of human metabolic energy expenditure.

Humans and birds use very different running styles. Unlike humans, birds adopt “grounded running” at intermediate speeds—a running gait where at least one foot always maintains ground contact. Avian grounded running is a paradox: Animals usually minimize locomotor energy expenditure, but birds prefer grounded running despite incurring higher energy costs. Using predictive gait simulations of the emu ( Dromaius novaehollandiae ), we resolve this paradox by demonstrating that grounded running represents an optimal gait for birds, from both energetics and muscle excitations perspectives. Our virtual experiments decoupled effects of posture and tendon elasticity, biomechanically relevant anatomical features that cannot be isolated in real birds. The avian body plan prevents (near) vertical leg postures, making the running style used by humans impossible. Under this anatomical constraint, grounded running is optimal if the muscles produce the highest forces in crouched postures, as is true in most birds. Shared anatomical features suggest that, as a behavior, avian grounded running first evolved within non-avian dinosaurs.

Locomotor energetics are an important determinant of an animal's ecological niche. It is commonly assumed that animals minimize locomotor energy expenditure by selecting gait kinematics tuned to the natural frequencies of relevant body parts. We demonstrate that this allows estimation of the preferred step frequency and walking speed of Tyrannosaurus rex , using an approach we introduce as the Natural Frequency Method. Although the tail of bipedal dinosaurs was actively involved in walking, it was suspended passively by the caudal interspinous ligaments. These allowed for elastic energy storage, thereby reducing the metabolic cost of transport. In order for elastic energy storage to be high, step and natural frequencies would have to be matched. Using a 3D morphological reconstruction and a spring-suspended biomechanical model, we determined the tail natural frequency of T. rex (0.66 s ⁻¹ , range 0.41–0.84), and the corresponding walking speed (1.28 m s ⁻¹ , range 0.80–1.64), which we argue to be a good indicator of preferred walking speed (PWS). The walking speeds found here are lower than earlier estimations for large theropods, but agree quite closely with PWS of a diverse group of extant animals. The results are most sensitive to uncertainties regarding ligament moment arms, vertebral kinematics and ligament composition. However, our model formulation and method for estimation of walking speed are unaffected by assumptions regarding muscularity, and therefore offer an independent line of evidence within the field of dinosaur locomotion.

In a recent paper, Kanstad & Kononoff ( Proc. R. Soc. A 471 , 20150287. ( doi:10.1098/rspa.2015.0287 )) presented a theoretical analysis of the mechanical energetics of a particular style of human walking and running. According to their analysis, the force of gravity provides energy when this style of horizontal walking/running is adopted. Furthermore, Kanstad & Kononoff suggested that uphill walking at zero energy cost is possible when the suggested style of walking is adopted. In this commentary, we argue that these claims violate the basic laws of thermodynamics, and are based on erroneous application of the basic laws of classical mechanics.

In this study, the effect of strapping rowers to their sliding seat on performance during 75 m on-water starting trials was investigated. Well-trained rowers performed 75 m maximum-effort starts using an instrumented single scull equipped with a redesigned sliding seat system, both under normal conditions and while strapped to the sliding seat. Strapping rowers to their sliding seat resulted in a 0.45 s lead after 75 m, corresponding to an increase in average boat velocity of about 2.5%. Corresponding effect sizes were large. No significant changes were observed in general stroke cycle characteristics. No indications of additional boat heaving and pitching under strapped conditions were found. The increase in boat velocity is estimated to correspond to an increase in average mechanical power output during the start of on-water rowing between 5% and 10%, which is substantial but smaller than the 12% increase found in a previous study on ergometer starting. We conclude that, after a very short period of adaptation to the strapped condition, single-scull starting performance is substantially improved when the rower is strapped to the sliding seat.