A theory of physiological similarity in muscle-driven motion

Labonte, David

doi:10.1073/pnas.2221217120

Cited by 16 publications

(72 citation statements)

References 64 publications

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“…The separation of the energy landscapes into these two regimes reconciles the debate between McHenry, Arnold and others Arnold et al (2011);McHenry and Summers (2011);McHenry (2010McHenry ( , 2012: both arguments are correct, but in opposite regimes of the physiological similarity index Γ = Γ 1 G −2 (see text for details). (Labonte 2023). This result is both elemental and crucial-muscle has not one, but two characteristic energy capacities.…”

Section: Resultsmentioning

confidence: 87%

“…max , is the dimensionless "physiological similarity index" , so called because musculoskeletal systems that operate with equal Γ put out equal fractions of their maximal displacement, speed, work and power capacity in a single contraction (Labonte 2023).…”

Section: Resultsmentioning

confidence: 99%

“…Here, we take McHenry's work as a starting point, and seek to develop a first principles framework to analyse the influence of the mechanical advantage on the mechanical energy output and mechanical energy flow in musculoskeletal systems. Our analysis builds on the theory of physiological similarity (Labonte 2023), and differs from earlier work in two key aspects: First, instead of an "elastic actuator" akin to a spring, we will analyse the dynamics of a system driven directly by muscle. This difference will enable us to show that variations in mechanical advantage can control how much work muscle can deliver, so reconciling Arnold et al's objection with McHenry's observation.…”

Section: Archimedes Of Syracusementioning

confidence: 99%

“…We use the conservation of energy to evaluate the flow of mechanical energy in the idealised model of a real musculoskeletal system that forms the basis of the theory of physiological similarity (Labonte 2023): a muscle with volume V m exerts a force F i (t), and acts on a mass m via an anatomical arrangement with characteristic constant mechanical advan-tage G; there are no in-series elastic elements (Figure 1). The muscle can apply a force of no more than F max , shorten by a distance of at most δ max , and no faster than with a maximum shortening velocity v max = L m εmax , where L m is a characteristic fascicle length, and εmax is a maximum strain rate in units muscle lengths per second.…”

Section: Model Formulation and Assumptionsmentioning

confidence: 99%

“…This result arises, because the idealised and the Hillmuscle become indistinguishable at the limits corresponding to vanishing and diverging G (see Labonte (2023) for further discussion).…”

Section: The Optimal Mechanical Advantage For Quadratic Dragmentioning

confidence: 99%

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Optimising the flow of mechanical energy in musculoskeletal systems through gearing

Polet,

Labonte

2024

Preprint

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Movement is integral to animal life, and most animal movement is actuated by the same engine: skeletal muscle. Muscle input is typically mediated by skeletal elements, resulting in musculoskeletal systems that are "geared": at any instant, the muscle force and velocity are related to the output force and velocity only via a proportionality constant G, the "mechanical advantage". The functional analysis of such "simple machines" has traditionally centred around this instantaneous interpretation, such that a small vs large G is thought to reflect a fast vs forceful system, respectively. But evidence is mounting that a complete analysis ought to also consider the mechanical energy output of a complete contraction. Here, we approach this task systematically, and use the theory of physiological similarity to study how gearing affects the flow of mechanical energy in a minimalist model of a musculoskeletal system. Gearing influences the flow of mechanical energy in two key ways: it can curtail muscle work output, because it determines the ratio between the characteristic muscle work and kinetic energy capacity; and it defines how each unit of muscle work is partitioned into different system energies, i.e. into kinetic vs. "parasitic" energy such as heat. As a consequence of both effects, delivering maximum work in minimum time and with maximum transmission efficiency generally requires a mechanical advantage of intermediate magnitude. This optimality condition can be expressed in terms of two dimensionless numbers, which reflect the key geometric, physiological, and physical properties of the interrogated musculoskeletal system, and the environment in which the contraction takes place. Illustrative application to exemplar musculoskeletal systems predicts plausible mechanical advantages in disparate biomechanical scenarios; yields a speculative explanation for why gearing is typically used to attenuate the instantaneous force output (G_opt < 1); and predicts how G needs to vary systematically with animal size to optimise the delivery of mechanical energy, in superficial agreement with empirical observations. A many-to-one-mapping from musculoskeletal geometry to mechanical performance is identified, such that differences in G alone do not provide a reliable indicator for specialisation for force vs speed- neither instantaneously, nor in terms of mechanical energy output. The energy framework presented here can be used to estimate an optimal mechanical advantage across variable muscle physiology, anatomy, mechanical environment and animal size, and so facilitates investigation of the extent to which selection has made efficient use of gearing as degree of freedom in musculoskeletal "design".

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Section: Resultsmentioning

confidence: 87%

Section: Resultsmentioning

confidence: 99%

Section: Archimedes Of Syracusementioning

confidence: 99%

Section: Model Formulation and Assumptionsmentioning

confidence: 99%

“…This result arises, because the idealised and the Hillmuscle become indistinguishable at the limits corresponding to vanishing and diverging G (see Labonte (2023) for further discussion).…”

Section: The Optimal Mechanical Advantage For Quadratic Dragmentioning

confidence: 99%

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Optimising the flow of mechanical energy in musculoskeletal systems through gearing

Polet,

Labonte

2024

Preprint

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Dynamic similarity and the peculiar allometry of maximum running speed

Labonte,

Bishop,

Dick

et al. 2024

Nat Commun

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Animal performance fundamentally influences behaviour, ecology, and evolution. It typically varies monotonously with size. A notable exception is maximum running speed; the fastest animals are of intermediate size. Here we show that this peculiar allometry results from the competition between two musculoskeletal constraints: the kinetic energy capacity, which dominates in small animals, and the work capacity, which reigns supreme in large animals. The ratio of both capacities defines the physiological similarity index Γ, a dimensionless number akin to the Reynolds number in fluid mechanics. The scaling of Γ indicates a transition from a dominance of muscle forces to a dominance of inertial forces as animals grow in size; its magnitude defines conditions of “dynamic similarity“ that enable comparison and estimates of locomotor performance across extant and extinct animals; and the physical parameters that define it highlight opportunities for adaptations in musculoskeletal “design” that depart from the eternal null hypothesis of geometric similarity. The physiological similarity index challenges the Froude number as prevailing dynamic similarity condition, reveals that the differential growth of muscle and weight forces central to classic scaling theory is of secondary importance for the majority of terrestrial animals, and suggests avenues for comparative analyses of locomotor systems.

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