Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa

Abstract

I used a simple mathematical model of the inverse dynamics of locomotion to estimate the minimum muscle masses required to maintain quasi-static equilibrium about the four main limb joints at mid-stance of fast running. Models of 10 extant taxa (a human, a kangaroo, two lizards, an alligator, and five birds) were analyzed in various bipedal poses to examine how anatomy, size, limb orientation, and other model parameters influence running ability. I examined how the muscle masses required for fast running compare to the muscle masses that are actually able to exert moments about the hip, knee, ankle, and toe joints, to see how support ability varies across the limb. I discuss the assumptions and limitations of the models, using sensitivity analysis to see how widely the results differed with feasible parameter input values. Even with a wide range of input values, the models validated the analysis procedure. Animals that are known to run bipedally were calculated as able to preserve quasi-static equilibrium about their hindlimb joints at mid-stance, whereas non-bipedal runners (iguanas and alligators) were recognized as having too little muscle mass to run quickly in bipedal poses. Thus, this modeling approach should be reliable for reconstructing running ability in extinct bipeds such as nonavian dinosaurs. The models also elucidated how key features are important for bipedal running capacity, such as limb orientation, muscle moment arms, muscle fascicle lengths, and body size. None of the animals modeled had extensor muscle masses acting about any one joint that were 7% or more of their body mass, which provides a reasonable limit for how much muscle mass is normally apportioned within a limb to act about a particular joint. The models consistently showed that a key biomechanical limit on running ability is the capacity of ankle extensors to generate sufficiently large joint moments. Additionally, the analysis reveals how large ratite birds remain excellent runners despite their larger size; they have apomorphically large extensor muscles with relatively high effective mechanical advantage. Finally, I reconstructed the evolution of running ability in the clade Reptilia, showing that the ancestors of extant birds likely were quite capable runners, even though they had already reduced key hip extensors such as M. caudofemoralis longus.

The gait dynamics of the modern broiler chicken: A cautionary tale of selective breeding

“…Havenstein et al, 1994a;Havenstein et al, 1994b;Lilburn, 1994), but under natural conditions is usually only seen in other Galliformes that require this large muscle to power a rapid take-off; e.g. grouse or partridges (Hartman, Step cycle (%) 3243 Gait dynamics of the broiler chicken wider pelvis (Pureline B birds), in combination with the large pectoral muscle mass (Hutchinson, 2004). Yet it remains unclear how other morphological changes may affect gait.…”

Terror birds on the run: a mechanical model to estimate its maximum running speed

“…According to a study on the running capabilities in bipeds and the leg extensor muscles mass, the increment of the body size implies a decline in the running speed (Hutchinson 2004). With this assumption, the estimated speed for the huge Phorursrhacinae gen. seems doubtful.…”

“…With this assumption, the estimated speed for the huge Phorursrhacinae gen. seems doubtful. However, the phororhacid group could have an apomorphically large extensor muscles like the fast running extant ratites (Hutchinson 2004 ). But this speed is only accessible for the fastest extant terrestrial tetrapod, the cheetah (Acynonix jubatus).…”

In vivostrains in the femur of river cooter turtles(Pseudemys concinna) during terrestrial locomotion: tests of force-platform models of loading mechanics

“…Alternatively, high limb bone safety factors, resulting from 'excessively' robust femora, may simply be a consequence of providing adequate surface area for the attachment of sufficiently large locomotor muscles to power locomotion and resist the high muscle forces that can be imposed during sprawling locomotion (Butcher and Blob, 2008). Such a scenario would suggest that skeletal design in the limb may be substantially influenced by the demands imposed by muscle arrangement and performance (Hutchinson and Garcia, 2002;Hutchinson, 2004).…”