Bipedal hopping is used by macropods, including rat-kangaroos, wallabies and kangaroos (superfamily Macropodoidea). Interspecific scaling of the ankle extensor muscle-tendon units in the lower hindlimbs of these hopping bipeds shows that peak tendon stress increases disproportionately with body size. Consequently, large kangaroos store and recover more strain energy in their tendons, making hopping more efficient, but their tendons are at greater risk of rupture. This is the first intraspecific scaling analysis on the functional morphology of the ankle extensor muscle-tendon units (gastrocnemius, plantaris and flexor digitorum longus) in one of the largest extant species of hopping mammal, the western grey kangaroo Macropus fuliginosus (5.8-70.5 kg post-pouch body mass). The effective mechanical advantage of the ankle extensors does not vary with post-pouch body mass, scaling with an exponent not significantly different from 0.0. Therefore, larger kangaroos balance rotational moments around the ankle by generating muscle forces proportional to weight-related gravitational forces. Maximum force is dependent upon the physiological cross-sectional area of the muscle, which we found scales geometrically with a mean exponent of only 0.67, rather than 1.0. Therefore, larger kangaroos are limited in their capacity to oppose large external forces around the ankle, potentially compromising fast or accelerative hopping. The strain energy return capacity of the ankle extensor tendons increases with a mean exponent of ~1.0, which is much shallower than the exponent derived from interspecific analyses of hopping mammals (~1.4-1.9). Tendon safety factor (ratio of rupture stress to estimated peak hopping stress) is lowest in the gastrocnemius (< 2), and it decreases with body mass with an exponent of -0.15, extrapolating to a predicted rupture at 160 kg. Extinct giant kangaroos weighing 250 kg could therefore not have engaged in fast hopping using 'scaled-up' lower hindlimb morphology of extant western grey kangaroos.

This meta-study investigated the relationships between blood flow rate ( _ Q; cm 3 s −1 ), wall shear stress (τ w ; dyn cm −2 ) and lumen radius (r i ; cm) in 20 named systemic arteries of nine species of mammals, ranging in mass from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varied between 3.7 µm in a cremaster artery of a rat and 11.2 mm in the aorta of a human. The 92 logged data points of _ Q and r i are described by a single second-order polynomial curve with the equation: log _ Q ¼ À0:20 log r 2 i þ 1:91 log r i þ 1:82. The slope of the curve increased from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci's rule ( _ Q/r 2 i ) applies to the main arteries and Murray's law ( _ Q/r 3 i ) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which _ Q is fairly constant, yielded the allometric power equation: _ Q ¼ 155r 2:49 i . These empirical equations allow calculation of resting perfusion rates from arterial lumen size alone, without reliance on theoretical models or assumptions on the scaling of wall shear stress in relation to body mass. As expected, _ Q of individual named arteries is strongly affected by body mass; however, _ Q of the common carotid artery from six species (mouse to horse) is also sensitive to differences in whole-body basal metabolic rate, independent of the effect of body mass.

If arteries penetrate bones through foramina, regional artery blood flow rates can be estimated from the foramen sizes. Femoral bone blood flow rates estimated from nutrient foramen sizes were previously not absolute, but only a relative blood flow index (Q i ), because the size relationship between the foramen and the occupying artery was unknown. The current study used vascular contrast and micro-computerized tomographic scanning to investigate femoral nutrient foramen and nutrient artery sizes in three groups of sub-adult chickens (non-laying hens, laying hens, and roosters) of similar ages. The results indicate that the cross-sectional area of the nutrient artery lumen occupies approximately 20.2 ± 4.1% of the foramen for femora with only one foramen. Artery lumen size is significantly correlated with foramen size. Vascular contrast imaging is capable of estimating blood flow rates through nutrient arteries, as blood flow rates estimated from artery lumen casts are similar to blood flow rates measured by infusion of fluorescent-labeled microspheres. Laying hens tend to have higher nutrient artery perfusion rates than non-laying hens, probably due to extra oxygen and calcium requirements for eggshell production, although the calculated blood flow difference was not statistically significant. Histological embedding and sectioning along with vascular contrast imaging reveal variable nutrient foramen morphology and nutrient artery location among femora with more than one nutrient foramen.

Brain metabolic rate (MR) is linked mainly to the cost of synaptic activity, so may be a better correlate of cognitive ability than brain size alone. Among primates, the sizes of arterial foramina in recent and fossil skulls can be used to evaluate brain blood flow rate, which is proportional to brain MR. We use this approach to calculate flow rate in the internal carotid arteries ( Q ˙ ICA ) , which supply most of the primate cerebrum. Q ˙ ICA is up to two times higher in recent gorillas, chimpanzees and orangutans compared with 3-million-year-old australopithecine human relatives, which had equal or larger brains. The scaling relationships between Q ˙ ICA and brain volume ( V br ) show exponents of 1.03 across 44 species of living haplorhine primates and 1.41 across 12 species of fossil hominins. Thus, the evolutionary trajectory for brain perfusion is much steeper among ancestral hominins than would be predicted from living primates. Between 4.4-million-year-old Ardipithecus and Homo sapiens , V br increased 4.7-fold, but Q ˙ ICA increased 9.3-fold, indicating an approximate doubling of metabolic intensity of brain tissue. By contrast, Q ˙ ICA is proportional to V br among haplorhine primates, suggesting a constant volume-specific brain MR.

The nutrient artery passes through the nutrient foramen on the shaft of the femur and supplies more than half of the total blood flow to the bone. Assuming that the size of the nutrient foramen correlates with the size of the nutrient artery, an index of blood flow rate () can be calculated from nutrient foramen dimensions. Interspecific is proportional to locomotor activity levels in adult mammals, birds and reptiles. However, no studies have yet estimated intraspecific to test for the effects of growth and locomotor development on bone blood flow requirements. In this study, we used micro-CT and medical CT scanning to measure femoral dimensions and foramen radius to calculate femoral during the in-pouch and post-pouch life stages of western grey kangaroos () weighing 5.7 g to 70.5 kg and representing a 12,350-fold range in body mass. A biphasic scaling relationship between and body mass was observed (breakpoint at ca. 1-5 kg body mass right before permanent pouch exit), with a steep exponent of 0.96±0.09 (95% CI) during the in-pouch life stage and a statistically independent exponent of -0.59±0.90 during the post-pouch life stage. In-pouch joeys showed values that were 50-100 times higher than those of adult diprotodont marsupials of the same body mass, but gradually converged with them as post-pouch adults. Bone modelling during growth appears to be the main determinant of femoral bone blood flow during in-pouch development, whereas bone remodelling for micro-fracture repair due to locomotion gradually becomes the main determinant when kangaroos leave the pouch and become more active.