Morphology of the nutrient artery and its foramen in relation to femoral bone perfusion rates of laying and non-laying hens.

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 (Qi ), 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.

Regional femoral bone blood flow rates in laying and non-laying chickens estimated with fluorescent microspheres.

The metabolic rate of vertebrate bone tissue is related to bone growth, repair and homeostasis, which are all dependent on life stage. Bone metabolic rate is difficult to measure directly, but absolute blood flow rate () should reflect local tissue oxygen requirements. A recent 'foramen technique' has derived an index of blood flow rate () by measuring nutrient foramen sizes of long bones. is assumed to be proportional to ; however, the assumption has never been tested. This study used fluorescent microsphere infusion to measure femoral bone in anaesthetized non-laying hens, laying hens and roosters. Mean mass-specific cardiac output was 338±38 ml min-1 kg-1, and the two femora received 0.63±0.10% of this. Laying hens had higher wet bone mass-specific to femora (0.23±0.09 ml min-1 g-1) than the non-laying hens (0.12±0.06 ml min-1 g-1) and roosters (0.14±0.04 ml min-1 g-1), presumably associated with higher bone calcium mobilization during eggshell production. Estimated metabolic rate of femoral bone was 0.019 ml O2 min-1 g-1. Femoral increased significantly with body mass, but was not correlated with nutrient foramen radius (r), probably because of a narrow range in foramen radius. Over all 18 chickens, femoral shaft was 1.07±0.30 ml min-1 mm-1. Mean in chickens was significantly higher than predicted by an allometric relationship for adult cursorial bird species, possibly because the birds were still growing.

Blood flow rate and wall shear stress in seven major cephalic arteries of humans.

Blood flow rate ( Q˙ ) in relation to arterial lumen radius (ri ) is commonly modelled according to theoretical equations and paradigms, including Murray's Law ( Q˙ ∝ ri3 ) and da Vinci's Rule ( Q˙ ∝ ri2 ). Wall shear stress (τ) is independent of ri with Murray's Law (τ âˆ  ri0 ) and decreases with da Vinci's Rule (τ âˆ  ri-1 ). These paradigms are tested empirically with a meta-analysis of the relationships between Q˙ and ri in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that Q˙ ∝ ri2.16 and τ âˆ  ri-1.02 , more consistent with da Vinci's Rule than Murray's Law. This meta-analysis provides standard values for Q˙ , ri and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.

Bone foramen dimensions and blood flow calculation: best practices.

Some blood vessels enter bones through foramina, leaving the size of the foramen as a gauge for estimating the rate of blood flow and hence the metabolic rate of the supplied tissues. Foramen dimensions have been measured using varied methods in previous foramen studies, to relate regional blood flows with associated physiological processes. With the increasing interests in this 'foramen technique', standard methods with minimized measurement errors are therefore required. This study provides details of microphotographic and micro-computerized tomographic methods, and introduces a new alternative method, which uses impression material to measure foramen dimensions. The three methods are compared and the results indicate that all of them are capable of obtaining precise and accurate foramen dimension values, although they all have limitations. A microphotograph of the external opening is suggested to be the standard method because of its ease of use, but the alternative methods provide more detailed information on foramen shape. If the foramen is mainly occupied by one artery, blood flow rates can be calculated from foramen size and artery wall-lumen ratio, which is evaluated from the literature survey in this study. If veins or nerves also penetrate the foramen, a relative index of blood flow rate is nevertheless possible for comparative purposes.

Cerebral blood flow rates in recent great apes are greater than in Australopithecus species that had equal or larger brains.

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 (Vbr) 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, Vbr 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 Vbr among haplorhine primates, suggesting a constant volume-specific brain MR.

Interspecific scaling of blood flow rates and arterial sizes in mammals.

This meta-study investigated the relationships between blood flow rate (Q̇; cm3 s-1), wall shear stress (τw; dyn cm-2) and lumen radius (ri; 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 [Formula: see text] and ri are described by a single second-order polynomial curve with the equation: [Formula: see text] 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 ([Formula: see text]) applies to the main arteries and Murray's law ([Formula: see text]) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which [Formula: see text] is fairly constant, yielded the allometric power equation: [Formula: see text] 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, [Formula: see text] of individual named arteries is strongly affected by body mass; however, [Formula: see text] 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.

Femoral bone perfusion through the nutrient foramen during growth and locomotor development of western grey kangaroos (Macropus fuliginosus).

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 (Qi) can be calculated from nutrient foramen dimensions. Interspecific Qi is proportional to locomotor activity levels in adult mammals, birds and reptiles. However, no studies have yet estimated intraspecific Qi 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 Qi during the in-pouch and post-pouch life stages of western grey kangaroos (Macropus fuliginosus) weighing 5.7 g to 70.5 kg and representing a 12,350-fold range in body mass. A biphasic scaling relationship between Qi 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 Qi 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.

Scaling of the ankle extensor muscle-tendon units and the biomechanical implications for bipedal hopping locomotion in the post-pouch kangaroo Macropus fuliginosus.

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.