Pulsatile blood flow, shear force, energy dissipation and Murray's Law

BACKGROUND: Murray's Law states that, when a parent blood vessel branches into daughter vessels, the cube of the radius of the parent vessel is equal to the sum of the cubes of the radii of daughter blood vessels. Murray derived this law by defining a cost function that is the sum of the energy cost of the blood in a vessel and the energy cost of pumping blood through the vessel. The cost is minimized when vessel radii are consistent with Murray's Law. This law has also been derived from the hypothesis that the shear force of moving blood on the inner walls of vessels is constant throughout the vascular system. However, this derivation, like Murray's earlier derivation, is based on the assumption of constant blood flow. METHODS: To determine the implications of the constant shear force hypothesis and to extend Murray's energy cost minimization to the pulsatile arterial system, a model of pulsatile flow in an elastic tube is analyzed. A new and exact solution for flow velocity, blood flow rate and shear force is derived. RESULTS: For medium and small arteries with pulsatile flow, Murray's energy minimization leads to Murray's Law. Furthermore, the hypothesis that the maximum shear force during the cycle of pulsatile flow is constant throughout the arterial system implies that Murray's Law is approximately true. The approximation is good for all but the largest vessels (aorta and its major branches) of the arterial system. CONCLUSION: A cellular mechanism that senses shear force at the inner wall of a blood vessel and triggers remodeling that increases the circumference of the wall when a shear force threshold is exceeded would result in the observed scaling of vessel radii described by Murray's Law

Determinants of inter-specific variation in basal metabolic rate

Basal metabolic rate (BMR) is the rate of metabolism of a resting, postabsorptive, non-reproductive, adult bird or mammal, measured during the inactive circadian phase at a thermoneutral temperature. BMR is one of the most widely measured physiological traits, and data are available for over 1,200 species. With data available for such a wide range of species, BMR is a benchmark measurement in ecological and evolutionary physiology, and is often used as a reference against which other levels of metabolism are compared. Implicit in such comparisons is the assumption that BMR is invariant for a given species and that it therefore represents a stable point of comparison. However, BMR shows substantial variation between individuals, populations and species. Investigation of the ultimate (evolutionary) explanations for these differences remains an active area of inquiry, and explanation of size-related trends remains a contentious area. Whereas explanations for the scaling of BMR are generally mechanistic and claim ties to the first principles of chemistry and physics, investigations of mass-independent variation typically take an evolutionary perspective and have demonstrated that BMR is ultimately linked with a range of extrinsic variables including diet, habitat temperature, and net primary productivity. Here we review explanations for size-related and mass-independent variation in the BMR of animals, and suggest ways that the various explanations can be evaluated and integrated