The Principle of Laplace and Scaling of Ventricular Wall Stress and Blood Pressure in Mammals and Birds

Abstract

Maximum left ventricular wall stress is calculated at end-diastolic volume and systemic arterial diastolic blood pressure, according to a thick-walled model for the principle of Laplace. Stress is independent of body mass and averages 13.9 kPa (+/-2.3; 95% confidence interval) in 24 species of mammals weighing 0.025-4,000 kg and 15.5 kPa (+/-4.7) in 12 birds weighing 0.014-110 kg. Birds have higher arterial blood pressures and larger hearts than mammals. Systolic and diastolic arterial blood pressures increase with body mass according to M(0.05) in mammals, and heart mass increases according to M(1.06) in the same species, further supporting the principle. However, blood pressure in birds is independent of body mass, and heart mass scales isometrically. End-diastolic stress values, calculated according to Laplace, are about one-third of peak stresses recorded in isolated mammalian myocardial preparations.

Blood flow to long bones indicates activity metabolism in mammals, reptiles and dinosaurs

“…Significant differences are bold. Blood flow to long bones R. S. Seymour et al 453 pressure in mammals increases significantly with body mass to the 0.05 power [22], it follows that maximum bone blood flow should be proportional to body mass to the 0.86 þ 0.05 ¼ 0.91 power. This value is indistinguishable from the 0.87 scaling exponent of mammalian exercise-induced MMR [23].…”

Testing Metabolic Theories

“…The assumption that the network tips are invariant with size has been argued to be inconsistent with the space-filling assumption, although the branching network model still predicts three-fourths power scaling if blood flow velocity increases with M 1/12 (Banavar et al 2010). Given that cardiac output of mammals scales as the product of heart rate ∝ M Ϫ0.23 (Seymour and Blaylock 2000) and stroke volume ∝ M 1.03 (Seymour and Blaylock 2000) and that aorta diameter scales with M 0.36 (Holt et al 1981), flow velocity through the aorta should scale as M 0.08 , which is very close to M 1/12 . WBE argued that, if cells were the terminal units of the circulatory system and not capillaries, metabolically active tissue density would have to vary with mass to the onefourth to match the observed mass-specific scaling of metabolic rate .…”

Allometric Analysis beyond Heterogeneous Regression Slopes: Use of the Johnson‐Neyman Technique in Comparative Biology

“…Given that the hearts of small (!4.26 kg) birds, the majority of which are capable of flight, are significantly larger than those of similarly sized mammals, it therefore seems appropriate to regress fliers (small birds) and nonfliers (small birds and large mammals) separately. Similarly, the blood pressures of mammals and birds are similar at large masses and diverge at small masses (Seymour and Blaylock 2000). The large hearts and high blood pressures of small birds therefore appear to be associated with the increased metabolic demands of flight.…”

“…In their study of the principle of Laplace and scaling of ventricular wall stress and blood pressure, Seymour and Blaylock (2000) found that the linear regressions relating log-transformed heart mass to log-transformed body mass (as the covariate) for mammals and birds had significantly different slopes. They noted that this prevented testing for significant differences in elevation but stated that "the bird hearts were obviously heavier within the range of similar body mass" and that "the scaling factor was twice as high at a body mass of 1 kg, but the data converge in larger species" (Seymour and Blaylock 2000, p. 395).…”