acteristics of the cardiovascular and respiratory systems, some of which have already been confirmed experimentally (Tables 1 and 2). E. Angiosperm trees An extension of their theory for broad-leaved angiosperm trees also makes some successful predictions, perhaps most notably that maximum possible tree heights should be on the order of 100 meters. This is in agreement with observations: the world’s tallest tree is a coastal redwood (Sequoia sempervirens) named “Hyperion” with a height of 116 meters (Enking 2022). For purposes of brevity, we do not discuss it here. However, interested readers may consult Enquist et al. (2000) for details. F.WBE ontogenetic growth theory West et al. (2001) also developed a general model for the ontogenetic growth of an organism, i.e., growth over the course of its lifetime. Their model partitions metabolic energy use between the energy needed to maintain existing tissue and the energy needed to produce new tissue: (12) The total basal metabolic rate B is the sum of the individual metabolic rates of the body’s cells, plus the rate at which energy is used to form new cells. The summation is over the different tissue types within the body. For each tissue type, there are Nc cells, each having a cellular metabolic rate of Bc, and Ec is the energy needed to form a new cell for that particular tissue type. WBE used Eq. (12) to derive an expression (see Appendix D for details) for an organism’s body mass m as a function of time: (13) 1 4 1 1 4 4 0 4 1 1 aM t m m e M M − − = − − Figure 6. Higher cardiovascular efficiency is obtained by using the “area-preserving” ⁻½ radius- scaling for wide blood vessels (smaller values of ), and the ⁻⅓ radius-scaling for thin blood vessels (higher values of ). After Figure 8 in West, Brown, and Enquist (2000). Variable Symbol Predicted Exp. Empirical Exp. Reference Aorta Radius 0 3/8 0.375 0.36, 0.41 Holt et al., Schmidt-Nielsen Pressure in Aorta Δ 0 0 0.00 0.032 Blood Velocity in Aorta 0 0 0.00 0.07 Blood Volume V .00 0.99, 1.00, 1.02 Günther, Prothero, Stahl Circulation Time T /4 0.25 0.25 Schmidt-Nielsen (calculated) Circulation Distance /4 0.25 ND Cardiac Stroke Volume .00 .04- .05 Günther Cardiac Frequency ω −/4 −0.25 −0.25, −0.26 Stahl, Günther Cardiac Output E 3/4 0.75 0.8 , 0.78–0.79 Stahl, Günther Number of Capillaries N 3/4 0.75 ND Supply Radius of Cells /2 0.083 ND Radius of Krogh Cylinder /8 0.25 ND Density of Capillaries −/2 -0.083 −0.095 Oxygen Affinity of Blood P50 −/2 −0.083 −0.089 Total Peripheral Resistance Z −3/4 −0.75 −0.76 Günther Womersley Number α /4 0.25 0.25 Metabolic Rate (O2 Uptake) B 3/4 0.75 0.76 Stahl Table 1. WBE predicted values of λ in cardiovascular allometric relationships Y Y0 Mλ, as well as experimentally-determined values (with references). HEBERT Allometric and metabolic scaling 2023 ICC 212
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