Table 1.

Values of allometric exponents for variables of the mammalian cardiovascular and respiratory systems predicted by the model compared with empirical observations. Observed values of exponents are taken from (2, 3); ND denotes that no data are available.

CardiovascularRespiratory
VariableExponentVariableExponent
PredictedObservedPredictedObserved
Aorta radiusr03/8 = 0.3750.36Tracheal radius3/8 = 0.3750.39
Aorta pressure Δp00 = 0.000.032Interpleural pressure0 = 0.000.004
Aorta blood velocity u00 = 0.000.07Air velocity in trachea0 = 0.000.02
Blood volume Vb1 = 1.001.00Lung volume1 = 1.001.05
Circulation time1/4 = 0.250.25Volume flow to lung3/4 = 0.750.80
Circulation distance l1/4 = 0.25NDVolume of alveolus VA1/4 = 0.25ND
Cardiac stroke volume1 = 1.001.03Tidal volume1 = 1.001.041
Cardiac frequency Ω-1/4 = -0.25-0.25Respiratory frequency-1/4 = -0.25-0.26
Cardiac output Ė3/4 = 0.750.74Power dissipated3/4 = 0.750.78
Number of capillaries Nc3/4 = 0.75NDNumber of alveoli NA3/4 = 0.75ND
Service volume radius1/12 = 0.083NDRadius of alveolus rA1/12 = 0.0830.13
Womersley number ω1/4 = 0.250.25Area of alveolus AA1/6 = 0.083ND
Density of capillaries-1/12 = -0.083-0.095Area of lung AL11/12 = 0.920.95
O2 affinity of blood P50-1/12 = -0.083-0.089O2 diffusing capacity1 = 1.000.99
Total resistance Z-3/4 = -0.75-0.76Total resistance-3/4 = -0.75-0.70
Metabolic rate B3/4 = 0.750.75O2 consumption rate3/4 = 0.750.76