Summary
This paper attempts to explain Kleiber's rule, which relates metabolic rate of mammals to their body mass, from the structure and function of the blood circulation system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a :
-
scaling factor
- Δ:
-
fractal dimension
- Δ:
-
hydrodynamic conductivity
- l n :
-
length of an arterial blood vessel at bifurcation level n
- M :
-
body mass
- N :
-
maximal number of bifurcation levels
- p :
-
pressure
- Q :
-
flow
- r :
-
size of Bohr effect
- r n :
-
radius of an arterial blood vessel at bifurcation level n
- V :
-
volume
- VO 2 :
-
rate of oxygen unloading
- Z n :
-
number of arterial blood vessels at bifurcation level n
References
Altmann PL, Dittmer DS (ed) (1964) Biology data book. Fed Am Soc Exp Biol
Barbee JH, Cokelet GR (1971) The Fahraeus effect. Microvasc Res 3: 6–16
Barbee JH, Cokelet GR (1971) Prediction of blood flow in tubes with diameters as small as 29 μ. Microvasc Res 3: 17–21
Buddenbrock W von (1967) Vergleichende Physiologie Bd 6: Blut und Herz. Birkhäuser, Basel Stuttgart
Burton AC (1972) Physiology and biophysics of the circulation: An introductory text. 2nd ed, Year Book Medical Publishers Inc., Chicago
Duncker HR, Günthert M (1985) The quantitative design of the avian respiratory system — from hummingbird to mute swan. BIONA report 3: 361–378
Duncker HR (1991) Constructional and ecological prerequisites for the evolution of homeothermy. In: Schmidt-Kittler N (ed) Constructional morphology and biomechanics: concepts and implications. Springer, Berlin Heidelberg New York
Eckert R, Randall D (1983) Animal physiology, mechanisms, and adaptation. 2nd ed, Freeman and Co., San Francisco
Fahreus R, Lindquist T (1931) The viscosity of the blood in narrow capillary tubes. Am J Physiol 96: 562–568
Fung YC (1984) Biomechanics: Mechanical properties of living tissues. Springer, New York
Fung YC (1981) Biodynamics: circulation. Springer, New York
Groat RA (1948) Relationship of volumetric rate of blood flow to arterial diameter. Fed Proc 7: 45
Hargens AR, Millard RW, Pettersson K, Johansen K (1987) Gravitational haemodynamics and oedema prevention in the giraffe. Nature 329: 59–60
Hemmingsen AM (1960) Energy metabolism as related to body size and respiratory surfaces and its evolution. Rep Steno Memorial Hosp Nord Insulinlab 9: 1–110
Kleiber M (1932) Body size and metabolism. Hilgardia 6: 315–353
Kleiber M (1961) The fire of life. An introduction to animal energetics. Wiley, New York
Krebs HA (1950) Body size and tissue respiration. Biochim Biophys Acta 4: 249–269
Mandelbrot BB (1983) The fractal geometry of nature. Freeman and Co, New York, p. 157
McMahon T (1973) Size and shape in biology. Science 179: 1201–1204
Prothero JW (1979) Maximal oxygen consumption in various animals and plants. Biochem Physiol 64 A: 463–466
Riggs A (1960) The nature and significance of the Bohr effect in mammalian hemoglobins. J Gen Physiol 43: 737–752
Rubner M (1883) Über den Einfluß der Körpergröße auf Stoff- und Kraftwechsel. Z Biol 19: 535–562
Schmidt-Nielsen K (1983) Animal physiology: Adaptation and environment. 3rd ed. Cambridge Univ. Press, Cambridge
Schmidt-Nielsen K (1984) Scaling: Why is animals size so important? Cambridge Univ. Press, Cambridge
Schmidt-Nielsen K, Larimer J (1958) Oxygen dissociation curves of mammalian blood in relation to body size. Am J Physiol 195: 424–428
Sernetz M, Gelléri B, Hofmann J (1985) The organism as bioreactor. Interpretation of the reduction law of metabolism in terms of heterogeneous catalysis and fractal structure. J Theor Biol 117: 209–230
Stahl WR (1965) Organ weights in primates and other mammals. Science 150: 1039–1042
Stahl WR (1967) Scalling of respiratory variables in mammals. J Appl Physiol 22: 453–460
Suwa N, Takahashi T (1971) Morphological and morphometrical analysis of circulation in hypertension and ischemic kidney. Urban and Schwarzenberg, München
Taylor CR (1982) Scaling limits of metabolism to body size: Implications for animal design. In: Taylor RC Johansen K, Bolis L (eds) A companion to animal physiology. Cambridge Univ Press, Cambridge
Taylor CR, Weibel ER (1981) Design of the mammalian resiratory system. I. Problem and Strategy. Resp Physiol 44: 1–10
Taylor CR, Maloiy GMO, Weibel ER, Langman VA, Kamau JMZ, Seeherman HJ, Heglund NC (1981) Design of the mammalian respiratory system: Scaling maximum aerobic capacity to body mass — wild and domestic mammals. Resp Physiol 44: 25–38
Thoma R (1901) Über den Verzweigungsmodus der Arterien. Arch Entwicklungsmech 12: 352–413
Weis-Fogh T, Alexander R McN (1977) The sustained power output from striated muscle. In: Pedley T (ed) Scale effects in animal locomotion. Academic Press, London New York San Francisco
Wieser W (1984) A distinction must be made between the ontogeny and the phylogeny of metabolism in order to understand the mass exponent of energy metabolism. Resp Physiol 55: 1–9
Wieser W (1986) Bioenergetik: Energietransformationen bei Organismen. Thieme, Stuttgart
Wilkie D (1977) Metabolism and body size. In: Pedley T (ed) Scale effects in animal locomotion. Academic Press, London New York San Francisco
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Spatz, HC. Circulation, metabolic rate, and body size in mammals. J Comp Physiol B 161, 231–236 (1991). https://doi.org/10.1007/BF00262303
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00262303