title: What can we learn from Einstein and Arrhenius about the optimal flow of our blood?
abstract: BACKGROUND
  The oxygen flow in humans and other higher animals depends on the erythrocyte-to-blood volume ratio, the hematocrit. Since it is physiologically favourable when the flow of oxygen transport is maximum it can be assumed that this situation has been achieved during evolution. If the hematocrit was too low, too few erythrocytes could transport oxygen. If it was too high, the blood would be very viscous, so that oxygen supply would again be reduced.
  
  
  METHODS
  The theoretical optimal hematocrit can be calculated by considering the dependence of blood viscosity on the hematocrit. Different approaches to expressing this dependence have been proposed in the literature. Here, we discuss early approaches in hydrodynamics proposed by Einstein and Arrhenius and show that especially the Arrhenius equation is very appropriate for this purpose.
  
  
  CONCLUSIONS
  We show that despite considerable simplifications such as neglecting the deformation, orientation and aggregation of erythrocytes, realistic hematocrit values of about 40% can be derived based on optimality considerations. Also the prediction that the ratio between the viscosities of the blood and blood plasma at high shear rates nearly equals Euler's constant (2.718) is in good agreement with observed values. Finally, we discuss possible extensions of the theory. For example, we derive the theoretical optimal hematocrit for persevering divers among marine mammals to be 65%, in excellent agreement with the values observed in several species.
  
  
  CONCLUSIONS
  These considerations are very important for human and animal physiology since oxygen transport is an important factor for medicine and physical performance.
authors.affiliation: Friedrich-Schiller-University, Department of Bioinformatics, Ernst-Abbe-Platz 2, 07737 Jena, Germany. Electronic address: stefan.schu@uni-jena.de.
authors.forename: Stefan
authors.initials: S
authors.lastname: Schuster
authors.forename: Heiko
authors.initials: H
authors.lastname: Stark
mesh_terms: D000818:Animals; D001692:Biological Transport; D001783:Blood Flow Velocity / Q000502:physiology*; D001809:Blood Viscosity; D004912:Erythrocytes / Q000502:physiology*; D006400:Hematocrit; D006801:Humans; D008962:Models, Theoretical; D010100:Oxygen / Q000097:blood
chemical_list: D010100:Oxygen
keywords: Blood flow; Einstein's viscosity equation; Hagen–Poiseuille law; Marine mammals; Optimal hematocrit; Viscosity of suspensions