What can welearn from Einstein andArrhenius abouttheoptimal flow of our blood

abstract Article history:Received 17 April 2013Received in revised form 27 August 2013Accepted 29 August 2013Available online 8 September 2013Keywords:Blood flowEinstein's viscosity equationHagen–Poiseuille lawMarine mammalsOptimal hematocritViscosity of suspensions Background:Theoxygenflowinhumansandotherhigher animalsdependsontheerythrocyte-to-bloodvolumeratio,thehematocrit.Sinceitisphysiologicallyfavourablewhentheflowofoxygentransportismaximumitcanbeassumedthatthis situation hasbeenachievedduring evolution.Ifthehematocritwastoolow,toofeweryth-rocytescouldtransportoxygen.Ifitwastoohigh,thebloodwouldbevery viscous,so thatoxygen supplywouldagain be reduced.Methods:Thetheoreticaloptimalhematocrit can be calculatedbyconsidering thedependence of bloodviscosityon the hematocrit. Different approaches to expressing this dependence have been proposed in the literature.Here,wediscussearlyapproachesinhydrodynamicsproposedbyEinsteinandArrheniusandshowthatespecial-ly the Arrhenius equation is very appropriate for this purpose.Results&conclusions:Weshowthatdespiteconsiderablesimplificationssuchasneglectingthedeformation,ori-entation and aggregation of erythrocytes, realistic hematocrit valuesof about 40% can be derived based on opti-malityconsiderations.AlsothepredictionthattheratiobetweentheviscositiesofthebloodandbloodplasmaathighshearratesnearlyequalsEuler'sconstant(2.718)isingoodagreementwithobservedvalues.Finally,wedis-cusspossibleextensionsofthetheory.Forexample,wederivethetheoreticaloptimalhematocritforperseveringdivers among marine mammals to be 65%, in excellent agreement with the values observed in several species.General significance: These considerations are very important for human and animal physiology since oxygentransport is an important factor for medicine and physical performance.© 2013 Elsevier B.V. All rights reserved.