HemodynamicsBioengineering 6000 CV PhysiologyHemodynamicsBioengineering 6000 CV PhysiologyHemodynamicsOverview and TerminologyArterioles• Parameters– Pressure– Velocity– Flow• laminar vs. turbulent– Resistance– Viscosity – Energy– Area– VolumeBioengineering 6000 CV PhysiologyHemodynamicsVessels of the Circulatory SystemEndotheliumElastic tissueSmooth MuscleFibrous TissueArteriole30 µmCapillary8 µmVenule20 µm6 µm 0.5 µm 1 µmDiameterWall thicknessAorta25 mmArtery4 mmVein5 mmVena Cava30 mm2 mm1 mm 0.5 mm 1.5 mmBioengineering 6000 CV PhysiologyHemodynamicsBlood Distribution• Velocities/Flows– Aorta: 30-50 cm/s– Capillaries: 0-1 cm/s or 5.5 hours/mm3 • Blood mass: 8% of body mass• Volumes (percent of total blood volume)– Systemic: 83%• Arteries: 11%• Capillaries: 5%• Veins: 67%– Pulmonary: 12%– Heart: 5%Aorta Arteries Arterioles Capillaries Venules Veins Venae CavaVelocityCross-sectional areaPressurePercent of blood volumeVelocityCross-sectional areaPressurePercent of blood volumeBioengineering 6000 CV PhysiologyHemodynamicsHemodynamics Basics• "The problem of treating the pulsatile flow of blood through the cardiovascular system in precise mathematical terms is insuperable" (Berne and Levy) – Blood is not Newtonian (viscosity is not constant)– Flow is not steady but pulsatile– Vessels are elastic, multibranched conduits of constantly changing diameter and shape.– Use equations qualitatively• Local control of blood flowR =P˙QC =VPL =P˙Q/t˙Q =(P1 P2)⇡r48⌘lR =8⌘l⇡r4(I =VR)Bioengineering 6000 CV PhysiologyHemodynamicsHemodynamic Parameters• Resistance• Compliance• Inertance• Poiseuille's Law– laminar flow– Newtonian fluid– rigid tube– works for small arteries and veinsQ = flow.P = pressure η = viscosityV = volumeBioengineering 6000 CV PhysiologyHemodynamicsResistance and Compliance• Veins vs. arteries– have 24 times the compliance of arteries– carry 65% of the blood– have even higher blood storage capacity• Autonomic control– alters resistance but not compliance (slopes of curves)– acts to shift blood volumeSympathetic inhibition0 100 200Arterial Pressure [mm Hg]Blood FlowNormalSympathetic stimulation0 70 140 Pressure [mm Hg]Blood VolumeArterialVenousC =VPR =P˙Q⌘ =⌧du/dy=F/AU/Y=Shear stressShear rateBioengineering 6000 CV PhysiologyHemodynamicsViscosityFUuyYADefinition for homogenous Newtonian fluid• Viscosity increases with– increased hematocrit– constrictions in vessels• Viscosity decreases with– increased flow velocity– vessel diameter below 300 µmPoor formula for viscosity in small vesselsHematocrit [%]Viscosity (water=1)10220 30 40 50 60 7046810WaterPlasmaBloodBioengineering 6000 CV PhysiologyHemodynamicsFactors that Affect Viscosity• Flow rate: as flow decreases, viscosity increases up to 10-fold. Mechanism: RBCs adhering to each other, and the vessel walls.• RBCs stick at constrictions, increase viscosity.• Concentration, distribution, shape, and rigidity of the suspended particles (e.g., RBCs drift to the center so velocity profile flattens from ideal parabolic)• Fahraeus-Lindqvist effect: reduced η when RBCs line up in small vessels (< 300 µm).• In very small vessels (< 20 µm), η increases as RBCs fill the capillaries, “tractor tread” motion• Temperature, blood pressure, presence of anticoagulants,• Measurement conditions: higher in vitro than in vivo.• History (pulsatile flow)˙Q =˙Qov = voPtot= Po= Pdo+ PloPd=12⇢v2o= PdoPl= PloBioengineering 6000 CV PhysiologyHemodynamicsVelocity and Pressure• Example: Aortic stenosis– increased velocity– decreased lateral pressure– reduced coronary flow– coronary ischemia˙Q =˙Qov = voPtot= PoPd= PdoPl= Plo˙Q =˙Qov = kvoPtot= Po= Pd+ PlPd=12⇢(kvo)2= k2PdoPl= Ptot Pd<PloBioengineering 6000 CV PhysiologyHemodynamicsAortic StenosisLeft ventricleCoronary arteryCoronary arteryPvPavoPao (lower than normal)• Pressure losses– kinetic energy conversion– energy loss (friction)Bioengineering 6000 CV PhysiologyHemodynamicsResistance of the Circulatory System• Resistance high where pressure drops• Arterioles have highest resistance• Paradox?– arterioles have more total area than arteries– vessels with larger area have smaller resistance– but arterioles have larger resistance than arteries?AortaArteriesArterioles Capillaries Venules Veins Venae CavaVelocityCross-sectional areaPressurePercent of blood volumeVelocityCross-sectional areaPressureAn,rn,RnRtRt=4Rw!Aw=4Anrw=2rn1Rt=4X1=11Rn=4RnRw=kr4w=k(2rn)4=k16r4n=14⇤k4r4n=Rt4Bioengineering 6000 CV PhysiologyHemodynamicsResistance-Area Paradox• Net flow must be constant• One vessel splitting to four increases total resistance!Aw,rw,RwR =8⌘l⇡r4=kr4Rt=Rn4=k4r4nRw= RtAt= 16An=4AwBioengineering 6000 CV PhysiologyHemodynamicsResistance Break Even Point• Break-even point at 16 to 1 (for Rw=Rt).• Capillaries have more than 16:1 ratio Aw,rw,RwAn,rn,RnRtBioengineering 6000 CV PhysiologyHemodynamicsLaminar Flow and Turbulence• Laminar flow– Parabolic profile• Pulsatile laminar flow– Velocity changes– May reverse direction• Turbulent flow– Nonaligned movement– Noisy (BP cuff)– Reynolds number• > 1000 = turbulence• > 200 = eddies possible– Rarely occurs in healthy vesselsVelocity