Hemodynamics Hemodynamics Bioengineering 6000 CV Physiology Overview and Terminology • Parameters – Pressure – Velocity Arterioles – Flow • laminar vs. turbulent – Resistance – Viscosity – Energy – Area – Volume Hemodynamics Bioengineering 6000 CV Physiology Structural Overview Intro to Circulation Bioengineering 6000 CV Physiology Functional Overview Arterial System Bioengineering 6000 CV Physiology Blood Distribution • Velocities/Flows Percent of blood Cross-sectional area volume – Aorta: 30-50 cm/s – Capillaries: 0-1 cm/s Velocity or 5.5 hours/mm3 • Blood mass: 8% of Pressure body mass • Volumes (percent of total blood volume) – Systemic: 83% • Arteries: 11% • Capillaries: 5% Aorta Arteries Arterioles Capillaries Venules Veins Venae • Veins: 67% Cava – Pulmonary: 12% Pressure Velocity – Heart: 5% Cross-sectional area Percent of blood volume Hemodynamics Bioengineering 6000 CV Physiology Velocity vs. Area • Flow is constant throughout • Flow =∫velocity * area Hemodynamics Bioengineering 6000 CV Physiology Hemodynamics 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 flow Hemodynamics Bioengineering 6000 CV Physiology Laminar Flow and Turbulence • Laminar flow – Parabolic profile • Pulsatile laminar flow – Velocity changes – May reverse direction • Turbulent flow – Nonaligned movement – Noisy (BP cuff) Velocity Profiles Velocity – Reynolds number • > 1000 = turbulence • > 200 = eddies possible – Rarely occurs in healthy vessels Hemodynamics Bioengineering 6000 CV Physiology Hemodynamic Parameters . P = pressure V = volume Q = flow η = viscosity ∆P • Resistance R = ∆Q˙ ∆V • Compliance C = ∆P ∆P • Inertance L = ∆Q/˙ ∆t ⇡r4 • Poiseuille's Law Q˙ =(P1 P2) – laminar flow − 8⌘l – Newtonian fluid V – rigid tube 8⌘l (I = ) – works for small R = R arteries and ⇡r4 veins Hemodynamics Bioengineering 6000 CV Physiology Hemodynamic Parameters . P = pressure V = volume Q = flow η = viscosity ∆P • Resistance R = ∆Q˙ ∆V • Compliance C = ∆P ∆P • Inductance L = ∆Q/˙ ∆t ⇡r4 • Poiseuille's Law Q˙ =(P1 P2) – laminar flow − 8⌘l – Newtonian fluid V – rigid tube 8⌘l (I = ) – works for small R = R arteries and ⇡r4 veins Hemodynamics Bioengineering 6000 CV Physiology Resistance and Compliance ∆P R = ˙ • Veins vs. arteries ∆Q – have 24 times the Normal compliance of arteries – carry 65% of the blood Blood Flow – have even higher blood 0 100 200 storage capacity Arterial Pressure [mm Hg] • Autonomic control Sympathetic inhibition Sympathetic stimulation – alters resistance but not compliance (slopes of ∆V C = curves) Venous ∆P – acts to shift blood volume Blood Volume Arterial 0 70 140 Pressure [mm Hg] Hemodynamics Bioengineering 6000 CV Physiology Viscosity U F A • Viscosity increases with u y Y – increased hematocrit – constrictions in vessels • Viscosity decreases with ⌧ F/A Shear stress – increased flow velocity ⌘ = = = du/dy U/Y Shear rate – vessel diameter below 300 µm Definition for 10 homogenous Newtonian fluid 8 Poor formula for viscosity in 6 small vessels Blood 4 2 Plasma Viscosity (water=1) Viscosity Water 10 20 30 40 50 60 70 Hematocrit [%] Hemodynamics Bioengineering 6000 CV Physiology Viscosity Hemodynamics Bioengineering 6000 CV Physiology Viscosity Shear Thinning or Thickening? Hemodynamics Bioengineering 6000 CV Physiology Factors 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) Hemodynamics Bioengineering 6000 CV Physiology Velocity and Pressure • Example: Aortic stenosis – increased velocity ˙ ˙ ˙ ˙ ˙ ˙ – decreased lateral Q = Qo Q = Qo Q = Qo pressure v = vo v = kvo v = vo – reduced coronary Ptot = Po Ptot = Po Ptot = Po flow = Pdo + Plo = Pd + Pl – coronary ischemia 1 2 1 2 Pd = ⇢v P = ⇢(kv ) P = P 2 o d 2 o d do 2 = Pdo = k Pdo Pl = Plo P = P P Pl = Plo l tot − d <Plo Hemodynamics Bioengineering 6000 CV Physiology Aortic Stenosis • Pressure losses P (lower than – kinetic energy ao conversion normal) – energy loss (friction) Pavo Coronary Coronary artery artery Pv Left ventricle Hemodynamics Bioengineering 6000 CV Physiology Resistance of the Circulatory System • Resistance high where Cross-sectional area pressure drops Velocity • Arterioles have highest resistance • Paradox? Pressure – arterioles have more total area than arteries – vessels with larger area have smaller resistance – but arterioles have larger resistance than arteries? Aorta Arteries Arterioles Capillaries Venules Veins Venae Cava Velocity Cross-sectional area Pressure Percent of blood volume Hemodynamics Bioengineering 6000 CV Physiology Resistance-Area Paradox An,rn,Rn Aw =4An Aw,rw,Rw rw =2rn Rt • Net flow must be 1 4 1 4 constant = = R R R • One vessel 8⌘l k t 1=1 n n R = = X splitting to four ⇡r4 r4 R k increases total n Rt = = 4 resistance! 4 4rn k k k 1 k Rt Rw = 4 = 4 = 4 = 4 = rw (2rn) 16rn 4 ⇤ 4rn 4 Rt =4Rw! Hemodynamics Bioengineering 6000 CV Physiology Resistance Break Even Point • Break-even point at 16 to 1 (for Rw=Rt). • Capillaries have more than 16:1 ratio An,rn,Rn Aw,rw,Rw Rt At = 16An =4Aw Rw = Rt Hemodynamics Bioengineering 6000 CV Physiology.