Hemodynamics. Overview and Terminology. Parameters. Pressure Velocity Flow. Resistance Viscosity Energy Area Volume. laminar vs.

Transcription

1 Overview and Terminology Parameters Pressure Velocity Flow laminar vs. turbulent Resistance Viscosity Energy Area Volume Arterioles

2 Structural Overview Intro to Circulation Functional Overview Arterial System

3 Velocities/Flows Aorta: 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% Blood Distribution Velocity Pressure Cross-sectional area Aorta Arteries Arterioles Capillaries Venules Veins Venae Cava Pressure Velocity Cross-sectional area Percent of blood volume Percent of blood volume Flow is constant throughout Flow = velocity * area Velocity vs. Area

4 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 Laminar 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 vessels Velocity Profiles

5 Hemodynamic Parameters. P = pressure V = volume Q = flow η = viscosity Resistance R = P Q Compliance C = V P Inertance L = P Q/ t Poiseuille's Law laminar flow Newtonian fluid rigid tube works for small arteries and veins Q =(P 1 P 2 ) r4 8 l R = 8 l (I = V r 4 R ) Hemodynamic Parameters. P = pressure V = volume Q = flow η = viscosity Resistance R = P Q Compliance C = V P Inductance L = P Q/ t Poiseuille's Law laminar flow Newtonian fluid rigid tube works for small arteries and veins Q =(P 1 P 2 ) r4 8 l R = 8 l (I = V r 4 R )

6 Blood Volume Blood Flow Resistance 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 volume R = P Q Arterial Pressure [mm Hg] Sympathetic inhibition Normal Sympathetic stimulation Venous C = V P Arterial Pressure [mm Hg] F y U A = du/dy = F/A U/Y Definition for homogenous Newtonian fluid Poor formula for viscosity in small vessels u = Shear stress Shear rate Viscosity (water=1) 10 Viscosity Y Viscosity increases with increased hematocrit constrictions in vessels Viscosity decreases with increased flow velocity vessel diameter below 300 µm Blood Hematocrit [%] Plasma Water

7 Viscosity Viscosity Shear Thinning or Thickening?

8 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) Velocity and Pressure Example: Aortic stenosis increased velocity decreased lateral pressure reduced coronary flow coronary ischemia Q = Q o v = v o P tot = P o = P do + P lo P d = 1 2 v2 o Q = Q o v = kv o P tot = P o = P d + P l P d = 1 2 (kv o) 2 Q = Q o v = v o P tot = P o P d = P do = P do P l = P lo = k 2 P do P l = P tot P d < P lo P l = P lo

9 Aortic Stenosis Pressure losses kinetic energy conversion energy loss (friction) P ao (lower than normal) P avo Coronary artery Coronary artery P v Left ventricle Resistance 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? Velocity Pressure Cross-sectional area Aorta Arteries Arterioles Capillaries Venules Veins Venae Cava Velocity Cross-sectional area Pressure Percent of blood volume

10 Resistance-Area Paradox A w,r w,r w A w =4A n r w =2r n A n,r n,r n R t Net flow must be constant One vessel splitting to four increases total resistance! R w = k r 4 w R = 8 l r 4 = k r 4 = k (2r n ) 4 = k 16r 4 n 1 R t = 4X 1=1 = 1 4 k 4r 4 n 1 = 4 R n R n R t = R n 4 = k 4r 4 n = R t 4 R t =4R w! Resistance Break Even Point Break-even point at 16 to 1 (for R w =R t ). Capillaries have more than 16:1 ratio A n,r n,r n A w,r w,r w R t A t = 16A n =4A w R w = R t