Rheology of blood circulation Law of Pascal Liquid column causes a pressure (hydrostatic pressure) that is directly proportional to the height of the liquid column (h), density of the liquid (p) and gravitational acceleration (g). Effect of gravity on arterial and venous pressure Per each 10 cm Ap=Ah.pklve.g = 0,1 . 1 065 . 9,81 = 1 045Pa = Law of Laplace Relation between distending pressure (P [N/m2]) and tension in the wall of hollow object (T [N/m]) : Characteristics of vessels ľ-1 p Ir ^ A—} P. R h P. R/h vessel P [kPa] radius tension (N/m) wall thickness tension (N/m2) aorta 13,3 13 mm nebo méné 170 2 mm 85000 arteries 12 5 mm 60 1 mm 60000 arterioles 8 150-62 pm 1,2-0,5 20 JLL1T1 40000 capillaries 4 4 jam 1,6.10-2 1 |Lim 16000 venules 2,6 10 |Lini 2,6.10-2 2 \im 13000 veins 3 200 (am a vice 0,4 0,5 mm 800 vena cava 1,33 16 mm 21 1,5 mm 14000 Continuity equation The volume of fluid flowing through a tube (vessel) per unit of time (Q [i/s]) is constant. v - velocity S - area Average blood velocity in vessels Qrest«5.6 l/min vessel aorta arterioles capilaries venules vena cava diameter - 2.6 cm 20-50 |um 4-9 jim -20 urn ~ 3 cm number 1 ~5x10e ~5x109 - 32X106 total area ~ 5.3 cm2 ~ 60 cm2 - 2000 cm2 -100 cm2 ~ 14 cm2 velocity Relation between total cross-sectional area of vessels and mean flow velocity aorta | arteries arterioles|capilares | venules veins 1 v. cava | Individual vessel diameter (cm) 2.6 Number 1 Increasing 0.16-109 5-109 0.5-109 Decreasing 2 Joint cross-sectional area (cm2) 5.3 20 3500 jOO 30 10 Mean flow velocity Va (cm-s 1) 6 Bernoulli's principle Law of energy conversation for fluid : P2 v2 Pi v1 TS 2 S1v1 = S2v2 a je-li S1v2 2* R2 \rf + Pl = \pV2+P2 Poiseuille - Hagen equation () t <- -► The flow of liquid in the cylindrical tube (Q) is directly proportional to the pressure difference between two ends of the tube (AP=PA-PB), to the fourth power of the tube radius (r) and inversely proportional to tube length (I) and to the viscosity of liquid (r|). Limitation: • For stationary flow in Newtonian fluids where viscosity is constant and independent on flow velocity. Vascular resistance (RJ: a consequence of the friction between fluid and vessel wall. _ Parallel arrangement of vessels Series arrangement of vessels Relation between vessel radius and peripheral resistance zTRheological features of blood Blood viscosity Effect of hematocrit Effect of diameter in small vessels Other factors causing increase of viscosity: • decrease of blood flow velocity • elevation of plasma proteins Velocity profile of the blood flow in vessels In small arteries the velocity profile of the flowing blood has a parabolic shape. In the bigger arteries it has a piston shape. The layer close to vessel wall is poor of erythrocytes. Laminar and turbulent flow Velocity profile in laminar and turbulent flow m The character of the flow is determined by Reynolds number Pathological states causing turbulent flow: decreased blood viscosity, aneurisma, stenosis, arteriosclerosis. Elasticity of vessels Pulse wave velocity (PWV) In aorta PWV = 4 - 6 m/s Mechanisms of venous return Blood circulation p lie.kapilár y plic. artérie Á a. pulmonale 100% 3 mm Hg pulmonary 100% circulation systemic circulation plic. vény 4 velké plieni vény 5% T (5%) 15 % (3%) 120/80 mm Hg 25% (50%) aorta artérie arterioly (4%) kapiláry duté žíly vény Low-pressure system (reservoir function) 20% (3%) High-pressure system £*] (supply function) Blood pressure Blood pressure (BP) is the pressure exerted by circulating blood upon the walls of blood vessels. svstolic Left ventricle Arteries Arterioles Capillaries P = Pd +—{Ps-Pd) mean 3 ^ J Dependence of blood pressure on cardiac output and vascular parameters AV = SV Model of blood pressure changes in aorta