Hemodynamics

Objectives Define resistance and understand the effects of adding resistance in series vs.in parallel in total resistance and flow. Describe the relationship between pressure, flow and resistance in the vasculature. Explain how Poiseuille’s law influences resistance to flow and define the factors that determine resistance. Describe the change in pressure along vascular tree and explain how flow to any organ is altered by change in resistance to that organ. Explain types of flow, laminar versus turbulent and the transition between them; Reynold’s number.

Hemodynamics: Factors affecting blood flow How much blood flow and what determines how much? Blood Flow: Volume of blood flowing through any tissue in a given time period (mL/min)

Relations of pressure, flow and resistance Change in Pressure Resistance Flow is: Directly proportional to pressure gradient Inversely proportional to resistance F = P R

Pressure differences or gradient ∆P ( the greater the ∆P, the greater the flow) Flow  ∆P P1 = 90 mmHg P2 = 40 mmHg ∆P = P1 – P2 = 50 mmHg

Resistance arises due to Resistance to BF (the higher the R, the smaller the flow). Flow  1/R Resistance arises due to interactions between the moving fluid and the stationary tube wall interactions between molecules in the fluid (viscosity) Factors determining the resistance: Vessel length Vessel radius Blood viscosity

1. Blood vessel length Resistance to Flow is directly proportional to the length the longer the length  the higher the resistance e.g. Obesity

-  viscosity ( dehydration, polycythaemia) 2. Blood viscosity Resistance is directly proportional to blood viscosity depends on:  ratio of RBCs to plasma vol.  conc. of proteins in plasma. -  viscosity ( dehydration, polycythaemia) -  viscosity ( RBCs or  Plasma prot.)

3. Size of the Blood vessel lumen (vessel radius) The resistance to flow is inversely proportional to the fourth power of the radius R  1/d4 ( the smaller the diameter the greater the resistance ------ if the diameter  by ½, the resistance  16 times) Therefore vessel radius is a major determinant of resistance to flow (happen in arterioles-vasoconstriction and vasodilatation)

Poiseuille’s Law } (FLOW)F = P F = R (P ) r 8nL R = 8  l  r4 F RADIUS DIFFERENCE IN PRESSURE VISCOSITY LENGHT

Some Implications of Poiseuille’s Law  r4 (P) F = P R = If P is constant, flow is very sensitive to tube radius r (10 - r/10)*100 Q/X [1 - (Q/Qr=10)]*100 10 0% 10,000 0% 9 10% 6,561 35% 5 50% 625 94% 1 90% 1 99.99% % decrease in flow % decrease in radius

What Can the Body Regulate to Alter Blood Flow and Specific Tissue Perfusion? = P = Mean Arterial Pressure – Mean Venous Pressure P, not subject to significant short term regulation R = 8  l  r4 R = Resistance 8, , l,  are not subject to significant regulation by body r4 can be regulated especially in arterioles, resistance vessels

Path of Blood Flow in the Circulatory System Heart (left ventricle) aorta arteries arterioles capillaries venules veins vena cava Heart (right atrium)

Velocity of blood flow Flow is a measure of volume per unit time Velocity is a measure of distance per unit time Velocity = Flow/Cross sectional area

CROSS SECTIONAL AREA AND VELOCITY A= 2cm2 10cm2 1cm2 F=10ml/s a b c V= 5cm/s 1cm/s 10cm/s V = F / A

Blood Vessel Diameter and Blood Velocity

Organization in the Circulatory System SERIES AND PARALLEL CIRCUITS

RESISTANCE TO FLOW IN SERIES VS IN PARALLEL Rt = R1 + R2 + R3…. SERIES RESISTANCE 1/Rt = 1/R1 + 1/R2 + 1/R3… PARALLEL RES. SERIES R1 R2 R3 R1 PARALLEL R3 R2

Then a series arrangement gives: RT = R1 + R2 + R3 RT = 12 PRU’s If: R1 = 2; R2 = 4; R3 = 6 PRU’s Then a series arrangement gives: RT = R1 + R2 + R3 RT = 12 PRU’s But a parallel arrangement gives: RT = =1.94 PRU’s 1 1 R1 1 R2 1 R3 + +

WHAT REALLY HAPPENS IN THE CVS? ARTERY ARTERIOLES CAPILLARIES LOWER R HIGHER R

LAMINAR VS TURBULENT FLOW THE REYNOLD’S NUMBER Nr = pDv / n p = density D = diameter v = velocity n = viscosity laminar = 2000 or less