HemodynamicsHemodynamics

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ObjectivesObjectives 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.

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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)

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Relations of pressure, Relations of pressure, flow and resistanceflow and resistance

Flow = Change in Pressure

Resistance

F = PR

Flow is: Directly proportional to pressure gradientInversely proportional to resistance

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Pressure differences or gradient ∆PPressure differences or gradient ∆P

( the greater the ( the greater the ∆P∆P, the greater the flow), the greater the flow)

Flow Flow ∆P ∆P

P1 = 90 mmHg P2 = 40 mmHg

∆∆P = P1 – P2 = 50 mmHgP = P1 – P2 = 50 mmHg

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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

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1. Blood vessel length1. Blood vessel length

Resistance to Flow is directly proportional to Resistance to Flow is directly proportional to the lengththe length

the longer the length the longer the length the higher the the higher the resistance resistance

e.g. Obesitye.g. Obesity

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2. Blood viscosity2. Blood viscosityResistance is directly proportional to blood Resistance is directly proportional to blood viscosityviscosity

depends on:depends on: ratio of RBCs to plasma vol. ratio of RBCs to plasma vol.

conc. of proteins in plasma.conc. of proteins in plasma.

- - viscosity viscosity ( dehydration, polycythaemia) ( dehydration, polycythaemia)

- - viscosity viscosity ( ( RBCs or RBCs or Plasma prot.) Plasma prot.)

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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)

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Poiseuille’s Law

} r

l

F R =8 l

r4

DIFFERENCEIN PRESSURE RADIUSVISCOSITY

(FLOW)F(FLOW)F = (P ) r

8nL

4

LENGHT

F = PR

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Some Implications of Poiseuille’s Law

8 l

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

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What Can the Body Regulate to Alter Blood Flow and Specific Tissue Perfusion?

8 l

r4

(P)F = P

R=

P = Mean Arterial Pressure – Mean Venous Pressure

P, not subject to significant short term regulation

R = Resistance R =8 l

r4

8, , l, are not subject to significant regulation by body

r4 can be regulated especially in arterioles, resistance vessels

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Path of Blood Flow in the Circulatory System

Heart (left ventricle)

aorta

arteries

arterioles

capillaries

venules

veins

vena cava

Heart (right atrium)

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Flow is a measure of volume per unit time

Velocity is a measure of distance per unit time

Velocity = Flow/Cross sectional area

Velocity of blood flowVelocity of blood flow

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CROSS SECTIONAL CROSS SECTIONAL AREA AND VELOCITYAREA AND VELOCITY

F=10ml/s

A= 2cm2 10cm2 1cm2

V= 5cm/s 1cm/s 10cm/s

V = F / A

a b c

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Blood Vessel Diameter and Blood Velocity

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SERIES AND

PARALLEL CIRCUITS

Organization in the Organization in the Circulatory SystemCirculatory System

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RESISTANCE TO FLOW IN RESISTANCE TO FLOW IN SERIES SERIES VS VS IN PARALLELIN PARALLEL

Rt = R1 + R2 + R3…. SERIES RESISTANCE

1/Rt = 1/R1 + 1/R2 + 1/R3… PARALLEL RES.

SERIESR1 R2 R3

R1PARALLEL

R3R2

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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

+ +

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WHAT REALLY HAPPENS IN THE CVS?

ARTERY

ARTERIOLES

CAPILLARIES

LOWER R HIGHER R LOWER R

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LAMINAR VS TURBULENT LAMINAR VS TURBULENT FLOWFLOWTHE REYNOLD’S NUMBERTHE REYNOLD’S NUMBER

Nr = pDv / n

p = densityD = diameterv = velocityn = viscosity

laminar = 2000 or less

LAMINARFLOW

TURBULENTFLOW

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