Lecture 9 Hemodynamics.pptx(1)

Hemodynamics

5/14/15 Cardiovascular Physiology

BENG 230C

Velocity and Flow

The terms "velocity" and "ow" can someGmes be confused and thought of as being interchangeable, but they are not.

Velocity is the distance an object (solid, liquid or gas) moves with respect to Gme (i.e., the distance traveled per unit of Gme) and is expressed in the units of cm/sec.

Flow, Q, Qdot or is the volume of a liquid or gas that is moving per unit of Gme, and is expressed in units of mL/sec

Review: Flow and Cross SecGonal Area

Q=V x A V=velocity Q=ow A=cross secGonal area

0

40

0

20

Aorta 23(mean)

Vena cava 15

Bloo

d ve

loci

ty (c

m/s

ec)0

10

100

1000

Tota

l cr

oss-

sect

ion

area

(cm

2 )

Aorta 4

Vena cava 7

Left

vent

ricle

Larg

ear

terie

s

Res

ista

nce

vess

els

Cap

illar

ies

Venu

les

Vein

s

Major Principle

Flow depends on Pressure Drop: For overall system, pressure drop: PA-PV

Resistance

5

Darcys Law: Pressure and Resistance Determine Flow

Pressure P1 Pressure P2

For laminar flow, Q is proportional to P1 - P2

Q = K ( P1 - P2 )

Putting in a proportionality factor K, called conductance:

This is called Darcys law of flow. Since resistance (R) is defined as 1/conductance:

Q = ( P1 - P2 ) R

(analogous to Ohms law, I=V/R)

Flow Q

Henry Darcy, Civil Engineer, Dijon, France

6

Example: use of Darcys to understand increased local flow through an individual

exercising muscle

Every tissue has the same perfusion pressures (PA PV) Therefore flow in an individual active muscle must be due to in its local vascular resistance R

A 20x fall in R within an individual exercising muscle (e.g. quadriceps, skiing) increases its blood flow 20x

Q (local flow) = (PA PV) Local R

7

PAT T ERNS OFBLOOD F LOW

Laminar

Bolus

Turbulent

Mostarteries,arteriolesvenulesand veins

Ventricles.Sometimesaorta,e.g. inpregnancy

Capillaries

Most arteries, arterioles, venules, veins

Ventricles. Sometimes aorta, e.g. in pregnancy. Atheroma (bruit)

Capillaries

There are 3 different patterns of

blood flow

Laminar vs Turbulent Flow

9

Shape of basic pressureflow relation

Pressure

Flow

Sir Osbourne Reynolds

Re

= 20

00

Laminar flow

Turbulent flow e.g. aorta at peak ejection in pregnancy in some women, espec. if anemic benign systolic murmur of pregnancy

Q P

Reynolds number Re = velocity x diameter x density / viscosity (anemia)

Understanding Darcys law: Pressure governs blood ow, Qdot = P/R

Pressure dierence across circulaGon depends upon: Arterial blood pressure Venous blood pressure

Resistance depends upon uid viscosity and the conduit (to be covered later in lecture -- Poiseuilles law).

Arterial Pressure: 3 relaGonships (1)

1. Pulse pressure: dierence between systolic and diastolic pressures. Systolic pressure = 120 mmHg

Diastolic pressure = 80 mmHg

Incisura

Pulse pressure = Systolic pressure Diastolic pressure


2. Compliance: Pulse pressure = ~stroke volume/compliance

Because arteries harden with aging (arteriosclerosis), this reduces compliance, so pulse pressure can double with aging.

13

Pulse pressure increases with age, due to arteriosclerosis of big elastic vessels.. Bigger oscillations around the mean. Mean BP increases due to resistance vessel changes.

0 10 20 30 40 50 60 70 80 900

20

40

60

80

100

120

140

160

180

200

Systolic

Mean

Diastolic

Age in years

Brac

hial

arte

ry p

ress

ure

(mm

Hg)

14

Stroke volume

Puls

e pr

essu

re

Art

eria

l pre

ssur

e

80

120

160

Volume of blood in elastic arteries

Compliance = volume/pressure

Arterial compliance curve is not linear

15

Stroke volume

Puls

e pr

essu

re

Art

eria

l pre

ssur

e

80

120

160

Volume of blood in elastic arteries

Arterial compliance curve is not linear

Compliance = volume/pressure Bigger pulse pressure

when stroke volume raised

Exercise

Hydraulic Filtering Creates Uniform Flow Over Time

Figure 7-1 (your text) When the arteries are normally compliant, blood ows through the capillaries throughout the cardiac cycle. When the arteries are rigid, blood ows through the capillaries during systole, but ow ceases during diastole.

Also reduces work At steady state, W = P x V; where W=work, P=pressure, V=volume Consider pumping 100 ml for 1s in a hypotheGcal rigid system (A and B): If conGnuous, lets say 100 mmHg: 100mmHg

* 100 ml/s = 10^4 mmHg*ml/s However, if intermihent, need to pump 200

ml/s for the 0.5 s acGvity and 0 ml/s for the 0.5 s of inacGvity. Because P=Q*R, pressure is therefore 200 mmHg during acGvity: 200 mmHg * 200 ml/0.5 s = 2*10^4 mmHg ml/ 0.5s acGvity

Therefore, intermihent pumping requires more work than conGnuous. Compliance compensates for intermiEent ow delivered by the heart, creaLng a nearly perfect ltering of the intermiEent ow. Therefore, W=100mmHg * 100ml/s = 10^4mmHg/ml/s

Reflected Wave

Model Descending Aorta

Point of reecGon e.g. bifurcaGon

Hodder Arnold / An IntroducGon to Cardiovascular Physiology 2010 J. Rodney Levick

The reflected wave in the human aorta varies with age and mean pressure

Why Does the Reected Wave Maher?

In young people, the reecGve wave returns slowly (system is more compliant)

The slow return increases diastolic pressure, increasing coronary artery perfusion (good)

In contrast, faster return in hypertension and elderly increases systolic pressure. This increases aPerload, hence cardiac work and O2 demand.


3. Mean Blood Pressure:

80

120

Time, t

Brachial arterypressure(mmHg) Mean

Pulse pressureMean pressure P A = 93.3

2/3rd

1/3rd

Mean BP = diastolic pressure + 1/3[pulse pressure]

What determines Mean Blood Pressure?

22

Applying Darcys law to whole systemic circulaLon, of total peripheral resistance TPR: Flow = Cardiac output C.O. = (PA-PV) / TPR

Since venous pressure (PV) is negligible compared with PA

C.O. P A / TPR

So, what determines PA is cardiac output, e.g. exercise

total peripheral resistance e.g. clinical hypertension

Therefore, Mean BP (PA) governed largely by CO & TPR



Resistance depends upon uid viscosity (to be covered later in lecture -- Poiseuilles law) and the conduit (also covered later).

24

The pressurevolume curve of veins

Typical venous pressures (mmHg)

Limb vein, heart level 810 Central venous pressure 0-7 Foot vein, standing 90

Relaxed

Venous pressure (cmH2O)

Volu

me

(ml)

Stimulated by sympathetic venoconstrictor nerves shifts blood centrally, supporting central venous pressure CVP

25

Vascular pressures

during standing

HeartHeart level

-35 mmHg

0-6 mmHg

90 mmHg

60 mmHg

95 mmHg

185 mmHg

Vein

s

Arte

ries

h=45

cm

h=11

5 cm

1 cm blood =1.06 cmH2O = 0.78 mmHg

(58)

(183)

*

h= 1

22 c

m b

lood

Blood-filledmanometer

Hg-filledmanometer

0-5 mmHg 95 mmHg

90 mmHg 185 mmHg

High local venous pressure in

upright position is reduced by

calf muscle pump

PV Low Pv increases local pressure gradient Pa-Pv, so flow

Displaced blood raises CVP, hence stroke volume (Starling LOH)

Low Pv reduces leg capillary pressure avoiding oedema formation


27

Central venous pressure



Resistance depends upon (Poiseuilles law): uid viscosity the conduit

29

Poiseuilles law tells us that 3 factors govern resistance

Length of tube

Radius of tube

Viscosity of liquid

Poiseuilles law denes R in Darcys law (Q = (PA-PV)/R)

30

Poiseuilles law: what governs resistance?

For laminar flow down a tube of radius r,

Resistance R = 8 L r 4

Length L Flow

Viscosity

Radius r Q

= (P1P2) r 4

8 L Q

Resistance depends on: radius r 4 viscosity length L

Since flow equals pressure drop (P1P2) divided by resistance,

Radius of arterioles is therefore a hugely powerful regulator of peripheral resistance (r4 eect)

31

Arterioles & the smallest arteries are the main site of resistance to blood flow.

Proof? the biggest pressure drop occurs between the conduit arteries and the arterial end of the capillaries.

Local arteriole radius therefore controls local blood flow in a given tissue. Doubling r increases flow 16x! Arteriole radius in the whole circulation controls TPR, and therefore mean arterial blood pressure. Hypertension is caused by narrowing of the resistance vessels. Remember the r4 effect!

The majority of the total peripheral resistance is situated in the microcirculaGon, more specically, in the arterioles, which are arterial vessels with diameters from 150 to 10 m. In the resGng condiGon, total peripheral resistance is primarily regulated at this level by the myogenic response, sympatheGc tone, paracrine factors (e.g., local metabolites), and humoral factors (e.g., ANG II) NEXT LECTURE


33

How arteriole radius affects both flow & BP (for a given cardiac work)

Capillaries

BP flow resistance

Resistance vessels

Artery Heart


34

How arteriole radius affects both flow & BP (for a fixed level of cardiac work)

Capillaries

BP flow resistance

flow BP

Resistance vessels

Artery Heart

resistance

35

PAT T ERNS OFBLOOD F LOW

Laminar

Bolus

Turbulent

Mostarteries,arteriolesvenulesand veins

Ventricles.Sometimesaorta,e.g. inpregnancy

Capillaries

Most arteries, arterioles, venules, veins

Ventricles. Sometimes aorta, e.g. in pregnancy. Atheroma (bruit)

Capillaries

There are 3 different patterns of

blood flow

Figure 6-17 Decrease in the viscosity of blood (in cenGpoise) at increasing rates of shear. The shear rate refers to the velocity of one layer of uid relaGve to that of the adjacent layers and is direcGonally related to the rate of ow. (Redrawn from Amin TM, Sirs JA: The blood rheology of man and various animal species. Q J Exp Physiol 70:37, 1985.)

Blood Rheology (Shear Thinning: Apparent viscosity decreases with increased stress)

Relative apparent viscosity of whole blood perfused through glass capillary tubes of varying diameters (the Fhraeus-Lindqvist effect).

Linea Natalie Toksvang, and Ronan M. G. Berg Advan in Physiol Edu 2013;37:129-133

2013 by American Physiological Society

Effective viscosity of blood in the circulation diameter is that of arterioles

Human red blood cells flowing through glass capillary tubes with different inner diameters.

Linea Natalie Toksvang, and Ronan M. G. Berg Advan in Physiol Edu 2013;37:129-133

2013 by American Physiological Society

Blood viscosity falls in narrow tubes! the Fhraeus-Lindqvist effect

Q

= P r4

8LPoiseuille's law, which describes the steady, laminar volume ow of a Newtonian uid through a uniform and rigid cylindrical, provides a useful starGng point:

Q is the volume ow through the tube, P is the pressure drop along the tube, L is the length of the tube, r is the tube radius, and is the viscosity of the uid.

When you get unexpected results you should be darn happy! If you always get the results you anGcipate you can never hope to discover anything new!

However, viscosity is not constant but is progressively reduced when the tube diameter decreases below 0.3 mm, therefore, Poiseuille's law does not apply to the ow of blood through tubes with a diameter of

41

Bolus flow in capillaries.

Plasma columns are trapped between the red cells;

the cells move like pistons along the capillary. Two factors that underline the Fahraeus-Lindqvist effect: (1) Axial streaming - migration of RBC to the middle of the stream, thus leaving cell-free plasma

near the vessel wall, reducing friction. (2) Bolus flow - reduction in viscosity due to RBC moving in single file w/ some plasma between

them, thus eliminates most of velocity profile, velocity shear and internal friction. The RBCs traverse the vessel at a higher velocity than the slower flowing marginal plasma stream. The consequent dilution of the blood at a given tube diameter furthermore reduces its viscous resistance, that is, the apparent viscosity of the flowing blood (the Fhraeus-Lindqvist effect)

42

Blood viscosity & disease

Hematocrit (4045%) typical tube is 4-5

mPA

Tube diameter (FhraeusLindqvist effect)

Red cell deformability

Velocity of blood (shear thinning)

Polycythemia (high ) Anemia (low )

Sickle cell anemia crises

Slow venous flow in immobile legs

Clinical aspects: Viscosity depends on:


43

Jean Lonard Marie Poiseuille (1779-1869)

Au revoir, mes enfants. Le fin!

Extra slides


45

Putting it all together: pressureflow relation in circulations in vivo

Saline Blood Blood

+ noradrenaline

Autoregulation: protects flow against pressure fluctuations brain, myocardium, kidneys

100 200 Blood pressure (mmHg)

Flow

0

46

Baylisss myogenic response of arterioles is cause of autoregulation

Flow

Pressure

Cross-sections of arteriole; resistance proportional to 1/r4

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Lecture 9 Hemodynamics.pptx(1)