Medical Physics 8

Principles of fluid mechanics

Ferenc Bariprofessor

October 27, 2016

Medical Physics • Principles of fluid mechanics (2016)

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Why are fluid mechanics important in medicine?

Circulation of bloodarterial systemcapillary systemvenous systemlymphatics

Respirationupper airwayslower airways

Other body fluids

Blood Pressure: Generated by Ventricular Contraction

Figure 15-4: Elastic recoil in the arteries

Major branches of the arterial tree

Medical Physics • Principles of fluid mechanics (2012)

aortic valve

William Harvey (1578-1657)

More Blood Pressures: Pulse and Mean Arterial Pressures

Figure 15-5: Pressure throughout the systemic circulation

Mean and Pulse Pressure

P P +1

3P - P )a d s d (

Mean Arterial Pressure

Q =P P

R

a v

P - P = Q Ra v

MAP = cardiac output x total resistance

Arterial Elasticity Stores Pressure and Maintains Flow

Factors Controlling Blood Pressure

Peripheral resistance mean arterial pressure

Cardiac output mean arterial pressure

Stroke volume pulse pressure

Arterial compliance pulse pressure

Heart Rate pulse pressure

Blood Volume arterial & venous

Systolic pressure

Diastolic pressure

Mean Arterial Pressure

Pulse pressure = systolic pressure - diastolic pressure

80

100

120

1 second

Pre

ssu

re [

mm

Hg

]

Aortic pulse wave

• MAP determined by resistance of peripheral arteries = Pd +1/3 PP

• Pulse pressure determined by elasticity of large arteries

Pulse pressure = systolic pressure - diastolic pressure

Systolic pressure

Diastolic pressure

Mean Arterial Pressure

80

100

120

1 second

Pre

ssure

[m

mH

g]

•

Normal Pulse (1/2)

– The normal central aortic pulse wave is characterized by a fairly rapid rise to a somewhat rounded peak.

– The anacrotic shoulder, present on the ascending limb, occurs at the time of peak rate of aortic flow just before maximum pressure is reached.

– The less steep descending limb is interrupted by a sharp downward deflection, coincident with AV closure, called incisura.

– The pulse pressure is about 30-40 mmHg.

Normal Pulse (2/2)

– As the pulse wave is

transmitted peripherally,

the initial upstrokes

becomes steeper, the

anacrotic shoulder becomes

less apparent, and the

incisura is replaced by the

smoother dicrotic notch.

Medical Physics • Principles of fluid mechanics (2012)

Noninvasive measurement of arterial pressure

The cuff method (Riva-Rocci, 1896)

the auscultatory technique (Korotkoff, 1905)

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Noninvasive measurement of arterial pressure: the principle

Nikolai Szergeievitch Korotkoff

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Noninvasive measurement of arterial pressure: mechanisms of the sounds

cavitationwall detachment turbulence

other theories and combinations

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Noninvasive measurement of arterial pressure: the setup

mic

BIOPAC STUDENT LAB SYSTEM

MP36

EKG

Pcuff

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Noninvasive measurement of arterial pressure: blood pressure measures

time

systolic (SBP)

diastolic (DBP)

A1

A2mean (MAP)

mean arterial pressure (MAP):

MAP=DSP+PP/3

(A1≈A2)

pulse pressure (PP):

PP=SBP-DBP

PP

Pressure and velocity in the different sites of the arterial tree

Medical Physics • Principles of fluid mechanics (2012)

systolic

diastolic

mean

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Noninvasive measurement of arterial pressure: the oscillometry principle

cuff pressure

Korotkoff sound

ECG

cuff pulse pressure

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

The oscillometry principle

cuff pressure

Korotkoff sound

ECG

cuff pulse pressure

1. Pulse pressure transmission is maximal at MAP

2. Pulse pressure transmission suddenly increases at SBP: MAP+2/3 PP

3. DBP is by 1/3 PP below MAP

Major branches of the canine arterial tree

Medical Physics • Principles of fluid mechanics (2012)

Internal cross-sectional areas (cm2) of the canine aorta and main branches

Medical Physics • Principles of fluid mechanics (2012)

aortic valve

aortic arch

diaphragm

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Cross-sectional area and velocity in the systemic circulation

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Blood pressure in the systemic circulation

Pressure and velocity in the different sites of the arterial tree

Medical Physics • Principles of fluid mechanics (2012)

systolic

diastolic

mean

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Ideal fluids: Bernoulli’s law

Daniel Bernoulli (1700-1782)

static pressure

dynamic pressure

hydrostatic pressure

v: velocityr: densityg: gravity

accelerationh: height

Medical Physics • Principles of fluid mechanics (2012)

Arterial and venous pressures – effects of gravity

heart level

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Arterial pressures – posture dependence

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Real fluids: friction

Newton’s law of friction

F: frictional forceh: viscosityA: surfaceDv/Dh: velocity gradient

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Laminar stationary flow in a tube

Medical Physics • Principles of fluid mechanics (2012)

Jean-Louis-Marie Poiseuille (1797-1869)

Gotthilf Heinrich Ludwig Hagen (1797-1884)

Dp/Dl: pressure gradientR: tube radiush: viscosity

The Hagen-Poiseuille law

volumetric flow rate:

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Real fluids: red blood cells

High velocity in the center results in low hydrostatic pressure (Bernoulli’s law) RBCs are concentrated

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Real fluids, steady flow: distortion of the parabolic profile

C: constant viscosity

A&B: viscosity increases inversely with radius

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Real fluids, dynamics: distortion of the parabolic profile

Sinusoidal pressure gradient and resulting velocity profiles at frequencies f and 2f.

Profile blunting and lagging reversal of flow near the axis

relative radius

f 2f

ph

ase

in t

he

cycl

e

Medical Physics • Principles of fluid mechanics (2012)

Relative viscosityhuman blood cells, rigid spheres, rigid disks, droplets and sickled RBC

Medical Physics • Principles of fluid mechanics (2012)

Red blood cells in mesentery capillaries

rabbit dog

Medical Physics • Principles of fluid mechanics (2012)

Aggregation of red blood cells

linear branched

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Real fluids: turbulence

Vocal chordsBronchial stenosisArtery narrowingBifurcationsAneurysms

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Turbulent flow

Critical velocity (vcrit) depends on the Reynolds number (Re), viscosity (h), density (r) and tube radius (r).

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Noninvasive measurement of arterial pressure

Medical Physics • Principles of fluid mechanics (2012)

Medical Physics • Principles of fluid mechanics (2012)

Riva-Rocci, 1896Korotkoff, 1905

Literature

Medical Biophysics. S. Damjanovich, J. Fidy, J. Szöllősi (editors). Medicina, Budapest 2009, pp. 209-224

Surface Tension

• http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html

water in bulk has many

binding partners

water at surface has

less, has exposed

charges left over

potential energy of

water at surface is

higher

deforming droplet to

increase surface area

takes work

Intermolecular forces acting on a molecule

а, б) – inside the volume of liquid

в) – in the surface layer

gas

liquid

If some alveoli were smaller and other large = smaller alveoli

would tend to collapse and cause expansion of larger alveoli

That doesn’t happen because:

Normally larger alveoli do not exist adjacent to small alveoli = because they

share the same septal walls.

All alveoli are surrounded by fibrous tissue septa that act as additional

splints.

Surfactant reduces surface tension = as alveolus becomes smaller surfactant

molecules are squeezed together increasing their concentration = reduces

surface tension even more.

“The pressure inside a balloon is calculated by twice the surface

tension, divided by the radius.”

Pressure to collapse generated by alveoli is inversely affected

by radius of alveoli

the smaller a bubble, the higher the pressure acting on the

bubble

Smaller alveoli have greater tendency to collapse