medical physics 8 principles of fluid mechanics - u-szeged.hu · medical physics • principles of...
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Medical Physics 8
Principles of fluid mechanics
Ferenc Bariprofessor
October 27, 2016
Medical Physics • Principles of fluid mechanics (2016)
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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
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Blood Pressure: Generated by Ventricular Contraction
Figure 15-4: Elastic recoil in the arteries
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Major branches of the arterial tree
Medical Physics • Principles of fluid mechanics (2012)
aortic valve
William Harvey (1578-1657)
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More Blood Pressures: Pulse and Mean Arterial Pressures
Figure 15-5: Pressure throughout the systemic circulation
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Mean and Pulse Pressure
P P +1
3P - P )a d s d (
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Mean Arterial Pressure
Q =P P
R
a v
P - P = Q Ra v
MAP = cardiac output x total resistance
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Arterial Elasticity Stores Pressure and Maintains Flow
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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
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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
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• 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]
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•
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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.
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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.
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Medical Physics • Principles of fluid mechanics (2012)
Noninvasive measurement of arterial pressure
The cuff method (Riva-Rocci, 1896)
the auscultatory technique (Korotkoff, 1905)
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Noninvasive measurement of arterial pressure: the principle
Nikolai Szergeievitch Korotkoff
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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
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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
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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
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Pressure and velocity in the different sites of the arterial tree
Medical Physics • Principles of fluid mechanics (2012)
systolic
diastolic
mean
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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
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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
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Major branches of the canine arterial tree
Medical Physics • Principles of fluid mechanics (2012)
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Internal cross-sectional areas (cm2) of the canine aorta and main branches
Medical Physics • Principles of fluid mechanics (2012)
aortic valve
aortic arch
diaphragm
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Cross-sectional area and velocity in the systemic circulation
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Blood pressure in the systemic circulation
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Pressure and velocity in the different sites of the arterial tree
Medical Physics • Principles of fluid mechanics (2012)
systolic
diastolic
mean
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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
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Medical Physics • Principles of fluid mechanics (2012)
Arterial and venous pressures – effects of gravity
heart level
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Arterial pressures – posture dependence
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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
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Laminar stationary flow in a tube
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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:
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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
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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
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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
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Medical Physics • Principles of fluid mechanics (2012)
Relative viscosityhuman blood cells, rigid spheres, rigid disks, droplets and sickled RBC
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Medical Physics • Principles of fluid mechanics (2012)
Red blood cells in mesentery capillaries
rabbit dog
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Medical Physics • Principles of fluid mechanics (2012)
Aggregation of red blood cells
linear branched
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Real fluids: turbulence
Vocal chordsBronchial stenosisArtery narrowingBifurcationsAneurysms
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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).
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Medical Physics • Principles of fluid mechanics (2012)
Riva-Rocci, 1896Korotkoff, 1905
Noninvasive measurement of arterial pressure
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Medical Physics • Principles of fluid mechanics (2012)
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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
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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
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Intermolecular forces acting on a molecule
а, б) – inside the volume of liquid
в) – in the surface layer
gas
liquid
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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.
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“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