Biomedical Engineering – Fluid Dynamics · 04.12.2014 1 Biomedical Engineering – Fluid Dynamics...
Transcript of Biomedical Engineering – Fluid Dynamics · 04.12.2014 1 Biomedical Engineering – Fluid Dynamics...
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Biomedical Engineering – Fluid Dynamics
PD Dr. Frank G. Zöllner Computer Assisted Clinical Medicine Medical Faculty Mannheim
PD Dr. Zöllner I Folie 118 I 9/9/2014
Overview
! Fluid Parameters: Pressure, Flow
! Fluids in Motion
! Flow of Fluids in Tubes
! Blood Pressure
! Measurement of Blood Pressure
! Pressure Sensor
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parameter Formula/Symbol
SI unit
Density: ρ=m/V [kg/m3]
Temperature T [K]
Velocity [m/s]
Pressure p=F/A [N/m2]
Fluid Parameters
PD Dr. Zöllner I Folie 120 I 9/9/2014
Pressure Conversion Factors
Atmosphere N/m2 = Pa mm Hg mm H2O
Atmosphere 1 1.01 x 105 760 10300
N/m2 = Pa 9.87 x 10-6 1 0.0075 0.102
mm Hg 0.00132 133 1 13.6
mm H2O 9.86 x 10-5 9.81 0.0735 1
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Pressure in the Body
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Hydrostatic Pressure
F A
H V
Force of Gravity of volume element dV:
pressure on ground element da:
" hydrostatic pressure distribution:
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Flow
v1, A1 v2, A2
flow: Q = dV/dt = Av
dV = A ds = A v dt
incompressible flow
continuity law: Q = v1 A1 = v2 A2 = const
general case: Q = V1 A1 + Qsource – Qdrain
Qsource
Qdrain
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Bernoulli‘s Equation
# used to determine kiquid velocities by means od pressure measurements
# „ideal liquid“, e.g. no force of viscosity
Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries
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Bernoulli‘s Equation
# Equation of continuity
Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries
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Bernoulli‘s Equation
# work done on the fluid entering the tube per unit time
# liquid in motion has also kinetic energy
Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries
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Bernoulli‘s Equation
# total work
Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries
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Fluids in Motion I
A
v(r)
Fr
liquid
η ... viscosity
Examples: fluid η [mNs/
m2]=[mPas]water 1.002 blood approx. 3-5 glycerin 1480 mercury 1.55
T = 20°
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PD Dr. Zöllner I Folie 133 I 9/9/2014
Fluids in Motion II
# laminar current: ! frictional force > accelerating
force # otherwise formation of turbulences
possible (where velocity gradient is strong)
distinction: Reynolds number:
• laminar flow: Re < 2300 • transient: 2300 < Re < 4000 • turbulent flow: Re > 4000
D ... characteristic length ... tube diameter
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Fluids in Motion II
Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries
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Flow of Fluids in Tubes I # due to symmetry the velocity of the
current is only depended on the distance to the axis!
# frictional force and resulting pressure force on the end surfaces are in equilibrium.
p1
p2
"
$"
"
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Flow of Fluids in Tubes II
Flow:
Poiseuille´s equation Resistance:
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Biomedical Engineering – Blood Flow & Pressure
PD Dr. Frank G. Zöllner Computer Assisted Clinical Medicine Medical Faculty Mannheim
PD Dr. Zöllner I Folie 138 I 9/9/2014
Physiological Basis
! blood: incompressible, laminar liquid
! pressure generator: heart
! cardiac output: volume that is pumped from one ventricle per time (minute)
! pumped volume per beat: approx. 70 cm3
! 60 beats per minute= 4,2 l/min
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The Heart
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Blood Pressure in Arterial Part strain phase
# chamber filled, contraction, closing by valve # increase of pressure: 0,27-1,47 kPa to
10,7 kPa (2-11 to 80 mm Hg) ejection phase # valve opens # max. pressure: 16 kPa (120 mm Hg)
relaxation phase ventricle pressure < aortic pressure # valve closes, ventricle pressure approx. 0 mm Hg, aortic pressure approx.
const. filling phase
# valves open, increase in pressure # dynamic area: 80-120 mm Hg
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Heart Phases
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Vascular System Human
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Arterial Blood Pressure
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Blood Pressure and Influences I ! normal values
- systolic pressure: age in years + 100 - diastolic pressure: 90
! depends from
- respiration (inspiration: decreasing, expiration: increasing) - physical stress - physical factors (sleep, filling of bladder (increases with filling), after
eating (higher)) - external temperature (colder = higher) - body temperature - time of day (minimum at 3 am, maximum at 3 pm) - muscle load - body position (lying: low, standing: high) - blood loss (decreasing) - measurement location - age (increasing)
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Blood Pressure and Influences II
# pathological: systolic pressure > 160, diastolic pressure > 95
# higher risk for defects of coronary arteries/heart infarct, brain infarct (cerebral apoplexy), damages of nerves, aneurisms
# hypertension: average blood pressure over 100 mm Hg
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Measurement of Blood Pressure
# Riva Rocci ! upper arm: fix cuff (arteria
brachialis) ! P > psys (200 mm Hg)
! no blood flow: photo sensor at finger
! pulsing flow: systolic pressure
! continuous flow: diastolic pressure
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Korotkoff I
# reduced cross section
! higher velocity v
! Re larger: turbulence
! curls: bump against wall: noise, pressure variation
! only open when blood pressure > external pressure
t open
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Korotkoff II
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Korotkoff III Problems: # Cuff must be at heart level to
obtain a pressure that is not influenced by gravity
# just possible to measure pressure in the arm (arteria brachialis)
# if cuff is left inflated for some time, the discomfort may cause an reflex raising the blood pressure
# incorrect size of cuff # incorrect speed of pressure
reduction # incorrect placement of cuff and
stethoscope membrane # difficulty to distinguish between
continuous and staccato sound
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Oscillometric Blood Pressure Measure I
# same principle # during measurement of pressure at cuff: oscillations # empirical criteria for systolic and diastolic pressure # determine amplitudes of oscillations # average pressure: cuff pressure where maximal amplitude
occurs # remainder over specific algorithms like
! A: amplitude; Asys = 45-57% of Am (normal value 50%): first occurrence of Korotkoff-sound
! Adia = 75-86% (normal value 80%) of Am: Korotkoff-sound vanishes
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Oscillometric Blood Pressure Measure II
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Oscillometric Blood Pressure Measure III
display
valve
pump
cuff
pressure m.
amplifier
low pass
high pass
A/D converter CPU
pressure
oscillations