Download Biomedical Engineering – Fluid Dynamics

04.12.2014
Biomedical Engineering –
Fluid Dynamics
PD Dr. Frank G. Zöllner
Computer Assisted Clinical Medicine
Medical Faculty Mannheim
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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Fluid Parameters
parameter
Formula/
Symbol
SI unit
Density:
ρ=m/V
[kg/m3]
Temperature
T
[K]
Velocity
[m/s]
Pressure
p=F/A
[N/m2]
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Pressure Conversion Factors
Atmosphere N/m2 = Pa
Atmosphere
mm Hg
mm H2O
1
1.01 x 105
760
10300
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
N/m2 = Pa
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Pressure in the Body
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Hydrostatic Pressure
Force of Gravity of volume element dV:
pressure on ground element da:
" hydrostatic pressure distribution:
F
A
H
V
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Flow
flow: Q = dV/dt = Av
v1, A1
v2, A2
Qsource
dV = A ds = A v dt
incompressible flow
continuity law: Q = v1 A1 = v2 A2 = const
general case: Q = V1 A1 + Qsource – Qdrain
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
Fr
A
v(r)
liquid
η ... viscosity
fluid
η [mNs/
m2]=[mPas]
water
1.002
blood
approx. 3-5
glycerin
1480
mercury
1.55
Examples:
T = 20°
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Fluids in Motion II
#  laminar current:
frictional force > accelerating
force
#  otherwise formation of turbulences
possible (where velocity gradient is
strong)
! 
distinction: Reynolds number:
D ... characteristic length
... tube diameter
•  laminar flow:
•  transient:
•  turbulent flow:
Re < 2300
2300 < Re < 4000
RePD>Dr. 4000
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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
p1
current is only depended on the distance
to the axis!
#  frictional force and resulting pressure
force on the end surfaces are in
equilibrium.
"
$"
p2
"
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Flow of Fluids in Tubes II
Flow:
Resistance:
Poiseuille´s equation
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Biomedical Engineering –
Blood Flow & Pressure
PD Dr. Frank G. Zöllner
Computer Assisted Clinical Medicine
Medical Faculty Mannheim
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
!  Re
velocity v
larger: turbulence
!  curls:
bump against wall:
noise, pressure variation
!  only
open when blood
pressure > external pressure
open
t
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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: Korotkoffsound vanishes
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Oscillometric Blood Pressure Measure II
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Oscillometric Blood Pressure Measure III
display
valve
pump
cuff
A/D
converter
pressure m.
low pass
pressure
amplifier
high pass
oscillations
CPU
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Problems
!  motion artifacts (pressure reduction in steps, 2
measurements per step, if the same: no disturbance
!  advantages
-  no acoustic measurements
-  good artifact detection and suppression
-  also applicable for newborns and babies
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