Biomedical Engineering – Fluid Dynamics · 04.12.2014 1 Biomedical Engineering – Fluid Dynamics...

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04.12.2014 1 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

Transcript of Biomedical Engineering – Fluid Dynamics · 04.12.2014 1 Biomedical Engineering – Fluid Dynamics...

04.12.2014

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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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PD Dr. Zöllner I Folie 119 I 9/9/2014

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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PD Dr. Zöllner I Folie 121 I 9/9/2014

Pressure in the Body

PD Dr. Zöllner I Folie 123 I 9/9/2014

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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PD Dr. Zöllner I Folie 124 I 9/9/2014

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

PD Dr. Zöllner I Folie 125 I 9/9/2014

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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PD Dr. Zöllner I Folie 126 I 9/9/2014

Bernoulli‘s Equation

# Equation of continuity

Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries

PD Dr. Zöllner I Folie 127 I 9/9/2014

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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PD Dr. Zöllner I Folie 128 I 9/9/2014

Bernoulli‘s Equation

# total work

Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries

PD Dr. Zöllner I Folie 132 I 9/9/2014

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

PD Dr. Zöllner I Folie 134 I 9/9/2014

Fluids in Motion II

Nicols & O‘Rourke, McDonald‘s Blood Flow in Arteries

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PD Dr. Zöllner I Folie 135 I 9/9/2014

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

"

$"

"

PD Dr. Zöllner I Folie 136 I 9/9/2014

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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PD Dr. Zöllner I Folie 139 I 9/9/2014

The Heart

PD Dr. Zöllner I Folie 140 I 9/9/2014

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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PD Dr. Zöllner I Folie 141 I 9/9/2014

Heart Phases

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Vascular System Human

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PD Dr. Zöllner I Folie 143 I 9/9/2014

Arterial Blood Pressure

PD Dr. Zöllner I Folie 144 I 9/9/2014

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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PD Dr. Zöllner I Folie 145 I 9/9/2014

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

PD Dr. Zöllner I Folie 146 I 9/9/2014

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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PD Dr. Zöllner I Folie 147 I 9/9/2014

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

PD Dr. Zöllner I Folie 148 I 9/9/2014

Korotkoff II

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PD Dr. Zöllner I Folie 149 I 9/9/2014

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

PD Dr. Zöllner I Folie 150 I 9/9/2014

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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PD Dr. Zöllner I Folie 151 I 9/9/2014

Oscillometric Blood Pressure Measure II

PD Dr. Zöllner I Folie 152 I 9/9/2014

Oscillometric Blood Pressure Measure III

display

valve

pump

cuff

pressure m.

amplifier

low pass

high pass

A/D converter CPU

pressure

oscillations

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PD Dr. Zöllner I Folie 153 I 9/9/2014

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