BLOOD PRESSURE BIOMEDICAL ENGINEERING 2006200401 TAE_EUI, KIM.

BLOOD PRESSURE

BIOMEDICAL ENGINEERING2006200401

TAE_EUI, KIM

Invasive BP measurementInvasive BP measurement

CatheterDome Diaphragm

Strain gages (usually Four)

Pressure Sensor

Po should be same as Pi

“Fluid Mechanics”

What affect the quality of PoWhat affect the quality of Po

• Catheter length should be shorter but there is

• Viscosity of liquid

• Diameter

• Elastic material for catheter

• Diaphragm itself should be elastic

• No air bubble

Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Sensor System– Sensor System

Electric Circuit Fluid Mechanics

Voltage , V [v] Pressure , P [pa]

Current , i [A] (Volume) Flow , f [m3/s]

Charge , q [c] Volume , V [m3]

R, L, C circuit Physics things

Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Resistance– Resistance

V RiV L

Ri A

Electrical resistance :

Liquid resistance : p R f LR

A

If viscosity is too big?

Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Capacitance or Compliance– Capacitance or Compliance

dPf C

dt ( AC flow )dv

i Cdt

AC

x Young's moduleC

The bigger Compliance, the bigger flow

Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Inductance or Innertance– Inductance or Innertance

div L

dt

dfP L

dt

2

mL

A

Equivalent Circuit ModelEquivalent Circuit Model

1 2 ( radius difference)R R

1 2 1 R R R

Catheter

iP 1R 2R

oP

Sensor

Equivalent Circuit ModelEquivalent Circuit Model

i c c o

div R i L v

dt

2

2

we need equation between and

Second-Order ODE (ordinary differential euation)

od

o oo c d c d i

i v

dvi C

dt

dv d vv R C L C v

dt dt

Catheter & Sensor are rigid but not diaphragm

Equivalent Circuit ModelEquivalent Circuit Model

2

2

2

2

2 1 ( ) ( )

o oo c d c d i

o in n

dv d vv R C L C v

dt dt

D Dv t Kv t

W W

max

1

( 1)2

1 > ( max freq. of (t) )

c d

c

n i

c d

K

R C

L

W W vL C

21

2

2d

c

RC

LC

CRL

CR

L

Frequency Transfer FunctionFrequency Transfer Function

2

2

122 2

2

2 2

2

1( )

( ) 2 1

1 =

1 ( ) 2

21

= tan

11 4

1 = t

1 4

o

i

n n

n n

n

nn n

n n

vH j

j jv

j

1 2an

n

n

Magnitude ResponseMagnitude Response

nWW

H

2

1

1

2

0.25 (under damped)

0.5 (critical damped)

1 (over damped)

Phase ResponsePhase Response

nWW

H

2

If higher , Phase is linear but high frequency discarded in terms of Magnitude

Trade off

ReferenceReference2

2

2

2

2

2

( 1)

LC(j )

1 H(j )= ( )

( ) ( ) 1

( ) ( ) { ( )}

( ) ( ) { }

( )

o

o o o i

o i

o o o o i

oD j

i

j t

j t

j

d vLC RC

dt

LCD v RCDv v v

LCD RCD v v

v RCj v RCj v v v

vH D

v LC j RC j

v j v t e dt v t

dv t dv te dt

dt dtdv t e

dt

F

F

( )( ) ( )

( ){ ( ) ( ) }

( ) ( ) }

0 { }

t j t j t

j t j t j t

j t j t

dv te v t e j

dtdv t d

e dt v t e j v t e dtdt dt

dv t e dt j v t e dt

dtj j

F

Steady State Frequency ResponseSteady State Frequency Response

1

1

( ) sin(2 )

( ) sin(2 )4

i

o

v t A f t

v t KA f t

2

2

( ) sin(2 )

( ) 0.1 sin(2 1.9 )i

o

v t A f t

v t A f t

R L

C

H H

0.1

K4

1.9

21f 2f

1f 2f

Steady State Frequency ResponseSteady State Frequency Response

1 1 2 2

1 1 1 1 2 2 2 2

( ) sin(2 ) sin(2 )

( ) sin(2 ) sin(2 )i

o

P t A f t A f t

P t K A f t K A f t

; Principle of Superposition

Transient ResponseTransient Response

( ) sin(2 ) ( ) ; Signal generated from a specific timeiv t A ft u t

; Principle of Superposition

( )iv t

1A 1KA

( )ov tTransient Property!

Transient Property!