ee 5340/7340, smu electrical engineering department, ©2004 1 carlos e. davila, electrical...

EE 5340/7340, SMU Electrical Engineering Department, ©2004

1

Carlos E. Davila, Electrical Engineering Dept.Southern Methodist University

slides can be viewed at: http:// www.seas.smu.edu/~cd/ee5340.html

EE 5340/7340 Introduction to Biomedical Engineering

Ultrasound Flowmetry II


2

A More Realistic Geometry

u

red bloodcell (RBC)

transmitted ultrasound

reflected ultrasound

t

r

ucos r

ucost

affects firstfrequency shift

affects secondfrequency shift


3

A More Realistic Geometry (cont.)

fc u

c ufr

tt

cos

cos

r

fuc

fd t r t cos cos

(see HW problems)

(1)

(2)

Doppler frequency shift: fd = fr - ft


4

Vector Notation

transmitted ultrasound

reflected ultrasound

t

r

kt

ukr

k kt t

t 2

k kr r

r

2


5

Vector Notation (cont.)

fc u

c ufr

tt

cos

cos

r

(1)

can be written as: f

ck

u k

ck

u k

frt

t

rr

t

1

1

since: x y x y cos

x

y

angle between thesevectors > 90o

(3)


6

Vector Notation (cont.)

fck

u kck

u k frr

rt

t t11

11

(3) becomes:

since: ck 2fand

we get: r r t tu k u k

or: d r t r tu k k


7

Transmitter/Receiver Configurations

the geometric configuration of the transmitter and receivercan greatly affect the sensitivity of the flowmeter:

d r tu k k

kt

kr

u

k kr t

d negative, sensitivity is maximized

assume k kr t , then Doppler shift depends primarily on angle between and

u

k kr t

u


8

Transmitter/Receiver Configurations (cont.)

kt

kr

u

k kr t 0

no sensitivity

kt

kr

u

k k ur t

no sensitivity

d r tu k k


9

Transmitter/Receiver Configurations (cont.)

kt

kr

u

tr

d r tu k k

u

k kr t

d negative, moderatesensitivity, also sensitive totransversal vessel wall motion


10

Angle of Transmitted Ultrasound

hand-held flow probes are calibrated assuming t = 45o.

if t is too small, ultrasound undergoes too much attenuation since it has a longer path from transmitter to reflector and back to sensor.

if t is too large (close to 90o), sensor becomes too sensitive to transverse motion.

error due to mispositioning the sensor away from 45o is not too severe (see HW).


11

Frequency Spectrum of Received Ultrasound

f

reflection from stationary objectstransverse vesselwall motion

forward blood flowreverse blood flow

sign

al p

ower

ft fd > 0 fd < 0


12

Doppler Frequency Shift Varies due to:

Acoustic beam illuminates a relatively large volume of blood within the vessel nonuniform velocity profile across section of vessel (e.g.

laminar flow has lower velocity near vessel walls) acoustic beam is nonuniform, effective angles t and r

vary over different locations If acoustic beam is focused so as to illuminate a very small

volume, then the reflector is seen for only a short period of time, this produces spreading in the frequency domain (e.g. in the limit the Fourier transform of an impulse function is a constant for all frequencies).


13

Continuous Wave (CW) Doppler Flowmeters-transmitter is excited continuously

skin

vessel

oscillator

transmitterRF amp

mixer audio

amp

speaker

zero-crossingdetector

LPF

recorder

LPFvr

vt vd va

2cos t t

2


14

CW Doppler Flowmeters (cont.)

v tt tcos

v tr t d cos

v t t

t td t t d

d t d

2

2

cos cos

cos cos

used trig identity:

cos cos cos cosu v u v u v 12


15

CW Doppler Flowmeters (cont.)

after LPF: v ta dcos note that flow direction is lost since

cos cos d dt t reverse blood flow cannot be distinguished from forward flow for ft in the 2 - 10 MHz range, fd varies from 10 Hz to 10 kHz,

corresponding to audio frequencies audible output devices are small, hand-held devices which are easy to

use. useful for diagnosis of vascular occlusion


16

Zero-Crossing Detectors

v ta dcos

zero-crossing detector output:

LPF output, crude flow signal:

t

t

t

hysteresis band

va must pass through entire hysteresis band to produce a pulse


17

Choice of Transmission Frequency

higher transmission frequencies tend to undergo better reflection (backscattering) when the reflectors are small relative the the wavelength of the ultrasound, as is the case with RBC’s, which produce Rayleigh scattering.

high frequencies are attenuated more than low frequencies. for shallow vessels, typically use ft = 4 - 10 MHz

for deeper penetration, use ft = 2 MHz

2 conflicting criteria:


18

Bi-directional Flowmeters: Quadrature Phase Detection

skin

vessel

oscillator

transmitterRF amp

mixer

vr

vt

LPFvd va

2cos t t2

90o phaseshift

2sin t t

2

LPFvdq vaq

-1

tan-1

d t


19

Quadrature Phase Detection (cont.)

v ta dcos

as seen before:

v tr t d cos

v t t

t tdq t t d

d t d

2

2

sin cos

sin sin

after LPF: v t taq d d sin sin

used trig identity: sin cos cos sinu v u v u v 12


20

Quadrature Phase Detection (cont.)

tan-1d t

sin

cos

d

d

t

t

t

d

sign of d is retained


21

Hardware for d Computation

+_

va

0

+_

vaq

0MMV

+_ LPFcomparator

comparator

differenceamp

arctan function not implemented in practice

d

“one shot”

a

b c

a’

d

e


22

Timing Diagram: Flow Towards Transducer

t

t

ta

a’

b

c

d

e

va

vaq

t

t

t

t

t


23

Timing Diagram: Flow Away From Transducer

t

t

ta

a’

b

c

d

e

va

vaq

t

t

t

t

t


24

Pulsed Doppler Flowmeters

Rather than CW excitation, the transducer is excited for a short time interval, a pulse of ultrasound is transmitted.

The resulting echoes reflect the Doppler shifts occurring along different locations within the vessel.

Can use the pulse echo information to image the flow profile along a section of the vessel.

Typically, transmit a 1 s pulse of 8 MHz ultrasound. Can use a single transducer for both transmission and

reception.


25

Pulsed Doppler Flowmeters (cont.)

transmitted pulse:

echo:

near-wallreflection

far-wallreflection

reflectionfrom vessel

center

vt

vr

eight cycles of 8-MHzultrasound

1 s

t

t

va va changes much slower than vrt


26


skin

vessel

oscillator

transmitterRF amp

mixer audio

amp

LPFvr

vt vd va

2cos t t

21-2n DEMUX

n-bitcounter

quadrature phase detection can also be used

“gating”


27


audio amp

va

1-8 DEMUX

3-bit counter

va scanned once for every transmitted pulse

scan

-1sc

an-2

scan

-3

cos d tn

t

vessel center

near wall

far wall


28

Pulse Repetition Rate

to avoid aliasing, t must satisfy the Nyquist criterion:

but 1/t is the pulse repetition rate, this imposes constraints on the maximum range, Rmax:

ft

fp d 1

2

Rcf

c t

pmax

2 2


29

Transit-Time Flowmeters

vesseluD

downstream transit time: tD

c udown cos

upstream transit time: tD

c uup cos

invasive


30

Transit-Time Flowmeters (cont.)

t t tDu

c u

Du

cdown up

2 2

2 2 2 2cos

cos

cos

since c u t is proportional to u

fudge factors: u u133.

u u107.

laminar flow

turbulent flow

u: average velocity along cross section of vessel


31

Stethoscope Pocket Doppler Flowprobe

Built-in probe Approximate 8 MHz frequency Operates on a standard 9 volt battery Stethoscope fitted to a Telex earphone outlet

courtesy of Park Medical


32

Pocket Doppler Flowprobe

Pocket Doppler FlowprobeBuilt-in signal processing for displaying recordings Factory set amplitude control Plug-in probes Dimensions: height: 3.8 cam width: 7.9 cam depth: 14.6 cam Built-in speaker Auto-shutoff Approximate 8 MHz frequency Operates on a standard 9 volt battery Auxiliary earphone output



33

Features:

Auto-shutoff Built-in speaker Auxiliary earphone output Rechargeable battery Low battery indicator Recorder output 8 MHz to 9.7MHz frequencies available Various welded-metal cases available Nondirectional



34

Bi-directional Flowmeter

Chart recorder Two chart speeds 5 mm / sec 25 mm / sec 40 mm chart paper Large speaker Auxiliary earphone output Rechargeable battery AC coupled pneumoplethysmograph DC coupled pneumoplethysmograph AC coupled photoplethysmograph DC coupled photoplethysmograph Dual frequency Approximate 8 MHz frequency

Approximate 4 MHz frequency


ee 5340/7340, smu electrical engineering department, ©2004 1 carlos e. davila, electrical...

Documents

sensitivity slide

frequency shift slide

ultrasound tt rr slide

f r f t

ultrasound f reflection

doppler frequency shift

doppler shift

ultrasound tt rr ucos