Laser Doppler Velocimetry · 2016. 6. 29. · • laser light reflected/scattered by moving blood cells, • partly back-reflected into laser cavity, • with Doppler-shifted frequency,

BioMedical Optics

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Biomedical Optics

Laser Doppler Velocimetry

F.F.M. de Mul

(University of Twente, Enschede, the Netherlands)

BioMedical Optics Biomedical Optics : course

FdM 2

Contents

1. - General Introduction

- Overview of existing techniques

2. - Light scattering, theoretical background

- Monte-Carlo + numerical assignment

- Photoacoustics

3. Experimental: focus on some techniques:

- Laser-Doppler perfusion

- Self-mixing velocimetry

BioMedical Optics Laser Doppler Velocimetry

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Contents:

1. LD for blood perfusion • Principles

• Monitoring

• Imaging

2. Self-mixing LD • Principles

• Experimental aspects

• Flow velocities

• Intra-arterial use

BioMedical Optics LDV: Principles

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Principle of laser Doppler:

vkk 0s

D

k0 and ks : incoming and

scattered wavevectors

v: particle velocity

D = 2 fD: Doppler frequency k0

ks

v k = ks-k0

21sin.2kk

cossin21

kvfD

Normally in tissue: is small : 0.95 < 15º

approx. k0 // v : only v-component k0 measured

BioMedical Optics LDV: Types of Instruments (1)

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(A) Differential (Dual-beam) Laser Doppler Velocimetry

Interference fringe pattern

Detection preferentially in

forward direction Scattered

intensity

burst

time

sin2 spacing Fringe s

/sin.2 frequencyDoppler

zvf

z


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(A) Differential (Dual-beam) Laser Doppler Velocimetry

Original frequency

[ 1014 Hz]

Doppler-shifted

frequency

+ D [ 1014 Hz]

Doppler frequency

D [


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(B) Laser Doppler Perfusion Velocimetry

laser

detector v

0

0

Averaged Doppler frequency:

Heterodyne mixing

= - 0

laser

detector v

0

1 2 Homodyne mixing

= 1 - 2

Averaging by: - random velocities

- (multiple) scattering in random directions

BioMedical Optics LDPV: Spectra (1)

FdM 8


0 D

f(D)

Doppler frequency spectrum

Heterodyne

peak

Heterodyne peak: due to large amount of non-Doppler shifted

scattered photons.

Doppler power spectrum

0 D

homodyne

heterodyne S(D)


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0 D

S(D)

Larger v

Larger c

Power spectrum

dependent on:

- concentration c

- velocity v

0

)(.

:spectrumPower

of Moments

dSM nn


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0 D

S(D)

Power spectrum dependent on:

- concentration c

- velocity v

0

)(.

:spectrumPower of Moments

dSM nn

Moments: n = 0 : ~ concentration of moving scatterers

n = 1 : ~ flux of moving scatterers

M1 / M0 : ~ velocity

BioMedical Optics LDPV

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Laser

Photodiode

fiber

BioMedical Optics LDPV: Skin Tissue

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(B) Laser Doppler Perfusion

Velocimetry

Schematic cross section of

Skin tissue

BioMedical Optics LDPV: Signals

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LD spectra of

finger tip

upon occlusion

of upper arm

Flux = 1st moment of power spectrum

Concentration = 0th moment

= flux/concentration

heart beat

heart beat

noise

20 sec

occlusion

BioMedical Optics LDPV: Types of Instruments

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(B) Laser Doppler Perfusion Velocimetry: Instrument design

laser detector

v

0

glass fibers (a) Glass fibers for light

transport

v

probe (b) Direct-contact velocimetry:

Laser and detector in one probe

Disadvantages:

• motional artefacts

• sensitive for local variations

• no motional artefacts

• local averaging

BioMedical Optics LDPV: New Instruments

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(B) Laser Doppler Perfusion Velocimetry: Instrument design

LD-monitor on-a-chip

provides miniature depth-sensitive

sensor.

Green: photodiode rows

Blue/red: electronics:

amplifiers/multiplexers

Red dot in yellow area:

VCSEL- laser diode

BioMedical Optics Clinical applications: (1) Plastic Surgery

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(B) Plastic and Reconstructive Surgery

Replantation and

Revascularization

N=68

Flaps: forearm, toe,

thumb, lateral arm,

fibula

Effects after

first half hour

Courtesy: L. van Adrichem, University Hospital Rotterdam

Resulting Inter-

vention level

(“alarm value”)

= 10


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Specificity and

Sensitivity of

LD Perfusion flowmetry

in the

replantation/

revascularization

group

“alarm value”,

intervention

level


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Characteristics of

Post-operative

monitoring devices


Figures:

instruments read-out

Red line:

Intervention level


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Cigarette smoking:

1.

Effect on flow through

healthy thumb.

2.

Effect on flow through

replanted digit.

BioMedical Optics Clinical Applications (2): PORH: Post-Occlusive Reactive Hyperemia

0

50

100

150

200

250

300

350

0 500 1000 1500 2000

time (sec)

perf

usio

n

FdM 20

Resting flux

PORH occlusion

Healthy person

BioMedical Optics PORH:

2002-01-25_Reindert: Flux in Dorsum with Perimed0.25

-10

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200 1400 1600 1800 2000

2001-08-10_Meijer: Flux in Dorsum with Perimed0.25

-5

0

5

10

15

20

0 200 400 600 800 1000 1200 1400 1600 1800 2000

2001-08-02_Smit: Flux in Dorsum with Perimed0.25

-10

0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1000 1200 1400 1600 1800 2000

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Diabetes Mellitus:

Medium rise, low top

Control group:

Fast rise, high top

PAOD:

Slow rise, low top

BioMedical Optics

PORH: Post-Occlusive Reactive Hyperemia

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Occlusion

position

Measurement

position

Leg arteries and veins

Capillaries

and shunts

Leg arteries and veins:

• Resistance R1

• Capacitance or

compliance C1

Capillaries/ shunts:

• Resistance R2 .. R4 • Capacitance or

compliance C2

Model: jump-response

after occlusion:

R1 R2

R3 R4 C1 C2 V1 V0 V2

BioMedical Optics

PORH: Post-Occlusive Reactive Hyperemia

hE

lrC

r

lR

2

3;

83

0

4

0

hEr

lRC

0

212

FdM 23

Model: jump-response after occlusion:

R1 R2

R3 R4 C1 C2 V1 V0 V2

V = pressure (voltage) [N/m2]

I = flow (current) [m3/s]

Q = volume (charge) [m3]

R = resistance = V / I [Ns/m5]

C = capacitance = Q / V [m5/N]

l = length of tube r0 = radius

= viscosity [Ns/m2] h = wall thickness

E = Young’s modulus [N/m2]

RC- circuits behave in time like : exp(-t / ): with characteristic time constant .

BioMedical Optics Post-Occlusive Reactive Hyperemia

214121

12

/

2

/

1

..,..,with

1;..1 21

CCRRfkk

kkekekIItt

rest

21 // 111 ttrestapprox eMReII FdM 24


R1 R2

R3 R4 C1 C2 V1 V0 V2

Exact model:

Measured perfusion:

Current I through R2.

Approximation: R4 >> R1 .. R3 (no shunts before entrance in capillary bed)

R1 C1


2

32

32

3222111 ;;

R

RRMR

RR

RRCCR

21 // 111 ttrestapprox eMReII

FdM 25


R1 R2

R3 R4 C1 C2 V1 V0 V2

Measured perfusion:


Approximation: R4 >> R1 .. R3 (no shunts before entrance in capillary bed)

R1 C1


21 // 111 ttrestapprox eMReII

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Approximation:

Measured perfusion:


t

1

0

MR

e -t/τ1

1-e-t/τ1

Assume: τ1


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Exact model Approximation


tR tM tH M/R

PAOD 6.5 58 149 3.1

Controls

BioMedical Optics Clinical applications (3): Iontophoresis

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tissue

Probe with

channel for

drug delivery

Measured:

Influence of drug delivery on flow.

Amp-meter measures amount of injected molecules.

Measure for diffusion coefficient of drug in tissue.

Fibers to LDF instrument

electrode

A Ampère-meter


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Measured:

Influence of drug delivery on flow.

Amp-meter measures amount of injected molecules.

Measure for diffusion coefficient of drug in tissue.

Example:

Women with pre-eclampsia (pregnancy poisoning):

- hypertension, proteinuria, oedema,

- due to endothelial dysfunction, changes in vascular reactivity and

permeability for macromolecules

Vasodilatation can be enforced by drugs:

- endothelial-dependent drugs: acetylcholine

- endothelial-independent drugs: nitroprusside

Question: relation between flow change and drug delivery.


FdM 31

Sponge pad

LDF-probe

(reference)

LDF-probe

(measurement)

BioMedical Optics

Clinical applications (3): Iontophoresis

Compounds in iontophoresis Activity

Capsaicin Neuropeptides

(Nor)epinephrine hydrochloride Vasoconstrictor

Sodium nitroprusside Vasodilator, to smooth muscle walls

Acetylcholin chloride Vasodilator, activating endothelial

vessel cells

Histamine Oedema and vasodilation

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BioMedical Optics Clinical applications (3): Iontoforesis

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-20

0

20

40

60

80

100

120

1 181 361 541 721 901 1081 1261 1441 1621 1801 1981

-50

0

50

100

150

200

250

300

1 212 423 634 845 1056 1267 1478 1689 1900 2111 2322

Per

fusi

on

Time (sec) Time (sec)

Acetylcholin chloride Sodium nitroprusside

5 Shots: Start ( ↓ ) at 600 sec, duration 20 sec each, intervals 90 sec

End ( ↑ ) at 960 sec

At end of recording: arterial occlusion.

Shown signal = measuring probe – reference probe

Acetylcholine washes out faster, due to vasodilation,

especially with women with pre-eclampsia.

BioMedical OpticsLD - Diffusion model for Iontophoresis 1. 1-Dimensional diffusion : c = concentration

2

2

z

cD

t

c

,

}4

exp{),(2

Dt

z

Dt

Qtzc

2. Decrease too slow: add decay term: - c

cz

cD

t

c

2

2

}4

exp{),(2

tDt

z

Dt

Qtzc

Assume:

excess (*) flow

F(t) ~ concentration (*) = above resting

flux level.

tntt

tDt

z

Dt

QsntF

n

n

nn

N

n

)1(

4exp)1(exp)(

20

1

3. Assume: N shots with interval t

s = shot saturation constant;

if s = 0: all shots contribute equally

if s >>1: only first shot contributes

D = diffusion

constant

= decay constant

BioMedical OpticsLD - Diffusion model for Iontophoresis

0

50

100

150

200

250

300

350

400

450

500

0 500 1000 1500 2000 2500

time (sec)

pe

rfu

sio

n (

a.u

.)

,

Fit results (2 Pre-eclampsia patients; SNP-administration): 9 shots; 90 sec. apart.

Parameters: χ2red = 1.15; 1 = 76 ± 10 s ; 2 = 408 ± 30 s ; s = 0.029 ± 0.014

χ2red = 1.90; 1 = 65 ± 12 s ; 2 = 252 ± 30 s ; s = 0.048 ± 0.028

BioMedical Optics SM-LDV: Self-mixing (1)

FdM 36

Principle:

• laser light reflected/scattered

by moving blood cells,

• partly back-reflected into laser cavity,

• with Doppler-shifted frequency,

• in cavity: mixing with “original” light,

• Doppler signal results,

• can be measured with photodiode

(C) Self-mixing Laser Doppler Velocimetry: Principle

Laser diode

Optical fiber

Photodiode

Moving cell

Velocity


FdM 37


Five-mirror setup:

- M1 and M2 : facets of laser crystal

- M3 and M4 : facets of fiber

- M5 : reflection at / scattering in moving object MO

MO: moving object

L1 and L2 : lenses

DL: diode laser +

photodiode

M1 M2 M3 M4 M5

fiber L1 DL L2

MO


FdM 38


0 10 20 30 40 50

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

am

plitu

de

, [m

V]

time, [s]

0 20 40 60 80 100

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

R rotating wheel

NR non rotating wheel

frequen

cy s

pectr

um

, [m

V]

frequency, [kHz]

Time signal Frequency signal

R

NR


FdM 39

(C) Self-mixing Laser Doppler Velocimetry:

Filter for directly reflected light

Reflected light will not be focussed onto laser crystal facet.

Only light returning through the fiber will be fed back into the laser cavity.

Laser

facet

No filter


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(C) Self-mixing Laser Doppler Velocimetry

0 100 200 300 400 500 600 700 800 900 100020

30

40

50

60

70

80

90

Cut-off frequency

Zero velocity

Doppler signal

Am

plitu

de

(

V)

Frequency (kHz)

Frequency / kHz

Sp

ectr

al i

nte

nsi

ty

Liquid flow: Cut-off frequency

provides maximum flow velocity

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

u/U

max

Fiber position, r (mm)

Flow profile in whole milk,

normalised on maximum value


FdM 41

(C) Self-mixing Laser Doppler Velocimetry

0 200000 400000 600000 800000 1000000

1E-5

1E-4

1E-3

0,01

0,1

frequency s

pectr

um

, a.u

.

frequency, [Hz]

Iliac

artery

Optical

fiber

Catheter

Basket

Branching in iliac artery of healthy pig

Cut-off frequency at 400 kHz corresponds with a velocity of 16 cm/s.

(Independent measurement using an electromagnetic probe: 14.5 1.0 cm/s)(

Flow – no flow

Cut-off frequency

BioMedical OpticsLaser Doppler Perfusion: Monitoring vs. Imaging

FdM 42

laser

detector

monitoring

fibers laser

detector

Scanning mirror

imaging

Scattering at moving cells causes Doppler frequency shift

BioMedical Optics

Laser Doppler Perfusion (Imaging)

FdM 43

Superficial perfusion of the

dorsal side of the hand,

characters UT written using

muscular balm.

Upper left: perfusion, not

normalized;

Upper right: DC-reflection

from tissue;

Lower left: perfusion,

normalized with DC

Lower right: perfusion,

normalized with DC2 .

BioMedical Optics


FdM 44

From: Bornmyr, “Laser Doppler flowmetry and imaging - methodological studies.

Dep of clinical hysiology”,thesis, Malmö, Sweden (1998);

Figure: courtesy: prof. G. Nilsson, Lisca, Linkoping, Sweden)

Typically the highest perfusion is in the boundary around

the ulcer, in inflammatory skin and in granulating tissue

inside the ulcer area.

Perfusion Image of a foot ulcer

BioMedical Optics


FdM 45

The effect of micro-trauma

Insertion of a micro-

dialysis fibre into the

skin.

The dialysis fibre

probe tip causes

hyperperfusion

No hyperperfusion

at the point of

introduction because

the skin is anesthetized.

After 30 minutes the

hyperperfusion is reduced.

(Courtesy: Lisca Sweden)

BioMedical Optics


FdM 46


Before treatment After treatment

Immediately One week 8.5 months later

Neo-vascularisation

in tumour area.

Inflammatory

response. Inflammatory response

with excessive perfusion. Back to normal.

Basal cell carcinoma

BioMedical Optics


FdM 47

Flow-Maps of a

Healing Wound

Day 1: wound creation

Day 4

Day 7

Day 10

Day 13

Black inc

marker on skin

Crust formation

in centre of wound Crust off Perfusion returning

to normal (Courtesy: Lisca Sweden)

BioMedical Optics


FdM 48

Day 2

Reduced perfusion

in burnt areas.

Increased perfusion

in surrounding skin.

Towards normalisation.

Day 13 Day 28

The healing process of a burn wound


BioMedical Optics Laser Doppler Perfusion (Monitoring) New developments

FdM 49

Low-coherent depth-sensitive LD-Monitoring

-5 0 5 10 15

0.0

0.2

0.4

0.6

0.8

1.0

experimental

MC simulation

No

rma

lize

d in

tensity

Optical path length [mm]

50:50

95:5

D

SLD

R

The reference mirror selects the depth in the sample from which a coherent Doppler-

shift signal will be measured.

BioMedical Optics

Laser Doppler Perfusion (Imaging) New developments:

FdM 50

Imaging using CMOS camera

to PC

CMOS

camera

lens

scattered light

sample

HeNe laser

illuminating beam

Remarks: - Beam diameter on the sample.....5 cm

- Sample-to-camera distance..........60cm

Advantage of CMOS over CCD camera:

CCD: serial read-out of collected photons

using shift registers

=> slow read-out

=> no dynamic response possible

CMOS: each pixel can be addressed separately,

enables fast dynamic 2D-response

Advantage of CMOS over scanning detector:

Scanning detector:

= measures dynamic signal

= slow imaging due to scanning

BioMedical Optics


FdM 51

New development:


Sample : Plastic box with 4 cylindrical holes

filled with Intralipid™ (moving particles)

35

mm

Full frame

Moving particles concentration, a.u.

0 255

Original False-color Smoothed

BioMedical Optics


FdM 52

New development:


Occlusion

After

image processing

Before

image processing

No occlusion

Moving blood cells concentration, a.u.

0 255

BioMedical Optics Laser Doppler Velocimetry

FdM 53

The End

Summary:

1. LD for blood perfusion • Principles

• Monitoring

• Imaging

2. Self-mixing LD • Principles

• Experimental aspects

• Flow velocities

• Intra-arterial use

Documents

Laser Doppler Velocimetry · 2016. 6. 29. · • laser light reflected/scattered by moving blood cells, • partly back-reflected into laser cavity, • with Doppler-shifted frequency,