Abstract

We have measured the velocity of blood flow in the femoral vein of a rabbit by detecting the Doppler shift of laser light introduced into the vein by means of a fiber optic catheter. A 0.5-mm diam optical monofiber inserted in the vein transmits both the incident light and collects the light scattered from the moving erythrocytes. The spectrum of heterodyne beat notes between the local oscillator, which originates at the end of the fiber, and the scattered light are measured using optical mixing spectroscopy.

© 1975 Optical Society of America

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References

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  1. D. L. Franklin et al., IRE Trans. Med. Electron. ME-6, 204(1959).
    [CrossRef]
  2. A. Menchimol et al., Am. Heart J. 78, 649(1969).
    [CrossRef]
  3. A. Kolin, Medical Physics, O. Glasser, Ed. (Chicago, 1960).
  4. E. M. Khouri, D. E. Gregg, J. Appl. Phys. 18, 224(1963).
  5. E. E. Selkurt, Am. J. Physiol. 193, 161 (1958).
  6. T. Tanaka, C. Riva, I. Ben-Sira, Science, in press.C. Riva, B. Ross, G. Benedek, Invest. Ophthal. 11, 936 (1972).
    [PubMed]
  7. G. B. Benedek, “Optical Mixing Spectroscopy with Applications to Problems in Physics, Chemistry, Biology and Engineering,” in Polarization, Matter and Radiation (Presses Universitaire de France, Paris, 1969).
  8. T. Tanaka, G. B. Benedek, in preparation.
  9. N. Anderson, P. Sekelj, Phys. Med. Biol., 12, 173(1967).
    [CrossRef] [PubMed]
  10. L. Landau, E. M. LifshitzHydrodynamics (Nauka, Moscow, 1965).

1969 (1)

A. Menchimol et al., Am. Heart J. 78, 649(1969).
[CrossRef]

1967 (1)

N. Anderson, P. Sekelj, Phys. Med. Biol., 12, 173(1967).
[CrossRef] [PubMed]

1963 (1)

E. M. Khouri, D. E. Gregg, J. Appl. Phys. 18, 224(1963).

1959 (1)

D. L. Franklin et al., IRE Trans. Med. Electron. ME-6, 204(1959).
[CrossRef]

1958 (1)

E. E. Selkurt, Am. J. Physiol. 193, 161 (1958).

Anderson, N.

N. Anderson, P. Sekelj, Phys. Med. Biol., 12, 173(1967).
[CrossRef] [PubMed]

Benedek, G. B.

G. B. Benedek, “Optical Mixing Spectroscopy with Applications to Problems in Physics, Chemistry, Biology and Engineering,” in Polarization, Matter and Radiation (Presses Universitaire de France, Paris, 1969).

T. Tanaka, G. B. Benedek, in preparation.

Ben-Sira, I.

T. Tanaka, C. Riva, I. Ben-Sira, Science, in press.C. Riva, B. Ross, G. Benedek, Invest. Ophthal. 11, 936 (1972).
[PubMed]

Franklin, D. L.

D. L. Franklin et al., IRE Trans. Med. Electron. ME-6, 204(1959).
[CrossRef]

Gregg, D. E.

E. M. Khouri, D. E. Gregg, J. Appl. Phys. 18, 224(1963).

Khouri, E. M.

E. M. Khouri, D. E. Gregg, J. Appl. Phys. 18, 224(1963).

Kolin, A.

A. Kolin, Medical Physics, O. Glasser, Ed. (Chicago, 1960).

Landau, L.

L. Landau, E. M. LifshitzHydrodynamics (Nauka, Moscow, 1965).

Lifshitz, E. M.

L. Landau, E. M. LifshitzHydrodynamics (Nauka, Moscow, 1965).

Menchimol, A.

A. Menchimol et al., Am. Heart J. 78, 649(1969).
[CrossRef]

Riva, C.

T. Tanaka, C. Riva, I. Ben-Sira, Science, in press.C. Riva, B. Ross, G. Benedek, Invest. Ophthal. 11, 936 (1972).
[PubMed]

Sekelj, P.

N. Anderson, P. Sekelj, Phys. Med. Biol., 12, 173(1967).
[CrossRef] [PubMed]

Selkurt, E. E.

E. E. Selkurt, Am. J. Physiol. 193, 161 (1958).

Tanaka, T.

T. Tanaka, C. Riva, I. Ben-Sira, Science, in press.C. Riva, B. Ross, G. Benedek, Invest. Ophthal. 11, 936 (1972).
[PubMed]

T. Tanaka, G. B. Benedek, in preparation.

Am. Heart J. (1)

A. Menchimol et al., Am. Heart J. 78, 649(1969).
[CrossRef]

Am. J. Physiol. (1)

E. E. Selkurt, Am. J. Physiol. 193, 161 (1958).

IRE Trans. Med. Electron. (1)

D. L. Franklin et al., IRE Trans. Med. Electron. ME-6, 204(1959).
[CrossRef]

J. Appl. Phys. (1)

E. M. Khouri, D. E. Gregg, J. Appl. Phys. 18, 224(1963).

Phys. Med. Biol. (1)

N. Anderson, P. Sekelj, Phys. Med. Biol., 12, 173(1967).
[CrossRef] [PubMed]

Other (5)

L. Landau, E. M. LifshitzHydrodynamics (Nauka, Moscow, 1965).

A. Kolin, Medical Physics, O. Glasser, Ed. (Chicago, 1960).

T. Tanaka, C. Riva, I. Ben-Sira, Science, in press.C. Riva, B. Ross, G. Benedek, Invest. Ophthal. 11, 936 (1972).
[PubMed]

G. B. Benedek, “Optical Mixing Spectroscopy with Applications to Problems in Physics, Chemistry, Biology and Engineering,” in Polarization, Matter and Radiation (Presses Universitaire de France, Paris, 1969).

T. Tanaka, G. B. Benedek, in preparation.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the scattering of laser light by a moving erythrocyte.

Fig. 2
Fig. 2

Experimental setup for the measurements of the blood flow velocities in vessels or in tubes.

Fig. 3
Fig. 3

The path of the laser light emitting from the exit of a fiber optics for different directions of the surface of the edge of the fiber optic catheter.

Fig. 4
Fig. 4

The effect of slit to exclude the light scattered with a large different angle from the exact backscattering direction.

Fig. 5
Fig. 5

Blood flow patterns around the fiber optics for two different types of exits. The dotted lines show the laser light beams.

Fig. 6
Fig. 6

The flow pattern around the fiber optics.

Fig. 7
Fig. 7

The electrocardiogram and the gate to open the correlator synchronously to the heart beat.

Fig. 8
Fig. 8

Correlation function of the scattered light by the blood flowing in a glass tube with a 6-mm diam. The solid circles are for the flow with average velocity of 1.8 cm/sec, and the white circles are for 0.18 cm/sec.

Fig. 9
Fig. 9

The inverse of the correlation width of the scattered light from flowing blood vs the average flow velocity given from the pumping rate to cause the flow.

Fig. 10
Fig. 10

The proportionality coefficients 1/τVav between the inverse of the correlation width τ and the average velocities Vav for different sizes of the tube diameters.

Fig. 11
Fig. 11

The correlation functions of the scattered light from the blood flow in the femoral vein of an albino rabbit. The lower curve is measured before the rabbit is killed, and the higher one is measured after its death.

Fig. 12
Fig. 12

The correlation function of the scattered light from the blood flowing in the femoral vein of a rabbit at 80 msec from a cardiac peak. The cyclic period of the electrocardiogram (ECG) was 240 msec.

Fig. 13
Fig. 13

The velocities of blood flow in the femoral vein of a rabbit as a function of the phase in the cardiac cycle.

Equations (24)

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r ( t ) = r 0 + v t .
E i = E o ( r ) exp [ i k i · r i ω o t ] .
E s = A f ( r ) E o ( r ) exp [ i ( k f k i ) · r ( t ) i ω o t ] .
K = k f k i .
E s = A f ( r ) E o ( r ) exp ( i K · r 0 i ω t ) .
ω = ω o + Δ ω , Δ ω = K · v = | K | · | v | cos θ .
Δ ω = ( 4 π v cos θ ) / λ ,
I ( t ) = Const | E s + E 1.0. | 2 = Const [ | E 1.0. | 2 + | E 1.0. · E s | + | E s | 2 ] .
I ( t ) = Const [ | E 1.0. | 2 + 2 E 1.0. · E s ] = I o + δ I ( t ) ,
δ I ( t ) = Const 2 E 1.0. · E s , δ I ( t ) = 2 Const ( A · E 1 ) E o ( r ) f ( r ) cos [ 4 π υ ( cos θ ) t / λ ] .
C υ ( t ) = δ I ( t ) δ I ( 0 ) = 4 Const 2 ( A · E 1 ) 2 E o 2 ( r ) f 2 ( r ) cos [ 4 π υ ( cos θ ) t / λ ] .
C ( t ) = Σ C υ ( t ) = d r ρ ( r ) C υ ( t ) = 4 Const 2 ( A · E 1 ) 2 d r ρ ( r ) E o 2 ( r ) f 2 ( r ) × cos { [ 4 π cos θ υ ( r ) / λ ] t } ,
E o 2 ( r ) = E o 2 ( 0 ) exp ( r / l o ) = E o 2 ( 0 ) exp ( z / l o sin θ ) ,
f 2 ( r ) = exp ( z / l o sin θ ) .
υ ( r ) = 2 V av ( 1 ( R z ) 2 / R 2 ) ,
C ( t ) = a 0 2 R exp ( α z ) cos [ β υ ( z ) t ] d z ,
υ ( z ) = 4 V av z / R ;
C ( t ) = a 0 exp ( α z ) cos ( γ z t ) d z ,
γ = ( 4 V av β ) / R = ( 16 π cos θ V av ) / ( λ R ) .
C ( t ) = ( a α ) / ( α 2 + γ 2 t 2 ) .
S ( ω ) = ( 1 / 2 π ) C ( t ) exp ( i ω t ) d t = [ a / ( 2 γ ) ] exp { [ ( α ω ) / γ ] } .
1 / τ = γ / α = [ ( 4 π sin 2 θ ) / R ] ( l o / λ ) ( V av ) .
( 1 / τ V av ) = [ ( 4 π l o sin 2 θ ) / λ ] ( 1 / R ) .
( R / τ V av ) calc = 7.8 kHz sec .

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