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WO2000016124A1 - Detection de la distribution d'une vitesse vectorielle - Google Patents

Detection de la distribution d'une vitesse vectorielle Download PDF

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Publication number
WO2000016124A1
WO2000016124A1 PCT/NL1999/000567 NL9900567W WO0016124A1 WO 2000016124 A1 WO2000016124 A1 WO 2000016124A1 NL 9900567 W NL9900567 W NL 9900567W WO 0016124 A1 WO0016124 A1 WO 0016124A1
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WIPO (PCT)
Prior art keywords
formula
calculated
aid
medium
transmitter
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PCT/NL1999/000567
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English (en)
Inventor
Arnoldus Petrus Gerardus Hoeks
Léon Armand Franciscus LEDOUX
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Universiteit Maastricht
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Universiteit Maastricht
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Publication of WO2000016124A1 publication Critical patent/WO2000016124A1/fr
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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/88—Sonar systems specially adapted for specific applications
    • G01S15/89—Sonar systems specially adapted for specific applications for mapping or imaging
    • G01S15/8906—Short-range imaging systems; Acoustic microscope systems using pulse-echo techniques
    • G01S15/8979—Combined Doppler and pulse-echo imaging systems
    • G01S15/8984—Measuring the velocity vector
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
    • G01F1/66—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters
    • G01F1/667—Arrangements of transducers for ultrasonic flowmeters; Circuits for operating ultrasonic flowmeters
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/88—Sonar systems specially adapted for specific applications
    • G01S15/89—Sonar systems specially adapted for specific applications for mapping or imaging
    • G01S15/8906—Short-range imaging systems; Acoustic microscope systems using pulse-echo techniques
    • G01S15/8979—Combined Doppler and pulse-echo imaging systems

Definitions

  • the present invention relates to a method for trifrp remote detection of the vectorial velocity distribution in a medium, wherein a signal is emitted towards the medium to be studied and wherein the said vectorial velocity distribution is calculated on the basis of a signal received back from the medium.
  • a method for trifrp remote detection of the vectorial velocity distribution in a medium wherein a signal is emitted towards the medium to be studied and wherein the said vectorial velocity distribution is calculated on the basis of a signal received back from the medium.
  • Such a method can be used in particular, but not exclusively, to measure the velocity distribution of blood in a blood vessel, which is why the present invention will hereinafter be explained in the context of this application.
  • velocity distribution is meant to indicate that the medium to be studied need not move as a plug, in which all the elements of the medium have exactly the same velocity, but that velocity variations can exist in the medium as a whole, so that the velocity components of different elements of the medium will exhibit a certain spread or distribution relative to one another.
  • a first drawback of this known method is that in determining the velocity component of the blood in the direction of the beam axis, use is made of a statistical model to calculate the most probable value of that velocity component. This implies that assumptions are made regarding the stochastic parameters of the signal which was received back. This means a restriction of the applicability of the known method.
  • An additional problem in this context is that sound attenuation in the medium to be studied is a function of the frequency of the sound used, so that a change in spectral bandwidth of the generated signal leads to deviations in the axial velocity component calculated on the basis of the statistical model.
  • a second drawback of the method described in the said publication is that the transverse velocity component is calculated on the basis of the rate at which changes in intensity occur in the signal which was received back. This, however, requires the beam width to be known at the location where the reflections occur, which, however, will in general not be the case .
  • a third drawback is that the application of this known method requires the existence of flow domains having a laminar flow pattern.
  • a fourth drawback of the method described in the said publication is that only an estimate is provided of the magnitude of the velocity vector, but that regarding the direction of the velocity vector no information is derived from the signal received back. With respect to the axial velocity component, the transverse velocity component, after all, still has a freedom of 360°. In the case of the method according to the said publication, it is therefore necessary for the three-dimensional direction of the velocity vector to be known beforehand, for example by the orientation of the flow duct (blood vessel) to be studied being known.
  • a further object of the present invention is to provide a method which allows, with as few assumptions as possible, the variables to be measured to be derived directly from the signals received back.
  • the present invention is based on an improved insight into the physical processes which lead to the measurable reflection signal. Based on this improved insight, the present invention provides a model describing the reflection signal, and formulae derived therefrom, with the aid of which the transducer parameters and the variables to be measured can be calculated directly from the measured reflection signals received back.
  • the present invention is thus capable of determining the variables to be measured more rapidly, more accurately and more consistently on the basis of the measured reflection signals, and of deriving more data from the observations. More in particular, the present invention is capable of deriving the local beam width from the observations .
  • the shape of the ultrasonic beam generated by the transmitter is assumed to be known. This is a reasonable assumption, since that beam is associated with the transmitter in question in a fixed way, and under normal conditions is reproducible, so that the shape of that beam can be measured in a test arrangement . On the basis of the beam shape, the local width of the beam can then be calculated from the signal received back itself .
  • An important advantage of the model proposed by the present invention is also that it does not make great demands on the measuring conditions and the measuring setup.
  • figure 1 schematically illustrates a specific measuring setup for measuring flow velocity in a flow duct
  • figure 2 schematically illustrates the principle underlying the measurement method
  • figure 3 shows a two-dimensional representation of an example of the envelope of reflection signals measured successively
  • figure 4 shows a schematic perspective view of a transducer in order to define a coordinate system.
  • FIG. 1 schematically illustrates a measuring setup 10 to measure the flow velocity in a flow duct 11.
  • the flow duct 11 forms part of a closed circuit 12 in which a medium 13 is recirculated by means of a pump 16.
  • the measuring setup 10 further comprises a measuring chamber 20 within which the flow duct 11 is situated.
  • a transducer 21 which is designed to generate a beam of ultrasonic pulses, as will be explained in more detail.
  • the distance between the transducer 21 and the flow duct 11 can be adjusted within certain limits, as can the angle between the beam axis and the axis of the flow duct 11.
  • FIG. 2 schematically illustrates the applied principle underlying the measurement.
  • the transducer 21 generates a brief sound pulse 22 in the direction of the medium 13 to be studied which comprises one or more reflection cores 14. If the emitted sound signal 22 reaches a reflection core 14, this will cause a reflected sound signal 23 to be emitted back to the transducer 21.
  • the reflected sound signal 23 is intercepted by the transducer 21, the latter generates an electrical signal 24 which is representative of the shape of the sound signal 23 received by the transducer 21; this electrical signal 24 is transferred, as known per se, to a signal-processing arrangement 30 with which a memory 31 is associated.
  • the signal -processing arrangement 30 samples the electrical signal 24 and stores the signal samples in the memory 31.
  • the signal samples are rendered analytic with the aid of a Hubert transformation.
  • the reflection signals are then complex numbers.
  • One advantage of working with analytic signals is that the correlation is not influenced by the carrier wave frequency, as will become evident from the following. This eliminates a source of interference. Possible random or secondary maxima in the correlation (see below) will then occur to a much lesser extent, or at least have a lower level.
  • the Hubert transformation to analytic signal samples can be carried out before the signal samples are stored in the memory 31, or when the signal samples are retrieved from the memory 31 for further processing, or in a separate intermediate step. Hereinafter, no distinction will be made between these options.
  • the sound signal 23 received back will normally be in the form of a single pulse, the time between emitting the transmission pulse 22 and receiving the reception pulse 23 being, on the basis of the sound velocity in the respective medium 13, a yardstick for the spatial distance between the transducer 21 and the reflective body or reflection core 14.
  • the medium 13 is a diffuse medium, i.e. it contains a multiplicity of randomly distributed particles 14 which may act as reflection cores. In practice this means that the signal 23 received back by the transducer 21 is a combination of many reflection pulses.
  • FIG. 3 illustrates an example of the envelope of a set of successive interference signals of this type, obtained in the example shown by measurement in a human carotid artery.
  • the strength of the electrical signal 24 emitted by the transducer 21, or alternatively the strenth of the reflection signal 23 received by the transducer 21, is plotted as a function of time (horizontal) . Since, as explained in the above, the time corresponds to distance, and in fact the distance is much more interesting to the observer than the time, the distance scale is shown at the horizontal axis. The vertical axis corresponds to the successive received reflection signals.
  • the strength of the electrical signal 24 emitted by the transducer 21 is represented by blackness (grey scale value) of a dot in the figure.
  • blackness grey scale value
  • a strong signal is represented by a dark dot
  • a weak signal is represented by a pale dot .
  • Each horizontal line of measured points in figure 3 represents the envelope of the electrical response of the transducer 21, after a single transmission pulse 22 has been emitted by the transducer 21.
  • the emission of a single transmission pulse 22 by the transducer 21 is repeated a number of times (at a predefined repeat rate) ; the electrical responses of the transducer 21 which are associated with the successive transmission pulses 22 (a number of horizontal lines of experimental points) are shown in figure 3 underneath one another; placed along the left-hand axis of figure 3 are serial numbers of these transmission pulses.
  • the constructive and destructive interference pattern (response to a transmission pulse) of the reflection signal changes as a function of time.
  • FIG 4 shows a transduceer array 121 comprising a multiplicity of juxtaposed transducers 21.
  • Each transducer 21 is able to emit a sound beam 22, whose beam axis 25 is assumed to be the Z-axis.
  • the X-axis is defined by a line connecting the transducers 21, so that the sound beams of all the transducers 21 are collectively situated in the XZ-plane.
  • the Y-axis is defined perpendicular to the XZ-plane defined by the transducers 21.
  • the first reflection signal RF 1#0 (t) received back by transducer 21 (t being the time after a sound pulse has been emitted by said transducer) can be described by formula (1) .
  • g(x,y,z) denotes the (three-dimensional) spatial distribution of the reflection cores 14 in the medium 13
  • f t (x,y,z) is the three-dimensional sensitivity function of the transducer in question.
  • the sensitivity function describes the three- dimensional pressure wave volume which contributes to the reflection signal at time t. It is further assumed that, even though the distribution of the reflection cores 14 in the medium 13 is stochastic, their movement is coherent within the three-dimensional sensitivity function.
  • P n T+p 12 in formula (2) is the time difference (unit ⁇ T EP ) between the transmission pulses associated with the reflection signals RF l ⁇ 0 (t) and RF 2 T (t).
  • the correlation between the initial reflection signal RF 1/0 (t) captured by the first transducer 21-, and the depth-shifted (T+l)th reflection signal RF 2 ⁇ (t+Z/f s ) captured by the second transducer 21 2 , denoted by R(T,Z), is defined by formula (3), wherein T denotes a time difference (unit ⁇ T EP ) , Z denotes a spatial differential distance, f s is the sampling frequency of the reflection signal, * means complex conjugate, and ⁇ > denotes mathematical expectation.
  • ⁇ g 2 > is the mean square of the spatial distribution of the reflection cores.
  • sensitivity function of a transducer The shape of the sensitivity function in the axial direction can be derived from the spectral distribution of the sound signal, whereas in the XY-plane local characteristics of the sound beam restrict the boundaries of the sensitivity function. These contributions to function are independent of one another and will be discussed independently of one another.
  • the spectral power density P(f) of an (analytic) reflection signal has an approximately Gaussian shape and in the normalized form can be written as formula (7) , wherein
  • f c is a central carrier wave frequency
  • BW EQ is the equivalent bandwidth of the spectral distribution.
  • equivalent bandwidth is meant the width of a rectangular distribution having the same area as the curve defined by the actual spectral distribution, the height of the equivalent function being equal to the height of the original function at f c .
  • the equivalent bandwidth can be written as formula (8) , wherein BW dB denotes the bandwidth at a specified level with respect to the maximum in decibels.
  • a reflection signal of this type can be written as formula (9) , where ⁇ is an arbitrarily chosen initial phase.
  • the beam dimensions contribute to the sensitivity function in the XY-plane.
  • the sensitivity functions can be approximated by Gaussian functions in accordance with formulae (11) and (12).
  • wx dB (z t ) and wy dB (z t ) denote the beam width in the x- and y- direction, respectively, at a depth z t , at a specified level in dB relative to the peak value.
  • Formula (13) only applies to plane waves, for which all the pressure waves in the XY-plane are in phase.
  • a curvature of the emitted wavefront occurs owing to path length differences ( ⁇ L) between the sound waves emitted from the centre of the transducer and from the edges.
  • This curvature can be approximated parabolically by formula (14) , the curvature at position (X,Y,z t ) being defined by the additional path length ⁇ X and ⁇ L Y in the x- and y-direction, respectively.
  • the sensitivity function f t ' (x,y,z) corrected for this curvature can be written as formula (15) .
  • This modified sensitivity function f t ' (x,y,z) can be written, according to formula (16) , as a product of independent x- , y- , and z-components .
  • R(T,Z) in formula (6) can be factored into x- , y- , and z-components according to formula (17) .
  • R X (T,Z) is the x-component (transverse direction) of the correlation function
  • R y (T,Z) is the y-component (height direction) of the correlation function
  • R Z (T,Z) is the z-component (axial direction) of the correlation function.
  • the correlation of the reflection signals is affected by noise.
  • the correlation function can be rewritten as formula (24), wherein the argument of R(T,Z) can be written as formula (25), and wherein the magnitude
  • the reflection signals received are sampled; the successive sampling points are denoted by the serial number ⁇ .
  • the successive sound pulses are distinguished by the serial number T.
  • the fth sampling point of a reflection signal after a rth sound pulse is denoted by RF( ⁇ ,$ " ) .
  • the reflection signals Prior to processing, the reflection signals are rendered analytic via a Hubert transformation. Such a transformation can be written as formula (27), wherein A(f) is the analytic frequency spectrum corresponding to the frequency spectrum S(f) of an actual signal, as will be explained below.
  • the two matrices are equal to one another .
  • an identical data window in the two matrices is defined having NZ sampling points in the f-direction and NT sampling points in the T-direction.
  • the data window associated with the signals captured by transducer 21 x is denoted by w 1 ( ⁇ , ⁇ .
  • the data window associated with the signals captured by transducer 21 2 is denoted by w 2 ( ⁇ ,f) .
  • the correlation coefficient R(T,Z) of signals from the two data windows, the difference between the serial numbers of the signals in both data windows being T and between the sampling points being Z, is defined according to formula (28) .
  • R(T,Z) from the sampled analytic reflection signals it is necessary to find a compromise between precision of the correlation coefficients on the one hand, and spatial and temporal resolution on the other hand.
  • a better resolution is obtained by selecting smaller values for NT and/or NZ, whereas better precision of the correlation coefficients is achieved by taking larger values for NT and/or NZ .
  • the axial movement S z can be estimated by means of formula (30), where ⁇ ⁇ T 2 .
  • An important aspect of formula (30) is that it is a relatively simple formula requiring relatively little computation time. This formula, however, is subject to a restriction, as is each formula which is based on the argument of a complex number, namely the so-called "aliasing" effect, caused by the fact that the argument of a complex number can only assume values between -180° and +180°. In practice, this means an upper limit for the velocity which can be estimated with the aid of formula (30) .
  • the present invention provides a solution even for this restriction, achieving this by providing the alternative formula (31) for the axial movement S 2 , wherein Z ⁇ Z 2 ⁇ Z 3 ⁇ Z 1# and T ⁇ 0.
  • This formula (31) is based on the magnitude of the correlation coefficients and therefore is not subject to an upper limit caused by aliasing.
  • a drawback of this formula (31) is that it is highly sensitive to variations in the amplitude of the reflection signals and consequently is somewhat less reliable.
  • the present invention therefore proposes that the two formulae (30) and (31) be combined with one another by first using formula (31) to estimate the velocity in a first approximation, an order of magnitude thus being obtained therefor, and by then using formula (30) for an estimate of the velocity in a second, more accurate approximation, the aliasing problem being eliminated since the order of magnitude is known.
  • the equivalent bandwidth BW EQ of the reflection signal can be estimated by means of formula (32) , wherein Z 1 ⁇ Z 2 ⁇ Z 3 ⁇ Z- L , and to avoid noise effects it is better to chose T ⁇ 0.
  • the normalized signal powers of the signals captured by the transducers 21 x and 21 2 are denoted by S ⁇ and S 2 , respectively.
  • V y of the velocity vector can be calculated.
  • V x and V y By combining V x and V y , the magnitude and direction of the transverse velocity vector V u ⁇ are then known.
  • the magnitude of S z can be estimated with the aid of the formulae (30) and (31) , from which the axial velocity component then follows.
  • S y can be estimated with the aid of formula (39) .
  • the term C B (z t ) can be determined by means of calibration. It should be noted, however, that using a single beam it is possible to determine the magnitude of the movement perpendicular to the beam axis, but not its direction in the plane perpendicular to the beam axis.
  • the field of application of the present invention is not limited to the example discussed of blood flow in a blood vessel. Rather, the present invention can be used for remote detection of the velocity of any collection of reflection cores which behave as a more or less coherent entity: an example to be considered in this context is that of water droplets in a cloud.
  • a Hubert transformation can be performed in a manner different from the example described.
  • the definition of different data sets can be carried out either before or after the signal samples have been recorded, and either before or after the reflection signals have been rendered analytic.
  • R(T,Z) J X J J J ft'(xN. z ) f + z (x , .y',z , )(g(x,y,z) g(x'-(p ⁇ T + Pl2 ) S x - ⁇ X,y'-(pdestinedT + p 12 ) S Y - ⁇ Y,z'-( Pl1 T + Pl2 ) s z ))dx dy dz dx' dy' dz 1 (4
  • R(T,Z) (g 2 ) f f f f l * (x 1 y,2)f t (x + (p u T + p réelle)S x + ⁇ X,y + ( Pl1 T + p, 2 )S ⁇ + ⁇ Y 1 z + (p 11 T + p 12 )S z )dxdydz (6)

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • General Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Electromagnetism (AREA)
  • Fluid Mechanics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

L'invention porte sur un procédé qui permet de détecter à distance la distribution de la vitesse vectorielle dans un milieu diffus (13). Par l'intermédiaire d'au moins un transducteur (21), un signal sonore à forme d'impulsions (22) est émis à destination du milieu (13), un signal de réflexion sonore (23) provoqué par le milieu (13) est détecté et converti en un signal électrique (24), lequel est échantillonné pour fournir des échantillons de signal RF (τ, z) enregistrés dans une mémoire (31). Les signaux de réflexion RF (τ, z) sont convertis en signaux analytiques et une fonction de corrélation R(T, Z) est calculée pour les signaux analytiques mesurés. L'invention porte en outre sur une formule fiable qui permet d'évaluer la distribution de la vitesse vectorielle du milieu sur la base d'un nombre réduit de coefficients de corrélation de ladite fonction de corrélation R(T, Z).
PCT/NL1999/000567 1998-09-10 1999-09-10 Detection de la distribution d'une vitesse vectorielle Ceased WO2000016124A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
NL1010061 1998-09-10
NL1010061A NL1010061C2 (nl) 1998-09-10 1998-09-10 Detectie van vectoriële snelheidsverdeling.

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WO2000016124A1 true WO2000016124A1 (fr) 2000-03-23

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5462058A (en) * 1994-02-14 1995-10-31 Fujitsu Limited Ultrasonic diagnostic system
WO1995032667A1 (fr) * 1994-05-31 1995-12-07 The Regents Of The University Of California Procede pour determiner la grandeur reelle de la vitesse du sang
US5522393A (en) * 1994-05-24 1996-06-04 Duke University Multi-dimensional real-time ultrasonic blood flow imaging apparatus and method
WO1998000719A2 (fr) * 1996-07-02 1998-01-08 B-K Medical A/S Dispositif et procede pour determiner les deplacements et les vitesses d'objets en mouvement

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5462058A (en) * 1994-02-14 1995-10-31 Fujitsu Limited Ultrasonic diagnostic system
US5522393A (en) * 1994-05-24 1996-06-04 Duke University Multi-dimensional real-time ultrasonic blood flow imaging apparatus and method
WO1995032667A1 (fr) * 1994-05-31 1995-12-07 The Regents Of The University Of California Procede pour determiner la grandeur reelle de la vitesse du sang
WO1998000719A2 (fr) * 1996-07-02 1998-01-08 B-K Medical A/S Dispositif et procede pour determiner les deplacements et les vitesses d'objets en mouvement

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
KAGEYOSHI KATAKURA ET AL: "A NEW LINEAR METHOD FOR ULTRASONIC FLOW VECTOR MEASUREMENT", PROCEEDINGS OF THE ULTRASONICS SYMPOSIUM, CANNES, NOV. 1 - 4, 1994, vol. 3, 1 November 1994 (1994-11-01), LEVY M;SCHNEIDER S C; MCAVOY B R (EDS ), pages 1727 - 1730, XP000525122 *

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