WO1997012256A1

WO1997012256A1 - Method of and device for measuring the velocity of moving matter by means of magnetic resonance

Info

Publication number: WO1997012256A1
Application number: PCT/IB1996/000949
Authority: WO
Inventors: Jan Frans Lodewijk De Becker; Thomas Leo Maria Hoogenboom; Miha Fuderer
Original assignee: Philips Electronics N.V.; Philips Norden Ab
Priority date: 1995-09-25
Filing date: 1996-09-16
Publication date: 1997-04-03
Also published as: EP0793810A1; US5773975A; JPH10509905A

Abstract

A method of determining a velocity of moving matter by means of magnetic resonance, in which a phase contrast method is applied in at least one measuring direction so as to determine a velocity. Upon determination of the velocity by means of phase contrast MRA, the cyclic nature of the phase introduces an ambiguity in the velocity determination. In accordance with the invention, this ambiguity is removed by performing an additional measurement in an additional direction and by combining the velocity measured in the additional direction with the previously determined velocity. It has also been found that there in an optimum direction for this additional measurement. The advantage of the method of the invention consists in that the velocities can be determined and corrected in the three basic directions. As a result, low flow velocities can be measured, so that slow liquid flows in small blood vessels can be made visible in an MR image.

Description

Method of and device for measuring the velocity of moving matter by means of magnetic resonance.

The invention relates to a method of determining a velocity of moving matter by means of magnetic resonance, in which a phase contrast method is applied in at least one measuring direction so as to determine in the measuring direction a velocity component but for a multiple of twice an encoding velocity.

The invention also relates to a magnetic resonance device for carrying out such a method.

A method of this kind is known from United States Patent US Re. 32,701. The known method is used in medical diagnostics, for example for phase-contrast magnetic resonance angiography. In phase-contrast MRA the phase contrast method is applied to determine the velocity components in three independent directions of moving matter in a number of voxels of a body, the encoding velocities of the three directions preferably being chosen so as to be equal. Subsequently, the velocity component in a direction to be selected is made visible in an image. It is a drawback of the known method that the velocity component measured in the measuring direction can be determined only but for a multiple of twice the encoding velocity of the measuring direction. Therefore, the known method does not enable measurement of an actual velocity component exceeding the encoding velocity in d e measuring direction. The encoding velocity, therefore, is defined as the highest actual velocity that can still be measured without such an error.

It is inter alia an object of the invention to determine the actual velocity component in the measuring direction also if the actual velocity is higher than the encoding velocity. To achieve this, the method in accordance with the invention for determining the velocity of moving matter by means of magnetic resonance is characterized in that a phase contrast method is applied in an additional direction, referred to as the dewrap direction, so as to determine a velocity component but for a multiple of twice a dewrap encoding velocity, and that an actual velocity component is determined in the measuring direction by combining the determinations of the velocity component in the measuring direction and the velocity component in the dewrap direction. The idea of the invention is based on the fact that a set of equations with a number of unknowns which is one larger than the number of equations cannot be solved and that by executing an additional measurement in the dewrap direction an additional equation can be formed with the same unknowns, said additional equation being added to die set of equations so that the set of equations can be solved.

A further advantage of die invention, when applied to, for example phase contrast MRA, consists in mat determination of me actual velocity, and hence the actual velocity component in me measuring direction, enables a reduction of the encoding velocity of the measuring direction and hence enhancement of me visibility of low flow velocities in small blood vessels in magnetic resonance images.

It is to be noted that the article "Dual Velocity Sensitive Tetrahedral Flow Encoding MR Angiography", by Y. Machida et al., published in Proceedings of die SMRM 1992, 2810, also proposes a method of extending a phase contrast measurement with an additional measurement. However, in the known method me additional measurement is used to obtain two MR angiography images: a first MR-A image with a sensitivity for a low velocity and a second MR-A image with a sensitivity for a high velocity. This method does not correct velocity measurements for errors amounting to multiples of twice the encoding velocity.

Preferably, me mediod in accordance with the invention is also characterized in mat projections of velocity components in the measuring direction or the measuring directions which amount to multiples of twice the encoding velocity do not coincide on an axis in the dewrap direction. This prevents coincidence of me results of the actual velocity on the axis in the dewrap direction.

A further method in accordance widi the invention is characterized in that a first velocity component is determined in a first direction with a first encoding velocity \^l _m and a second velocity component is determined in a second direction with a second encoding velocity V² _^,., me second direction extending substantially peφendicularly to die first direction, a direction coefficient of d e dewrap

direction being determined by l:(2m+l)

V ' a²ic in which m is a positive integer. The number m is determined by me number of phase wraps to be dewrapped, i.e. for which it holds d at (2m+ l) times the encoding velocity is greater than the maximum actual velocity component to be measured in the measuring direction. Furthermore, d e dewrap direction is situated in a plane defmed by the measuring directions. If the direction coefficient of me dewrap direction is chosen

in conformity with the ratio

it is ensured diat the possible results for the velocity components have a different projection on a line irough the origin of a coordinate system in me dewrap direction. Moreover, the projections of multiples of the encoding velocities are men equidistantly situated on die line in the dewrap direction. Anodier version of the method in accordance with the invention is characterized in that phase contrast measurements are applied to determine a first velocity component in a first direction with a first encoding velocity V¹^, a second velocity component in a second direction with a second encoding velocity V²^,., and a diird velocity component in a third direction with a third encoding velocity V³^, die mree directions extending substantially perpendicularly to one another, and that the direction coefficients of the dewrap direction are determined by

in which m is a positive integer. The number m is determined by the number of phase wraps to be dewrapped, i.e. for which (2m + 1) times me encoding velocity is greater than the actual velocity component to be measured in a measuring direction. This step constitutes an extension of the measurement for determining the actual velocity by measurement of two velocity components in two substantially peφendicular directions. This step ensures at the projections of the possible results of the velocity components on a line dirough the origin differ in the dewrap direction. Moreover, the projections of multiples of the encoding velocities in the measuring directions are equidistantly situated on the line in the dewrap direction.

The invention also relates to a method of determining a derivative of a velocity by means of magnetic resonance, in which a phase contrast method is applied in at least one measuring direction so as to determine in the measuring direction a measured component of the derivative of the velocity but for a multiple of twice an encoding value, characterized in mat a phase contrast method is applied in an additional direction, being the dewrap direction, so as to determine a component of a derivative of me velocity but for a multiple of twice a dewrap encoding value, and mat an actual value of the derivative is determined by combining me determinations of the components of the derivatives of me velocity and the component of the derivative in the dewrap direction. Using die phase contrast measurements, first-order and higher-order derivatives of the velocity of the moving matter can also be determined, for example die acceleration, die first-order derivative of the moving matter and the jerk, a second-order derivative of the velocity of die moving matter. Because the derivative of d e velocity is also a vector quantity, the actual value of a first-order or higher-order derivative of the velocity can be determined in me same way as the actual velocity of the moving matter. As in the measurement of the velocity, ambiguity due to die cyclic nature of die phase is thus removed by way of an additional measurement in an additional direction. The encoding value is then die maximum actual value which can be measured without an error amounting to a multiple of twice the encoding value. An MR device for determining a velocity of matter by means of magnetic resonance in accordance wid me invention comprises a) means for sustaining the static magnetic field, b) means for generating RF pulses, c) means for generating temporary magnetic gradient fields, d) a control unit for generating control signals for the means for generating the RF pulses and for the means for generating the temporary magnetic gradient fields, e) means for receiving, demodulating and sampling the MR signals,

0 a processing unit for processing the sampled MR signals, the control unit also being arranged to apply a phase contrast method in at least one measuring direction so as to determine in the measuring direction a velocity component but for a multiple of twice an encoding velocity, characterized in that me control unit is also arranged to apply a phase contrast method in an additional direction, being the dewrap direction so as to determine a velocity component but for a multiple of twice an encoding velocity, and that an actual velocity component is determined by combining the determinations of the velocity components in the measuring directions and the dewrap direction. These and odier aspects of the invention will be apparent from and elucidated wi reference to me embodiments described hereinafter.

In the drawings:

Fig. 1 shows an MR device for the imaging of objects, Fig. 2 shows a pulse sequence for generating a gradient echo, Fig. 3 shows the actual velocity and the measured velocity in a measuring direction, Fig. 4 shows die components of the velocity along the axes of a 2D coordinate system and die dewrap direction a,

Fig. 5 shows the optimum dewrap direction in a 2D application, Fig. 6 illustrates me determination of the accuracy, and Fig. 7 shows a bipolar temporary magnetic gradient field widi a second- order moment.

Fig. 1 shows a magnetic resonance device which is known per se. The MR device 100 comprises a first magnet system 101 for generating a static magnetic field, a second magnet system 102, 103, 104 for generating temporary magnetic gradient fields in three orthogonal directions, and power supply units 110 for the second magnet system 102, 103, 104. The power supply for the first magnet system 101 is not shown. The system comprises an examination space which is large enough to receive a part of a body 106 to be examined. As is customary, in this Figure and in is description die z-direction of me coordinate system shown denotes me direction of the static magnetic field. An RF transmitter coil 105 serves to generate RF fields and is connected to an RF source and modulator 107. The RF transmitter coil 105 is arranged around or against or near a part of the body in the examination space. A receiver coil 114 is used for the reception of a magnetic resonance signal. This coil may be the same coil as the RF coil 105. The RF transmitter-receiver coil 105 is connected, via a transmitter-receiver circuit 108, to a signal amplifier and demodulation unit 109. In the signal amplifier and demodulation unit 109 a sampled phase and a sampled amplitude are derived from the MR signals received. Subsequently, the sampled phase and the sampled amplitude are applied to a processing unit 112. The processing unit 112 processes the applied phase and amplitude by way of, for example a two- dimensional Fourier transformation in order to form an image. This image is displayed by means of a monitor 113. The magnetic resonance device 100 also comprises a control unit 111. The control unit 111 generates control signals for the RF transmitter 107, the power supply units 110 and me processing unit 112.

When the magnetic resonance device is switched on while me body 106 is arranged in me magnetic field, a small majority of nuclear spins in the body is oriented in me direction of the magnetic field. In the state of equilibrium this results in a net magnetization M₀ of me material of the body 106, which magnetization is parallel to the direction of the magnetic field. This macroscopic magnetization MQ can be modified by subjecting the body 106 to RF pulses of a frequency equal to the Larmor frequency of the nuclear spins. The nuclear spins are thus excited and d e direction of the magnetization M_o is changed. When the body is exposed to suitable RF pulses, the macroscopic magnetization vector is rotated, the angle of rotation being referred to as the flip angle. Introduction of changes in die magnetic field by application of temporary magnetic gradient fields locally influences the resonant frequency and me magnetization. When suitably chosen pulse sequences are used, comprising RF pulses and temporary magnetic gradient fields, MR signals are generated in die body. The MR signals provide information as regards given types of nuclei, for example hydrogen nuclei and me material containing me hydrogen nuclei. Information regarding internal structures of the body is obtained by analysis of die MR signals and me presentation thereof in the form of images. A more detailed description of the magnetic resonance imaging and magnetic resonance devices can be found in the book "Practical NMR Imaging", by M.A Foster and J.M.S. Hutchison, 1987, IRL Press.

Fig. 2 shows a customary pulse sequence for the generating of MR signals in order to form an image. The pulse sequence 200 comprises an excitation RF pulse 201 which excites the nuclear spins in a part of the body. The excitation pulse is rendered spatially selective by means of a first temporary magnetic gradient field 210 whereby a slice extending peφendicularly to the z-direction is selected. Using a second temporary magnetic gradient field 220, a phase encoding is introduced into the MR signal 240. By increasing the strength of the second temporary magnetic gradient field 220 in successive pulse sequences, for example from a minimum value to a maximum value in 256 steps, a spatial encoding can be achieved in me echo signals for the entire slice. A third temporary magnetic gradient field 230, having a gradient direction extending in the x-direction, dephases and rephases, after a period r,, the nuclear spins so that the MR signal 240 arises. Moreover, the third temporary magnetic gradient field 230 introduces frequency encoding into the MR signal 240. The MR signal 240 received is sampled in the receiver and demodulation device 106. In practice a value of from 64 to 512 is chosen for the number of samples. Each sample comprises a sampled phase and a sampled amplitude. Using a two-dimensional Fourier transformation, an image of, for example the density of die nuclear spins in the selected slice is derived from the sampled phases and amplitudes.

In a known phase contrast measurement, for example a phase contrast measurement as known from the cited Patent Specification Re. 32,701, in order to obtain a flow-sensitive phase in me MR signal 240 a bipolar temporary magnetic gradient field 250 is included in me pulse sequence 200 for generating the MR signal by means of me third temporary gradient field 230. The gradient direction of the first bipolar temporary magnetic gradient field is chosen to extend in a measuring direction which corresponds to the direction of a velocity component of a flow to be measured in a voxel, for example the x-direction 270, d e y-direction 260 or the z- direction 250. The measured phase is subsequently dependent on the magnitude of the velocity component in the direction chosen. If the bipolar temporary magnetic gradient field contains a first-order moment Mj, the phase shift is given by: φ=yM,v (1) in which φ is a phase shift and y is the gyromagnetic constant of die nuclear spins, for example the hydrogen nuclei of die moving matter. In order to prevent phase errors due to odier causes, moreover, a reference measurement is carried out utilizing a second bipolar temporary magnetic gradient field whose gradient direction corresponds to me gradient direction of the first bipolar magnetic gradient field, said second bipolar temporary magnetic gradient field having a first-order moment which deviates from that of the first bipolar temporary magnetic field. Subsequently, d e velocity component in the voxel is determined in d e measuring direction by the complex difference of the reference measurement and me phase contrast measurement. The velocity component in the voxel in the measuring direction is then given by:

It is a drawback of the known phase contrast measurement that the velocity component in the measuring direction can be determined only but for multiples of twice the encoding velocity.

This encoding velocity is determined by V _ =— — - (3).

In a version of the method in accordance with the invention an additional phase contrast measurement is inserted in an additional direction, being me dewrap direction, the dewrap encoding velocity being chosen so as to be higher than the velocity component to be expected in the voxel in d e dewrap direction. The measured velocity component in the dewrap direction is subsequentiy used to determine the actual velocity component in the measuring direction, so diat the actual velocity is then known. The determination of me actual velocity from the measured velocity components in me measuring direction and the dewrap direction will be described in detail wid reference to Fig. 3.

Fig. 3 shows an actual velocity v associated wid a voxel, a measured velocity component v_α ^m in the dewrap direction a, and a measured velocity component v_x ^min the x- direction. An infinite set of feasible values mus exists for me actual velocity component v_x to be determined in me x- direction. Thus, me following holds for the actual velocity component v^ : v, +2I_XV ) ⁽⁴⁾

in which l_x represents integers and V_enc represents me encoding velocity in die measuring direction. The projection of me actual velocity vector v on an axis in the dewrap direction a, however, also results in v_α ^ra . If v_α ^m and v_z are known, me actual velocity vector ^"v can be simply calculated. In Fig. 3 me actual velocity is represented by die vector v whose projection on the x-axis has me value v_Jt ^m+2V_βlc and whose projection on the axis in the dewrap direction is coincident wid die measured v_β. The actual velocity in a two- dimensional example can be determined analogously. This two-dimensional example will be illustrated with reference to Fig. 4.

Fig. 4 shows a velocity v in an orthogonal system X,Y with a measured component v,™ in the x-direction, a measured component v_y in the y-direction, and a measured component v_α ^min the dewrap direction α. Furthermore, the encoding velocities in me x-direction and the y-direction are chosen so as to be equal; however, this is not necessarily so. Furthermore, the limits of the possible velocities v, being a combination of multiples of twice the encoding velocity in the x-direction, v_x ^m+2 _ιV_βιc and twice d e encoding velocity in the y-direction v_y ^m+2/_>V_enc are represented by a circle. In Fig. 4 die actual velocity is represented by die vector v whose projection on the X-axis has the value v ™+2 and whose projection on the Y-axis has the value v₎ ^m+2V_CT(. , its projection on d e axis in d e dewrap direction corresponding to v_α ^m .

Furthermore, anomer version of the method in accordance widi the invention can be used to measure velocity components in three substantially peφendicular directions in a voxel of a selected slice. To diis end, phase contrast measurements are carried out to determine the phases in three directions, for example the directions corresponding to the axes of an orthogonal system X,Y,Z. Furthermore, a reference phase measurement is carried out again. The velocity components along the d ree axes are determined by me complex difference between the reference measurement and me three respective phase contrast measurements. The velocity components in the x-direction, the y-direction and d e z- direction, respectively, are then given by:

V_r.~(Φ,- _rjW_χ (5)

v,=(Φ_z- _rfVyM_z (7) Using the four phase contrast measurements, me velocity components in successive measuring directions can be determined only but for multiples of twice an encoding velocity of the associated measuring direction. In me present example the encoding velocities in die mree orthogonal directions are chosen to be equal. In a method in accordance widi the invention an additional phase contrast measurement is carried out in an additional direction, being the dewrap direction; me dewrap encoding velocity is then higher than the velocity component to be expected in the dewrap direction. Subsequentiy, die velocity component measured in me dewrap direction is used to determine the actual velocity component in the x- direction, the y-direction or the z-direction, respectively. The determination of me actual velocity components is performed in the same way as the actual velocity components in the two-dimensional example. If me velocity, represented by v=(v_x,v_>,v_z) is given and if v_Λ ^m,v₎ ^m and v, represent the measured velocity components associated with a voxel in me x-direction, the y- direction and the z-direction, respectively, an infinite set of feasible values exists for the actual velocity ^"v=(v_x,v ,v_z) Therefore, for the actual velocity v it holds diat:

^■S{(v,"+2/_JtVi_fv_jr₊2^Vi,v_z-^* ₊2 _IV₄ )} (8)

in which k_x,k_y,lς are integers and \*_m, V⁵^, V¹^ are die encoding velocity in die x- direction, the y-direction and die z-direction, respectively.

The result v_α of the additional measurement in the dewrap direction α^* is die projection of the actual velocity vector v on an axis in the dewrap direction. If v_x ^m, v_y ^m , ™ and x ™ are known, me actual velocity components v_x,v_y,v_r can be simply determined. Assume that a phase error occurs only due to one phase cycle; v_x is dien situated in the interval [-3V^* _C ,3V^* _C ] , v_y in the interval [-3V_m ^y _c ,3V^ ] , v₂ in the interval [-3V^ ,3V^_C ] and k_x,k,,k_z € { -1 ,0,1} . It is also assumed that, moreover, no phase errors occur in the measurement in the additional direction due to a velocity higher than V_enc in die dewrap direction, so v_c ^m = v_α .

An optimum choice of the dewrap direction a is important for the execution of die dewrap measurement. Generally speaking, the dewrap direction a is chosen so that the projections on an axis through the origin of a coordinate system in the dewrap direction a of the feasible combinations of the various encoding velocities along the axes are not coincident. The dewrap direction is also dependent on me magnitude of the actual velocity to be measured, so on d e number of times that the encoding velocity is to be added to die measured velocity. One way of determining the dewrap direction will be described on die basis of a three-dimensional application. In a 3D application me dewrap direction

(α_x,α_y,α-) can be determined as follows. The measured velocity in die dewrap direction a is given by:

Furthermore, the velocity measured in die dewrap direction is lower than me encoding velocity in d e dewrap direction. The velocity, moreover, is determined by me velocity components v_x ^m, v_y ^m en v ™ along the d ree axes X,Y,Z of die orthogonal system X,Y,Z. Subsequently, combinations of the velocity components measured along me three axes X,Y,Z are projected, with the multiples of twice die encoding velocity, on a line through the origin of the coordinate system in the dewrap direction. The projection v can then be written as:

The relation between the two values for v_α is dien given by:

V v This equation can be solved by determining or _x,Qf_v— —,a,— — for which the sum

' aic ' aic

unambiguously determines the values l_x,l_y,l_z. Equal values of a_x,a_y

do not lead to a solution, because projections then coincide. Therefore, it is assumed that

This can be done witiiout loss of generality and anodier assumption as regards diis inequality is also possible. For ^y = 1, = 0 the feasible values for a I +α > — —y +α ^z I- —_v —z are -1 , 0, 1.

' aic * ate

For l_z = 0 there are the foilowing feasible values of

-α_y ^y

For suitable separation of the various projections of the velocity components v_x , v_y ^m en v,_z ^m moreover, the values (12) are chosen to be equidistant and the difference between two successive values is 1 , so d at

Analogously, a value is determined for _z. The projections are then situated at a distance from one another which is chosen to be 1; the values of me projections are then determined by me feasible values of

These values are -4-p, -3-p, -2-p, -1-p, -p, 1-p, 2-p, 3-p, 4-p , -1, 0, 1, 2, 3, 4, - 4+p, -3+p, -2+p, -1+p, p, 1+p, 2+p, 3+p, 4+p, where . From the mutually

equal distance, again being 1, it d en follows that5=-4+/? ^•*=» p=9 and a =9— V ~L .

V ' e^znc For the determination of an actual velocity which is lower than ti ree times the encoding velocity and for which, moreover, it holds that the encoding velocities in the measuring directions are equal, it suffices to carry out one additional measurement whose measuring direction is determined by

(1,3,9) or a permutation mereof. Generally speaking, it holds mat if a velocity component v, is situated in the interval -(2m+\)VL, (2m+l)VL for i=x,y of z, the ratio of α_x, α_y, α. is determined by

The derivative has been performed for a 3D measurement, but it is analogous for a 2D measurement or a ID measurement. For a 2D measurement the direction coefficients are 1:3 and 1:5 for actual velocity components smaller than three times and five times, respectively, the encoding me velocity. The preferred direction a for a 2D measurement is also shown in Fig. 5. Fig. 5 shows an orthogonal system X,Y with die encoding velocity V_enc in die x-direction and me encoding velocity V_^ in the y-direction, and with multiples mereof; because in this example the maximum actual velocity may amount to mree times the encoding velocity, only d e combinations of die velocity components 0 + 21_xV_enc,0 + 21^_^ for l_x,l_y= -1 ,0, 1 are shown. Furthermore, the projections on the line in the measuring direction a are represented by means of an "x". For a ID measurement the optimum dewrap direction is die same as the measuring direction. The advantage of a ID measurement or a 2D measurement over a 3D measurement consists in that the requirements as regards precision can be more readily satisfied. The determination of me precision requirements imposed on the phase contrast measurement will be described widi reference to Fig. 6. Fig. 6 shows an orthogonal system X,Y with the encoding velocity in the x-direction and die encoding velocity in the y-direction. The minimum encoding velocity in die dewrap direction is determined by the projection on a line in the dewrap direction of (2m + 1) times encoding velocities along d e axes. The actual velocity component in the x- direction, the y-direction or the z-direction is then limited by (2m + 1) times the encoding velocity. In Fig. 6 d e direction coefficient of the dewrap direction a is determined by tan a. The projection on the dewrap direction is determined by the vector sum of the encoding velocity in d e x-direction and the encoding velocity in die y-direction and equals cos(45° -a).{(2tn+l)*_v/2^~V_jic } . This velocity corresponds to the minimum encoding velocity in me dewrap direction. For adequate distinction of two adjacent projections on the line in the dewrap direction, a minimum distance S is required. The distance S is given by sin(α).V_CTC. The actual precision in the dewrap direction is then determined by die ratio of half the distance S to the value of the dewrap encoding velocity; diis is expressed by d e following formule:

For a 3D measurement witii an optimum dewrap direction for which the ratio 1:3:9 holds, i.e. me maximum acmal velocity components along the orthogonal axes are smaller than three times the encoding velocity, it men follows from (12) that me velocity measurement requires a precision of 1.7% of me encoding velocity in me dewrap direction. An actual velocity component to be measured, amounting to at me most five times the encoding velocity, tiien implies a ratio of 1:5:25 and, in conformity with (12), a measurement with 0.4% of the encoding velocity is tiien required. The requirements are less severe for a 2D measurement. The requirements following from (12) are then 4.2% for a measurement up to three times the encoding velocity and 1.7% for a measurement up to five times the encoding velocity. In die case of an MR device whose signal-to-noise ratio is too poor for 3D measurements, 2D measurements can be performed so as to satisfy the precision requirements. Carrying out a ID measurement mree times is also possible. A ID measurement requires a precision of only 16.7% for a measurement up to three times the encoding velocity and of 10% for a measurement up to five times the encoding velocity.

Furdiermore, the mediod of the invention can also be used in phase contrast measurements utilizing a bipolar temporary magnetic gradient field having a higher- order moment, for example a second-order moment. Such a phase contrast measurement enables measurement of an acceleration of the motion of the matter. An acceleration measurement of this kind is also known from the cited Patent Re. 32,701. an example of a waveform of a bipolar temporary magnetic gradient field having a second-order moment is illustrated by Fig. 7. Fig. 7 shows a bipolar temporary magnetic gradient field 700 having a second-order moment M₂. The phase is dependent on die acceleration as follows:

φ=yM,a (15) where φ is the phase, γ is the gyromagnetic constant and a is the acceleration. The bipolar temporary magnetic gradient field 700 having the second-order moment M₂ can be used in die pulse sequence 200 instead of die bipolar temporary magnetic gradient field 250. The bipolar temporary magnetic gradient field 700 is symmetrical with respect to a symmetry line 701. The actual acceleration can then be determined in the same way as described wid reference to Fig. 4.

Claims

CLAIMS:

1. A method of determining a velocity of moving matter by means of magnetic resonance, in which a phase contrast method is applied in at least one measuring direction so as to determine in the measuring direction a velocity component but for a multiple of twice an encoding velocity of die measuring direction, characterized in that a phase contrast method is applied in an additional direction, referred to as the dewrap direction, so as to determine a velocity component but for a multiple of twice a dewrap encoding velocity, and tiiat an actual velocity component is determined in the measuring direction by combining the determinations of the velocity components in the measuring direction and die dewrap direction.

2. A method as claimed in Claim 1, characterized in that the projections of multiples of twice the encoding velocity in the measuring direction or in the measuring directions do not coincide on a line in the dewrap direction.

3. A method as claimed in Claim 1 or 2, characterized in that a first velocity component is determined in a first direction witii a first encoding velocity V¹,,,,. and a second velocity component V² _^ is determined in a second direction, which second direction extends substantially peφendicularly to die first direction, and a direction coefficient of the dewrap direction is determined by

V l:(2m+l)— — , in which m is a positive integer.

V ' a²te

4. A method as claimed in Claim 1 or 2, characterized in diat phase contrast measurements are applied so as to determine a first velocity component in a first direction with a first encoding velocity V¹ _^, a second velocity component in a second direction with a second encoding velocity V^, and a third velocity component in a third direction with a third encoding velocity V³^, the three directions extending substantially peφendicularly to one another, and that the direction coefficients of die dewrap direction are determined by , in which m is a positive integer.

5. A method of determining a derivative of a velocity by means of magnetic resonance, in which a phase contrast method is applied in at least one measuring direction so as to determine in the measuring direction a component of the derivative of the velocity but for a multiple of twice an encoding value of the measuring direction, characterized in tiiat a phase contrast method is applied in an additional direction, being the dewrap direction, so as to determine a component of the derivative of d e velocity but for a multiple of twice a dewrap encoding value, and that the actual derivative of the velocity is determined by combining the determinations of the components in the measuring direction and the dewrap direction of the derivatives of the velocity.

6. An MR device for determining a velocity of matter by means of magnetic resonance, comprising a) means for sustaining the static magnetic field, b) means for generating RF pulses, c) means for generating temporary magnetic gradient fields, d) a control unit for generating control signals for the means for generating the RF pulses and for die means for generating the temporary magnetic gradient fields, e) means for receiving, demodulating and sampling the MR signals, f) a processing unit for processing the sampled MR signals, the control unit also being arranged to apply a phase contrast method in at least one measuring direction so as to determine in the measuring directions a velocity component but for a multiple of twice an encoding velocity, characterized in that a phase contrast method is applied in an additional direction, being the dewrap direction, so as to determine a velocity component but for a multiple of twice the dewrap encoding velocity, and that an actual velocity component is determined by combining the determinations of the velocity components in the measuring directions and the dewrap direction.