JPH0714387B2 - Measurement method of magnetization distribution using nuclear magnetic resonance - Google Patents

Description

The present invention relates to an inspection apparatus that non-destructively obtains the spin distribution, relaxation time distribution, etc. (hereinafter referred to as magnetization distribution) in a target object using nuclear magnetic resonance. In particular, the present invention relates to an apparatus that images a distribution of an object at high speed.

[Background of the Invention]

The closest known technology to the present invention is, for example, Journal of Physics C (J.Phys.C), Solid.
State State Phys. No. 10
There is an echo planar method proposed by P. Mansfield, which is introduced in Volumes, pp. 55-58. The typical RF and gradient magnetic field application timings to realize this method
Shown in the figure. The figure shows the sequence for selecting and measuring a cross section perpendicular to the Z-axis. A gradient magnetic field that is constantly applied in one direction, such as Gy in the figure, and vibration in the direction perpendicular to this, such as Gx, in the figure. The spin distribution is measured by applying a gradient magnetic field. This method requires switching of the gradient magnetic field with large amplitude and high speed, but in principle an image can be constructed using the NMR signal measured by applying 90 ° pulse once.

However, unless special post-processing is performed, a rectangular wave must be used as the oscillating waveform of the oscillating gradient magnetic field, which imposes a heavy burden on this gradient magnetic field generating power source and requires a large frequency. In this case, the gradient magnetic field generating coil also needs a special device.

[Object of the Invention]

An object of the present invention is to use a sinusoidal periodic waveform without switching a rectangular gradient magnetic field in an inspection apparatus that non-destructively obtains a magnetization distribution in a target object by using nuclear magnetic resonance. Therefore, it is to provide an apparatus capable of capturing data required for image reconstruction at high speed.

[Outline of Invention]

Assuming two-dimensional imaging, let the image plane be the (x, y) plane. When the gradient magnetic field is driven as Gx (t) = G ₀ cosωt−G ₀ ωtsinωt Gy (t) = G ₀ sinωt + G ₀ ωtcosωt, the obtained nuclear magnetic resonance signal is S (t) = ∫ρ (x, y) exp [iγ {G ₀ t (xcosωt + ys
inωt)}] dxdy (2).

The data sequence obtained from the above equation is a spatial frequency domain of ρ (x, y) sampled in a spiral shape as shown in FIG. The spiral sampling in the Fourier domain is described in Journal of magnetic resonance, Vol. 54, 33.
Although it is suggested in pages 8-343 (1983), the above-mentioned document does not discuss more than suggestions regarding methods such as an image reproducing method.

The present invention is characterized by an image reproduction method for spirally measured data, a data measurement method for applying this image reproduction, and a data measurement method with a small load on a gradient magnetic field drive derived from the image reproduction method. To do.

First, the image reconstruction will be described. Sampling interval of signal measurement, that is, the sampling interval Δ of the AD converter that gives the computer the measured signal digitally.
t Then, as shown in FIG. 2, the measurement points are arranged at equal intervals on a straight line forming an angle θ with the k _x axis. (Sampling points are indicated by circles in the figure.) The time when the spiral lines intersect these straight lines is It is represented by. Substituting into equation (1), S (▲ t ^θ _n ▼) = ∫ρ (x, y) exp [iγ {G ₀ ▲ t ^θ _n
▼ (xcosθ + ysinθ)}] dxdy (2). If ▲ t ^θ _n ▼ is regarded as a continuous variable and is represented as t ^θ , Here, sgn (t) = 1 t0 −1 t <0. Here, S (t ^θ ) is the angle θ in FIG.
It refers to a group of data arranged on a radial line such as. After that t
Performing the calculation regarding ^θ means grouping the data on the spiral into data groups on radial vectors having different θ. In order to clarify this, the data on the radius vector with the angle θ is expressed as S _θ (t ^θ ). Taking the Fourier transform of both sides of equation (3), Here, * means convolution. Also And this P _θ (f) is ρ given on the frequency axis.
It is a projection of (x, y) in the θ direction. From equations (3) and (4), Get the expression. Therefore, the projection of the angle θ is obtained from the equation (6), and ρ (x, y) is reconstructed from P (f) of 0 to 360 °.

Reconstruction is performed as follows.

Fourier transform P _θ (f) with respect to f. This is F _θ
When written as (R), Therefore, ρ (x, y) can be reproduced by performing the following calculation on this F _θ (R). That is, Is. By the way, the calculation of the equation (6-2) is usually divided into two. That is, Is calculated first, Is a method of asking for. In particular, the calculation of the equation (6-4) is called back projection. Here, (6), (6-1),
Looking at (6-3), Also, W _θ (u) can be obtained. This (6-
The method using the equation (5) is a method of directly determining W _θ (u) by grouping the data on the spiral into data on the radial of each angle, weighting the data in the radial direction and then performing Fourier transform. , (6), (6-1), and (6-3), the Fourier transform calculation can be saved twice for each angle of data.

Example of Invention

 An embodiment of the present invention will be described below with reference to screens.

FIG. 3 is a schematic configuration diagram of an inspection apparatus using nuclear magnetic resonance (hereinafter, simply referred to as “inspection apparatus”) according to an embodiment of the present invention.

In FIG. 3, 1 is an electromagnet that generates a static magnetic field H ₀ , 2
Is a target object, 3 is a coil for detecting a signal generated from the target object 2 at the same time as generating a high frequency magnetic field, 4x, 4
y and 5 are gradient magnetic field generating coils for generating gradient magnetic fields in the X, Y and Z directions, respectively. As the gradient magnetic field generating coil 5, a circular ring wire is used so that currents flow in opposite directions. Reference numerals 6, 7 and 8 are drive devices for supplying currents to the gradient magnetic field generating coils 4x, 4y and 5, respectively. Reference numeral 9 is a computer, 10 is a power source for the electromagnet 1 for generating a static magnetic field, and 11 is an object volume measuring device.
The intensity of the gradient magnetic field generated by the gradient magnetic field generating coils 4x, 4y, 5 can be changed by a command from the object capacity measuring device 11.

Next, the operation of this inspection apparatus will be described with reference to a schematic diagram.

The high frequency magnetic field for exciting the nuclear spins of the target object 2 is generated by waveform shaping and power amplification of the high frequency generated by the synthesizer 12 by the modulator 13 and supplying a current to the coil 3. The signal from the target object 2 is received by the coil 2, passes through the amplifying device 14, and is then quadrature detected by the detector 15 and input to the computer 9. After the signal processing, the computer 9 displays an image corresponding to the nuclear spin density distribution or relaxation time distribution on the CRT display 16. Reference numeral 17 is a memory for storing data in the middle of calculation or final data.

FIG. 4 shows a measurement sequence according to an embodiment of the present invention, where RF is a high-frequency magnetic field waveform, Gz, Gx, and Gy are gradient magnetic field emission in the z, x, and y directions, and AD is a signal sampling period.

First, by applying a 90 ° high-frequency pulse and a gradient magnetic field Gz, spin in a desired slice of the subject is induced. Next, when time τ has passed from the peak of the 90 ° C high frequency pulse, 180 °
A high frequency pulse is applied so that a transverse magnetization signal of the spin at the point (t = 0) after the time τ has elapsed is obtained again. From t = 0, the gradient magnetic field is generated with the waveform shown in equation (1).
Gx and Gy are applied and signal sampling is started.

As mentioned before, the AD sampling interval Δt is And the measured data (M is an integer) And divide it into groups. That is, the data are grouped for each radial data having different angles. Data of the dynamic diameter upper as the angle theta _m is denoted as S.theta _m. here And Δθ = 2π / M.

Data string for each m Is subjected to the discrete Fourier transform with respect to n, and according to the equation (6), after phase correction, the real part is taken to obtain Pθ _m (f). This calculation is performed for each m, and from Pθ _n (f) at each angle, equations (6-1) to (6-4),
Alternatively, the image is reconstructed by the back projection method defined by the equation (6-5).

According to the above sequence, a magnetic field distribution showing the spin density distribution of the subject can be obtained by applying a gradient magnetic field having a sinusoidal periodic waveform without vibrating the rectangular gradient magnetic field as in the conventional echo planer method. Is obtained. Note magnetization distribution image including the effect of the longitudinal relaxation time T ₁ distribution of spin of an object (T ₁
In order to obtain an enhanced image), as is well known, a 180 ° high frequency pulse is applied a predetermined time before the 90 ° high frequency pulse is applied to perform spin reversal in advance, and the longitudinal relaxation at t = 0 is performed. It suffices if a transverse magnetization signal including the effect can be obtained. Also the signal When sampling at intervals other than, the angle θ _m (m = 0,1, ...,
The Fourier transform may be performed after obtaining the radial data of (M-1).

Several modifications can be considered for this image reproduction method.
First, a method for obtaining projection directly after combo Reuse Chillon performs weighting with respect S.theta (t ^theta) instead of using the equation (6).

When the frequency characteristic of the convolution weight is (t), the projection Wθ (f) after the convolution is Determined by. The expression (7) corresponds to the expression (6-5). Where (t9 is the transverse relaxation of the spin (T ₂ deca
Considering the effect of y), the average T ₂ of the sample is set to _2. Therefore, the effect of lateral relaxation can be reduced to some extent.

By the way, when considering the non-uniformity of the static magnetic field in the visual field, this effect can be corrected by devising the back projection. This will be described below.

Assuming that the non-uniformity of the static magnetic field in the visual field is E (x, y), when this is taken into account, the equation (1) is S ′ (t) = ∫ρ (x, y) exp [iγ {G ₀ t (Xcosωt + ysinωt + E (x, y) t)}] dxdy (1) ′, and by the same derivation, And To get Equation (3) ′ shows that E (x, y) causes a frequency shift in the projection data, and E
It can be corrected by selecting the data considering (x, y). This correction will be described below. The relationship between the image plane and the frequency axis during back projection is shown in FIG. In the figure, fc is
It is the resonance frequency at the center of the visual field. In normal backprojection, as shown in the figure, backprojection data from the angle θ to the point (x, y) is taken from the frequency position indicated by _B below. Although _{B = γG (xsinθ + ycosθ)} / 2π + c, the resonant frequency of the point under the influence of nonuniformity of the static magnetic field (x, y) rather than above equation _B, the _B '= _B given by _B + c'. Therefore, if the magnetic field inhomogeneity is known, the effect of the static magnetic field inhomogeneity can be corrected by using this _B ′ instead of _B in the coordinate calculation of the back projection.

By the way, in the above description, the method of performing image reproduction from P _θ (f) at 0 to 360 ° has been described, but S ^θ (▲ t ^θ _n ▼)
When By connecting and Fourier transforming P
_{If θ} (f) is obtained, in this case, P from 0 to 180 °
_The image can be reproduced by _θ (f). However, as shown in FIG. 2, Sθ (▲ t ^θ _n ▼), In both cases, since the measurement points are unequal intervals near the origin, it is necessary to estimate equidistant data points by interpolation.

Now, if we introduce T that ω = 2π / T and let the radius of the field of view be R, Have a relationship. If the image matrix is J × J, the resolution Δγ = 2π / J, and at the same time, Therefore, from these expressions To get At this time, the maximum amplitude G _max of Gx and Gy is given by G _max = G ₀ ωt _max = πJG ₀ (10). For example, if R = 15 cm, T = 0.25 ms and J = 128, then G ₀ = 0.016 gauss / cm and G _max = 6.4 gauss / cm. It is very difficult to realize the combination of the values of T and G _max with an actual device.

To avoid this difficulty, the gradient magnetic fields Gx and Gy can be expressed by the following equations.

Here, the phase φ of the sine wave and cosine wave, which are the elements of this gradient magnetic field waveform, is changed at equal intervals and the measurement of the sequence of FIG. 4 is repeated a plurality of times to obtain a set of data on a plurality of evenly-spaced spirals. To get Next, similarly to the embodiment described with reference to FIG. 4, the data on the radial vector at each angle may be divided into groups and Fourier-transformed to reconstruct the image. Φ in Fig. 5
But An example in which signals on four different spirals are sampled will be described.

Now, if we reconstruct the image using D spirals, It can be seen that the condition for G _max is relaxed by D times.

Further, the present invention can be realized particularly easily when the subject can be rotated, such as an NMR microscope.

That is, such a case is shown in FIG. In the figure, the subject is rotating within the visual field, and the center of rotation and the center of the visual field coincide. A fixed coordinate system (x,
y). Instead of the rotating magnetic fields Gx and Gy shown in FIG. 4, as shown in FIG. The gradient magnetic fields Gx and Gy indicated by are applied.

That is, two gradient magnetic fields that are orthogonal to each other are applied one steadily and one in proportion to time, and the proportional constant is divided by the magnitude of the steadily applied gradient magnetic field. The subject is rotated at an angular velocity corresponding to. By doing this, the coordinate system fixed to the rotating subject is x _r , y _r ).
Then, Becomes here, Substituting into equation (14) When the integral is calculated, S (t) = ∫ρ (x _r , y _r ) exp [iγ {x _r G ₀ tcosωt + y _r G ₀ tsinωt}] dx _r dy _r (17). That is, the same spiral sampling as shown in FIG. 2 can be executed by rotating the subject and applying the gradient magnetic field shown in FIG.

Therefore, the sampling interval of the signals is set to 1 / integral of the rotation period of the subject, and the grouping of the obtained sampling signals and the image reconstruction processing are performed in the same manner as described in FIG. The spin density distribution of the sample is obtained. If the sampling interval of the signal is not an integral fraction of the rotation cycle of the subject, a signal corresponding to the integral division of the rotation cycle may be calculated by interpolation before the grouping and image reconstruction processing.

Furthermore, when the application timing of the gradient magnetic fields Gx and Gy shown in FIG. 8 is changed with respect to the rotation angle of the subject and a plurality of measurements are performed, as shown in FIG. Sampling data on the line is obtained. This data is also the same as in the above-described embodiment in that the image plane configuration can be performed.

〔The invention's effect〕

According to the present invention described above, by adopting a new method of sampling Fourier space in a spiral shape, it is necessary to perform image reconstruction at high speed without performing high-speed oscillation of a rectangular gradient magnetic field. It is possible to capture data, and it is possible to relax the restrictions on the apparatus of the apparatus that nondestructively obtains the spin distribution or relaxation time distribution in the target object.

[Brief description of drawings]

FIG. 1 is a pulse sequence for realizing an echo planar method, which is a known technique close to the present invention, FIG. 2 is an example of how measurement points are arranged according to the present invention, and FIG. 3 is an apparatus configuration example of an embodiment of the present invention. FIG. 4 is an application sequence of RF and a gradient magnetic field according to an embodiment of the present invention, FIG. 5 is another example of how to arrange measurement points according to the present invention, and FIG. 6 is a relationship between an image plane and a frequency axis during back projection. FIG. 7 is a coordinate system of another embodiment of the present invention for rotating the subject, and FIG. 8 is a pulse sequence of the embodiment of FIG.

Claims (17)

[Claims] 1. A first step of preparing a transverse magnetization signal of a desired region of a subject placed in a substantially uniform static magnetic field, and a second step of measuring the transverse magnetization signal under application of a gradient magnetic field. Process, including a third process of reconstructing a magnetization distribution image from the measured signal, wherein the gradient magnetic field has an oscillating waveform constituted by a combination of sine wave or cosine wave functions, and the signal in the second process At the measurement point draws a spiral in the spatial frequency domain, and the period of the sine wave or cosine wave function
A method of measuring the magnetization distribution using nuclear magnetic resonance, wherein the value divided by the sampling interval of the signal in the process of is an integer. 2. The third step obtains signals at measurement points at intervals having an integer ratio with the cycle of the sine wave or cosine wave function by interpolation from the signal sampled in the second step. The method for measuring a magnetization distribution using nuclear magnetic resonance according to claim 1, further comprising a step of calculating. 3. The third step is a step of grouping data of measurement points distributed on the spiral into one-dimensional data for each radial direction, and Fourier transform after weighting the one-dimensional data. The method of measuring the magnetization distribution using nuclear magnetic resonance according to claim 1, including the step of reconstructing an image by back-projecting the result of Fourier transform. 4. The magnetization distribution using nuclear magnetic resonance according to claim 3, wherein data relating to a static magnetic field distribution in the visual field is used for coordinate calculation of the backprojection data in the backprojection. Measurement method. 5. The method according to claim 1, wherein the first and second steps are repeated a plurality of times by changing the phase of the sine wave or cosine wave function which is a constituent element of the vibration waveform. A method for measuring a magnetization distribution using nuclear magnetic resonance according to. 6. A first step of preparing a transverse magnetization signal of a desired region of a subject placed in a substantially uniform static magnetic field, and a second step of measuring the transverse magnetization signal under application of a gradient magnetic field. The gradient magnetic field has an oscillating waveform constituted by a combination of sine wave or cosine wave functions, and the sine wave or cosine wave function is included in the gradient magnetic field. The method of measuring the magnetization distribution using nuclear magnetic resonance, characterized in that the first and second steps are repeated a plurality of times by changing the phase. 7. The method for measuring the magnetization distribution using nuclear magnetic resonance according to claim 6, wherein the signal measurement point in the second step draws a spiral line in the spatial frequency domain. . 8. A value obtained by dividing a period of a sine wave or a cosine wave function, which is a constituent element of the vibration waveform, by a sampling interval of the signal in the second step is an integer. A method for measuring magnetization distribution using nuclear magnetic resonance according to the sixth item. 9. In the third step, by interpolating the signal sampled in the second step, signals at measurement points at intervals whose ratio to the cycle of the sine wave or cosine wave function is an integer are obtained. The method for measuring a magnetization distribution using nuclear magnetic resonance according to claim 6, further comprising a step of calculating. 10. The third step is a step of grouping data of measurement points distributed on the spiral into one-dimensional data for each radial direction, and Fourier transform after weighting the one-dimensional data. The method of measuring magnetization distribution using nuclear magnetic resonance according to claim 7, including the step of reconstructing an image by back-projecting the result of Fourier transform. 11. The magnetization distribution using nuclear magnetic resonance according to claim 10, wherein in the back projection, data regarding a static magnetic field distribution in the visual field is used for coordinate calculation of the back projection data. Measurement method. 12. A first step of preparing a transverse magnetization signal of a desired region of a subject placed in a substantially uniform static magnetic field, the subject being rotated, and the subject being rotated under the application of a predetermined gradient magnetic field. The method includes a second step of measuring a transverse magnetization signal and a third step of reconstructing a magnetization distribution image from the measured signal, wherein the gradient magnetic field has a constant first gradient magnetic field component and the first gradient magnetic field component. Applying in the orthogonal direction, the second of which the size changes in a certain increment
A method for measuring magnetization distribution using nuclear magnetic resonance, which is characterized by comprising a gradient magnetic field component. 13. The nuclear magnetic resonance according to claim 12, wherein the signal measuring point in the second step draws a spiral line in the spatial frequency domain relating to the rotating subject. The method of measuring the magnetization distribution. 14. The nuclear magnetic resonance according to claim 12, wherein a value obtained by dividing the rotation cycle of the object by the sampling interval of the signal in the second process is an integer. The method of measuring the magnetization distribution. 15. The third step is a step of calculating signals of measurement points at intervals whose ratio to the rotation cycle of the subject is an integer, by interpolation from the signals sampled in the second step. 13. The method for measuring a magnetization distribution using nuclear magnetic resonance according to claim 12, characterized in that 16. The third step is a step of grouping data of measurement points distributed on the spiral into one-dimensional data for each radial direction, and Fourier transform after weighting the one-dimensional data. 14. The method for measuring a magnetization distribution using nuclear magnetic resonance according to claim 13, including the step of reconstructing an image by back-projecting the result of Fourier transform. 17. The method according to claim 12, wherein the application timing of the gradient magnetic field is changed with respect to the rotation of the subject to repeat the first and second steps a plurality of times.
A method for measuring a magnetization distribution using nuclear magnetic resonance according to item 13 or 13.