WO1993014414A1

WO1993014414A1 - Gradient field control

Info

Publication number: WO1993014414A1
Application number: PCT/GB1993/000082
Authority: WO
Inventors: Peter Simon Aptaker; Paul Beasley; David Arthur Morris
Original assignee: Oxford Instruments (Uk) Limited
Priority date: 1992-01-15
Filing date: 1993-01-15
Publication date: 1993-07-22
Also published as: EP0621955A1; AU3265093A; JPH07502671A; GB9200812D0

Abstract

A control system for a gradient field generator, suitable for example for an NMR apparatus, includes filters which modify the field demand signal. The modification shapes the gradient field profile typically to compensate for the response characteristics of the NMR apparatus. Current generators (3a, 3b) supply currents to a plurality of individually magnetisable windings. The filters include different filters (F0, F1) corresponding to matrix currents (I0, I1) of different orders. The outputs of the different filters are summed to provide a control input for one of the current generators, and subtracted to provide the control input for the other of the current generators. The system thereby provides substantially decoupled control of the different field orders.

Description

GRADIENT FIELD CONTROL

TECHNICAL FIELD

The present invention relates to a method and apparatus for controlling the gradient field in an NMR apparatus. It is applicable to any type of NMR apparatus including superconducting, resistive electromagnetic or permanent magnetic systems.

BACKGROUND

In typical NMR imaging and spectroscopy apparatus a main magnet is provided for generating a homogeneous steady axial field. In addition, a number of gradient coil sets are also provided. These superimpose gradients on the main field in order to localise a working volume of uniform magnetisation within the apparatus for investigation of the sample at that position.

In use, a pulse is applied to the gradient coils and the subsequent free induction decay (FID) signal from the sample is sensed. While ideally the output of the coil would vary as a step function, in practice imperfections in the dynamic response of the gradient coils means that the shape of the output field pulse tends to be degraded. In particular, it may be found that a large z₀ term, equivalent to a time-varying shift in the main magnetic field B₀, is generated as a result of eddy currents in the apparatus. These fields occur, for example, in the metal components making up the coil housing or NMR apparatus.

It has previously been proposed to use compensation techniques of the type known in control engineering as "feedforward" in order to compensate for these imperfections in the dynamic response of the gradient field coils. This is widely known as pre-emphasis where the flux lags the current and emphasis is needed on the current to give a flat flux response. At their simplest, these techniques might involve the insertion of a multi- exponential signal shaping network in the feed to the existing gradient coil. Typically between two and five time constants are set based on a mixture of measurement and empirical methods.

US-A-4585995 in the name of Flugan, for example, discloses a system in which an overshoot current is provided to a gradient coil during gradient switching. The shape of the pre-emphasis signal is determined by a time constant network.

With simple pre-emphasis techniques of the type described above, it is not possible fully to compensate for the imperfections in the response of the gradient coil. This results, in part, from the cross-coupling of the different spatial orders of the field in the gradient coils. This means, in a z gradient for example, changes in the z field will also alter the z₀, X, Y fields and even higher field orders.

In an attempt to overcome the limitations of these simple pre-emphasis techniques, it has been proposed to shape the signals applied to multiple coils. In the paper by P. Jehenson et al published at pp 264-248, Journal of Magnetic Resonance 90, (1990) a system is described in which there is provided an additional z₀ coil. Separate pre-emphasis networks independently shape the signals fed to both the gradient coils and to the additional z₀ coil (see for example Fig. 3(A) of the cited paper).

These prior art systems have a number of limitations. The cross-coupling compensation cannot in general be exact since the approaches adopted rely upon the assumption that certain cross-coupling terms are small. Secondly, they require the use of an extra winding which adds an extra degree of coupling control, e.g., a z₀ winding to compensate for z₀ cross-coupling effects. This is not always possible in practice. A further limitation is that the prior art techniques can only approximately model the eddy currents using a finite number of coupled coils and the use of a larger number of coils can make the Laplace transform method unwieldy, requiring that a large number of time constants should be used for the filter network.

SUMMARY OF THE INVENTION According to a first aspect of the present invention, there is provided a control system for a gradient field generator for use in an NMR apparatus, the control system including filter means arranged to modify a field demand signal so as to shape the gradient field profile, and current generators arranged to supply current to a plurality of individually magnetisable windings, in which the filter means include different filters corresponding to dynamic matric currents (I^I,) of different orders, and in which the outputs of the different filters are summed to provide the control input for one of the current generators, and subtracted to provide the control input for another of the current generators, the system thereby providing substantially decoupled control of a plurality of individually magnetisable windings. The method of the present invention, by contrast with the prior art system, provides decoupled control of the different fields orders using the combination of a number of individually magnetisable windings without requiring the use of any additional coils. This is achieved by decoupling the real current feeds for the windings into "dynamic matrix currents" corresponding to respectively even and odd order terms of the fields to be generated by the windings. Separate filters can then be provided for each of the matrix currents. The outputs of the different filters are then summed to give the current input for one winding and the difference taken to provide the current input for the other winding. In this manner the control system provides decoupled control of the different field orders. The method of the present invention can be applied to any type of magnet producing a DC field which has a gradient field superimposed. The actual form of the windings depends on the particular application and the preferred field strength, order of the field gradient, pulsed field profile, heating effects, and complexity of the power supply and control system.

Preferably the plurality of windings comprise different parts of a single gradient coil.

The different windings may be provided, for example, by the left and right parts of the axial (z) gradient coil or, for example, by the inner and outer parts of an x gradient coil or a y gradient coil. The different halves of such coils are readily accessed using centre taps. In the example described in further detail below, for the axial z gradient the sum of current inputs to the two parts of the winding (labelled A and B) produce odd order terms and these are used to generate the required z gradient. The difference windings of A and B produce even order terms and it is these which are used to compensate for the z₀ field shift. In practice of course the nature of the physical connection to the different windings remains unchanged and "sum" or "difference" connections are effected by an appropriate change in the signs of the feeds to the respective windings.

The filter means may comprise a number of discreet analogue filters with appropriately chosen time constants, or may be implemented by appropriate digital signal processing controlled by software.

As a preferred option, the control system may further comprise a feedback loop arranged to sense a variation in a particular field order generated by the plurality of windings and to modify the corresponding matrix current accordingly.

A further major advantage of the present invention is that by providing decoupling it makes it possible to construct feedback loops for individual field orders. The flux associated with a particular order can be measured from the induced EMF in the winding, or alternatively an equivalent search coil may be provided for this purpose. Other techniques having suitable dynamic response and sensitivity may be used. In particular, it may be advantageous to measure the individual field orders directly on the basis of NMR measurements.

Preferably the feedback loop includes an AC coupled integrator.

Since perfect control of the feedback loop is not possible the DC level will eventually become arbitrary. For this reason it is preferred that the integrator should be AC coupled. The filtering of the AC coupled integrator is then allowed for in the overall control strategy.

A variety of different methods may be used to set the filter values for the control system but it is much preferred that this is done by measuring the frequency response of the system and calculating complementary response curves. The response curves may then be used directly to modify the feed signal in the case of a digitally implemented signal, or for a system using discrete analogue filters the time constants may be fitted to the curve using, e.g., a least-squares method. In either case, this approach avoids the inaccuracies resulting from attempting to identify eddy-current time constants. In the case of the directly digitally modified signal this method avoids altogether the need to identify filter time constants. This novel approach to determining values for the filters is not limited in application to control systems in accordance with the first aspect of the present invention but can also advantageously be used to determine the filter values for different types of feedforward control systems for gradient field generator windings.

According to a second aspect of the present invention, there is provided a method of determining the filter values for a feed forward control system for a gradient field generator for use in an NMR system, comprising injecting currents into windings of the gradient field generator at a number of different frequencies, measuring the field strength at the different frequencies so as to determine response curves, calculating the inverses of the response matrix at the different frequencies, determining from the inverse values corresponding inverse response curves, and setting the filter means in the feed forward control system to give response characteristics substantially matched to the inverse response curves.

The steps of injecting current at different frequencies and measuring the response may carried out directly on the control circuits or alternatively may be carried out using a computer model of the system, in which case the steps are implemented by equivalent mathematical operations.

According to a third aspect of the present invention, there is provided a method of controlling a gradient field generator for use in a NMR apparatus, the method including determining response characteristics of the apparatus and modifying a field demand signal so as to compensate for the response characteristic, in which different elements of the matrix having dimensions corresponding to different orders of the field demand and different orders of the field response respectively are determined and the field demand signal is subsequently modified in accordance with the inverse of the matrix.

Although it is preferred that this third aspect of the present invention is used in combination with the first and second aspects above, nonetheless the use of matrix inversion techniques still give advantages in otherwise conventional NMR gradient field generators, such as those disclosed in the prior art documents cited above. As discussed in further detail below, the demand signal may be modified in accordance with the inverse matrix either by direct matrix inversion using filters corresponding to the elements of the inverted matrix, or by combining the use of filters with feed back of all cross-coupling terms. The filters are then in feed back loops and these loops cannot be guaranteed to be stable. In practice however in most instances especially when cross-coupling is modest, stability is possible. The filter network with feedback then responds exactly as the inverse matrix system.

BRIEF DESCRIPTION OF THE DRAWINGS One example of system in accordance with the present invention will now be described in detail and the theoretical background to the invention further discussed with reference to the accompanying drawings, in which:

Figure la is a diagram showing schematically the transforming of matrix currents I₁ I₀ to the winding currents;

Figure lb is a diagram showing the relationship between the matrix currents and the different field orders;

Figure lc shows the ideal inverse matrix compensation network;

Figure Id shows an alternative implementation of the matrix inversion using feedback;

Figure 2 is a circuit diagram for an analogue filter for use in the systems of Figure 1; Figures 3a - 3h are response curves for the system;

Figures 4a - 4h are inverse response curves;

Figure 5 is a diagram showing a shielded gradient winding;

Figure 6 is a schematic showing the transfer function of a typical multiexponential filter;

Figures 7a and 7b are diagrams showing typical axial z gradient and axial x gradient coils respectively;

Figure 8 is a circuit diagram and schematic of coil windings; Figures 9a and 9b are a circuit diagram of a first printed circuit board used in the preferred embodiment; and

Figures 10a and 10b are a circuit diagram of a second circuit board used in the preferred embodiment.

DESCRIPTION OF PREFERRED EXAMPLE

Figure la shows schematically one example of a control system embodying the present invention. The system has an input 1 which receives a magnetic field demand signal. In the presently described example, the demand signal contains only a first order term B,, since the required field response is a step function in the field gradient, without any change in the constant zeroth order field B₀. Accordingly in practice the second demand input 1' would not be used unless required for a more general gradient control system.

The demand signal is fed to a filter system 2. This comprises a first filter pair F₁ which provides an output which determines the first order matrix current I, and a second filter pair F₀ which provides the output determining the zeroth order matrix current I₀. The sum of the outputs of F₁ and F₀ provide the control input to a first current amplifier 3A. The difference between the outputs of F₀ and

F, similarly provide the control input to a second current amplifier 3B. These amplifiers feed respective windings z_A and z_B which in the present example are two halves of the axial z gradient winding. In use, typically a step function is applied as the input signal at the input 1.

This results in a generally corresponding rise in the outputs from the current amplifiers feeding the respective windings.

The field generated by the windings however does not perfectly track the rise in the applied current, but includes in addition time-varying fields resulting from eddy currents in the coils, and in other portions of the apparatus.

In the formalism adopted for the theoretical discussion below, the total field B generated in the system is related to the current I in the windings by a function G. In the feed forward technique adopted in the present invention the filters used to shape the field demand signal are arranged to have a response equivalent to G . Then, in the ideal case, the field generated by the windings perfectly tracks the demand signal. Consider a set of m-, windings whose currents can be represented as a vector

CI]=[I₁ I₂ ..i_m....i_mi]^T

The magnetic field can be analysed in, say m_g components (eg Legendre components Z,X,Y,XX, or fields at key points)

[B]=[B₁.. B ...Bu_g]

For such a system the steady state the two can be related by the matrix [G_ss] :

[B]=[G_SS][I] Where the input is dynamic, however, and the co-efficients are a function of frequency and it is necessary to take a frequency transform such as the Fourier Transforms:

[B(jω]=[G(jω)[Ijω)]

The "jω" must be replaced for other transform (eg "s" for Laplace transform) .

Conversely, the current response may be determined from the demanded field as:

[I(jω]=[G(jω)]^"1[B(jω)]=[H(jω)[B(jω)]

If one has the same number of degrees of freedom (m,-) and variables to control (m_g) then ^m_g and a matrix of filters

[G(jω)]^" will enable one to control the individual field components exactly. Where m^π-_g there is more than one exact solution while when ,<m_g approximate solutions may be found using the pseudo-inverse matrix (least squares) . In practice, even if there are enough degrees of freedom, one is only going to implement the filters "approximately". In the classical pre-emphasis techniques used in the prior art, the eddy currents are modelled as a multi- exponential function and the required filter characteristics determined accordingly. For example, assuming only one eddy-current time constant, the normalised step response is

Bfiyistcp=(l-κe-^,τ)

(6) This is governed by a Laplace transform, but any frequency transform is applicable

For a flat response a filter is required equivalent to

I (s) /B (s) so

1(a) (l+s(l-r)τ)

(8 )

This has a step response k -ι/(l-κ)τ

G(D = ι ^+"πr^e

(9) In practice between 2 and 5 time constants are set based on a mixture of measurement and empirical methods.

As discussed above in relation to the prior art, in general such systems can only imperfectly compensate for the response characteristics of the apparatus.

The approach adopted in the present invention is based on the control of "dynamic matrix currents".

In our simplest example we have an axial gradient winding whose left and right hand winding [optionally actively shielded] can be separately magnetised with currents I_A and I_B. By utilising these two degrees of input freedom we are able to have almost decoupled control of two orders z₀ and z. with currents.

The matrix currents I₀ and I. are then defined as:

«0 =0.5 1)

111 U 'J Ϊ (1

It follows from system symmetries that, in the steady state, I₀ will only effect even orders and I, odd orders. The fields are, therefore, related to the currents by equation

However, dynamic responses necessitate taking the frequency transform, the Fourier transform being used here. Furthermore, other effects, such as structural conductor asymmetry and winding imperfection mean that the cross terms are relevant and one gets

B_o0ω) βϋθOω) βθ|Uω) BιOω)J ( 13 ) 1-Slo0∞) β| l()ω) . IlOω)J

which can be represented in matrix terms as: [B(jω)]=[G(jω)][I(jω)]

This approach relies upon the fact that gradient and shim windings are built of components which can usually be separated into symmetrical physical sections. The sections then are separated into two halves A and B. For example, a Z gradient might be separated into a left and right half. In an X gradient it is separation into two facing sections 180° apart that is relevant for the present purposes.

The fields due to any section may be analysed by Legendre polynomials into coefficients of given orders (m,n) . The effective winding principle takes advantage of the separation of odd and even orders in the physically and electrically symmetrical A and B sections.

Note that the sign convention is arbitrary so, for example. Section B may have both signs inverted. It would then be the Difference that produces the "desired" orders.

Section A={odd in m and/or n} + {even in m and or n} Section B = {odd in m and/or n} - {even in m and or n} Sum = {odd in m and/or n} [desired component] Difference = {even in m and/or n} [not desired]

Examples for Z and X Gradients

(1) Z gradient : ideally produced (m,n)=(0,l) but, at best, will produce other terms (0,odd)

Z_A = (m=0,n=odd) + (m=0,n=even) Z_B = (m=0,n=odd) - (m=0,n=even)

Sum = (Z_A + Z_B) = {m=0,n=odd} Difference = (Z _A -Z_B) = {m=0,n=even} (2) X gradient: ideally produces (m,n)=(l,l) but, at best, will produce other terms (odd,odd)

X_A = {m=odd,n=odd} + {m=even,n=even} X_B = {m=odd,n=odd} - {m=even,n,even}

Sum =%(X_A+X_B) = {m=odd,n=odd}

Difference = (X_A - X_B) = {m=even,n=even}

Tables la and lb show for the different orders of the Legendre polynomial expansion the contributions to the field of the A and B sections, together with the sum and difference of those contributions. Table la and the corresponding Figure 7a relate to a typical axial Z gradient, while Table lb relates to a typical transverse X gradient. Considering, for example Table la, it can be seen that the difference windings produce large even order fields while the sum winding produces primarily the first order z field.

In the present example the values for the different filters are determined by exciting the windings with matrix currents of different frequencies and measuring the frequency response. Different frequencies of 10 are injected and the strength of the resulting zeroth and first order fields measured, giving the response curves shown in Figures 3a and 3b respectively. Similarly different frequencies of II are injected and the zeroth and first order responses measured, giving plots 3c and 3d. At any given frequency these four plots correspond to a 2 x 2 matrix. These matrices are inverted to give the inverse response curves shown in Figures 4a to 4d. In the present example discreet filters are used, with the values of the filters chosen to approximate the inverse response curves by use of exponential fitting methods in the time domain, so that the filter has the same step response. If S(t) is a square wave of unity amplitude and h(jω) is the filter required, then the frequency response of the filter to the step input is (18) y(jo>) ^*■*■ h(jα>) S(jω) and the time response of the filter is found from the inverse Fourier transform, -I y(l)«-F ( Uω)Sϋω))

In a digitally implemented system these curves may then be applied directly to shape the demand signal.

Figure 6 shows a schematic for an analogue filter made up of the sum of a number of first order exponential filters. The FFT may be implemented using a discrete Fourier transform. The sample time for the transform must be less than the time constants of interest and the square wave must be of a long enough wavelength such that the slow time constants will have decayed.

Plots f-j in Figures 3 and 4 show the response curves and inverse curves in the time domain.

The above method is applicable equally to shielded and unshielded windings. Figure 5 shows a shielded gradient winding in which a secondary winding is positioned outside the primary winding. The matrix currents may be combined in the primary and secondary windings in a number of different configurations, as shown in Table 2 which relates to an axial gradient. (In the sign convention chosen the current sense is equal to the axial field sense) . For the preferred options 1 and 2 listed in the table both the primary and secondary coils are used to generate the B₀ field. Equivalent IA and IB can be produced by connecting the primary and secondary pairs in an uncrossed or crossed configuration. Option 1 shown in Figure 5 uses an uncrossed connection so that the real current in each of the secondaries is opposite in sign to that in the primary, thereby maintaining the active shielding.

As an alternative to the direct matrix inversion method shown schematically in Figure 1(c), feedback may be used to provide a system have the desired matrix inverse characteristics. This is shown schematically in Figure 1(d). Also, the system may be extended to take account of coupling between fields in different directions. Thus, for example, although the systems are described above for correction of the cross-coupling of different spatial orders of the axial (z) field in practice a change in the z field will also be cross-coupled to changes in the x and y fields. The dashed lines in Figures 1(c) and (d) show how connection for the cross-coupling to and from different directions may be added to the basic system. Figure 2 shows a typical analogue implementation of a compensation filter incorporating three time constants. In practice each block, such as filter element .. in Figure 1 may be implemented by such a filter. The general form of the analogue filters can be represented by the sum of a DC component k₀ and the sum of exponential filters. In terms of Laplace transforms one gets:

^{£ij o+}k i⁺ «i where the gains k,- and the time constants t_f can be found from the components in the circuit of Figure 2 as:

where a refers to the wiper setting of the potentiometers (adjustable resistance RVl_{ and RV2,) which varies from zero to unity. Typical component values for the circuit are shown in Table 3.

Figures 9 and 10 show in detail one example of a complete circuit incorporating the compensating filter. The different components of the circuit are described below. Because of the limited space available to mount the circuit, it is spread over two PCBs.

Board 1 (Figure 9) Power Supply

The power input to the PCB is an unregulated +/- 23 volt supply. Integrated circuit U15 is a +15 volt regulator and together with CIO, C18, D5 and D7 supply +15 volt power to the circuit. Similarly U17 is a -15 volt regulator and together with Cll, C19, D6 and D8 provide the -15 volt power to the circuit. There are a large number of decoupling capacitor spread evenly about the two PCBs.

Demand Input

The gradient demand input is a differential signal on connector PI alO and clO pins. A 5 volt level between these two pins will constitute a maximum gradient demand. Integrated circuit Ul receives this signal and this is summed with the shim demand by U3. Test Point 6 (TP6) is a monitor point that is the sum of both the gradient demand and the shim demand.

Shim Demand Input

The shim demand input on connector PI pins al4 and al5 is received by the differential amplifier U2. This signal is then limited in frequency by the low pass filter R9 and

C24 with a 3db point of 1.6 Hz. The shim signal is summed with the gradient demand by U3.

Stop Circuit A 0 volt level on connector pin PI all will reduce the gain of the amplifier U3 to a very small level thereby removing any large gradient demand. This occurs whenever the gradient amplifier is in the STANDBY condition.

BO Circuit

The BO compensation circuits are similar to the cross term circuits. The demand for the BO circuit is only the uncompensated DEMAND signal. There are five signals summed by U10 to form the BO compensation signal BO_OUT. U8a forms a signal that is linearly proportional to the DEMAND signal with a gain set by RV25 between -1 and +1. The four circuits associated with C9 to C12 are similar to the cross term circuits described above. Circuit U10 sums each of the five BO compensation signals at TP9 to TP12 and TP15. Each compensation is a maximum of +/- 10% of the DEMAND signal. The three signals CT1_0UT, CT2_OUT and B0_0UT are presented to the connector PI pins cl6, cl7, c3 respectively and passed on the amplifier control circuits to drive the required gradient coils.

Slew Rate Limit

When driving an inductive load the demand signal has to be rise time limited to keep the output voltage of the amplifier within its working range. The circuit combination of U4 and U5 generate a linear ramp on the rising and falling edges of the demand signal. The slew rate limit is adjusted by the RV2 potentiometer over a range of 0.1 millisecond to over 1 millisecond of time to full demand.

Eddy Current Compensation

As described above, eddy current compensation is required to get the optimum performance from a MRI system. Depending on the exact requirements of the system this compensation may be required to pre-emphasize or de- emphasize the current demand. The modification is constructed with four available time constants made from four independent circuits associated with capacitors CI, C2, C3 and C4. Each time constant is adjusted with potentiometers RV3, RV5, RV7 and RV9 respectively. The time constants are buffered by U6a, U6b, U7a and U7b. The gain of each time constant can be varied from -1 to +1 with potentiometers RV4, RV6, RV8 and RV10 respectively. Each of the four compensation signals can be monitored on test points TP9, TP10, TPll and TP12. Cross Term Demands

Two outputs to the cross term and BO compensation circuits these are DEMAND taken from the slew rate limited input signal but before any compensation is added. CR_DEM is the same signal as the gradient demand output and contains all of the compensation signals as programmed.

Gradient Demand Output

The demand output presented to connector PI cl and monitored on TP17 is the sum of the demand input, shim input and any combination of eddy current compensation and cross term combination required. Links LK5 to LK16 together with the adjustment potentiometers are used to program the desired compensation signal.

Power Monitor

The gradient amplifier may be able to deliver larger power than the gradient coil can withstand. A protection circuit is incorporated to monitor the gradient demand signal and to set the amplifier into standby mode if the demand is higher than a set level. Circuit U9, U10 and the associated components form a precision rectifier, TP6 signal is the absolute value of the demand signal. Ull is a transconductance amplifier that is used as a squarer circuit its output is the square of the demand signal. U12 low pass filters this signal. The signal at TP14 is proportional to the square of the output current. This signal level is monitored by the level detector U13. If the TP14 signal becomes more +ve than the level set at TP15 by RVll then the TP15 signal and connector Pi pin c20 goes to a low (0 volt) level and sets the amplifier in the STANDBY state.

Board 2 (Figure 10) Cross Term Circuit

The "piggy back" board contains eight cross term circuits in two sets of four. Each of the eight circuits is identical except for the value of the compensation capacitors Cl to C8. The links LK27 and LK28 select which of the two demand signals are required for the cross compensation. Either the uncompensated DEMAND signal is selected with LK27 or the compensated output demand CR_DEM with LK28.

Referring to one circuit. The time constant is set by the Cl, RVl combination and is buffered by Ulb. RV2 sets the compensation gain between -1 and +1. The circuit associated with U7 sums the four compensation signals at TP1 to TP4. The required compensation being selected by the links LK1 to LK8. TP13 forms the first cross term signal CT1_0UT. Each of the compensation circuits can be set to a maximum of +/- 10% of the demand signal. Similarly for the second cross term signal CT2_OUT the compensation is set with C5 to C8 and RV9 to RV15 components, U8 sums the signals from TP5 to TP8, links LK9 to LK16 select the desired compensation signals.

As noted above, one preferred aspect of the present invention uses feedback based on NMR measurements. In this case the NMR response from a known sample volume is measured across an array of many sampling points. The response is compared with the expected response to derive an error signal which is used in the feedback loop to modify the matrix currents.

TABLE 1

Numerical Example of Effective Windings of A Z and X Gradient la LEGENDRE POLYNOMIAL EXPANSION FOR BZ FROM A TYPICAL AXIAL Z GRADIENT

Note: The sum of windings A and B produce the odd order terms required to generate the Z gradient. The difference windings of A and B produce even order terms which can be used to compensate for field shifts.

lb LEGENDRE POLYNOMIAL EXPANSION FOR BZ FROM A TYPICAL TRANSVERSE X GRADIENT

Note: The sum of windings A and B produce the odd order terms required to generate the X gradient. The difference windings of A and B produce even order terms which can be used to compensate for field shifts.

TABLE 2

Virtual Currents in a Split Gradient Winding

TABLE 3

Typical Circuit Component Values

R2i=10K;R5=10K;

No. Rli RVli Cl τ_f (approx) R4i *^~

n/a n/a n/a n/a 10K -1 to 1

99K 1M0 4μ7 0.5 to 5 s 10OK -.1 to .1

99K 1M0 lμO 0.1 to 1 S 100K -.1 to .1

99K 1M0 0μ22 0.02 to .24 s 100K -.1 to .1

Claims

1. A control system for a gradient field generator for use in an NMR apparatus, the control system including filter means (2) arranged to modify a pulsed magnetic field spatial profile as a function of time, and current generators (3A,3B) arranged to supply current to a plurality of individually magnetisable windings, characterised in that the filter means include different filters (F^F,) corresponding to dynamic matrix currents (1,₅,1,) of different orders, the outputs of the different filters being summed to provide the control input for one of the current generators (3A) , and subtracted to provide the control input for another of the current generators (3B) , the system thereby providing substantially decoupled control of a plurality of individually magnetisable windings.

2. A system according to claim 1, in which the plurality of windings comprise different (Z_A,Z_B) parts of a single gradient coil.

3. A system according to claim 1 or 2, further comprising a feedback loop including means for sensing a variation in a particular field order generated by the plurality of windings, and means for modifying the corresponding matrix current in response to the sensed variation.

4. A system according to claim 3, in which the feedback loop includes an AC-coupled integrator.

5. A system according to claim 3, in which the means for sensing a variation in a particular field order are arranged to do so on the basis of an NMR measurement.

6. A method of controlling a gradient field in an NMR apparatus including a plurality of individually magnetisable windings, and current generators arranged to supply current to the windings, the method including the steps of modifying a field demand signal so as to shape the gradient field profile, and controlling the current generators in accordance with the modified field demand signal characterised by the steps of applying the field demand signal to different filters corresponding to-matrix currents of different orders, summing the outputs of the different filters to provide the control input for one of the current generators, and subtracting the outputs of the different filters to provide the control input for another of the current generators, the method thereby providing substantially decoupled control of a plurality of individually magnetisable windings.

7. A method according to claim 6, further comprising sensing a variation in a particular field order generated by the plurality of windings, and modifying the corresponding matrix current accordingly.

8. A method according to claim 7, in which the variation is sensed by making an NMR measurement.

9. A method according to claim 6, 7 or 8, further comprising the steps of measuring the frequency response of the NMR system, and calculating complementary response curves, the filters for the field demand signal being determined in accordance with the complementary response curves.

10. A method according to claim 9, in which the step of measuring the frequency response comprises injecting currents into the windings of the gradient field generator at a number of different frequencies, measuring the field strength at the different frequencies and thereby determining a matrix of response curves, and in which the step of calculating complementary response curves comprises determining the inverses of the response curve matrix at the different frequencies, determining from the inverse values corresponding inverse response curves, and setting the filter means to give response characteristics substantially matched to the inverse response curves.

11. A method according to claim 9, in which the step of injecting current at different frequencies and measuring the response are carried out on a computer model of the NMR system.

12. A method of determining the filter values for a feed forward control system for a gradient field generator for use in an NMR system, characterised by injecting currents into windings of the gradient field generator at a number of different frequencies, measuring the field strength at the different frequencies so as to determine response curves, calculating the inverses of the response matrix at the different frequencies, determining from the inverse values corresponding inverse response curves, and setting the filter means in the feed forward control system to give response characteristics substantially matched to the inverse response curves.

13. A method of controlling a gradient field generator for use in an NMR apparatus, the method including determining response characteristics of the apparatus and modifying a field demand signal so as to compensate for the response characteristic, characterised in that different elements of the matrix having dimensions corresponding to different orders of the field demand and different orders of the field response respectively are determined and the field demand signal is subsequently modified in accordance with the inverse of the matrix.