Acta Polytechnica Vol. 43 No. 412003 A Magnetic Resonance Measurement Technique for Rapidly Switched Gradient Magnetic Fields in a Magnetic Resonance Tomograph K. Bartu5ek. E. Gescheidtovd This paper fuscribes a method for measuring of the gradient rnagnetic f,eld, in Nuclear Magnetic Resorurnce (NMR) tomography, whiclt. k one of tlrc modem rnedical diagnosti,c methods. A aery important prerequisite for high quality inagtng is a gradient magnetic field in the 'instrurnent with exactly dcf.ned properties. Nuckar magnetic resonance enables us to measure the pulse gra.dient magnetic fi,eld characteristics uith high accurec). These interesting precise nethod; uere designed, realised, and tested at the Institute of Scientific Instruments (ISI) of the Acadcmy of Sciences of the Czech Republic. The first of themuas the Instantaneous Frequency (lF) method, uhich uas deueloped into the Instantaneous Frequency of Spin Echo (IFSE) and the Instantaneo,us Frequmcy of Spin Echo Series (IFSES) mcthods. The aboae named metltods are desribed in this paper and their a comparison'is also presented. Keywords: nucLear magnetic reslnance, gradient magnetic fiel.d, w,gnetic resonance tomography, instantaneous frequency methods, spin echo. I Notation Bo(r) Induction of the basic magnetic field G(t) Gradient of the magnetic field Go(t') Gradient of the magnetic field in the cr direction (cr is the r, y, or z direction) M1(l) Macroscopic vector of the magnetisation of the nuclei rn Vector of the spatial nucleus magnetisation y Gyromagnetic ratio of the nucleus s(l) MR signal s(zZ) Digitalised MR signal f(t) Instantaneous fiequency of MR signal O(t) Instantaneous phase of MR signal T2 Spin relaxation time TE Echo time - time of the spin echo creation 2 Introduction The quality of the gradient magnetic fields is an im- portant property of devices exploiting the phenomenon of magnetic resonance for imaging or localised spectroscopy. Besides the homogeneity of the gradient field causing shape distortion of the MR image, the behaviour of the magnetic field during its time changes is also important. The time char- acteristics of the magnetic field in the instrument influence the amplitude of the scanned MR signal and the prolongation of the scanning time of the MR image. Gradient changes induce eddy currents in nearby con- ducting arrangement, potentially causing image artef;act, localization errors, and signal distortion. While the use of actively shielded gradients has greatly reduced the magni- tude of eddy currents, signifrcant distortion often still remains especially in short time interval after gradient switch off. Residual eddy currents may require further reduction. This is frequently achieved by preemphasis correction in relevant gradient canal and in the homogeneous 8o shim. Rise time of 30 the impulse of a magnetic field or its decrease to the level of non-homogeneity of a basic magnetic field should be as short as possible (< 100 ps). Settings of the amplitude and time constants for pre- emphasis correction are based on the iterative process until eddy currents effects are minimized. This process uses one or more of the following measurement methods: output of a pick up coil, which needs special hardware and repositioning of the pickup coil [1, 2]; measuring multiple FIDs of a sample after a gradient is switch o[ which needs precise sample positioning [3, 4]; mapping eddy current characteristics in the magnet for a small sample, which is a time-consuming procedure; or mapping along projections and adjusting the parameters for eddy current compensation by the automatic shimming technique [5, 6], which in measurement process uses all three gradients and doesn't allow measured for short time after the end of the gradient [7]. The basic idea of the MR gradient measurement method is to acquire the MR signal after selective excitation of a thin layer of the specimen and after the end of the gradient pulse [8]. At this point, the time gradient characteristic is propor- tional to the instantaneous frequency of the MR signal, which has a small signal to noise (S/N) ratio. The time magnetic field induction characteristic in a lim- ited layer is proportional to the instantaneous frequency of the complex MR signal, which is the sum of the FID signal originated after the application of the n impulse and spin echo a(zo't7=@(zo't) ' (l) v In conductive parts of the MR device eddy currents in- duce, causing inconvenient retardation of the time changes of the magnetic field. The rise time of the impulse of the magnetic field or its decrease to the level of non-homogeneity of the basic magnetic field should be as short as possible (< 100 ps), The influence of eddy currents can be eliminated Acta Polytechnica Vol. 43 No. 412003 by an inverse filte4, put into the way of the signals derermin- ing the time sequence of rhe generared gradienr pulses. The constants of the digital inverse filrers, so called preemphasis constants, are computed from the time courses of the disap- pearing gradient magnetic frelds. These time characteristics must be measured very exactly for a sufficiently long time. If this condition is not fulfilled, significant errors are introduced during the calculations of the preemphasis consrants and the compensation of the eddy currents is not sufficient. For this reason we try to measure the drop of the magnetic fields for as long a time period as possible. An accurate method that is appropriate for time charac- teristics measurement is a method based on NMR, called the Instantaneous Frequency method [8]. The measurement can be performed on a commercial NMR instrument r.vith adjusted preemphasis compensarion. This method can be used to find out the quality of the gradienr magneric fields with sufficient precision. The disadvantage of the IF merhod lies in the very limited time interval - about to 2.5 ms - in which we are able to acquire an MR signal for further process- ing. For this reason the basic IF method is extended with spin echo, and is thus converted into the Instantaneous Frequency of Spin Echo (IFSE) method. The spin echo rvas crcared by us- ing a n exciting pulse. The IFSE method enables scanning of the MR signal for an l8 ms time period. The latest modifi- cation of the methods based on instantaneous frequency measurement is the Instantaneous Frequency of Spin Echoes Series (IFSES) method, which partially eliminates the main disadvantage of the nr'o methods mentioned above. Its basic principle is the same as for the IFSE method [9]. The differ- ence is that IFSES is based on the sum of rhe MR signals wirh echoes, measured at di{ferent echo times in order to extend the MR signal scanning time up to 80 ms. 3 IF method Direct measurement of the magnetic field gradients in the whole space of the tomograph is not possible because rhe MR signal, called the Free Induction Decay (FID) signal, carrier of the information about the gradient field time characteristics, decays rapidly (100 ps). The FID signal is a complex signal, whose magnitude rapidly decreases, especially in the first part of the time domain. This effect is a consequence of rapid MR signal dephasing under the presence of a high gradient amplitude. The gradients are computed fiorn the amplitudes of the magnetic field induction in a thin layer of the investigated material, placed at a distance -rzo from the centre of the gradients. In this case the FID signal lasts for a significantly longer time period. The location of a thin excited layer is determined by offset of the selective radio frequency pulse applied before the end of the gradient rectangular pulse. The pulse sequence of the IF method is shown in Fig. l. At first the gradient pulse of 2 s length is initiated on the basis of the selected direction. After stabilisation of the eddy currents in the conductive parts of the MR magnet the nuclei are excited in the presence ofthe gradient by the selective n/2 radlo fre- quency (RF) pulse of 1.8 ms length. By adjusting the exciting coils current the basic magnetic field induction Bo is set up to its maximum homogeneity. The zero gradientBo(l) is given by the sum of inductions of the magnetic field in positions *zo o"to Time Fig. l: Pulse sequence for the IF method and -26, and the difference of the rwo parts determines the module of the magnetic field gradient. I Bo(t) =;la(zs,t) + B(-zs,t)], (2) G"(r) =.- [r(zo,t) -B(-zs,t)]. (3) 9z-"0 The local magnetic field is proportional ro rhe instanra- neous frequency of the FID signal; the frequency can be computed as a time derivative of the digitaiised FID signal phase. During the digitalisation of the FID signal, the Shan- non theorem has to be fulfilled. The digitalised FID signal is: s (zr) =Rs (5 (nr)) + jIm(s (rzr)) . (4) The instantaneous phase of s (rzT) is: o1,;=u,.,r[14'-@I)1. (5)"[Re(s @D) ) The instantaneous frequenry is given by the time deriva- tive of s (n 7): '(r)=9o1r;-e!)-e(r:O. (6)dtT The gradient G"(t), in the axis q, direction, and induction .Bn(t) are computed using equations (2) and (3). The require- ment is that the frequency of nuclei without the gradient pulse influence has to be set up into resonance. The process of instantaneous frequency measurement is implied in the block diagram, Iig. 2. The FID signal is at first processed by an anti-aliasing filter (low-pass filter), followed by the A,/D converter. The digitalised FID signal s (zZ) is filtered by two digital filters. Between these two frlters the in- stantaneous frequency computation block (IFC) takes place. The first filter (DFl) processes the FID signal in the time domain, the second (DF2) in the instantaneous frequency domain. Fig. 2: Block diagram for the IF method J1 Acta Polytechnica Vol. 43 No. 4/2003 Filtering a noised FID signal with variable frequency using ' classical digital filters is a big problem; parricularly in the sec- ond part in the time domain, the FID signal has a very small S/N ratio. The output signal has a large distortion, which is caused by the transient response of the common FIR filters used [0]; the error of measuremenr is too iarge. This dis- advantage can be removed by the adaptive digital filtering method. 4 IFSE method The principle of the IFSE method is identical to rhe IF method. The pulse sequence of the IFSE method is illustrated in Fig. 3. Frrst a gradient pulse of 2 s length is initiated based on the selected direction. After stabilisation of the eddy cur- rents in the conductive parts of the MR magnet the nuclei are excited in the presence of the gradient by the selective n/2 high frequency pulse of 1.8 ms length. After time TE (4 ms) the nuclei subside and FID quickly drops. The second selected pulse I (3.6 ms) turns the direction of the nuclei rota- tion and after a certain time spin echo will be created. The MR signal obtained during the measurement is con- sequently processed in the MATLAB environmenr. The instantaneous fiequency is determined from the time deriva- with a single rhin spectral line to achieve suflicient precision of the measurement. The time gradient characteristic is proportional to the in- stantaneous frequency of the complex MR signal. The MR signal used for later processing is the sum of the FID signal after the n pulse and the spin echo. For consecutive MR signal processing it is important that the spin echo continually extends the FID signal and together they form a continuous signal. The shape and position of the envelope of the spin echo is not important for the process of measuring the magnetic field decay. It is important that the MR signal with suflicient signal to noise ratio lasts as long as possible and that the enve- lope does not pass zero. At intersection with zero, the phase changes by a step and results in undesired impulse errors in the sequence of the instantaneous frequency of the MR sig- nal and in the measured time characteristic of the gradient magnetic field. The time characteristic of the decaying gradi- ent magnetic field can be measured to a maximum of l8 ms. 5 IFSES method The IFSES method is a modification of the IFSE method and partially eliminates its main disadvantage. The basic principle of the IFSES method is the same as for the IFSE method [2]. The difference between rhese two merhods is rhar IFSES is founded on the sum of the MR signals with echoes, measured at variable echo times 'f" in order to extend the MR signal scanning time. By generating and adding of the spin echoes in di{ferent times we receive a continuous MR signal. The times 7, are chosen so that the individual echoes overlap each other. The pulse sequence of the IFSES method is pre- sented in Fig.4. The shape and position of the spin echo envelope are not important for the measurement of a decrease in magnetic field. It is substantial that the MR signal with a high S/N ratio s (fl o(r) Fig. 4: Pulse sequence for the IFSES method disappears for a suffrciently long time and its envelope does not go through zero. Ifthe envelope passes through zero it results in a step change of the FID signal phase, and in an undesirable impulse error in the sequence of the insranra- neous frequency. The computed time characteristics of the gradient magnetic field are not correct in this case. Fig. 3: Pulse sequence for the IFSE method tion of the phase of the digitalised complex MR signal [l]. The total of the magnetisation vectors z of particular excited nuclei in the whole excited space is represented by an inte- gral. In our case the excited space is a thin circle layer placed in location xo and in coordinater. The spin echo arises in the location ,' = Tt. We measure signal s (t') and for one echo it is: The centre of the spin echo occurs in time Tru (10 ms). The spin echo is not symmetrical and does not have a maxi- mum in fEafter termination of pulse n, as in the case in classi- cal MR spectroscopy. This is caused by the dropping ampli- tude of the gradient magnetic field. We have to use a sample 32 (7) tt -! r(t')= I lm.e Iz IT slite Acta Polytechnica Vol. 43 No. 4/2003 I'ft')= f'{r). '-'E urin 20 30 40 50 Time [ms] Fig. 5: Example of an MR signal for ir G, gradient IF METHOD 30 40 50 Time [ms] I FID The time characterisrics of a decreasing magnetic field in an ISI tomograph can be measured up to 80 ms, whenthe S/N ratio of the FID signal is suffrciently high for consecurive processing. An example of an MR signal for a.G" gradient is presented in Fig. 5. The MR signal obtained during the measurement is consequently processed in the MAILAB en- vironment. The instantaneous frequency is determined from the time derivation of the phase of the digitalised complex MR signal []. The total MR signal of all echoes is: I -0 (t) hl (8) -1 80706010 S12 .E, d10 o) ?8 E a4 b 18 16 ._-l E '' - tz k tu =o(ro 18 16 14 E E r lfl Ceov =Eo 4 2 n IFSE METHOD Time [ms] Fig. 6: Comparison of gradient Gr decay time characteristics measured by IF, IFSE, and IFSES methods JJ Acta Polytechnica Vol. 43 No. 4/2003 6 Experimental results An MR tomograph with a field intensity of 4.7 T is equipped with a gradient system with an inner diameter of 200 mm composed of four gradient coils (G,, Gr, G"ancl Bo). The gradient coils G, and G, are constructed on a printed circuit board, coils G" and Bo are cylindrical and they are wound around with a copper conductor. All gradient coils are placed in the instantaneous vicinity of the non-conductive wall of the cryostat. Conductive layers in the viciniry of the gradient system are formed with a skeleton of the supra-con- ductive magnet, its temperature-shielding layers and other parts of the magnet. The maximum currenr going through the gradient coils, /*= +60 A ilduces the gradient of the magnetic field G*o=-1100 m?m. The measurement was realised at the gradient Go= 'r20 m?m (a is a direction of the used gradient -f;, ) or z), 'lhe pulse sequence presented in Frg. 4 was used during the measurement. A thin layer was excited by a rectangular n/2 RF pulse. For a gladient at rhe amplitude of 20 mT/m the thickness of the excited layer is 0.94 mm. Reversing the RF n pulse will create a spin echo, and the MR signal is formed by resonating nuclei in the layer 0.47 mm in thickness. For offset of 6000 Hz and a gradient of 20 mT/m the excited layer was at a distance of 9.4 mm from the centre of the measured specimen, formed with a sealed glass ball with a diameter of 36 mm, filled with distilled water. Homogeneity was achieved with tuning of the basic magnetic field l.t0-7 on the ball with a diameter of 36 mm. The MR signal was taken for 80 ms, which is 100 ps before switching off the gradients. To prevent the influence of noise, the MR sig- nal was accumulated five times. The time characteristics of the decay times of the G,, G,, G, gradients of the magnetic field and the induction of the basic magnetic field.Bo were measured by the IFSES m€rhod in the working space of the tomograph without the assessment of preemphasis. Double adaptive filtration and averaging were used for the MR signal processing. A comparison of the G, gradient time decay characterisrics obtained by the I[ IFSE, and IFSES methods is presented in Fig. 6. From the courses of the curves, it is obvious that all three methods give the same results in the interval up to 2.5 ms including systematic errors of measurement, The IFSES method gives the same results in the time interval of up to 18 ms as the IFSE method, but it enables measurement of time characteristics of the fields even 80 ms after the gradient pulse disappears. This interval is sufficiently long for accurate computation of the preemphasis constants, The time charac- teristic measured by the IFSES method is not complete; the G* gradient field decreases to a level of 29 Vo in the course of l8 ms after the end of the pulse. The gradient declines to the inhomogeneity level up to I s, or 2 s. 7 Conclusion From a comparison of the IF method and the hvo merh- ods with spin echo for measurement of the gradient magnetic field time characteristics in MR systems, it is clear that the application of spin echo prolongs the interval when the time characteristics are measurable with sustained accuracy. A comparison of the IFSE and IFSES methods gives the same results, including systematic errors of measurement, in the 34 interval to 18 ms. From the results obtained by measurement it follows that both methods are convenient for simple and quick characterization of the gradienr magnetic field in MR tomographic magnets. The IFSES method prolongs the inrerval of gradient mag- netic field time decay characteristics measurement four times more than the IFSE method. This prolongation is substantial for the computatiorr of preemphasis constants and for their accuracy. An MR signal up to 80 ms after the end ofa gradient has a suffrciently high S/N ratio, and the resuhs are sufficient for subsequent processing. The described measurement techniques enabled exact adjustment of preemphasis constanrs in the MR system in the Institute of Scientific Instnrments. This adjustment shows a significant sensibility to the exactness of the gradient fields course rneasurement. It was achieved, in comparison with other published techniques, the adjusrment of preemphasis especially in the area up to I ms after the end of a gradient pulse. Acknowledgment This study has been supported by Grant No: A2065201 of the Grant Agency of the Academy of Sciences of the Czech Republic. References tll Chanklj, J., Lefevre, J. 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Karel Bartuiek, DrSc. e-mail: bar@isibrnci.cz Academy of Sciences of the Czech Republic Institute of Scientific Instrurnenrs Krdlovopolskd 147 :, 612 64 Brno, Czech Republic Ing. Eva Gescheidtov6, CSc. e-mail: gescha@feec.vutbr.cz Department of Theoretical and Experimental Electrical Engineering Brno University of Technology Faculty of Electrical Engineering and Communication Purkyfiova ll8 612 00 Brno, Czech Republic 35 Scan1 30 Scan1 31 Scan1 32 Scan1 33 Scan1 34 Scan1 35