Patent Application: US-97520707-A

Abstract:
a method for homogenizing a static magnetic field with a magnetic field distribution b 0 for nuclear magnetic resonance spectroscopy by adjusting the currents c i through the shim coils , thus creating spatial field distributions c i · s i , where r stands for one , two , or three of the spatial dimensions x , y , and z , and said magnetic field distribution b 0 has only a field component along z , in a working volume of a magnetic resonance apparatus with one or more radio frequency coils for inducing rf pulses and receiving rf signals within a working volume , said rf coils having a spatial sensitivity distribution of magnitudes b 1 k , and with shim coils for homogenizing the magnetic field within the working volume , said shim coils being characterized by their magnetic field distributions per unit current s i and having components only along z , includes the following steps : mapping the magnetic field distribution b 0 of the main magnetic field , calculating a simulated spectrum i s based on the sum of the magnetic field distribution b 0 and the additional field distributions c i · s i generated by the shim coils , and on the sensitivity distributions b 1 k of the rf coils , optimising a quality criterion derived from the simulated spectrum i s by using an optimisation procedure within a search range with the shim currents c i as a set of parameters , whereby for each new set of parameter values step has to be repeated , realising the found optimum of the quality criterion of step by generating the associated target field distribution b 0 t . in this way a direct one - to - one link is obtained between a set of shim currents and the associated nmr spectrum the quality of the desired nmr spectra can be improved with this method .

Description:
fig1 shows the main building blocks of the nmr spectrometer . the nmr spectrometer comprises an experimental magnet area 1 , a spectrometer area 2 with electronic components , and a computer 3 for controlling and evaluating the experiment . the experimental parameters such as gradient pulses and rf pulses and shim values as requested by the computer 3 are realised by gradient coils 4 , rf coils 5 and shim coils 6 respectively within the magnet area 1 via the spectrometer area 2 . the nmr signal received from a sample 7 is transferred to the computer 3 , usually in a digitised form . in most cases , rf coils 5 and gradient coils 4 are part of a probe head , whereas the shim coils 6 are mounted in the magnet bore . fig2 shows a flow chart of the iterative approach used with conventional search and gradient shimming methods . from the data obtained in an nmr measurement a criterion is calculated . if the result fulfils the requirements the procedure is stopped , otherwise new shim currents are calculated according to an algorithm . after setting the new shim values , the nmr data is updated etc . each iteration consists of spectrometer operation ( hatched box ) as well as calculations ( white box ). with search methods the optimisation happens during the iterations . with gradient shimming the “ optimum ” choice of the shim values happens implicitly during a single run while iterating aims at benefiting from an increasingly improved homogeneity . in fig3 a flow chart of the procedure for optimising the simulated nmr line shape is shown . the structure is in complete analogy to conventional shimming with a parameter search . only the parts of the “ spectrometer operation ” are replaced by simulation . from the input field maps b 0 and b 1 the simulated spectrum is calculated . the criterion derived from the spectrum enters the optimisation algorithm ( elements marked with bold lines ). after new shim values were determined , the application of them is simulated by adding the accordingly weighted shim functions to b 0 . the results associated with the found optimum are a set of shim values and the residual b 0 used as a target field in the subsequent shimming procedure . fig4 shows a flow chart of the iterative approach for gradient shimming with a target field . after mapping the field an absolute criterion is calculated and the procedure is stopped for a satisfying result . otherwise the optimisation ( bold frame , see fig3 ) is performed with the desired criterion resulting in a target field distribution associated with the found optimum solution . after setting the new shim values the fitting iteration loop is entered . field mapping is followed by comparison of the current with the target field by means of the fit criterion , e . g . the sum - of - least - squares . the fit procedure is iterated until the measured field is close enough to the target to ensure the fulfilment of the determined optimum solution . as an alternative to stopping at this stage the optimisation loop can be entered again ( dashed line ). this outer loop aims at benefiting from a potentially improved homogeneity as similar done with conventional gradient shimming ( see fig2 ). differences between optimisation and fit loop are emphasised with bold letters . the enclosing boxes correspond to those in fig2 . here , the calculation of a simulated spectrum is described for the simple excitation - acquisition nmr experiment . more complicated experiments require the simulation being adapted accordingly . the present approach consists of refinement of the measured data , calculation of the density - of - states ( dos ), and convolution with the natural spectrum . in the following description it is assumed that the b 0 ( r ) map is given in frequency units of the nucleus of interest . spatial refinement means interpolation between neighbouring data points of the measured b 0 ( r ) map . it is necessary in order to prevent rapid field variations being reflected in the dos as discontinuities . the smallest width δf of a natural line used for the spectrum serves as a basis to determine the required degree of refinement . furthermore , in order to save computation time the degree of refinement can be varied locally depending on the field gradient present in the b 0 ( r ) map . with and without refinement each data point must be weighted according to the size of the represented volume element . the dos of the refined b 0 ( r ) map is calculated as a histogram of the b 0 values present in the map . a reasonable bin size is chosen in dependence on δf . when calculating the dos the influence of the ( normalised ) b 1 sensitivity must be taken into account by weighting a b 0 data point at a location r with with the first factor accounting for the excitation of maximum flip angle α and the second one for the signal reception . the final spectrum is calculated as the convolution of the spectrum consisting of the lines of natural width with the dos . the natural width should be selected such as to reflect the width of the expected lines in the real sample to be measured . in doing so the optimisation is not irritated by variations of the dos not relevant for the result of interest . the grid size of the frequency axis is again chosen based on δf . beside the commonly used criteria such as maximum height or full width at different heights of the spectrum , more sophisticated criteria are required to judge the shape of the line , for example smoothness , symmetry , or the envelope of a spectral line . the aim is to penalise deviations of the spectral line from a smooth shape , e . g . extra peaks or bumps . assuming a single spectral line i ( f ), the basic idea is to compare a line with a smoothed version of itself i smooth ( f ). however , simple smoothing of the line would flatten also the main peak which is not desired . therefore smoothing of a spectral line is performed in the following way : 1 . the spectrum is separated into the two parts to the left and to the right of the maximum intensity value . 2 . each part is smoothed separately with a kernel of given maximum size ( e . g . δf ). however , the kernel size is limited to twice the distance from the border that is the closer one to the frequency point to be smoothed . thus for points very close to a border less smoothing is performed . 3 . the two parts are merged again to form i smooth ( f ). the symmetry criterion compares the two parts to the left and to the right of the maximum intensity of the spectral line , which is located at f max . the sums run from f = 0 up to f = f border , where the latter is limited by that spectrum border that is closer to f max . useful envelope shapes for spectral lines are e . g . lorentz , gauss or tsallis [ 5 ] curves , which have the advantage that they can be described in a closed mathematical form with the parameters position , width , and maximum height or integral . only the tsallis function has the additional parameter q that determines the transition between lorentz and gauss function . in contrast to that e . g . the voigt curve cannot be described in such a simple manner , thus leading to a considerably larger computational effort . the main property of the envelope of a spectrum is that it must fit closely to the spectrum while never running below it . in order to find the envelope env ( f ) of a given shape fitting best to a spectrum i ( f ) the parameters are varied by means of an optimisation algorithm to minimise the difference between the two curves while for all available frequencies the intensity of the spectrum must not be larger than that of the envelope . to enable the use of a simple optimisation algorithm working on a smooth , continuous criterion for this task , the penalty function to be minimised is defined in the following way : the parameters “ course ” and “ fine ” serve for adjusting the strictness of the envelope condition , where “ course ” controls the overall fit and “ fine ” may be used to accept or not to accept small deviations from the condition . reasonable values are e . g . course = 4 and fine = 100 . useful criteria derived from the envelope are e . g . the height , the full - width - at - half - maximum or the remaining difference between envelope and spectrum : multiple criteria crit i can be combined in various ways , e . g . by simple weighted addition with weighting factors weight i , to enable using them in an optimisation algorithm with a single criterion : important aspects of the optimisation procedure are the start values , the search range , the selection of a reasonable set of shim functions , and an the conditioning of the problem . the start values for the shim currents , which determine the centre in the search space around which the optimisation should happen , are reasonably solutions proposed by the lsq algorithm weighted with w ( r ). multiple optimisations with start values based on different weightings could be performed and compared . the search range used by the optimisation should reflect the available range of the current supply of the shim system . on the one hand , strict limitations to shim currents and power given by the shim system hardware can be taken into account by using an algorithm that constrains the search parameters . on the other hand , the order of magnitude of reasonable changes must be provided . also , the relative range of the currents for the different shim functions is of particular importance . therefore , a measure for the “ effect per effort ”, or efficiency of a shim function is required , where both effect and effort can be chosen in different ways . the direct approach to the effect of a certain shim function is the change it can cause to the chosen criterion starting from the field distribution b 0 start ( r ) created with the start values . effect i = criterion ( b 0 start ( z )+ c i s i ( z ))− criterion ( b 0 start ( z )) depending on the limitations of the shim current supply the current applied to or the power dissipated in the shim coil can serve as the effort . effort i = c i or effort i =√{ square root over ( p i )}=√{ square root over ( r i c i 2 )}= c i √{ square root over ( r i )} or effort i = p i in this way the efficiency becomes a function of the current c i and a threshold for the efficiency can be used to determine the search range for each shim function . however , this approach requires calculation of the effect , i . e . the criterion , for several values of c i which can be avoided by making the effect linearly dependent on the current . as an approximation to the problem the starting b 0 is assumed to be zero and the weighted lsq sum is used as a criterion , thus the effect becomes in case of the current being used as the effort , the efficiency is then independent of c i and it can be used for setting the relative range of the different shim functions . the efficiency can furthermore be utilised to automatically select the shim functions that are reasonable to apply in a situation determined by the current b 0 inhomogeneity . to this end the efficiency of each shim is put into relation to the standard deviation of the current b 0 ( r ) weighted in the same manner , and a threshold is applied for the selection of the shims to be used . in the iterative procedure this leads to the order of the shimming being increased for successive iterations of the optimisation . finally , the condition of the optimisation problem and hence the convergence of the applied algorithm may be improved by orthogonalising the selected set of shim functions with or without weighting by w ( z ). an important part of the gradient shimming method is the determination of the shim maps , i . e . the spatial distribution of the fields generated by the shim coils . conventionally this is performed with the same nmr mapping procedure as the b 0 field map employing the gradient coil ( s ) mounted on the probe head . however , there are several disadvantages coming along with this approach : 1 . performing the mapping for all shim functions is a time - consuming procedure , in particular if three spatial dimensions are resolved . 2 . reusing shim maps for a different probe head is not trivial . this is due to potentially ( i ) different position and angular orientation of the gradient coil with respect to the shim system , and ( ii ) different spatial characteristics of the gradient fields leading to image distortions . 3 . reusing shim maps with the probe head they were acquired with after detaching and reattaching it may be hampered by changes in position or orientation . 4 . measured shim maps are prone to errors such as noise and phase wrapping . furthermore , the obtained information is limited to the sample range and the sensitive range of the rf coil used for acquisition . especially in the border regions with relatively low sensitivity large errors can occur . on the other hand , in these regions often very large b 0 distortions are present making them particularly important for shimming . 5 . a further image distortion error is introduced by the mere presence of b 0 field inhomogeneity that superposes the imaging gradient . this effect is non - negligible when shim functions of high order are mapped with a relatively weak imaging gradient . in this case strong local field gradients shift the respective data points to a considerable degree . as usually the b 0 field map is acquired using the gradients mounted on the probe head , the centre of the map is identical with the gradient centres ( defined by a zero field value ). moreover , the image axes are given by the orientation of the gradient axes . in order to enable reusing the shim maps acquired with a certain probe head their position and orientation must be given with respect to a coordinate system attached to the shim system . a suitable set of shim functions can serve to define this coordinate system by mapping their 1d projections onto the gradient axes . this means that a certain current is applied to the respective shim coil and 1d mapping is performed with one of the probe head gradients . ( as usual , a reference map without the shim function applied is also required .) depending on the possible motional degrees of freedom and the number of spatial dimensions of the maps this approach leads to a couple of 1d mapping procedures that can be accomplished for each probe head in a relatively short time . the different sets of projections are then used to match the shim maps with the field map of the current probe head . as an example , in the case of the single translational degree of freedom of a shift along z a suitable shim function to use for position calibration is e . g . the quadratic function z 2 . the map of this function allows identifying the centre of the shim system in the z dimension , i . e . the position of the extremum of the parabola . due to various restrictions gradient coils built into probe heads do not provide a perfectly linear field in the sensitive range of the rf coil . therefore maps acquired with such a gradient suffer from distortions leading to non - equidistant positions of the data points , in particular in the important border regions . in order to match the field data with the shim maps acquired with a different probe head equipped with a different gradient coil , the positions of both the field and the shim maps must be corrected using knowledge of the actual fields generated by the gradient coils . the latter can be obtained either by calculation from the coil geometry or by some kind of nmr or other field measurement . distortions caused by the b 0 inhomogeneity itself have the awkward property to be different for each shim and field map . therefore , in principle the data grids for different maps never match . however , usually the introduced shift is far below the distance of the data points and hence negligible . nevertheless , there may be situations where it plays a considerable role , e . g . for the mapping of high order shim functions or b 0 fields with strong gradients at the ends of the rf coil . in these cases the pixel shifts can be corrected for in a first - order approach by taking into account the local gradient derived from the b 0 map itself . finally , it is proposed to completely dispense with the mapping of the shim functions and use theoretical maps instead . the latter can e . g . be obtained by magnetostatic calculations using the geometrical and electrical properties of each shim coil . furthermore , the influence of the surrounding ( e . g . superconducting magnet coil and dewar ) can be taken into account . this approach requires application of the described methods for position calibration , gradient non - linearity correction , and possibly b 0 field distortion correction to match the acquired field maps with the coordinate system of the given theoretical shim maps . slight differences between the theoretical and the actual field distribution are compensated in an iterative approach as described above the advantages of this approach are considerable time - savings and the availability of shim maps of unlimited range and free of measurement errors . the basis for a good results from gradient shimming obtained one way or the other are good nmr field map data . this requires the sequence parameters being chosen optimally . however , the optimal choice of some parameters depends on the b 0 inhomogeneity to be mapped itself . therefore , it is proposed to adapt certain parameters during an iterative gradient shimming procedure based on the latest field map information available . thus the required data quality is achieved in the minimum measurement time . as a measure for the b 0 inhomogeneity e . g . either its standard deviation can serve or the maximum field gradient observed in the map , depending on which parameter should be optimised . in particular , the signal - to - noise - ratio ( snr ) of the field map must be adapted to the variations of the map itself and to the order of the shim functions used . this can be accomplished amongst others by modification of the number of averages , the receiver bandwidth ( associated with the strength of the imaging gradient ), and the difference of the two echo times δte . however , all of these parameters have contradictory effects making their optimisation important . increasing the snr with more averages increases the measurement time . increasing the snr by reducing the bandwidth leads to an increased acquisition time and a lower gradient strength . the former causes signal loss due to dephasing and an increased measurement time while the latter gives more emphasis to distortion problems . the echo time difference again needs snr optimisation in itself , as a large δte gives larger phases differences for a certain field offset but also favours signal dephasing . furthermore , unwrapping strong phase wraps may become too difficult . simulations were performed based on nmr data acquired with a one - dimensional ( 1d ) field mapping procedure . the b 0 inhomogeneity and the b 1 field of the coil were resolved along the direction z of the main magnetic field . as a “ virtual ” sample free protons were used . in the nmr experiment a 90 - degree excitation was followed by the acquisition . six polynomial shim functions up to the fifth order were used , including a constant function . for the optimisation an unconstrained simplex algorithm was used . fig5 a shows an 1d map of the static magnetic field distribution b 0 and fig5 b shows an 1d map of the b 1 sensitivity of the rf coil . both maps are the result of an nmr field mapping procedure acquired at 300 mhz . b 0 ( z ) was derived from the phase and b 1 ( z ) from the magnitude data , assuming that shimming and the nmr experiment are performed with the same coil . the z dimension is along the direction of the b 0 field as well as the sample axis . the b 0 field is given in frequency units for protons . simulated spectra are shown in fig6 a - e . the simulation was performed for a single proton line of lorentzian shape with a width of 0 . 3 hz using six polynomial shim functions up to the fifth order , including a constant function . the intensity of all spectra is given in arbitrary but equally scaled units . the spectrum shown in fig6 a has been obtained with a weighted least - squares ( lsq ) algorithm . the lsq line is relatively narrow but shows a splitting of the main peak , an extra peak at 1 . 3 hz , and a slight bump on the left hand side of the line , which are unfavourable properties . spectra obtained with shape optimisation with various criteria applied are shown in fig6 b - e . all results show an improved shape without any compromise towards height or width . optimisation of the line shape in fig6 b was performed by minimising the difference from an envelope with a tsallis shape [ 5 ] with q = 1 . 5 . without much change in width or height of the line the peak splitting is greatly reduced and the extra peak is removed , however , at the price of an increase of the bump . for obtaining the spectrum shown in fig6 c a criterion for quantifying the smoothness of the line was added to the difference criterion of used in fig6 b . as a result , the peak splitting as well as the bump is completely removed . in the spectrum of fig6 d a symmetry criterion was added to the spectrum of fig6 c resulting in a slightly more symmetrical shape . finally , adding the width of the envelope as a further criterion in fig6 e leads to a slightly narrower line , however , at the price of some distortion of the shape . a selection of b 0 fields associated with the spectra is depicted in fig7 a - c . fig7 a shows the b 0 field associated with the simulated spectrum of fig6 a which has been obtained with a weighted least - squares ( lsq ) algorithm . in fig7 b the b 0 field is shown which has been is associated with the spectrum of fig6 d and shows an optimised line shape with a criterion combined from envelope difference , smoothness , and symmetry . fig7 c shows the comparison of the spectra of fig7 a and fig7 b displayed with a zoomed b 0 axis . it shows only little differences of the two results , however , leading to important differences in the spectra . u . s . pat . no . 5 , 218 , 299dunkel r . method for correcting spectral and imaging data and for using such corrected data in magnet shimming . 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