Patent Application: US-89780610-A

Abstract:
a method for position dependent change in the magnetization in an object , according to a requirement in a magnetic resonance measurement , wherein radio - frequency pulses are irradiated in conjunction with supplementary magnetic fields that vary in space and over time and are superposed on the static and homogeneous basic field of a magnetic resonance measurement apparatus along a z - direction , is characterized in that non - linear supplementary magnetic fields are used , whose spatial gradient of the z - component is not constant at least at one instant of the irradiation , and that the radio - frequency pulses to be irradiated are calculated in advance , wherein progressions over time of the field strengths of the supplementary magnetic fields in the region of the object that are calculated and / or measured position - dependently are included in this calculation . this enables change in the magnetization with an at least locally spatially higher resolution and / or shorter irradiation duration of the rf pulses and supplementary magnetic fields than is feasible with linear supplementary magnetic fields produced by conventional gradient systems . in particular , this is possible under the technical and physiological conditions that currently constrain the performance of the known methods using linear supplementary fields .

Description:
fig1 schematically shows an mr measurement apparatus that is suitable for performing the inventive method . the system contains the main magnet m , with which the essentially homogeneous and static basic magnetic field is produced in a volume under examination v . the part of the object under examination that is contained in the volume under examination will subsequently be referred to as the object under examination or simply the object o . surrounding this volume under examination v , a global gradient system , comprising three sets of gradient coils gx , gy , and gz , and a local gradient system are put into the bore of the main magnet m with which different variants of local additional fields , local gradients , can be implemented by switching coils , usually multiple coils , to form coil combinations g 1 , g 2 . global and local gradient systems do not have to be implemented as separate devices but may access shared gradient coils . fig3 shows examples of 2 such coil combinations , g 1 and g 2 . in both gradient systems , additional magnetic fields with controllable duration and strengths can be superposed on the basic field . with gradient amplifiers ax , ay , az , a 1 , and a 2 that are controlled by a sequence control unit seq to produce gradient pulses at the right instant , the gradient coils sets gx , gy , gz , g 1 , and g 2 are supplied with electric power to produce the additional fields . within the gradient field system , there are multiple transmission elements , ta 1 to tan , that are together termed the transmission antenna equipment . they surround an object under examination o and are powered from multiple independent rf power transmitters tx 1 . . . txn . the rf pulses produced by these rf power transmitters tx 1 . . . txn are determined by the sequence control unit seq and triggered at the correct time . with the transmission elements ta 1 to tan , rf pulses are irradiated onto the object under examination o in the volume under examination v , where they excite nuclear spins . the magnetic resonance signals caused by this are converted into electrical voltage signals with one or more rf reception elements ra 1 , . . . , ram , but are then fed into a corresponding number of reception units rx 1 , . . . , rxm . the reception elements ra 1 , . . . , ram are together termed the reception antenna equipment consisting of m reception elements rx 1 , . . . , rxm . they are also located within the gradient coils gx , gy , gz , and surround the object under examination o . to reduce the complexity of the apparatus , the transmission and reception antenna equipment can be designed and connected in such a way that one or more of the transmission elements ta 1 to tan are also used to receive the magnetic resonance signals . in this case , which is not shown in fig1 , switchover between transmission and reception modes is assured by one or more of the electronic transmission - reception switches controlled by the sequence control unit seq , that is , that during the rf transmission phases of the executed pulse sequence , this antenna or these antennas are connected with the corresponding rf power transmitter or transmitters and disconnected from the allocated reception channel or channels , while , for the reception phases , transmitter disconnection and reception channel connection is performed . with the reception units rx 1 to rxm shown in fig1 , the signals received are amplified and converted to digital signals using known signal processing methods and passed on to an electronic computer system comp . in addition to reconstruction of images , spectra and derived quantities from the measured data received , the control computer system comp is used to operate the entire mr measurement apparatus and to initiate execution of the pulse sequences by appropriate communication with the sequence control unit seq . user - guided or automatic execution of programs for adjusting the measurement apparatus characteristics and / or for generating magnetic resonance images is also performed by this control computer system comp , as are visualization of the reconstructed images and storage and administration of the measurement and image data and control programs . for these tasks , this computer system is equipped with at least one processor , a working memory , a computer keyboard kb , a pointing device pntr , for example , a computer mouse , a monitor mon , and an external digital storage unit dsk . an explanation of how the inventive method can be performed with such an mr measurement apparatus is given below using a specific embodiment . the results shown were obtained by calculated simulation of an mr experiment in which a postulated position dependent initial magnetization is converted to a position dependent target magnetization in an object under examination by irradiation of rf pulses and the simultaneous effect of supplementary magnetic fields according to the inventive method . according to the invention , at least two supplementary magnetic fields are used ( fig2 ) that have a spatial gradient of the z - component that is not constant because the z - component depends non - linearly on position . the z - component of the superposition of these supplementary magnetic fields also has a non - constant gradient at all instants at which at least one of these supplementary fields is active . as an example of the situation described in a dependent claim , two equivalent positions are shown . it is demonstrated below for this example that if one transmission antenna is used at these two positions , an identical , and therefore only mutually dependent change in the magnetization is performed and the desired position dependent change in the magnetization is only partially implemented . moreover , it is demonstrated that when eight transmission antennas with different spatial transmission profiles are used , according to the inventive method , a different , mutually independent change in the magnetization at these two positions can be effected and the desired change in the magnetization can therefore be implemented at both positions . fig2 shows the spatial dependences of the two supplementary magnetic fields used f 1 and f 2 that can be produced with coils g 1 and g 2 of the local gradient system in fig1 , while fig3 shows the temporal progression of the amplitudes a 1 and a 2 of these fields during transmission of the rf pulses . by way of example , this therefore provides the basis for the calculation of the rf pulses according to the independent claim . the initial situation for this embodiment is magnetization m ( 0 , r ) that is position dependent in two dimensions within the object under examination , wherein the magnetization is oriented in the z - direction at each position of the two - dimensional object on a grid of 96 × 96 points with the extent 6 cm × 6 cm . the strength of this z - component corresponds to the value m z ( 0 , r )= m 0 =) cos ( 0 °)= 1 . the specific position - dependent change in the magnetization with the inventive method is to be effected in such a way that , due to the combined application of the supplementary magnetic fields and of the rf pulses , the x - component of the magnetization is given the distribution shown in fig4 , also referred to as target distribution m t ( r ). here , the areas shown in white correspond to a non - vanishing component m x of ) sin ( 90 °)= 1 and the areas shown in black represent m x = 0 . the z - component of the magnetization is to be reduced to m z = cos ( 90 °)= 0 in the white areas , while m y is to remain unchanged at zero everywhere . an essential part of the inventive method is determination of the temporal progressions of the radio - frequency pulses to be irradiated . one possible procedure for this calculation is described below , for example , without going into varied alternatives and variations that are obvious to persons skilled in the art . first of all , to solve the bloch equation iteratively below , a small - angle pulse is required as the starting point . the phase φ onto which the infinitesimal transverse magnetization produced at instant t is superposed by the supplementary magnetic fields while these fields are still being applied , is required for calculation of the small - angle pulse . this calculation is performed explicitly according to the inventive method from the known , in this case , electrodynannically calculated , spatial progressions of the supplementary magnetic fields f 1 and f 2 and the temporal progressions a 1 and a 2 defined by the sequence control of the mr measurement apparatus as herein , s l ( r ) are the transmission profiles of the rf transmission antenna associated with rf pulse shape i l ( t ). fig7 shows the relative amplitudes of the transmission profiles used . further , r denotes the position variable ; t , the time variable ; m , the magnetization ; γ , the gyromagnetic ratio of the proton ; and t = 83 . 1 ms , the total duration of the rf pulses and the application of the supplementary magnetic fields . the target magnetization distribution m xy ( r ) for the small - angle pulse design is derived from the target distribution described above ( see also fig4 ) that is set in the white areas m x = sin ( 10 °= 0 . 17 . m y is unchanged at zero . in the small - angle pulse design , m z is also assumed to be constant over time . the solution of the design equation ( 9 ) according to the eight rf pulse shapes i l ( t ) is obtained numerically after discretization and conversion into a quadratic minimization problem with the generally known conjugate gradient method . the small - angle pulses obtained in this way ( totality of the eight rf pulse shapes ) is now scaled by a factor of 9 , that is , with the ratio between the desired flip angle of the position dependent magnetization ( here 90 °) and the postulated flip angle of the position dependent magnetization in the small - angle calculation ( here 10 °). the scaled rf pulse is the starting point for the following iterative optimization by means of optimal control . the following iteration steps are now repeated until the deviation λ ( r ) of the simulated position dependent magnetization of a particular iteration from the desired position dependent magnetization is sufficiently small ( see step 2 ). the transmission field b 1 ( t , r ) is calculated from the eight rf pulse shapes and the eight transmission profiles by δ b 0 ( t , r )= f 1 ( r ) a 1 ( t )+ f 2 ( r ) a 2 ( t ) ( 11 ) is calculated from the spatial and temporal progressions . with these functions , the bloch equation starting from the initial magnetization m ( 0 , r ) is numerically integrated forward in time at each position r until total duration t , with the result m ( t , r ). here , b 1 , x ( t , r ) and b 1 , y ( t , r ) are the real and imaginary part of the transmission field and the dependence of m ( t , r ) is stored for each instant and position . by calculating the vector difference between the position dependent magnetization obtained in step 1 and the target magnetization , the deviation is calculated . if the mean value of the squares of the absolute values of λ is less than 0 . 025 over all positions , that is , the mean square deviation is therefore below 2 . 5 %, the iteration is terminated at this point and the eight pulse shapes of the current iteration are the result of the large - angle rf pulse calculation . otherwise , the calculation moves onto step 3 . is integrated backward in time using the transmission fields and the superposition of the supplementary magnetic fields from step 1 at each position r ( i . e . λ = λ ( t , r )) is the starting point for integration in negative time increments until t = 0 ), and the dependence of λ ( t , r ) for each instant and position is stored . according to the known principles of calculus of variations which are the basis for optimal control methods , improved large - angle rf pulse shapes i l ( t ) opt are calculated from the transmission profiles and progressions of m ( t , r ), λ ( t , r ) and i l ( t ) by where an increment μ = 2 . 5 × 10 − 8 was chosen . with the improved rf pulse shapes i l ( t ) opt , the calculation now continues with step 1 . fig8 shows the result of a simulation of the position dependent change in the magnetization according to a method that corresponds to the inventive method except for the number of transmission coils used . the result of using exactly one transmission coil with homogeneous transmission profile shows an unwanted multiplication of the target pattern because , if only one transmission coil is used , independent change in the magnetization is not possible at equivalent positions , such as r 1 and r 2 ( see fig5 ). the result of a simulation of the position - dependently modified magnetization according to the inventive method is shown in fig9 . implementation of the target magnetization is enabled by the additional spatial selectivity of the eight transmission antennas used , ta 1 to ta 8 in fig1 . the characteristic of a non - constant gradient of the supplementary magnetic fields can also be advantageously used to effect the change in the magnetization , according to an dependent claim , with spatially varying resolution , as is illustrated in fig1 to 12 . the change in the magnetization is initially effected according to the inventive method as shown in the above example , with the difference that the position dependent target magnetization is replaced by the pattern shown in fig1 . the result of simulation of position dependent magnetization modified in this way is shown in fig1 . by comparison with this , fig1 shows magnetization modified according to the prior art using linear supplementary magnetic fields , whose maximum amplitude in the object matches that from the inventive method . it can be seen that the spatial resolution in fig1 varies in space and that the inventive method can implement the magnetization in the edge regions of the mapping area according to the resolution of the target magnetization , whereas the method according to prior art is unable to achieve this at any point . xu , d . ; king , k . f . ; zhu , y . ; mckinnon , g . c . ; liang , z . p . : designing multichannel , multidimensional , arbitrary flip angle rf pulses using an optimal control approach , magnetic resonance in medicine 59 ( 2008 ), 547 - 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