Patent Application: US-64550509-A

Abstract:
a method for accelerating data acquisition in mri with n - dimensional spatial encoding has a first method step in which a transverse magnetization within an imaged object volume is prepared having a non - linear phase distribution . primary spatial encoding is thereby effected through application of switched magnetic fields . two or more rf receivers are used to simultaneously record mr signals originating from the imaged object volume , wherein , for each rf receiver , an n - dimensional data matrix is recorded which is undersampled by a factor r i per selected k - space direction . data points belonging to a k - space matrix which were not recoded by a selected acquisition schema are reconstructed using a parallel imaging method , wherein reference information concerning receiver coil sensitivities is extracted from a phase - scrambled reconstruction of the undersampled data matrix . the method generates a high - resolution image free of artifacts in a time - efficient manner by improving data sampling efficiency and thereby reducing overall data acquisition time .

Description:
the present invention achieves an increased efficiency and thus time saving in spatial encoding of mr signals based on a combination of the non - linear spatial modulation of the phase of the signals with efficient signal reception using an rf receiver coil array . the scope of the present invention extends beyond the combined use of linear gradients for primary spatial encoding and quadratic phase modulation to achieve phase scrambling ; indeed non - linear magnetic fields , as in patloc approach [ 12 ] or a combination of those fields with linear gradients may be used for primary spatial encoding in combination with a phase modulation function having a significantly non - linear representation in the distorted coordinate space defined by the primary encoding fields . e . g . phase modulation of the third or fourth order may be used in combination with a quadrupolar encoding fields . additionally , more than a single phase modulation function can be applied to the different steps of the primary spatial encoding . for the sake of clarity , only the quadratic phase modulation combined with the linear gradient spatial encoding is described in more detail below . the following section considers , without loss of generality , the case of one - dimensional spatial encoding of a sample placed within a homogeneous rf coil ; multidimensional mri formulation and extension to receiver coil arrays follow as trivial generalizations of the described approach . k - space signals of a sample with a magnetization density β ( x ) ignoring relaxation , b 0 and b 1 inhomogeneities can be expressed as follows : where integration is performed over the sensitive volume of the receiver coil ; k max and δx are the k - space sampling extent and resolution in image space and are introduced into the right hand equation based on the k - space sampling definition , where k max δx ≡ 1 . upon introduction of dimensionless variables : s ( η k max )=∫ ρ ( ξδ x ) exp (− iπη 2 ) exp (− iπξ 2 ) exp ( i π ( η − ξ ) 2 ) δ xdξ . ( 4 ) by defining a chirp function g ( θ )= exp ( iπθ 2 ), modulated spin density and modulated k - space signal variables can be introduced as : which enables to simplify greatly equation ( 4 ). indeed , modulated signal intensity can now be expressed as a convolution of the modulated spin density with the chirp function as : the chirp function used as a convolution kernel in equations ( 6 ) and ( 7 ) is a pure phase term , which upon using the fourier convolution theorem and explicit fourier transform of a gaussian function , permits one to formulate the image reconstruction problem in terms of a convolution with a conjugated chirp : the above derivations of the convolution interpretation of mr image reconstruction are entirely equivalent to the traditional fourier transform . however , the presence of a convolution with an explicit kernel invites study of properties of this convolution kernel in more detail and investigation of the possibilities of changing this kernel to subsequently modify properties of image reconstruction . noteworthy is also that equation ( 8 ) describes a transformation from the frequency to the spatial domain without a fourier transform . to efficiently calculate equation ( 8 ) a fourier convolution theorem may be applied making it equivalent to equation ( 9 ) in [ 11 ]. in analogy with this publication , we consider a convolution kernel modified as : where α is the scaling parameter , defining the resolution and fov of the reconstructed image . as shown previously by us [ 13 , 14 ], sampling properties such as aliasing can be directly observed from a discretization of the modified kernel in equation ( 9 ). in order to be able to suppress aliasing with scaled kernels , a further modification of the kernel is required : where w α ( θ ) is a window function normalized accordingly to preserve the resulting image intensity . a variety of window functions can be employed , e . g . a fermi band - pass filter . for the convolution reconstruction with a windowed kernel to work properly , e . g . to be able to create an alias - free full fov image , the window size must be large enough for the kernel to be able to reallocate the k - space signals to the appropriate positions in image space . for zoomed - in image reconstruction with the scaling parameter α & gt ; 1 , the window function must have an extent smaller than the full image fov to suppress aliasing . correspondingly , in order to allow for the image intensity to be correctly transferred from k - space to image space with the windowed kernel , k - space echo locations from different image regions need to be modified . this can be achieved by inducing a phase modulation prior to the primary gradient encoding . the induced k - space echo shift in pixels must be large enough for signals from all image locations : where δk ( x ) is a k - space echo shift for the location given by x , and w is a distance from the window function center to its cut - off edge . equation ( 11 ) shall be fulfilled either for + or − sign on the right hand side . it is essential to the present invention that mr signals are treated prior to or during the signal acquisition process in such a way that the recorded k - space signals are reallocated compared to the normal untreated situation , when signals in the source space are typically assumed to have approximately zero phase . the goal of this signal treatment is to separate k - space echoes originating from different locations within the object . the correlations between k - space and object space are combined with those introduced by use of a plurality of inhomogeneous receiver coils comprising the receiver coil array to allow for an accelerated spatial encoding , resolution and snr improvement and suppression of residual artifacts . the most trivial way to fulfill equation ( 11 ) is to prepare the mr signals for the k - space echo shift to be proportional to the position in object space . according to the fourier shift theorem , k - space shift is proportional to the local gradient of the signal phase . therefore the desired k - space signal allocation can be achieved if the derivative of the signal phase in object space is proportional to the coordinate . a quadratic phase modulation function where β describes the strength of the applied modulation , clearly fulfills this requirement . the strength of the quadratic phase modulation controls the extent of the k - space echo offset and defines the maximum resolution of the alias - free image reconstructed using the convolution method . in accordance with the present invention , the applied phase modulation should be sufficient to describe the sensitivities of the used receiver coils with accuracy sufficient for artifact - free image reconstruction . excessive phase modulation in the object will result in intravoxel signal dephasing . for the given resolution and imaging settings , a range of optimal phase modulation exists , where the modulation readily provides additional information but does not cause intravoxel dephasing . phase modulation rules can be generalized to the case , where non - linear magnetic fields are used for the primary spatial encoding . in this case in addition to the object space and the k - space , an additional so - called encoding space is defined , whose geometry and topology is characterized by the encoding fields used [ 15 ]. hence , phase modulation applied to the object shall approximate equation ( 12 ) in the encoding space . alternative phase modulation functions might be of advantage to improve conditioning of the image reconstruction . amongst them , a pseudo - random modulation deserves special mention . this modulation will result in pseudo - random k - space echo shifts , essentially distributing signals over k - space . if this modulation is too strong , signal loss due to intravoxel dephasing in object space will result . however , for moderate modulations , low - resolution artifact - free images may be recovered from a fraction of k - space data . in accordance with the present invention , as depicted in fig1 , acquisition of the image of an object begins with a selective or non - selective excitation of the spins , followed by or combined with modulation of the phase of the exited magnetization . the modulation function has the special property of being significantly non - linear with respect to the spatial coordinates . in case of the non - linear magnetic fields used for the primary spatial encoding , the modulation function is required to have a non - linear representation with regard to the encoding coordinate system defined by the primary encoding fields used . a single or several modulation functions can be used for different steps of the primary spatial encoding . in accordance with the present invention , parameters of the primary spatial encoding can be chosen for the resolution and / or fov of the image recovered by an inverse fourier transform of the recorded data to be lower than desired and possibly resulting in aliasing artifacts . mr signals are recorded by a receiver coil array containing two or more receiver coils with inhomogeneous sensitivities . in addition to the inverse fourier reconstruction , phase - scrambled reconstruction is also applied to the same raw data to recover images with fov and resolution different to the nominal values . the essence of the present invention lies in the observation that , in the presence of the non - linear phase modulation , the two reconstructions produce significantly different images characterized by different artifacts . combination of the two reconstructions enables one to recover an image combining the best properties of the two reconstructions , e . g . higher spatial resolution with larger fov . fig2 presents a schematic diagram of a 2d gradient echo imaging sequence , where an additional electrically controllable coil is used to induce phase modulation . the three gradient coils g slice , g phase and g read are driven by electric currents in accordance with the diagram to provide the primary spatial encoding . the aforementioned additional modulation coil is characterized by a non - linear spatial field dependence in the coordinates defined by the primary spatial encoding . depending on the realization and the performance of the modulation coil and the driving electronic circuitry , the phase modulation can be realized as one or several pulses or as a continuous current of a lower amplitude , as long as it serves the purpose of inducing a desired phase modulation across the imaged object up to the time point of the gradient echo . the method can be trivially extended to a 3d encoding scheme by adding a phase encoding gradient table to the slice axis . fig3 presents a schematic diagram of a 3d spin echo imaging sequence , where the accelerated spatial encoding in accordance with the present invention may optionally be applied to phase encoding , slice ( partition ) encoding or both encoding directions simultaneously . the three gradient coils g slice , g phase and g read are driven by electric currents in accordance with the diagram to provide the primary spatial encoding . the desired non - linear phase modulation is induced by means of either one or several additional coils characterized by non - linear field dependencies in the coordinate system defined by the primary spatial encoding . depending on the realization and the performance of the modulation coils and the driving electronic circuitry , the phase modulation can be realized as one or several pulses or as continuous currents of lower amplitude as long as it serves the purpose of inducing a desired phase modulation across the imaged object in one or multiple spatial dimensions up to the time point of the echo . the method can be trivially converted to a 2d encoding scheme by removing the phase encoding gradient table from the slice axis . a generalized concept of combining tailored rf excitation to perform spatial selection and modulation , optionally followed by or combined with an additional modulation using one or several magnetic field modulation coils ; followed by a generic 2d or 3d spatial encoding module , which may incorporate one or several refocusing pulses and optionally one or several phase modulation pulses is presented in fig4 . the described tailored excitation module can be realized by means of one or several rf pulses with constant or modulated amplitudes , constant or swept carrier frequencies , played out on a single or several rf transmitter channels , applied prior , during or interleaved with gradient or modulation fields . in the most general case , the described magnetization preparation and modulation module may be combined with an arbitrary signal readout module . a image space reconstruction flow chart for the undersampled data is presented in fig5 . in accordance with the nyquist sampling condition , application of the inverse fourier transform to the undersampled data results in images with reduced fov and thus undesired aliasing artifacts . however , the images originating from the different rf receivers are modulated with the sensitivities of the corresponding receiver coils , and this modulation occurs prior to the signal aliasing . for the k - space data acquired with the appropriate non - linear phase modulation , a phase - scrambled reconstruction can be applied , to recover low - resolution full fov images of the object . the low - resolution images of the object originating from different rf receivers are modulated by the sensitivities of the corresponding received coils . based on the fact that coil sensitivities are rather smooth , they can be estimated based on the low - resolution images resulting from the phase - scrambled reconstruction . the sensitivities recovered from the same undersampled k - space data are then used to unwrap aliased images via an application of the sense algorithm or a modification thereof to recover a high - resolution full fov image . as an optional finishing step , the high - resolution image can be combined with the low - resolution intermediate image to further improve snr of the resulting reconstruction . a schematic k - space reconstruction flow chart is presented in fig6 . in the first step , a phase - scrambled reconstruction is applied to the undersampled k - space data to recover a plurality of low - resolution alias - free images corresponding to the different rf receivers used to record the data . these low - resolution images , carrying information of the receiver coil sensitivities , are then fourier - transformed to create a synthetic k - space dataset . the dataset corresponds to the center of the fully - sampled k - space data , and hence can be used to estimate the correlations between the neighboring k - space lines arising due to use of the receiver coil array . the synthetic dataset is then used to calculate the reconstruction coefficients ( weights ) for the grappa algorithm . these weights are then applied to the original k - space data to interpolate the missing lines and thereby create an approximation of the fully - sampled k - space . optionally , the synthetic k - space center restored by the phase - scrambled reconstruction can be used to fill a fraction of the data . an inverse fourier transform is then applied to the interpolated k - space data followed by a multi - channel coil combination method of choice to recover the combined high - resolution full fov image . fig7 presents exemplary images acquired from a normal human volunteer on a tim trio 3t scanner ( siemens healthcare , erlangen , germany ) with a standard 12 channel head receiver coil array . presented is a single slice of a 3d gradient echo acquisition . fully - encoded raw data with 256 2 matrix , fov = 256 mm , 16 2 mm thick partitions were acquired with tr = 150 ms , fa = 15 ° and retrospectively undersampled to simulate accelerated acquisitions . with the a22 second order shim current offset to the maximum , te = 25 ms was required to achieve a sufficient quadratic phase modulation . the image reconstructed by fourier - transforming the fully encoded data comprising 256 k - space lines is presented in fig7 a . to test the performance of the standard sense reconstruction , a block of 32 densely sampled k - space lines in k y direction close to the k - space center was extracted to reconstruct low - resolution images and calculate coil sensitivities . the original dataset was then undersampled and fourier - transformed to produce aliased images . these images were then unwrapped according to the sense algorithm by using the calculated coil sensitivities , with the resulting image presented in fig7 b . to assess the performance of the standard grappa reconstruction , a block of 32 densely sampled k - space lines in k y direction close to the k - space center was extracted and used to calculate grappa weighting coefficients . the original dataset was then undersampled and the missing k - space lines were interpolated according to the grappa approach . the resulting k - space data were then fourier - transformed and combined into a single composite image presented in fig7 c . note that image 7 a was reconstructed using 256 k - space lines , whereas images 7 b and 7 c using 144 k - space lines , respectively . the following images 7 d - f are all reconstructed using 128 k - space lines based on the same undersampled dataset . in fig7 d , a phase - scrambled reconstruction of the undersampled dataset is presented . the fov recovery is apparent , however , the image has a lower spatial resolution and some aliasing artifacts originating from sharp edges in the image may be observed . fig7 e presents the result of the image space reconstruction in accordance with the present invention . recovery of both image resolution and fov is apparent . a certain noise increase in the areas of no signal is associated with an inferior algorithm used to extrapolate the sensitivity maps and is not an intrinsic limitation of the present approach . in fig7 f , the result of k - space reconstruction in accordance with the present invention is presented . the resolution , fov and general image quality recovery appear to be optimal , making fig7 f practically indistinguishable from fig7 c . images in fig7 e and 7f demonstrate the ability of the present invention to recover high - quality high - resolution full fov images from the undersampled k - space data sets without requiring additional receiver coil calibration measurements . further increase in image quality is expected by using specialized , more efficient phase modulation techniques and combined reconstruction strategies . at this juncture a considerable potential is attributed to iterative reconstruction techniques , which enforce a consistency between the reconstructed images and the measured data . larkman dj , nunrs r g . parallel magnetic resonance imaging . review . phys med biol 52 : r15 - r55 ( 2007 ). shannon c e . communication in the presence of noise . proc . institute of radio engineers 37 ( 1 ): 10 - 21 ( 1949 ). sodickson d k , manning w j . simultaneous acquisition of spatial harmonics ( smash ): fast imaging with radiofrequency coil arrays . magn reson med 38 ( 4 ): 591 - 603 ( 1997 ). pruessmann k p , weiger m , scheidegger m b , boesiger p . sense : sensitivity encoding for fast mri . magn reson med 42 ( 5 ): 952 - 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