Abstract:
A magnetic resonance image of a subject is generated by acquiring k-space samples by sampling an elliptical central area of k-space, k-space having a plurality of points. Each point is representative of a potential sample. An elliptical peripheral area of k-space which peripheral area surrounds the central area is partially sampled. Respiratory motion of the subject is detected and the magnetic resonance image of the subject is reconstructed using the k-space samples acquired before the detection of respiratory motion.

Description:
CROSS-REFERENCE TO PRIOR APPLICATIONS 
     This application is the U.S. National Phase application under 35 U.S.C. §371 of International Application No. PCT/IB2013/051449, filed on Feb. 22, 2013, which claims the benefit of U.S. Provisional Patent Application No. 61/612,522, filed on Mar. 19, 2012. These applications are hereby incorporated by reference herein. 
    
    
     TECHNICAL FIELD 
     The invention relates to the field of magnetic resonance imaging of a subject. 
     BACKGROUND OF THE INVENTION 
     Magnetic resonance imaging (MRI) methods use the interaction between magnetic field and nuclear spins with the purpose of forming two-dimensional or three-dimensional images. These methods are widely used these days, notably in the field of medical diagnostics. The advantages of the MR methods are that they do not require ionizing radiation and they are usually not invasive. MRI is used for example as imaging technique to visualize structural abnormalities of the body, e.g. tumour development. 
     An MRI apparatus uses a powerful magnetic field to align the magnetization of some atomic nuclei in the body, and radio frequency fields to systematically modify the alignment of this magnetization. This causes the nuclei to produce a rotating magnetic field detectable by a scanner. This information is recorded to construct an image of the sampled area of the body. Magnetic field gradients cause nuclei at different locations to rotate at different speeds. By using gradients in different directions 2D images or 3D volumes can be obtained in arbitrary orientation. 
     According to the MR method in general, the body of a patient or in general an object to be examined is arranged in a strong, uniform magnetic field B 0  whose direction at the same time defines an axis, normally the z-axis, of the coordinate system on which the measurement is based. 
     Any temporal variation of the magnetization can be detected by means of receiving RF antennas, which are configured and oriented within an examination volume of the MR device in such a manner that the temporal variation of the magnetization is measured in the direction vertically to the z-axis. 
     Spatial resolution in the body can be realized by switching magnetic field gradients. They extend along the three main axes and are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving antennas then comprises components of different frequencies which can be linked to different locations in the body/subject. 
     The signal data obtained by the receiving antennas matches to the spatial frequency domain and are called k-space data. The k-space data generally include multiple lines acquired with different phase encoding. Each line is digitized by collecting a number of samples. A set of samples of k-space data is transformed to an MR image, e.g. by inverse Fourier transformation. 
     Furthermore the document “Combined compressed sensing and parallel MRI compared for uniform and random cartesian undersampling of k-space” by D. S. Weller et al. (2011 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing. Prague, Czech Republic, May 2011, pp. 553-6) discloses the combination of compressed sensing and variable density random k-space sampling. Combining both methods enables imaging with greater undersampling than accomplished previously. 
     United States Published Application US 20090274356 A1 describes a method for generating a magnetic resonance image of a subject. The disclosed invention relates to magnetic resonance imaging using compressed sensing which allows recovery of a sparse signal, or a signal that can be made sparse by transformations, from a highly incomplete set of samples, and thus has the potential for significant reduction in MRI scan time. 
     SUMMARY OF THE INVENTION 
     The invention provides for a method, a medical apparatus, and a computer program product that are claimed in the independent claims. Embodiments are given in the dependent claims. 
     In accordance with embodiments of the invention a sampling strategy for magnetic resonance imaging with incomplete breathholds is provided which supports the reconstruction of images from data acquired up to any point in time. It proposes to combine a segmented acquisition with global sampling density variation and local Poisson disk sampling. The sampling strategy is thus compatible with compressed sensing and parallel imaging for accelerated scanning, and adaptable to target functions of the spatial resolution over time. The onset of respiratory motion is either detected with external or internal sensors, or is based on metrics applied to a series of images, produced from successively more data. 
     In accordance with embodiments of the invention a method of generating a magnetic resonance image of a subject is provided comprising the acquisition of k-space samples by sampling an elliptical central area of k-space, wherein the k-space has a plurality of points, each point being representative of a potential sample and partially sampling an elliptical peripheral area of k-space, wherein the peripheral area surrounds the central area. The method further comprises the detection of respiratory motion of the subject and reconstruction of the magnetic resonance image of the subject using the k-space samples acquired before the detection of respiratory motion. 
     Embodiments of the invention are particularly advantageous as they provide a reconstruction of images from data acquired during breathholds with a priori unknown length. This reconstruction avoids artifacts and thus a decrease in image quality resulting from previously methods in the case of early onset of respiratory motion. It relies on a specific profile order which makes it possible to exclude data acquired after the onset of respiratory motion from the reconstruction. 
     In accordance with one embodiment of the invention the central area is fully sampled. 
     In general, artifacts resulting from incomplete breathholds are less severe if respiratory motion occurs during sampling of the periphery of k-space, rather than the center of k-space. Thus, embodiments of the invention are particularly advantageous as they sample the central k-space fully and early on, thus reducing the risk of more severe motion artifacts. 
     In accordance with one embodiment of the invention the method further comprises increasing the half-axes of the peripheral area during the acquisition over time for increasing spatial resolution over time. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that the sampling density increases over time, corresponding to a decreasing average reduction factor over time leading to a higher image quality. 
     In accordance with one embodiment of the invention the method further comprises that the partial sampling is performed by random or pseudo-random selection of a subset of the plurality of points being located in the peripheral area. 
     In accordance with one embodiment of the invention the likelihood of selecting one of the plurality of points that has not been previously selected is defined by a k-space and time variant target sampling density. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that the sampling density becomes locally nearly homogeneous, facilitating a parallel imaging reconstruction leading to a higher quality of the reconstructed image. The term sampling density means herein the density of the sampled points. 
     In accordance with one embodiment of the invention the selection of one of the plurality of points that has not been previously selected is based on k-space and time variant minimum distances to all points that have already been selected. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that the quality of the reconstructed image becomes better due to the above mentioned sampling density which is locally nearly homogenous. 
     In accordance with one embodiment of the invention the sequence of selected points is grouped into subsequences, wherein the selected points in each subsequence are permuted to minimize artifacts resulting from system and acquisition imperfections. 
     In accordance with one embodiment of the invention the points in each subsequence are permuted to minimize the distance in k-space between points acquired in immediate succession. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that eddy current effects in the acquisition can be minimized leading to reduced artifacts arising from eddy currents. 
     In accordance with one embodiment of the invention the number of selected points in each subsequence is defined with a target maximum average reduction factor. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that the reduction factor is successively reduced which also provides a better image reconstruction. 
     In accordance with one embodiment of the invention the sampling density decreases towards the periphery of k-space. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that the fully sampled central area increases over time leading to the best available image. 
     In accordance with one embodiment of the invention the respiratory motion is detected using a magnetic resonance navigator, wherein moving of the diaphragm or the abdomen of the subject is detected, wherein the detection is performed simultaneously or interleaved with the imaging and wherein the acquisition is automatically stopped when respiratory motion of the subject is detected. 
     The duration an individual patient can actually hold his/her breath is unknown and generally unpredictable. Embodiments of the invention are particularly advantageous as they relieve the operator from guessing this duration prior to the examination and from repeating the examination in case of an overestimation. 
     In accordance with one embodiment of the invention the magnetic resonance images are reconstructed by using the k-space samples acquired before a certain point in time, wherein this point in time is successively increased, and the last image without significant artifacts is taken as the result, wherein a compressed sensing or parallel imaging reconstruction, or a combination of both, is employed for generating the magnetic resonance image. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that it enables an efficient reconstruction of images from sparse, incomplete data using both compressed sensing and parallel imaging. 
     In accordance with one embodiment of the invention the k-space samples are acquired using a magnetic resonance gradient-echo, spin-echo, echo-planar imaging or diffusion-weighted imaging sequence. 
     Embodiments of the invention are particularly advantageous as they provide a procedure that enables the users to use the best technique for a specific application. The advantage of gradient-echo techniques is primarily a faster acquisition, while spin-echo sequences provide a stronger signal and are more robust against artifacts. Echo planar imaging is even faster than conventional gradient-echo techniques, at the expense of even more artifacts. Diffusion-weighted imaging provides unique contrast between tissues and insights into cellular architecture at the millimeter scale, which is of particular interest in the field of oncology. 
     The invention provides a medical apparatus for generating a magnetic resonance image of a subject comprising the acquisition of k-space samples by sampling an elliptical central area of k-space, wherein the k-space has a plurality of points, each point being representative of a potential sample and partially sampling an elliptical peripheral area of k-space, wherein the peripheral area surrounds the central area. The medical apparatus further comprises the ability for detection of respiratory motion of the subject and reconstruction of the magnetic resonance image of the subject using the k-space samples acquired before the detection of respiratory motion. 
     The invention provides a computer program product for generating a magnetic resonance image of a subject comprising the acquisition of k-space samples by sampling an elliptical central area of k-space, wherein the k-space has a plurality of points, each point being representative of a potential sample and partially sampling an elliptical peripheral area of k-space, wherein the peripheral area surrounds the central area. The computer program product further comprises the ability for detection of respiratory motion of the subject and reconstruction of the magnetic resonance image of the subject using the k-space samples acquired before the detection of respiratory motion. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following embodiments of the invention will be described, by way of example only, and with reference to the drawings in which: 
         FIG. 1  is a block diagram of a magnetic resonance imaging apparatus. 
         FIG. 2  is a scheme illustrating the creation of k-space data through the sampling of the MR signal. 
         FIG. 3  shows the spatial resolution as function of the iterations. 
         FIG. 4  shows the reduction factor as function of the iterations. 
         FIG. 5  shows the density of sampling points and the corresponding sampling pattern after 1, 2 and 3 iterations. 
         FIG. 6  shows the density of sampling points and the corresponding sampling pattern after 5, 10 and 15 iterations. 
         FIG. 7  is a flowchart illustrating the sampling strategy for accelerated magnetic resonance imaging with incomplete breathholds. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       FIG. 1  is a block diagram of a magnetic resonance imaging apparatus. The magnetic resonance imaging apparatus comprises main magnet coils  100  being appropriate to produce a static magnetic field required for magnetic resonance imaging. The apparatus further comprises gradient coils  102 . These gradient coils  102  enable to selectively image different voxels (volume picture elements) of a subject. A patient or more generally a subject  104  is located within a typically cylindrical core of the main magnetic coils  100 . Parts of the body of the patient  104  are imaged using a coil  106 . Such a coil may comprise a transmit coil and a receiver coil, or alternatively a transmit coil being separated from the receiver coil may be additionally provided. 
     The main magnet coils  100  are controlled by a main coil power supply  108  and a power supply control  110 . The gradient coils  102  are controlled by a gradient coils control unit  116 . Also provided is a transmit coil amplifier  114 , This transmit coil amplifier  114  is connected to the coil  106 . The coil  106  itself can be adapted as a coil comprising many element coils. 
     The power supply control  110 , the transmit control amplifier unit  114  and the gradient coils control unit  116  are connected to a receiver  112 . The receiver  112  comprises an Analogue-Digital-Converter  118  being adapted to convert radio frequency (RF) signals received from the coil  106  into digital signals. Using a digital down converter  120 , the digitized MR signals can be down converted in order to reduce the data rate from the Analogue-Digital-Converter to a factor 50 or less (from e.g., 50 MHz to 1 MHz). An encoder and/or compressor  122  may even further reduce the bandwidth by making use of the MR signal properties. 
     The receiver  112  further comprises an element based merge unit  124 . The element based merge unit  124  serves the purpose of merging MR data and status data incoming to the receiver with the acquired MR data and the local status and to provide said merged information for further processing to the system. This is especially necessary, when multiple coils are connected to the receiver  112  or when multiple receivers are interlinked. 
     The receiver  112  further comprises an interface  126 . Thereby, the interface  126  is adapted for transmitting for example the down converted digital signal through a communication link over a network  128  to an RF-chain slave subsystem  130 . Thereby, the RF-chain slave subsystem  130  also possesses an interface  132 . Such kind of interface may be an over the air interface for wireless data transmission or an optical fiber. 
     The RF-chain slave subsystem  130  comprises an RF scan control unit  136  and a system based merge unit  134 . The system based merge unit  134  serves the purpose of merging MR data and status information incoming to the interface  132  from multiple receivers. It also serves the purpose of broadcasting control and status commands to all incoming fibers, said fibers incoming to the interface  132 . 
     The RF-chain slave subsystem  130  is connected to a data processing system  138 . The data processing system  138  comprises a screen  140 , an input device  142 , a memory  144 , an interface  146  and a processor  148 . The processor  148  comprises a computer program product  150 . The computer program product  150  comprises a reconstruction module  152  which reconstructs the magnetic resonance image by using an inverse 2D Fourier Transformation to transform the k-space data into a magnetic resonance image. 
       FIG. 2  is a scheme illustrating the creation of k-space data through the sampling of the MR signal.  FIG. 2  shows the principle of reconstruction of a magnetic resonance image. The k-space is the denotation for the raw data matrix in magnetic resonance imaging. These raw data are converted into an MR image using inverse 2D or 3D Fourier transformation. The measured signal includes two informations. Firstly, the frequency encoding gradients include data on the origin of the signal in the x-direction. Secondly, the phase encoding gradients include data on the origin of the signal in the y-direction (and optionally further directions). 
     All subsampling in the herein disclosed embodiments are performed along the phase encoding direction(s), while the frequency encoding direction is usually fully sampled and processed separately. As a consequence, the described sampling pattern apply primarily to 3D imaging, with frequency encoding direction k x , and phase encoding directions k y  and k z , where the described sampling pattern is applied to points in the k y -k z  plane, where each point actually represents a k-space line along k x  that is fully sampled. 
       FIG. 3  shows the spatial resolution as function of the iterations. One sampling procedure with predefined half-axes is called iteration. In detail, this means that the second sampling with the second length of half-axes is the second iteration; the third sampling with the third length of half-axes is the third iteration, and so on. The spatial resolution is restricted by the maximum average reduction factor R and the number of subsets the acquisition is segmented into after sampling the elliptical central area of k-space. Assuming that each subset contains N samples and takes a time T, the spatial resolution increases as
 
 y   i ∝( iNR+N   0 ) +1/2  and  z   i   =y   i   z   0   /y   0  
 
wherein i is the number of subsets, N 0  is the number of samples in the central elliptical area and y i  and z i  are the half-axes after i subsets. The reduction factor is the factor by which the number of k-space samples is reduced. In  FIG. 3  the development of the spatial resolution for a maximum reduction factor of 8 and 40 subsets, for an image with N y =185 and N z =102 is plotted. The first phase encoding direction (k y ) and the second phase encoding direction (k z ) are shown.
 
       FIG. 4  shows the reduction factor as function of the iterations. As in the description of  FIG. 3  mentioned the values are based on a maximum reduction factor of 8 and 40 subsets, for an image with N y =185 and N z =102. Two cases are distinguished in  FIG. 4 , the reduction factor as a function of the interations with a calibration area and without a calibration area. The underlying nominal number of samples is calculated to the momentary spatial resolution. 
       FIG. 5  shows the density of sampling points and the corresponding sampling pattern after 1, 2 and 3 iterations. As described also in the description of  FIG. 3 , the first iteration means the time interval in which the sampling of a peripheral area with predefined half-axes is executed ( FIG. 5A ). After this sampling the length of the half-axes can be increased and the time interval for the sampling of this peripheral area is the second iteration ( FIG. 5B ).  FIG. 5C  shows the third iteration which means that the half-axes are further increased and this defined peripheral area is sampled. The  FIGS. 5A, 5B and 5C  show the density of the sampling points. The  FIGS. 5A ′,  5 B′ and  5 C′ show the sampling pattern in k-space. The distribution of the density of sampled points results from two conditions: the spatial resolution steadily increases over time and the sampling density monotonically decreases toward the periphery of k-space. To generate the sampling pattern a Poisson disk sampling is used herein. Poisson disk sampling is a random distribution of samples with the additional constraint that neigbouring samples must not fall below a defined distance. Due to the above mentioned a central area of k-space is fully sampled. This area may increase over time. The sampling density drops to zero at the edge of the peripheral area respectively at the edge of the half-axes which defines the peripheral area. The random respectively pseudo-random selection of the plurality of points being located in the peripheral area leads to a nearly locally homogeneous subsampling of the peripheral area. 
       FIG. 6  shows the density of sampling points and the corresponding sampling pattern after 5, 10 and 15 iterations. As described before in the description of  FIG. 5 , iteration means the time interval in which the sampling of a peripheral area with predefined half-axes is executed. The fifth iteration is the sampling of the peripheral area after the length of the half-axes was increased for the fifth time ( FIG. 6A ). The tenth iteration is the sampling of the peripheral area after the length of the half-axes was increased for the tenth time ( FIG. 6B ). And finally  FIG. 6C  shows the density of sampling points and the corresponding sampling pattern after 15 iterations. The  FIGS. 6A, 6B and 6C  show the density of the sampling points. The  FIGS. 6A ′,  6 B′ and  6 C′ show the sampling pattern in k-space. The distribution of the density of sampled points results from two conditions: the spatial resolution steadily increases over time and the sampling density monotonically decreases toward the periphery of k-space. The maximum spatial resolution is defined by the user and the radius of the k-space respectively the length of the half-axes are not increased anymore at a certain point in time when this maximum spatial resolution has been reached. To generate the sampling pattern a Poisson disk sampling is used herein as described above. Both the maximum sampling density near the center of k-space and the decay rate toward the periphery of k-space are adapted in the course of the acquisition, while the averaged reduction factor is successively reduced, as illustrated in  FIG. 6 . This is continued until the patient starts to breathe again, which can be detected with a respiration sensor, a navigator, or in a series of images produced from successively more data, among others. If the patient is able to hold his/her breath for a really long time then it can be possible that also the peripheral area is fully sampled. 
       FIG. 7  is a flowchart illustrating the sampling strategy for accelerated magnetic resonance imaging with incomplete breathholds. The method starts in step  700  at which the sampling  702  and the detection of respiratory motion  710  start. The sampling  702  comprises the sampling of the central area of k-space  704 , followed by the sampling of the peripheral area of k-space  706 . After the sampling of the peripheral area of k-space  706 , the half-axes of the peripheral area can be increased  708 , and the peripheral area of k-space  706  with adapted half-axes is sampled again. This can be repeated until the predefined maximum length of the half-axes is reached and the enclosed k-space area is fully sampled. In addition or alternative to increasing the half-axes of the peripheral area from iteration to iteration, the k-space variant target sampling density can be adapted. During the sampling the respiratory motion is detected in parallel  710 . If no respiratory motion is detected the sampling procedure goes on, until respiratory motion is detected. If respiratory motion occurs the sampling will be stopped in step  712 . In step  714  the MR image is reconstructed by using the k-space samples acquired before respiratory motion occurred. 
     The invention has been described with reference to the preferred embodiments. Modifications and alterations may occur to others upon reading and understanding the preceding detailed description. It is intended that the invention be constructed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.