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Patent Issued for Method and Device for Uniform Radial Data Acquisition in Three-Dimensional K-Space in an MR Measurement for a Magnetic Resonance...

February 27, 2014



Patent Issued for Method and Device for Uniform Radial Data Acquisition in Three-Dimensional K-Space in an MR Measurement for a Magnetic Resonance System

By a News Reporter-Staff News Editor at Computer Weekly News -- A patent by the inventors Piccini, Davide (Erlangen, DE); Zenge, Michael (Nuremberg, DE), filed on October 26, 2010, was published online on February 11, 2014, according to news reporting originating from Alexandria, Virginia, by VerticalNews correspondents.

Patent number 8648594 is assigned to Siemens Aktiengesellschaft (Munich, DE).

The following quote was obtained by the news editors from the background information supplied by the inventors: "The present invention concerns a method and a device for radial data acquisition in three-dimensional k-space in an MR measurement for a magnetic resonance system. Moreover, the present invention concerns a magnetic resonance system with the device described above.

"In recent years radial three-dimensional data acquisition in k-space has become popular in the field of magnetic resonance tomography for a number of reasons. First, the data acquisition is very robust with regard to a movement (for example the movement of a patient in an MR examination) since, in the prevalent radial three-dimensional methods, each readout process (process in which multiple points of k-space are detected in one step) proceeds through the center of k-space. Moreover, radial three-dimensional data acquisition very simply enables a radial sub-sampling, so the sampling density (detected points per volume unit) is relatively low at the edges of k-space while it is relatively high in the environment of the center and in the center itself.

"However, the radial three-dimensional data acquisition has the following two problem areas:

"According to a widely accepted approach to radial data acquisition in three-dimensional k-space, the data acquisition is composed of multiple readout processes, and wherein points along a spoke (i.e. a straight line segment) are detected per readout process, wherein this spoke is defined by a point on a sphere and the center point of this sphere. In other words, each spoke on which the points in k-space are detected by the corresponding readout process runs through this center point (which is located in the center of k-space) and through the corresponding point on the sphere. A spoke is thus differentiated from the other spokes by the corresponding point on the sphere since each spoke runs through the center point.

"The points on the sphere (which respectively each define one of the spokes) lie on a trajectory which possesses the shape of a three-dimensional Archimedean spiral. The more points in k-space that are sampled, the more spokes exist and the more windings that the Archimedean spiral on the sphere has, so the separation of adjacent windings of the Archimedean spiral is reduced. In an interleaved procedure, for each acquisition step only every m-th spoke is sampled (when m corresponds to the number of acquisition steps). In other words--for example for the first acquisition step--the points on the spokes 1, (m+1), (2*m+1), (3*m+1) etc. are acquired while the points on the spokes k, (m+k), (2*m+k), (3*m+k) etc. are acquired for the k-th acquisition step (k.ltoreq.m).

"In this procedure a significant interleaving, i.e. m>>1, leads to a large gradient change of the magnetic field at the transition from one spoke to the next, which disadvantageously leads to artifacts which occur due to the effects of the eddy current.

"For a radial data acquisition in three-dimensional k-space wherein the data are acquired by means of 1600 spokes, the points 1 defining these spokes are shown on a sphere 4 in FIGS. 1a, 1b and 1c. FIG. 1a shows the sphere 4 from above and FIG. 1b shows the sphere 4 at an angle from above. The depicted points 1 lie on a three-dimensional Archimedean spiral which forms the trajectory by means of which the order in which the individual spokes are processed is determined.

"FIG. 1c depicts the trajectory 15 for one of these acquisition steps for the case that the entire data acquisition consists of 20 acquisition steps. The straight line segments thereby represent the transition from one spoke to the next. Since these straight line segments are relatively large at least in part, this leads to a relatively large variation in the gradient of the magnetic field that is necessary for data acquisition, which in turn induces strong eddy currents, which ultimately leads to artifacts in the imaging depending on the data acquisition.

"However, the approach described above for radial data acquisition in three-dimensional k-space has the advantage of an extremely uniform sampling, so a compensation of the sampling density is significantly facilitated. The compensation of the sampling density is understood as the process in which the different sampling density (high in the center and low at the edge of k-space)--as noted above--for the imaging is compensated, such that the density of the image points (pixels) (determined from the acquired data) in the entire sampled volume is optimally uniform.

"An additional approach to radial data acquisition in three-dimensional k-space is described in 'Temporal Stability of Adaptive 3D Radial MRI Using Multidimensional Golden Means', R. W. Chan et al., Magnetic Resonance in Medicine 61, Pages 354-363, 2009. The proposed method executes (at least in a time period) a uniform sampling of a two-dimensional normalized space, so the concept of the golden segment is used together with a modified Fibonacci series in order to distribute the points 1 on a sphere 4, wherein these points 1 respectively define a spoke for radial data acquisition. This sampling pattern is transferred to a spherical surface by the coordinates of the planar sampling points being coupled with the polar angle and the azimuthal angle within the three-dimensional space. The result of such a pattern is shown in FIG. 2a as a view of the sphere 4 from above and in FIG. 2b as a view of the sphere at an angle from above.

"This approach is aimed at an optimally uniform sampling in the time curve. Nevertheless, with a Voronoi analysis the result is reached that the sampling distribution is not particularly uniform within a time frame. This approach consequently requires a complicated compensation of the sampling density. Ultimately, exposures are not optimally avoided with this approach.

"In summary it is to be noted that the approaches to radial data acquisition in three-dimensional k-space according to the prior art are optimized either with regard to a uniform sampling density (spatial or temporal) or with regard to a suitable compensation of eddy currents (with regard to avoiding eddy currents that are too large). In most cases a complicated compensation of the sampling density is required."

In addition to the background information obtained for this patent, VerticalNews journalists also obtained the inventors' summary information for this patent: "An object of the present invention is to provide a method and device for radial data acquisition in wherein both a uniform spatial sampling density and an avoidance of overly large eddy currents are ensured, and wherein only a simple compensation of the sampling density is required.

"This object is achieved in accordance with the present invention by a method for radial data acquisition in three-dimensional k-space in an MR measurement for a magnetic resonance system. Data in k-space are acquired along straight-line spokes. Each of these spokes is defined by a point on a sphere and the center point of this sphere (i.e. the point on the sphere and the center point lie on this spoke), with the center point of the sphere corresponding to the center of k-space. The points are arranged on the sphere or spherical surface such that the points or the distribution of the points corresponds to the spiral phyllotaxis, in particular the Fibonacci (spiral) phyllotaxis.

"As used herein 'phyllotaxis' means the leaf position or the leaf state in plants. The 'leaf position' means the arrangement of leaf-like organs of a plant. Leaf-like organ includes leaves and carpels of a plant, for example the scales of a pine cone, the fruit of a banana plant and the seeds in a sunflower bloom. The arrangement of the leaf-like organs according to phyllotaxis is frequently also spiral-shaped, and the structure of these spirals obeys specific rules. These rules are defined according to the spiral phyllotaxis; as described in 'A Collision-based Model of Spiral Phyllotaxis', D. R. Fowler et al., Proceedings of SIGGRAPH 1992, in Computer Graphics, July 1992, ACM SIGGRAPH, New York, pages 361-368.

"In the spiral phyllotaxis a divergence angle that exhibits an arbitrary point relative to its predecessor point is always constant. The divergence angle is defined relative to a center point in which a spiral that is formed by the point winds. Expressed otherwise, the divergence angle describes an angle that occurs at a center point in a triangle which is constructed from the point, it predecessor point and the center point.

"In the present invention, the points lie on a spherical surface. If the position of an arbitrary one of these points is determined by means of spherical coordinates (coordinate origin=center point of the sphere), for the case that the points are arranged on a sphere according to the spiral phyllotaxis it then applies that a difference angle always has the same value or is constant between the azimuthal angle of an arbitrary one of these points and the azimuthal angle of its predecessor point. This difference angle can also be viewed as the divergence angle.

"The Fibonacci phyllotaxis is a special case of the spiral phyllotaxis, wherein the divergence angle in the Fibonacci phyllotaxis corresponds to one of the golden angles (see Equations (1) and (2) below).

"For a better comprehension of the Fibonacci phyllotaxis, also refer in this context to 'A Better Way to Construct the Sunflower Head, H. Vogel, Mathematical Biosciences 44: Pages 179-189, 1979.

"If, for definition of the spokes, the points are arranged on the sphere or spherical surface corresponding to the spiral phyllotaxis, in particular corresponding to the Fibonacci phyllotaxis, the distribution of the sample points is more uniform than is the case given the approach which is described in 'Temporal Stability of Adaptive 3D Radial MRI Using Multidimensional Golden Means', R. W. Chan et al., Magnetic Resonance in Medicine 61, Pages 354-363, 2009. A reduction of the eddy current effects advantageously results relative to the approach in which the points are arranged on the sphere in the form of an Archimedean spiral.

"In order to arrange the points on the sphere corresponding to the spiral phyllotaxis (in particular the Fibonacci phyllotaxis) to define the spokes, the points can be arranged either by means of the Voronoi diagram or by means of the 'Contact Pressure Model' (see 'Contact pressure models for spiral phyllotaxis and their computer simulation', H. Hellwig et al., Journal of Theoretical Biology 240 (2006), Pages 489-500).

"A Voronoi diagram designates a decomposition of space in regions that are defined by a predetermined set of points of the space which are designated as centers. Every region is defined by precisely one center and comprises all points of the space that, in relation to Euclidean metrics, lies closer to the center of the region than to every other center. Such regions are also designated as Voronoi regions. The Voronoi diagram is created from all points that possess more than one nearest center and thus form the limits of the regions.

"According to a preferred embodiment of the invention, N spokes are processed for data acquisition of three-dimensional k-space, meaning that the number of processed spokes is N. Each point on the sphere by which one of these spokes is defined is defined by the center point of the sphere via a polar angle and an azimuthal angle. In other words, assuming a Cartesian coordinate system with the origin equal to the center point of the sphere, the polar angle describes that angle between the positive x-axis of this coordinate system and the spoke defined by the corresponding point while the azimuthal angle defines the size between the positive z-axis of this coordinate system and this spoke. The polar angle of the spoke n or n-th spoke is dependent on (for example proportional to) the root of n or, respectively, n or dependent on (for example proportional to) the root of the number of spokes (N) or N. It is also possible that the polar angle is dependent both on (for example proportional to) n and on (for example proportional to) N.

"According to a further embodiment according to the invention, the azimuthal angle of the nth spoke is dependent on (for example proportional to) n or dependent on (for example proportional to) the golden angle. Moreover, it is possible that the azimuthal angle is both dependent on (for example proportional to) n and dependent on (for example proportional to) one of the golden angles. In the present invention, what is thereby understood by a golden angle .psi. is either what is known as the small golden angle .psi..sub.1 or what is known as the large golden angle .psi..sub.2. The small golden angle .psi..sub.1 is defined according to the following Equation (1):

".PSI..times..degree..times..degree..apprxeq..times..degree. ##EQU00001##

"The large golden angle .psi..sub.2 is defined according to the following Equation (2):

".PSI..times..degree..apprxeq..times..degree. ##EQU00002##

"According to a preferred embodiment according to the invention, the polar angle .theta..sub.n of the spoke n or, respectively, the nth spoke is determined corresponding to the following Equation (3):

".THETA..pi..times..times. ##EQU00003##

"According to a further preferred embodiment according to the invention, the azimuthal angle .phi..sub.n of the spoke n or, respectively, the nth spoke is determined corresponding to the following Equation (4): .PHI..sub.n=mod(n.times..PSI.,2.times..pi.) (4)

"In other words, according to the invention two different definitions of the azimuthal angle .phi..sub.n exist. In the first definition the azimuthal angle .phi..sub.n is defined with the small golden angle (i.e. .psi.=.psi..sub.1) and in the second definition the azimuthal angle .phi..sub.n is defined with the large golden angle (i.e. .psi.=.psi..sub.2). In particular in the definition of the points on the spherical surface (and therefore of the spokes) only the first definition of the azimuthal angle .phi..sub.n or only the second definition of the azimuthal angle .phi..sub.n is thereby used.

"Both the polar angle and the azimuthal angle in a closed shape can be calculated with the aid of Equations (3) and (4) depending on the total number of spokes N and depending on the respective index n of the respective spoke to be determined, whereby the respective spoke is then defined. A time-consuming iteration or optimization to determine the distribution of the points on the spherical surface is advantageously avoided.

"According to the invention it is also possible that, instead of the small golden angle .psi..sub.1, or instead of the large golden angle .psi..sub.2, a small angle .psi..sub.1' or a large angle .psi..sub.2' is used in Equation (4) which essentially corresponds to the small golden angle or, respectively, the large golden angle in that the small angle .psi..sub.1' obeys the following Equation (5) and the large angle .psi..sub.2' obeys the following Equation (6): 0.9*.psi..sub.1.ltoreq..psi..sub.1'.ltoreq.1.1*.psi.1 (5) 0.9*.psi..sub.2.ltoreq..psi..sub.2'.ltoreq.1.1*.psi.2 (6)

"According to one embodiment according to the invention, all spokes which are to be processed for radial data acquisition are subdivided into M sets. Corresponding to a predetermined order of the spokes, the spokes are assigned to one of the M sets such that the k-th spoke, the (k+M)-th spoke, the (k+2*M)-th spoke . . . belongs to the k-th set. In the data acquisition the data in k-space are first acquired for all spokes of one of these sets before the data of all spokes for the next set are acquired. The number M of sets is advantageously selected such that it is a Fibonacci number. Since the Fibonacci numbers also comprise the number 1, it is accordingly also possible that all spokes belong to the same set.

"If the number M corresponds to a Fibonacci number, the predetermined order of two successive spokes of the same set advantageously exhibits a corresponding interval. The change between a magnetic field gradient to acquire the one of these two spokes and a magnetic field gradient to acquire the other of these two spokes is advantageously small, such that only slight eddy current effects occur so that a compensation of these eddy current effects by means of a complicated algorithm can be omitted.

"It is naturally also possible that the order in which the spokes of a specific set (one of the M sets) are processed for data acquisition is determined such that the distance between spokes that is processed in direct succession is minimal. For example, that order in which the sum of the distances between two spokes processed in direct succession exhibits a minimum could be determined by means of an optimization method. The distance between two spokes could be defined by the line which connects the two points (via which the respective spoke is defined) on the spherical surface.

"In one example according to the invention, every N spokes are defined with the aid of Equations (2) and (3), wherein the order is established by the index n. In other words, according to this predetermined order the spoke which is defined by the polar angle .theta..sub.n+1 and the azimuthal angle .phi..sub.n+1 is directly that spoke which is defined by the polar angle .theta..sub.n and the azimuthal angle .phi..sub.n. These spokes defined in such a manner are now divided up into M different sets so that the spoke with index 1 (defined by the polar angle .theta..sub.1 and the azimuthal angle .phi..sub.1), the spoke with index (1+M) (defined by the polar angle .theta..sub.1+M and the azimuthal angle .phi..sub.1+M), the spoke with index (1+2*M) (defined by the polar angle .theta..sub.1+2*M and the azimuthal angle .phi..sub.1+2*M), the spoke with index (1+3*M) (defined by the polar angle .theta..sub.1+3*M and the azimuthal angle .phi..sub.1+3*M) etc. are present in the set 1. Accordingly, the spoke with the index k (defined by the polar angle .theta..sub.k and the azimuthal angle .phi..sub.k), the spoke with index (k+M) (defined by the polar angle .theta..sub.k+M and the azimuthal angle .phi..sub.k+M), the spoke with index (k+2*M) (defined by the polar angle .theta..sub.k+2*M and the azimuthal angle .phi..sub.k+2*M), the spoke with index (k+3*M) (defined by the polar angle .theta..sub.k+3*M and the azimuthal angle .phi..sub.k+3*M) etc. are located in the k-th set.

"If the number M corresponds to a Fibonacci number, the spokes of an arbitrary one of the M sets are processed in an order which is provided by the index. In other words, for the k-th set the spoke with the index k is processed first, then the spoke with the index (k+M), then the spoke with the index (k+2*M), then the spoke with the index (k+3*M). Due to the fact that the spokes are defined with the use of Equations (2) and (3), it is then ensured that almost no eddy current effects occur between two successive spokes.

"If, in contrast to this, the number M does not correspond to a Fibonacci number, large gradient changes normally exist between two successive spokes, such that it is advisable to not define the order in which the spokes of a set are processed as the same as that order which is provided by the index. In this case the order can be selected such that the distances between two successive spokes is respectively as small as possible, which naturally can indicate a complicated optimization.

"Within the scope of the present invention, a device is also provided for a magnetic resonance system for radial data acquisition in three-dimensional k-space in an MR measurement. The device has a control unit to control the magnetic resonance system; a receiver device to receive MR data acquired by the magnetic resonance system; and an evaluation device to evaluate the MR data. The device is designed such that data in k-space are acquired along spokes running in straight lines. Each spoke is defined by a point on the sphere and the center point of the sphere, wherein the center point of the sphere corresponds to the center of k-space. The device arranges the points on the spherical surface such that the distribution of the points obeys the spiral phyllotaxis (even better the Fibonacci phyllotaxis).

"The advantages of the device according to the invention essentially correspond to the advantages of the method according to the invention which have been described in detail in the preceding.

"Moreover, the present invention encompasses a magnetic resonance system that includes the device according to the invention that is described in the preceding.

"The present invention embodies an electronically readable data storage medium--for example a DVD, a magnetic tape or a USB stick--on which is stored electronically readable control information, in particular software. All embodiments according to the invention of the method that is described in the preceding can be implemented when this control information (software) are read from the data medium and stored in a controller or, respectively, computer of a magnetic resonance system.

"The programming instructions of the computer-readable storage medium include, for example, libraries and auxiliary functions in order to realize the corresponding embodiments of the method. The programming instructions represent software with which any of the embodiments of the method according to the invention that are described above can be executed. The software can thereby be a source code (for example in C++) that must still be compiled and linked or that must merely be interpreted, or it can be an executable software code that is merely to be loaded into the corresponding computer for execution.

"The present invention is particularly suitable for radial data acquisition in three-dimensional k-space in an MR measurement (magnetic resonance measurement) Naturally, the present invention is not limited to this preferred apparatus field since the present invention could also be used in other imaging methods, for example (x-ray computer tomography, positron emission tomography, for example)."

URL and more information on this patent, see: Piccini, Davide; Zenge, Michael. Method and Device for Uniform Radial Data Acquisition in Three-Dimensional K-Space in an MR Measurement for a Magnetic Resonance System. U.S. Patent Number 8648594, filed October 26, 2010, and published online on February 11, 2014. Patent URL: http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=50&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=2497&f=G&l=50&co1=AND&d=PTXT&s1=20140211.PD.&OS=ISD/20140211&RS=ISD/20140211

Keywords for this news article include: Software, Siemens Aktiengesellschaft.

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