Magnetic resonance trajectory correcting with GRAPPA operator gridding

Apparatus, methods, and other embodiments associated with magnetic resonance (MR) trajectory correcting using GRAPPA operator gridding (GROG) are described. One example method includes identifying an on angle or regular portion of a projection in an MR trajectory and then computing base GROG weights for that portion. The example method includes identifying a shift direction and a shift amount for the projection. The shift direction is configured to shift the projection towards a desired point in k-space and the shift amount is configured to shift the projection by a desired amount in the shift direction. With a shift direction and amount available, the example method corrects for a gradient delay by manipulating the MR source signal data using the shift direction and the shift amount. In one embodiment, a gradient delay can be determined and used to calibrate an MRI apparatus.

BACKGROUND

Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) is described in Griswold, et al., Proceedings of the ISMRM, Vol. 7, Issue 6, Pg. 1202-1210 (2002). GRAPPA facilitates generating uncombined coil images for coils in an array of receive coils used by a parallel magnetic resonance imaging (pMRI) apparatus. GRAPPA reconstructs missing lines in coil elements by forming linear combinations of neighboring lines to reconstruct individual missing data points. The weights for these linear combinations are derived by forming a fit between additionally acquired lines using a pseudo-inverse operation.

GRAPPA Operator Gridding (GROG) is described in Seiberlich, et al., Non-Cartesian data reconstruction using GRAPPA operator gridding (GROG), Magn Reson Med. 2007 December; 58(6): 1257-65. GROG facilitates gridding data sampled along a non-Cartesian trajectory. GROG facilitates shifting acquired data points to another (e.g., nearest) Cartesian location to facilitate converting non-Cartesian to Cartesian data. GROG synthesizes the net weight for a shift from a basis set of weights along logical k-space directions. GROG employs local averaging because the reconstructed points fall upon the Cartesian grid. This facilitates not having to calculate and apply a density compensation function (DCF).

Magnetic resonance imaging (MRI) pulse sequences manipulate gradient fields by controlling gradient coils. Gradient coils are physical things that have physical properties including, for example, a delay time and a slew rate. The delay time describes how quickly a gradient coil may respond to a direction to change the state of the gradient coil. The slew rate describes the rate of ascent or descent of a gradient from zero to its maximum amplitude once it has begun to respond to the direction to change its state. Having a faster slew rate allows the gradient to slew from zero to its maximum amplitude in less time, which in turn facilitates having faster gradients and shorter echo spacing. Unfortunately, different gradient coils may have different delay times and may have different slew rates, which may introduce artifacts into magnetic resonance images.

FIG. 1illustrates a square wave100and a non-square wave110. Square wave100and non-square wave110represent the amplitude of a gradient field being produced by a gradient coil. In theory a gradient coil would respond instantaneously to produce a gradient field whose amplitude would then transition like square wave100. In practice, due to slew rate, a gradient coil responds less than instantaneously and produces a gradient field whose amplitude transitions more like wave110.

FIG. 2illustrates a non-square wave200that represents the amplitude of a gradient field produced by a gradient coil. Non-square wave200illustrates the effect of both slew rate and delay. For example, a gradient coil may receive an input at time T20that is intended to cause the gradient coil to change its state. However, the gradient coil may not begin to slew until time T21. The delay may be caused, for example, by switching, by a capacitor charging, or by other factors. Once the gradient coil begins to slew at T21, the gradient field amplitude continues to change until time T22where the gradient field amplitude achieves steady state. At a later time T23the gradient coil may slew in the other direction until the gradient field returns to its original state at time T24.

MRI pulse sequences may manipulate multiple gradients at the same time. Thus, the situation illustrated inFIG. 3could occur.FIG. 3illustrates the amplitude of a gradient field300transitioning as controlled by a gradient coil GXand the amplitude of a gradient field310transitioning as controlled by a gradient coil GY. While gradient coils GXand GYhave similar slew rates, they have different delay times.

Both GXand GYmay be controlled to change their state at time T30. GXmay begin to respond at time T31while GYdoes not begin to respond until time T32. GXachieves steady state at time T32while GYdoes not achieve steady state until T33. Between T33and T35, both gradient fields are in steady state. A trajectory associated with the two gradient fields GXand GYmay be stable during this period of time. Both GXand GYmay be controlled at time T34to change their state. Once again GXmay respond more quickly and begin to change state at T35while GYdoes not respond until a later time. Eventually both GXand GYachieve their original steady state.

During the period of time36between T31and T32, only the GXgradient field is active and that field has not yet achieved steady state. During the period of time37between T32and T33, both the GXand the GYgradients are active but the GYfield has not yet achieved steady state. Thus, a trajectory associated with GXand GYmay not be stable during the period of time between T31and T33. Once GXand GYachieve steady state at T33the trajectory may be stable during, for example, period of time38. The situation illustrated inFIG. 3could be even further complicated if GXand GYalso had different slew rates.

FIG. 4illustrates a radial projection associated with a system where gradient coils reacted identically and without delay. The radial projection includes a portion400OUTthat extends directly out from the center of k-space. The radial projection also includes a portion400BACKthat returns directly through the center of k-space. Note that the projection angle θ is the same for both400OUTand400BACK.

FIG. 5also illustrates a radial projection. But inFIG. 5the radial projection is associated with a system where gradient coils did not react identically and did not react instantaneously. The radial projection includes a portion500OUTthat extends out from a position offset from the center of k-space. The radial projection also includes a portion500BACKthat returns but not directly through the center of k-space. Once again note that the projection angle is the same for both500OUTand500BACK.

FIG. 6illustrates a trajectory that would be experienced by the radial projection that includes500OUTand500BACK. Once the gradients reach steady state, the projection is stable and lies along the desired projection angle. However, the projection does not originate from the center of k-space nor does it pass back through the center of k-space. This may lead to artifacts in an image reconstructed from the radial projection.

FIGS. 5 and 6illustrate how gradient delays and stewing can cause a trajectory desired by a pulse sequence to not be exactly where it was intended to be. The trajectory may proceed at the correct angle during an “on angle” portion, but it may not pass through desired points (e.g., center of k-space). Ideally, a projection would go out and back passing through the same points. InFIG. 6, since the X gradient reacts more quickly than the Y gradient, the projection first gets shifted to the right in the X direction and then gets shifted to the left in the X direction. Although neither500OUTnor500BACKare exactly where they are supposed to be, they are still useful because they are on the desired projection angle θ.

To summarize, gradient timing delays may cause mismatches between a desired trajectory and an actual trajectory. In radial scanning, individual projections may be shifted along the direction of the projection or may be translated in k-space so that they do not pass through the center of k-space. These shifts may cause artifacts in reconstructed images. Conventional systems may attempt to address the shifts by measuring the trajectory using a separate acquisition. Making a separate acquisition takes additional time, during which conditions may change. These conventional approaches assume that shifts are consistent between measurements. However, the assumption may not hold due to gradient coupling, patient motion, or other factors. Even if the assumption holds during the additional acquisition, the conventional approaches may still only provide a partial solution. The extra measurement may not address k-space signals that are being used for additional purposes including, for example, self-gating signals acquired from repeatedly sampling the echo peak.

DETAILED DESCRIPTION

Example apparatus and methods account for trajectory shifts caused by gradient delays in magnetic resonance imaging (MRI). Accounting for the trajectory shifts may include correcting for trajectory errors, determining a location for the center of k-space, and other actions. Unlike conventional systems, example apparatus and methods do not employ an additional acquisition to account for trajectory shifts.

Example apparatus and methods may rely on GRAPPA Operator Gridding (GROG) to provide base weights for use in shifting a trajectory. ConsiderFIG. 5, where the projection angle θ of the shifted projection will be correct during portions of the trajectory. Gradient delays may shift the projection so that it is off center. GROG may facilitate shifting the projection back to on center. Gradient delays may cause a shift either along a projection or perpendicular to the projection and thus some parts at the beginning of the projection may not have the desired projection angle θ. However, once the gradients have achieved their desired gradient amplitude in the steady state, the projection angle θ of the trajectory will be correct and the projection may be linear or substantially linear.

Because the projection angle θ will be correct and consistent for a portion of a trajectory, and because the projection will be linear or substantially linear, GROG base weights can be determined for the portion for which the projection angle θ is correct and consistent. These GROG base weights can then be used to selectively shift a trajectory. The GROG base weights can also be used to facilitate finding the center of k-space relative to the k-space points sampled by the shifted trajectory. After the center of k-space is located, the trajectory can be shifted by an appropriate amount and in an appropriate direction so that it will pass through a desired location (e.g., center of k-space).

Example apparatus and methods may also determine gradient delays. If consistent gradient delays can be established for an operating MRI apparatus, then the MRI apparatus may be calibrated. The calibrating may include, for example, adapting pulse sequences for that particular MRI apparatus to reduce the period of time where gradients are not working as desired. For example, if a GYcoil is found to consistently react more slowly than a GXcoil, then a pulse sequence for that particular machine may be altered to account for the discrepancy.

FIG. 7illustrates one example data flow700associated with MR trajectory mapping using GROG. The data flow700starts with source signals705. The source signals705may be, for example, multi-channel non-Cartesian data. As described above, a projection may have an on angle portion and an off angle portion. Therefore data flow700includes, at710, identifying an on angle portion of a trajectory. GROG weights715are then calculated for points in this on angle portion. Data flow700also includes, at720, establishing an initial location for a supposed center of k-space. In one embodiment, the initial/supposed center of k-space is selected as the point having the maximum measured echo-peak magnitude (EPM). With a set of GROG weights available, and with an initial guess for the center of k-space available, data flow700may proceed to apply GROG weights at725to produce a new candidate set of points780. The candidate set of points780will be shifted by a fractional GROG weight (e.g., 0.1Δk, 0.25Δk) in various directions. While 8 directions are illustrated, a greater or lesser number of directions may employed. Additionally, while the 8 directions are uniformly distributed around a compass, non-uniform distributions may employed.

Having prepared candidate points780, data flow700then proceeds, at730, to evaluate those candidate points780to determine whether there is a new best guess for the center of k-space. Evaluating the candidate points780may include, at730, calculating characterizing values for the candidate points780and retrieving information from those characterizing values at735. In one example, the characterizing values may be computed using a sum-of-squares (SoS) approach where SoS are computed for candidate points780across different, and potentially all, available data channels. The evaluation at735may analyze whether a computed SoS indicates that one point in the candidate points780is better than another and better than those seen so far (e.g., current estimate of center of k-space). If the answer at735is no, then the presumed center of k-space has been identified and that presumed center can be established as “the center of k-space” at755. If the answer at735is yes, then further action may be undertaken.

For example, at740a determination may be made concerning a shift direction indicated by the superior SoS information. The shift direction is indicated in candidate points780′ as being up and to the right. This shift direction may then be employed at745to re-establish the guess for the center of k-space associated with the echo-peak maximum (EPM). In an iterative process it may not make sense to allow the process to backtrack. Therefore data flow700may include, at750, removing some shift directions or future candidate points from consideration. Candidate points780″ illustrate removing the point down and to the left since that is the point from which the candidate points780′ were shifted.

Data flow700may then continue until a best guess for the center of k-space is identified. In one example, data flow700may be associated with an iterative gradient ascent approach. Other approaches may be employed.

Some portions of the detailed descriptions that follow are presented in terms of algorithms and symbolic representations of operations on data bits within a memory. These algorithmic descriptions and representations are used by those skilled in the art to convey the substance of their work to others. An algorithm is considered to be a sequence of operations that produce a result. The operations may include creating and manipulating physical quantities that may take the form of electronic values. Creating or manipulating a physical quantity in the form of an electronic value produces a concrete, tangible, useful, real-world result.

Example methods may be better appreciated with reference to flow diagrams. For simplicity, the illustrated methodologies are shown and described as a series of blocks. However, the methodologies may not be limited by the order of the blocks because, in some embodiments, the blocks may occur in different orders than shown and described. Moreover, fewer than all the illustrated blocks may be required to implement an example methodology. Blocks may be combined or separated into multiple components. Furthermore, additional or alternative methodologies can employ additional, not illustrated blocks.

FIG. 8illustrates an example method800associated with MR trajectory correcting. Method800includes, at810, identifying an on angle portion of a set of MR source signal data associated with a projection in an MR trajectory. In one example, the set of MR source signal data may be multi-channel non-Cartesian (e.g., radial) data. In one example, identifying the on angle portion of the set of MR source signal data includes identifying where the linearity of the projection meets a linearity threshold or identifying where the projection has a desired projection angle. A projection that initially wanders off course while gradients are delayed may become sufficiently regular (e.g., linear) or may maintain a desired projection angle after the gradients achieve steady state.

Method800also includes, at820, determining a set of base GROG weights for the on angle portion.

Method800also includes, at830, identifying a shift direction for the projection. Computing the shift direction facilitates shifting the projection towards a desired point in k-space. The final shift direction may be computed by traversing a path from a starting point to an ending point. Thus, in one example, identifying the shift direction includes determining an initial estimate for the center of k-space and then iteratively examining other possible estimates for the center of k-space using a travelling approach (e.g., gradient ascent). While a travelling approach (e.g., gradient ascent) is described, in one embodiment a large number of candidate points in a finite data space could be examined collectively in one pass. In one example, determining the estimate for the center of k-space comprises determining a measured echo-peak magnitude (EPM) for the set of MR source signal data.

Examining the other possible estimates may include first generating a set of candidate points from the on angle portion of the set of MR source signal data so there is something to which the initial estimate can be compared. In one example, generating the set of candidate points may include creating N different candidate points in N different locations in k-space. The N different locations may be determined by shifting a point in the on angle portion of the set of MR source signal data along a set of N candidate shift directions by a fractional amount of the base GROG weights. N may be, for example, 2, 4, 8, 16, 32, or other integer values. The fractional amount may be, for example, 0.1Δk, 0.25Δk, or other amounts.

Once the candidate points are available for comparison, an instant or local shift direction can be selected for a step along a path based, at least in part, on re-determining the estimate for the center of k-space using the set of candidate points. In one example, re-determining the estimate for the center of k-space includes computing a sum of squares value for a member of the set of candidate points and then, if the sum of squares value indicates that the member of the set of candidate points is more likely the center of k-space than the estimate for the center of k-space, making the member of the set of candidate points the new estimate for the center of k-space. In one example, computing the sum of squares value for the member is based, at least in part, on information associated with multiple different channels associated with acquiring the set of MR source signal data.

After a number of iterations during which a number of instant shift directions are acquired, an overall shift direction may be identified. Thus, in one example, method800may include iterating through the determining, generating, and selecting involved in identifying a shift direction under the control of a gradient ascent algorithm. The gradient ascent algorithm termination condition may include determining that the estimate for the center of k-space has not improved between iterations.

Method800also includes, at840, identifying a shift amount for the projection. Computing the shift amount facilitates shifting the projection by a desired amount in the shift direction. In one example, identifying the shift amount includes comparing an initial estimate for the center of k-space and a final estimate for the center of k-space.

Method800also includes, at850, manipulating the set of MR source signal data based, at least in part, on the shift direction and the shift amount. In one example, manipulating the set of MR source signal data comprises shifting the MR source signal data in the shift direction by the shift amount.

FIG. 9illustrates another embodiment of example method800. This embodiment includes actions810,820,830, and840, does not include correcting image data, but does include additional calibration and adaptation actions.

This embodiment of method800includes, at860estimating a gradient delay for a gradient coil associated with an MR apparatus that acquired the set of MR source signal data. In one embodiment, estimating the gradient delay is based, at least in part, on analyzing shift directions or shift amounts determined for two or more projections. The gradient delay may be determined because the amount by which a projection is shifted varies directly with the gradient delay. If a consistent shift amount is found, then there may be a consistent gradient delay.

Since a consistent gradient delay may be present, this embodiment of method800may also include, at830, calibrating an MR apparatus based, at least in part, on the gradient delay. Calibrating the MR apparatus can include different actions. In one embodiment, if there is a consistent gradient delay, calibrating the MR apparatus may include manipulating a pulse sequence as a function of the gradient delay. For example, an instruction to control a gradient to change its state may be issued sooner so that the gradient changes state at a desired time. ConsiderFIG. 3again. If the GYgradient coil is consistently slower to respond than the GXgradient coil, then the control point for the GYgradient coil may be moved to the left of T30to a point T29that would allow the GYgradient coil to begin to react at T31instead of at T32. In this way, the gradient coil shifting may be avoided and may not need to be corrected for.

Calibrating the MR apparatus may also include, for example, controlling the MR apparatus to use the estimate of the center of k-space as a portion of a navigator signal for a retrospective self-gated image acquisition.

FIG. 10illustrates an example MRI apparatus1000configured with an MR trajectory correcting apparatus1099. The MR trajectory correcting apparatus1099may be configured with elements of example apparatus or circuits described herein or may perform example methods described herein. In one embodiment, apparatus1099may provide means for identifying a gradient delay that created an artifact in an image reconstructed from image data acquired during a multi-channel non-Cartesian acquisition by the MRI system1000. The means may include, for example, circuits, programmed logics, and a special purpose computer. In one embodiment, apparatus1099may also include means for correcting the image data to account for the gradient delay using GROG weights calculated from the image data. These means may also include circuits, programmed logics, a special purpose computer, and other apparatus described herein.

The apparatus1000includes a basic field magnet(s)1010and a basic field magnet supply1020. Ideally, the basic field magnets1010would produce a uniform B0field. However, in practice, the B0field may not be uniform, and may vary over an object being imaged by the MRI apparatus1000. MRI apparatus1000may include gradient coils1030configured to emit gradient magnetic fields like GS, GP, and GR. The gradient coils1030may be controlled, at least in part, by a gradient coils supply1040. In some examples, the timing, strength, and orientation of the gradient magnetic fields may be controlled, and thus selectively adapted, during an MRI procedure. Ideally the actual gradient magnetic fields produced would perfectly faithfully represent the desired gradient magnetic fields and would be created identically with consistent, matching slew rates, and with consistent, matching delay times. Since these ideals may not be attained, MR trajectory correcting is performed to account for trajectory shifts due, for example, to gradient delays.

MRI apparatus1000may include a set of RF antennas1050that are configured to generate RF pulses and to receive resulting nuclear magnetic resonance (NMR) signals from an object to which the RF pulses are directed. In one embodiment, the RF antennas1050are arranged as an array of parallel transmission coils that are individually controllable. How the pulses are generated and how the resulting MR signals are received may be controlled and thus may be selectively adapted during an MR procedure. Separate RF transmission and reception coils can be employed. The RF antennas1050may be controlled, at least in part, by a set of RF transmission units1060. An RF transmission unit1060may provide a signal to an RF antenna1050. The RF transmission unit1060may provide different signals to different RF antennas to produce different RF excitations from the different members of the array of parallel transmission coils.

The gradient coils supply1040and the RF transmission units1060may be controlled, at least in part, by a control computer1070. In one example, the control computer1070may be programmed to control an NMR device as described herein. Conventionally, the magnetic resonance signals received from the RF antennas1050can be employed to generate an image and thus may be subject to a transformation process like a two dimensional Fast Fourier Transform (FFT) that generates pixilated image data. The transformation can be performed by an image computer1080or other similar processing device. The image data may then be shown on a display1090.

FIG. 11illustrates an embodiment of an MR trajectory correcting apparatus1099. Apparatus1099may be a computer, electronic, or other apparatus that is configured to control an MRI apparatus (e.g., apparatus1000).

Apparatus1099may include a first logic1110that is configured to access MR trajectory data that has been affected by a gradient delay. The gradient delay may have occurred in an MR apparatus (e.g., apparatus1000) that acquired the MR trajectory data. Recall that a gradient delay may cause a projection to shift but may leave the projection angle intact. Thus, in one embodiment, the first logic1110is also configured to identify a portion of an MR trajectory described by the MR trajectory data that represents an on angle portion of a projection in the MR trajectory. Identifying the on angle portion may include analyzing a projection angle associated with the MR trajectory and determining whether the actual projection angle falls within a threshold amount of a desired projection angle.

In one embodiment, the first logic1110is also configured to control the MR apparatus to acquire the MR trajectory data. The MR trajectory data may be acquired, for example, as multi-channel non-Cartesian data.

Apparatus1099may include a second logic1120that is configured to compute GROG weights for a portion of the MR trajectory data. In one example, the GROG weights may be computed for just the on angle portion of the projection.

Apparatus1099may include a third logic1130that is configured to compute a shift direction and shift amount for the MR trajectory data. The shift direction and the shift amount may be selected to correct the MR trajectory data. Correcting the MR trajectory data may account for a shift caused, by the gradient delay, which may in turn facilitate mitigating artifacts associated with gradient delays.

In one embodiment, the third logic1130is configured to identify the center of k-space by applying an iterative gradient ascent to the MR trajectory data to locate a maximum. While a gradient ascent is described, other point location algorithms may be employed. Gradient ascents and descents begin somewhere and end somewhere and take a series of steps along a path between the beginning point and ending point. Thus, third logic1130may be configured to identify a starting point by calculating an initial echo-peak magnitude (EPM) computed in the MR trajectory data. The steps may be taken from a current estimated best point to a member of a set of candidate best points. Third logic1130may continue to produce candidate points and to evaluate those candidate points until the gradient ascent terminates. The third logic1130may produce candidate gradients points by shifting an actual point in multiple directions by an amount determined by a fractional GROG weight. The third logic1130may evaluate candidate points using, for example, a SUM of squares based approach. While a sum of squares based approach is described, one skilled in the art will appreciate that other comparison techniques may be employed.

Once the gradient ascent has terminated and the determined center of k-space has been computed, the third logic1130may then compute the shift direction and the shift amount by comparing the determined center of k-space calculated by apparatus1099to the initial EPM. In one example, the third logic1130may be configured to compute a gradient delay as a function of the shift amount or shift direction.

Apparatus1099may include a fourth logic1140that is configured to manipulate the MR trajectory to account for the gradient delay. Accounting for the gradient delay may include using the shift amount and the shift direction to manipulate image data to reposition a projection associated with the MR trajectory data. The projection may be repositioned to, for example, pass through a desired point (e.g., the center) in k-space. Thus, the fourth logic1140may be configured to manipulate the MR trajectory by applying the shift amount in the shift direction to the MR trajectory data to make the MR trajectory appear to pass through the desired point in k-space.

The following includes definitions of selected terms employed herein. The definitions include various examples or forms of components that fall within the scope of a term and that may be used for implementation. The examples are not intended to be limiting. Both singular and plural forms of terms may be within the definitions.

An “operable connection”, or a connection by which entities are “operably connected”, is one in which signals, physical communications, or logical communications may be sent or received. An operable connection may include a physical interface, an electrical interface, or a data interface. An operable connection may include differing combinations of interfaces or connections sufficient to allow operable control. For example, two entities can be operably connected to communicate signals to each other directly or through one or more intermediate entities (e.g., processor, operating system, logic, software). Logical or physical communication channels can be used to create an operable connection.

“User”, as used herein, includes but is not limited to one or more persons, software, computers or other devices, or combinations of these.