Systems and methods for generating optimized gradient direction sets for magnetic resonance imaging

Abstract

A method of controlling a magnetic resonance (MR) imaging system includes: receiving a diffusion tensor imaging (DTI) command, the command including a number of gradient vectors; obtaining a set of gradient vectors according to the number in the command, by: (i) selecting an initial set of gradient vectors; (ii) adjusting each gradient vector in the set, to generate a set of adjusted gradient vectors; (iii) determining a cost function based on the set of adjusted gradient vectors, the cost function indicating an impact of the set of adjusted gradient vectors on diffusion tensor variance; (iv) repeating the selecting, the adjusting, and the determining until an optimization condition is met, to obtain a final set of gradient vectors; and controlling the MR imaging system to capture a set of images based on the final set of gradient vectors.

Description

Agent Docket: P12854PC00SYSTEMS AND METHODS FOR GENERATING OPTIMIZED GRADIENT DIRECTION SETS FOR MAGNETIC RESONANCE IMAGINGFIELD

[0001] The specification relates generally to magnetic resonance imaging (“MRI”) systems, and specifically to systems and methods for generating optimized gradient direction sets for MR imaging systems.BACKGROUND

[0002] Diffusion tensor imaging (DTI) is a method of MR imaging involving the capture of a reference image, and a set of diffusion-weighted images with various different gradient magnetic fields. A composite image can be generated from the reference image and the diffusion-weighted images, which enhances the visibility of fluid flow in the imaged tissues. For example, DTI images can be used to visualize white matter tractography in the brain. Certain methods of selecting gradient field directions may result in suboptimal gradient field directions, which can negatively affect the quality of the resulting composite image.SUMMARY

[0003] An aspect of the specification provides a method of controlling a magnetic resonance (MR) imaging system, the method comprising: receiving a diffusion tensor imaging (DTI) command, the command including a number of gradient vectors; obtaining a set of gradient vectors according to the number in the command, by: (i) selecting an initial set of gradient vectors; (ii) adjusting each gradient vector in the set, to generate a set of adjusted gradient vectors; (iii) determining a cost function based on the set of adjusted gradient vectors, the cost function indicating an impact of the set of adjusted gradient vectors on diffusion tensor variance; (iv) repeating the selecting, the adjusting, and the determining until an optimization condition is met, to obtain a final set of gradient vectors; and controlling the MR imaging system to capture a set of images based on the final set of gradient vectors.Agent Docket: P12854PC00BRIEF DESCRIPTIONS OF THE DRAWINGS

[0004] Embodiments are described with reference to the following figures.

[0005] FIG. 1 is a diagram of a system for generating optimized gradient direction sets for magnetic resonance (MR) imaging.

[0006] FIG. 2 is a diagram showing example gradient vectors for use in the system of FIG. 1.

[0007] FIG. 3 is a flowchart of a method of generating optimized gradient direction sets forMR imaging.

[0008] FIG. 4 is a flowchart of a method for performing block 315 of the method of FIG. 3.

[0009] FIG. 5 is a diagram of an example performance of the method of FIG. 4.DETAILED DESCRIPTION

[0010] FIG. 1 depicts a system 100 for generating optimized gradient direction sets for magnetic resonance (MR) imaging. The system 100 includes an imaging device 104 such as an MR scanner having a housing that defines a bore 108 into which a patient or other imaging target can be placed. The scanner 104 includes, as will be apparent to those skilled in the art, a plurality of coils controllable to generate magnetic fields, to generate excitation pulses, and to detect signals emitted by the imaging target in response to the magnetic fields and excitation pulses.

[0011] The system 100 also includes a computing device 112, which is illustrated as a physically distinct device from the scanner 104, but in other embodiments may integrated with the scanner 104. The device 112 is configured, in general, to control the scanner 104, e.g., to initiate scan sequences, receive data collected during such scan sequences, and generate images therefrom. A wide variety of scan sequences can be implemented by the scanner 104. An example class of scan sequences is diffusion tensor imaging (DTI), a subset of diffusion-weighted imaging (DWI) techniques. To capture DTI images, the device 112 can be configured to control the scanner 104 to capture a reference image, e.g., using a primary magnetic field Bo, and to subsequently capture a plurality of additional images, applying a distinct gradient magnetic field for each additional image. For example, the sequence can include at least six, and as many as two hundred, additional images (in some examples, fewer than six or more than two hundred additional images can also be captured).Agent Docket: P12854PC00

[0012] Each additional image, as a result of the corresponding gradient field, exhibits signal drop-out in regions with fluid diffusion in a direction substantially matching the direction of the gradient field. Thus, for imaging targets such as white matter (e.g., neurons and myelin sheaths in the brain of a patient being imaged) each additional image may exhibit differential signal variations corresponding to a subset of fluid flows in the imaged tissue. By combining the additional images, the computing device 112 can generate a DTI image that visualizes anisotropic fluid flow, e.g., corresponding to neural tracts in the patient tissue.

[0013] Generating the DTI image includes, at the computing device 112, a diffusion tensor for each voxel of the reference image. The diffusion tensor may be, for example, a 3x3 matrix indicating the direction and magnitude of fluid flow at that voxel. Various mechanisms to determine diffusion tensors based on comparisons between the reference image and the additional gradient images. Due to noise and / or other artifacts in each of the images, the above comparisons may each yield different diffusion tensors in isolation. Determining the diffusion tensor for each voxel of the DTI image is therefore an optimization problem, e.g., seeking to minimize a cost function indicative of variance in the diffusion tensor estimates.

[0014] Various factors contribute to imaging noise and the resulting variance in diffusion tensors, and therefore to the quality of the DTI image. Among those factors, a factor that has received relatively little attention in previous systems is the orientation of the gradient fields used to capture the additional images. Various processes may be used for generating gradient vectors that define the orientations of the above-mentioned gradient vectors. For example, gradient vectors can be selected based on a simulation of electrostatic repulsion, by simulating each gradient vector as a point charge at the end of a segment extending from a central point. The point charges repulse one another, and when the position of each point charge stabilizes in such a simulation, the directions of the corresponding segments are stored as gradient vectors. In other examples, gradient vectors can be selected based on predetermined polyhedra, e.g., with each gradient vector represented by a segment extending from the center of mass of a polyhedron to a corresponding vertex of the polyhedron. The above approaches, however, can result in suboptimal gradient vectors and thus in noisy DTI images. The polyhedral approach may also be relatively inflexible, in that it may not be suitable to dynamically generate a polyhedron for any arbitrary number of gradient vectors. The electrostatic repulsion-based approach may yield sets of gradient vectors thatAgent Docket: P12854PC00 are relatively equally spaced, but such equally spaced sets of vectors may not be optimal for image quality.

[0015] The computing device 112 is therefore configured to implement functionality for generating optimized gradient direction sets for MR imaging. Before discussing the functionality implemented by the device 112, certain internal components of the device 112 will be introduced. The device 112 includes a processor 116, such as one or more central processing units (CPU), one or more graphics processing units (GPUs), or other integrated circuit components configured to execute programming instructions. The processor 116 is interconnected with a non-transitory computer readable storage medium such as a memory 120. The processor 116 and the memory 120 are generally comprised of one or more integrated circuits (ICs). The memory 120 can include any suitable combination of volatile memory (e.g. Random Access Memory (“RAM”)) and nonvolatile memory (e.g. read only memory (“ROM”), Electrically Erasable Programmable Read Only Memory (“EEPROM”), flash memory, magnetic computer storage device, or optical disc).

[0016] The device 112 can also include a communications interface 124 interconnected with processor 116. The interface 124 enables the device 112 to communicate with other devices, including the scanner 104, via one or more networks (e.g., local area networks (LAN), wide area networks (WAN), personal-area networks (PAN), or any suitable combination thereof), and / or via local input / output interfaces (e.g., Universal Serial Bus (USB), and the like). The interface 124 thus includes any necessary hardware for such communications such as radios, network interface controllers (NICs) and the like. The device 112 can also include one or more input devices 128, such as a keyboard, mouse, touch screen, microphone, or the like. The device 112 can also include an output such as a display 132.

[0017] The memory 120 stores a plurality of computer-readable instructions, executable by the processor 116 to implement the gradient selection functionality mentioned above. In the illustrated example, the memory 120 stores a gradient selection application 136, whose execution by the processor 116 configures the device 112 to select optimized gradient vectors, e.g., for generation of DTI images. The memory 120 can also store, as shown in FIG. 1, a repository 140 of previously determined gradient vectors and / or other configuration data for use in controlling the scanner 104. Those skilled in the art will appreciate that the functionality implemented by the processor 116 via the execution of the application 136 may also be implemented by one or moreAgent Docket: P12854PC00 specially designed hardware and firmware components, such as FPGAs, ASICs and the like in other embodiments.

[0018] Turning to FIG. 2, the bore 108 of the scanner 104 is illustrated, along with a primary magnetic field 200 with a direction 204 (which may be represented by a unit vector in a predetermined coordinate system of the scanner 104). Four example gradient vectors 208-1, 208- 2, 208-3, and 208-4 are also illustrated (also referred to collectively as gradient vectors 208, and generically as a gradient vector 208; similar nomenclature may also be used for other elements herein). FIG. 2 also illustrates a polyhedron 212 (e.g., a twelve-faced polyhedron) that can be used for gradient vector selection. For example, gradient vectors 208-5 and 208-6 extend from a center of the polyhedron 212 to respective vertices of the polyhedron 212.

[0019] Turning to FIG. 3, a method 300 of generating optimized gradient direction sets for magnetic resonance imaging is shown. The method 300 is described below in conjunction with its performance by the device 116, e.g., via the execution of the application 136 by the processor 116.

[0020] At block 305, the device 116 is configured to receive, e.g., via the input device 128, an imaging command including a number of gradient vectors. The command can be a command to initiate, for example, a DTI capture sequence. The number of gradient vectors can be selected, e.g., by an operator of the device 116, or generated automatically based on other parameters of the DTI capture sequence that are not directly relevant to the performance of the method 300. The number of gradient vectors in the imaging command, as will be apparent to those skilled in the art, may vary depending on the nature of the imaging target, the diagnostic goal of the DTI capture sequence, and the like. Example numbers of gradient vectors may fall in a range between about six and about two hundred, although as noted earlier, other numbers of gradient vectors outside that range may also be used.

[0021] At block 310, the device 116 is configured to determine whether the repository 140 contains a set of gradient vectors corresponding to the number received at block 305. The device 116 can be configured, in some embodiments, to store the results of previous gradient vector set generation, to reduce or eliminate the need to regenerate such gradient vector sets in response to later requests. For example, the repository 140 can be implemented as a lookup table containing, for each of a plurality of numbers of gradient vectors, a set of gradient vector definitions. TheAgent Docket: P12854PC00 determination at block 310 can therefore include determining whether the repository 140 contains a record corresponding to the number of gradient vectors received at block 305.

[0022] When the determination at block 310 is affirmative, the device 116 can proceed to image capture at block, retrieving the previously stored gradient vector set from the repository 140. When the determination at block 310 is negative, however, the device 116 proceeds to block 315. At block 315, the device 116 is configured to generate a set of gradient vectors equal in number to the number from the command. Generation of gradient vectors will be described in greater detail below in conjunction with FIG. 4.

[0023] At block 320, the device 116 is configured to store the gradient vectors generated at block 315, e.g., in the repository 140 in association with the number of gradient vectors from the request received at block 305. At block 325, the device 116 is configured to initiate capture of a DTI image using the set of gradient vectors.

[0024] Turning to FIG. 4, a method 400 of generating a set of gradient vectors at block 315 is shown. At block 405, the device 116 is configured to obtain a number of gradient vectors to generate. For example, the number obtained at block 405 can be obtained from the request received at block 305. In other examples, the method 400 can be performed independently of the method 300, e.g., to generate one or more sets of gradient vectors to populate the repository 140, prior to imaging operations.

[0025] At block 410, the device 116 is configured to obtain an initial set of gradient vectors. The initial set of gradient vectors can be selected via any of a variety of selection processes. For example, the initial set can be selected via electrostatic repulsion, or as vectors defined by the segments extending from center to vertices of a predetermined polyhedron. In some examples, the device 116 can store sets of vectors based on the polyhedral selection mechanism, and at block 410 can determine whether one of the stored polyhedral sets matches the number of gradient vectors from block 405. When no such polyhedral set is available, the device 116 can select the initial set using electrostatic repulsion. In other examples, the device 116 can select the initial set of gradient vectors at random. In further examples, the initial set can be a number of identical vectors.

[0026] At block 415, the device 116 is configured to determine and apply adjustments to at least some of the set of vectors from block 410. In this example, the device 116 is configured toAgent Docket: P12854PC00 select a random adjustment vector (e.g., a unit vector of random orientation) for each gradient vector in the initial set. In some examples, the adjustment vectors can be constrained, e.g., to be orthogonal to the corresponding initial gradient vector. That is, the adjustment vector for a given initial gradient vector can be selected at random within a plane orthogonal to the corresponding initial gradient vector.

[0027] FIG. 5 illustrates an example set of initial gradient vectors 500-1, which in this example contains six vectors. FIG. 5 also illustrates a set of six corresponding adjustment vectors 504-1. Each adjustment vector is applied to the corresponding vector in the set 500- 1 to generate a set of adjusted gradient vectors 508-1. For example, the first vector in the set 500-1 is adjusted according to the adjustment vector “al” to yield an adjusted first vector (e.g., [xl’, yl’, zl’]). Various techniques can be used to apply the adjustments to the initial vectors. For example, where the adjustment vectors are selected at random, e.g., without the above-mentioned orthogonality constraint, a given adjusted vector can be obtained according to Equation 1, below:

[0028] Equation 1

[0029] In Equation 1, Vmis the adjusted vector (e.g., the first vector in the set 508-1), V is the initial vector, e.g., the first vector in the set 500-1, and U is the adjustment vector (e.g., the vector al of the set 504-1). Further, a is an adjustment factor, which can be initialized at block 410, and determines how aggressively sets of gradient vectors are adjusted during the performance of the method 400. The above computation is repeated for each vector of the set 500-1, to generate the set 508-1.

[0030] In other examples, where the adjustment vectors are constrained to be orthogonal with the corresponding vectors of the set 500- 1 , a given adjusted vector can be obtained according to Equation 2, below:

[0031] Vm- 1 — a2V + aU Equation 2

[0032] Referring again to FIG. 4, at block 420 the device 116 is configured to determine a cost function based on the set of adjusted gradient vectors 508-1. The cost function indicates an impact of the set of adjusted gradient vectors 508-1 on diffusion tensor variance. The cost function used herein provides an analytical, rather than heuristic, representation of diffusion tensor variance, and thus enables consistently reproducible estimations of gradient vectors via the method 400. PreviousAgent Docket: P12854PC00 gradient vector selection mechanisms such as electrostatic repulsion are heuristic, and assessing the relative performance of two different sets of gradient vectors obtained via electrostatic repulsion may not be feasible.

[0033] The cost function used at block 420 is shown below:

[0034] Equation 3

[0035] In equation 3, A is a 5-dimensional vector constructed in the following way:

[0037] In equation 4, C is a 3x3 matrix built from second order moments of the set of K gradient direction vectors {g} according to equation 5 below:

[0038]

[0039] Equation 5

[0040] Further, in equation 3, B is a 5x5 matrix constructed according to equation 6:

[0041] Equation 6

[0042] In equation 6, GA is a K-row 5 -column matrix constructed according to Equation 7 below:

[0043] Equation 7

[0044] In equation 7, MSA; is a 5-dimensional vector build from i-th gradient direction vector defined by equation 8:Agent Docket: P12854PC00

[0046] In equation 9, MA; is a 3x3 matrix built from the i-th gradient vector according to Equation 10:

[0047] Equation 10

[0048] FIG. 5 illustrates an example cost 512 determined via the cost function above. At block 425, the device 116 is configured to determine whether the cost 512 from block 420 is smaller than a cost from a previous iteration. Following the first performance of block 420 during a given instance of the method 400, block 425 may be omitted. In other examples, a cost may be determined for the initial set 500-1, and the comparison at block 425 can be a comparison between the cost 512 and the initial cost.

[0049] When the determination at block 425 is negative, indicating that the adjusted gradient vector set 508-1 is less optimal than the initial set 500-1 (or, more generally, than the previous set assessed), the device 116 proceeds to block 430. At block 430, the device 116 is configured to discard the adjusted gradient vectors from block 415, reverting to the previous gradient vectors (e.g., the initial set 500-1, or the preceding adjusted set). The device 116 can also be configured to update a parameter such as the adjustment factor a. For example, the device 116 can maintain a step size, or multiplier, value, e.g., a value greater than one (e.g., two). The adjustment factor can be reduced based on the multiplier value (e.g., by dividing the adjustment factor by the multiplier value) at block 430. As will be apparent, reducing the adjustment factor leads to future adjustments of the gradient vectors making smaller changes to the gradient vectors.

[0050] When the determination at block 425 is affirmative, indicating that the adjusted gradient vector set 508-1 is more optimal than the initial set 500-1 (or, more generally, than the previous set assessed), the device 116 proceeds to block 435. At block 435, the device 116 is configured to store the adjusted vectors from block 415 as the current gradient vectors. In other words, as shown in FIG. 5, when the cost 512 is below a previous cost (e.g., a cost associated with the initial set 500-1), the set 500-1 can be discarded, and the set 508-1 can be used for any subsequent iterations. At block 435, the device 116 can also update the adjustment factor, e.g., byAgent Docket: P12854PC00 increasing the adjustment factor according to the multiplier value (e.g., by multiplying the adjustment factor by the multiplier value).

[0051] At block 440, the device 116 is configured to determine whether an optimization condition has been met. The optimization condition can include performing a predetermined number of iterations of blocks 415 to 435. For example, the number of iterations can be included in the request from block 305, or otherwise obtained at or before the performance of block 405. In other examples, the optimization condition can include comparing the cost 512 to a predetermined threshold and determining whether the cost 512 is below the threshold.

[0052] When the determination at block 440 is affirmative, the device 116 is configured to determine new adjustment vectors and repeat the adjustment and cost determination. For example, as shown in FIG. 5, the device 116 can determine a set 504-2 of adjustment vectors bl to b5 and apply the vectors of the set 504-2 to the gradient vector set 508-1 to generate an adjusted gradient vector set 508-2. The device 116 can then repeat the determination of a cost function at block 420, and determine whether to retain the set 508-2 or revert to the set 508-1 for the next iteration.

[0053] The scope of the claims should not be limited by the embodiments set forth in the above examples, but should be given the broadest interpretation consistent with the description as a whole.

Claims

Agent Docket: P12854PC00CLAIMS1. A method of controlling a magnetic resonance (MR) imaging system, the method comprising: receiving a diffusion tensor imaging (DTI) command, the command including a number of gradient vectors; obtaining a set of gradient vectors according to the number in the command, by:(i) selecting an initial set of gradient vectors;(ii) adjusting each gradient vector in the set, to generate a set of adjusted gradient vectors;(iii) determining a cost function based on the set of adjusted gradient vectors, the cost function indicating an impact of the set of adjusted gradient vectors on diffusion tensor variance;(iv) repeating the selecting, the adjusting, and the determining until an optimization condition is met, to obtain a final set of gradient vectors; and controlling the MR imaging system to capture a set of images based on the final set of gradient vectors.

2. The method of claim 1, wherein adjusting each gradient vector in the set includes, for each gradient vector: determining an adjustment vector specific to the gradient vector; and applying the adjustment vector to the gradient vector.

3. The method of claim 1, wherein determining the adjustment vector includes selecting a random vector.

4. The method of claim 3, wherein adjusting each gradient vector in the set includes determining an adjusted gradient vector Vmaccording to:wherein V is a corresponding one of the initial gradient vectors, U is the adjustment vector, and a is an adjustment factor.Agent Docket: P12854PC005. The method of claim 3, wherein selecting the random vector includes randomly selecting a vector that is orthogonal to the gradient vector.

6. The method of claim 5, wherein adjusting each gradient vector in the set includes:Vm= 1 - a2V + aU; wherein V is a corresponding one of the initial gradient vectors, U is the adjustment vector, and a is an adjustment factor.

7. The method of claim 1, wherein determining the cost function is based on:

8. The method of claim 1, wherein the optimization condition includes a number of repetitions of the selecting, the adjusting, and the determining.

9. The method of claim 1, wherein the optimization condition includes a cost function threshold.

10. The method of claim 1, wherein selecting the initial set of gradient vectors is based on one of: electrostatic repulsion; a predetermined polyhedron; random selection of the initial set; and generation of a plurality of identical gradient vectors.

11. A computing device, comprising: a memory; and a processor configured to perform the method of any one of claims 1 to 10.

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