Method and apparatus for determining a motion field from k-space data

Abstract

The invention relates to a motion determination device for determining a motion of an object. The motion determination device comprises a magnetic resonance (MR) information providing unit (2, 5) for providing MR images of the object (6) and for providing non-image MR data of the object, the non-image MR data having been acquired at different acquisition times, and a motion determination unit (9) for determining a motion field describing the motion of the object (6) from the provided non-image MR data acquired at the different acquisition times and from the provided MR images. Since the non-image MR data, which are preferably k-space data, are directly used for determining the motion field, i.e. without intermediate reconstruction of MR images based on the non-image MR data, the motion field can be determined with a very high temporal resolution.

Description

Technical Field

[0001] This invention relates to a motion determination apparatus, method, and computer program for determining the motion of an object. The invention also relates to a magnetic resonance (MR) therapy system, method, and computer program for treating an object based on the determined motion. Background Technology

[0002] The article "Ultrafast volumetric cine MRI (VC-MRI) for real-time3D target localization in radiation therapy" by W. Harris et al. (Proceedings of the International Society for Magnetic Resonance in Medicine, ISMRM, 24 th The Annual Meeting and Exhibition, Singapore, number 3210 (2016) disclosed a deformation of volumetric MR images based on two-dimensional cinematic MR images (i.e., based on several MR images acquired at several acquisition times) and according to a respiratory model based on patient principal component analysis (PCA).

[0003] The article “Automatic Correction of Motion Artifacts in Magnetic Resonance Images Using an Entropy Focus Criterion” by D. Atkinson et al. (IEEE Transactions of Medical Imaging, Vol. 16, pp. 903-910 (1997)) discloses the automatic correction of motion artifacts in MR images using an entropy focus criterion.

[0004] For example, according to the article "Hybrid two-dimensional navigator correction: a new technique to suppress respiratory-induced physiological noise in multi-shot echo-planar functional MRI" by R.L. Barry et al. (NeuroImage, volume 39, pages 1142-1150 (2008)), several MR images of a moving object can be generated at different times, and these MR images can be registered to each other to determine the object's motion. This process of determining the object's motion only allows motion determination at a relatively low temporal resolution. Summary of the Invention

[0005] Therefore, an object of the present invention is to provide a motion determination device, method, and computer program that allows for the determination of the motion of an object with increased temporal resolution. Another object of the present invention is to provide an MR treatment system, method, and computer program for treating an object based on the determined motion.

[0006] In a first aspect of the invention, a motion determining device for determining the motion of an object is presented, wherein the motion determining device comprises:

[0007] - An MR information providing unit is used to provide MR images of the object and to provide non-image MR data of the object, wherein the non-image MR data has been acquired at different acquisition times and is k-space data.

[0008] - A motion determination unit is configured to determine a motion field describing the motion of the object based on non-image MR data acquired at the different acquisition times and a provided MR image, wherein the motion determination unit is adapted to directly use the non-image MR data to determine the motion field.

[0009] Since the motion determination unit only needs the provided MR images and the provided non-image MR data acquired at the different acquisition times, and does not require several MR images to determine the motion field and thus the motion of the object, it does not require, for example, acquiring a relatively large amount of k-space data at different acquisition times, reconstructing several MR images for different acquisition times based on the acquired k-space data, and registering and reconstructing several MR images for motion determination. This allows for increased temporal resolution in the determination of the object's motion.

[0010] The object is preferably a living organism (i.e., a human or animal) or a part of a living organism (such as an organ like the heart, lungs, pancreas, kidneys, etc.). The object can also be a technological object. The motion field is preferably a three-dimensional motion field describing motion in three spatial dimensions. However, a motion field can also be a two-dimensional motion field describing motion in two spatial dimensions.

[0011] The motion determination unit is not adapted to use non-image MR data to reconstruct several MR images for different acquisition times, and then determine the motion field based on the reconstructed MR images. Instead, the motion determination unit is adapted to directly use non-image MR data as k-space data to determine the motion field, i.e., without intermediate reconstruction of MR images based on the non-image MR data. The motion of the object determined by the motion determination unit is therefore the motion of the object between different acquisition times of the non-image MR data that have been acquired. The determined motion field can therefore describe the motion of the object over a time period spanning the different acquisition times of the non-MR data that have been acquired as k-space data.

[0012] The MR information providing unit can be a storage device in which non-image MR data and MR images are stored, and from which non-image MR data and MR images can be retrieved to provide the same content. The MR information providing unit can also be a receiving unit for receiving and providing the received non-image MR data and MR images. For example, the MR information providing unit can be adapted to receive non-image MR data from an MR data acquisition device and MR images from an MR image generation unit adapted to generate MR images based on MR data acquired by the MR data acquisition device. The MR information providing unit can also be an MR data acquisition device having an MR image generation unit. The MR data acquired by the MR data acquisition device and used to reconstruct MR images is preferably k-space data. Non-image MR data is also k-space data.

[0013] In one embodiment, the motion determination device further includes a dynamic MR image generation unit for generating a dynamic MR image of the object based on a provided MR image and a determined motion field. The dynamic MR image of the object can be represented as a series of different static MR images for different times, wherein the series of static MR images illustrates the motion of the object during time periods covered by the different times. Therefore, the dynamic MR image of the object generated based on the provided MR image and the determined motion field illustrates the motion of the object over time periods spanning different acquisition times of non-image MR data already acquired as k-space data. Since generating a corresponding static MR image at a corresponding time does not require, for example, acquiring a relatively large amount of k-space data typically needed to reconstruct a static MR image for that time, but only requires, for example, acquiring a relatively small amount of non-image MR data at the corresponding time, a significant reduction in the time required to acquire the MR data needed to generate the dynamic MR image can be achieved, thereby allowing for increased temporal resolution of the dynamic MR image.

[0014] The MR image provided by the MR information providing unit can be referred to as a "reference MR image". The reference MR image is preferably a static MR image. The reference MR image can be reconstructed based on MR data acquired at a specific acquisition time or during a specific motion phase when the object is moving, or based on MR data acquired when the object is not moving. Furthermore, the MR information providing unit is preferably configured to provide a steady-state MR image (i.e., a steady-state magnetized MR image) as the reference MR image, and / or provide steady-state non-image MR data (i.e., steady-state magnetized non-image MR data) as the non-image MR data. Therefore, the non-image MR data is preferably k-space data acquired during the readout interval when the magnetization is in a steady-state condition. Furthermore, the provided MR image is preferably reconstructed from k-space data acquired during the readout interval when the magnetization is in a steady-state condition. Furthermore, preferably, both a) the k-space data for the non-image MR data and b) the k-space data used to reconstruct the provided MR image are acquired during the same steady-state period, i.e., by using the same type of sequence. If the provided reference MR image is a steady-state MR image, and if the non-image MR data is steady-state non-image MR data, the determined motion is less affected by the dynamic magnetization process. This can lead to improved accuracy in the determined motion.

[0015] The MR information providing unit is configured to provide k-space data as the non-image MR data. Therefore, the MR image providing unit is configured to provide different sets of k-space data as non-image MR data, wherein the different sets of k-space data (i.e., different k-space datasets) have been acquired at different acquisition times. The motion determination unit is configured to determine the motion field based on the provided k-space datasets acquired at different acquisition times and the provided MR images. Specifically, the MR information providing unit is preferably configured to provide k-space data that does not completely fill the k-space, such that the provided k-space data is undersampled compared to the k-space data already used to generate the provided MR images. Specifically, the spatial resolution of the provided MR images limits the resolution of the k-space (i.e., data points) due to the Nyquist criterion. Therefore, preferably, the spatial resolution of the provided MR images, together with the Nyquist criterion, limits a fully sampled k-space. The non-image MR data does not need to adhere to this sampling scheme; that is, they do not need to be according to the Nyquist criterion and can be acquired in a sparser manner. In one embodiment, the MR information providing unit is configured to provide the k-space data, i.e., the non-image k-space data, such that it fills less than five percent of the k-space, i.e., less than five percent of the entire space, more preferably less than one percent of the k-space, i.e., more preferably less than one percent of the entire k-space. Therefore, at each acquisition time, corresponding k-space data can be acquired, filling less than five percent of the entire k-space, more preferably less than one percent of the entire k-space. Specifically, the k-space is formed by the data point locations where data points (i.e., k-space data) can be acquired. The reference MR image (i.e., the provided MR image) is preferably reconstructed based on k-space data for all data point locations (i.e., based on a fully filled k-space). The non-image k-space data filling less than five percent of the entire k-space preferably corresponds to less than five percent of all data point locations in the entire k-space. In other words, the number of data point locations acquired at a specific acquisition time for determining the non-image k-space data of the sports field is preferably less than five percent of the number of data point locations acquired in the entire k-space for reconstructing the reference MR image. By using such a small amount of k-space data, the acquisition time can be further reduced. This can lead to a further increase in the temporal resolution of the movement of objects.

[0016] The k-space data for non-image MR data is acquired using a gradient field and therefore spatial encoding. However, as explained above, this k-space data is preferably undersampled, i.e., below the Nyquist rate, where this is irrelevant because, also as explained above, this k-space data (i.e., non-image MR data) is not used to reconstruct an image for determining the motion field, but rather it is used directly to determine the motion field. Furthermore, the provided MR image and non-image MR data do not need to originate from the same acquisition. Therefore, in one embodiment, the provided MR image and non-image MR data originate from different acquisitions, where, and in this case, preferably, a) the k-space data for non-image MR data and b) the k-space data for reconstructing the provided MR image are both acquired during the same steady-state period, i.e., by using the same kind of sequence.

[0017] More preferably, the MR information providing unit is configured to provide the k-space data such that they form a spiral trajectory in the k-space. If the k-space data acquired at a given time forms a spiral trajectory, motion can be determined with further increased accuracy. However, the k-space data can also be provided such that they form a trajectory with a different shape in the k-space.

[0018] In a preferred embodiment, the motion determination device further includes a) a motion model providing unit for providing a motion model for modeling the motion field, and b) a non-image MR data function providing unit for providing a non-image MR data function that describes non-image MR data based on MR images and the provided motion model for different acquisition times. The motion determination unit is configured to determine the motion field by adjusting the motion model such that, given a provided MR image, the non-image MR data function generates provided non-image MR data acquired at the different acquisition times. By using the motion model and the non-image MR data function, and by adjusting the motion model such that, given a provided MR image, the non-image MR data function generates provided non-image MR data acquired at different acquisition times to determine the motion field and thus the motion, motion can be determined with further increased accuracy and relatively low computational cost.

[0019] In a preferred embodiment, the non-image MR data function providing unit is configured to provide the non-image MR data function according to the following

[0020]

[0021] Among them, s jLet q(r) represent the non-image MR data acquired at the time indicated by index j, q(r) represent the MR image values ​​of the provided reference MR image at different spatial locations r, k represent the gradient trajectory in the k-space, and u j (r) represents the motion model defined by the spatial position of a portion of the object at the acquisition time indicated by the index j, the spatial position of the portion of the object being indicated by the corresponding spatial position r. The reference MR image q(r) can be defined according to the following formula:

[0022] q(r)=ρ(r)m(r), (2)

[0023] Where ρ(r) represents the spin density of the object at spatial position r, and m(r) is a variable indicating the unit magnetization at spatial position r (i.e., having the static MR equilibrium condition m = (0,0,1)).

[0024] The motion determination unit is adapted to precisely use formula (1) or an approximation of it as a non-image MR data function. By precisely or approximately using this specific non-image MR data function, the accuracy of determining the motion of the object can be further increased.

[0025] In one embodiment, the motion model providing unit is configured to provide an affine motion model as the motion model. Furthermore, in one embodiment, the motion determining unit is configured to use a gradient-based minimization algorithm (particularly a Newton-type minimization algorithm) to adjust the motion model such that, given a provided MR image, a non-image MR data function generates the provided non-image MR data acquired at different acquisition times.

[0026] In another aspect of the invention, an MR therapy system is provided for disposing of an object that is a living organism or part of a living organism, wherein the MR therapy system comprises

[0027] The motion determining device for determining the motion of the object as described in claim 1

[0028] A device for disposing of the object according to a determined motion disposal.

[0029] In one embodiment, the treatment device is configured to emit treatment energy along the direction of the object by taking into account the determined motion. Specifically, the treatment device may include a linear particle accelerator (LINAC) for emitting treatment energy in the opposite direction of the object. Because the motion can be determined with increased temporal resolution and because the treatment device treats the object according to the determined motion, the treatment device can respond more accurately to the movement of the object, thereby resulting in improved quality of the treated object and reduced therapeutic side effects.

[0030] In another aspect of the present invention, a motion determination method for determining the motion of an object is presented, wherein the motion determination method includes:

[0031] The MR information providing unit provides MR images of the object and non-image MR data of the object, wherein the non-image MR data has been acquired at different acquisition times and is k-space data.

[0032] The motion determination unit determines the motion field describing the motion of the object based on the provided non-image MR data for the different times and based on the provided MR images.

[0033] In one aspect of the invention, an MR treatment method for disposing of an object as a biological organism or a part of a biological organism is provided, wherein the MR treatment method comprises:

[0034] Determining the motion of the object as described in claim 11,

[0035] The object is disposed of by using a disposal device according to a determined motion.

[0036] In another aspect of the invention, a computer program for controlling a motion determination device as claimed in claim 1 is presented, wherein the computer program includes program code modules that, when the computer program is run on a controller controlling the motion determination device, cause the motion determination device to perform the motion determination method as claimed in claim 11.

[0037] In another aspect of the invention, a computer program for controlling the motion determination device as claimed in claim 9 is provided, the computer program including program code modules that, when the computer program is run on a controller controlling the MR therapy system, cause the MR therapy system to perform the MR therapy method as claimed in claim 12.

[0038] It should be understood that the motion determination device as claimed in claim 1, the MR therapy system as claimed in claim 9, the motion determination method as claimed in claim 11, the MR therapy method as claimed in claim 12, the computer program for controlling the motion determination device as claimed in claim 13, and the computer program for controlling the MR therapy system as claimed in claim 14 have specific preferred embodiments similar to and / or identical to those defined in the dependent claims.

[0039] It should be understood that the preferred embodiments of the present invention can also be any combination of the dependent claims or the above embodiments and the corresponding independent claims.

[0040] These and other aspects of the invention will be apparent and will be elucidated with reference to the embodiments described below. Attached Figure Description

[0041] In the following figures:

[0042] Figure 1 An embodiment of a motion determination device for determining the motion of an object is illustrated schematically and exemplary.

[0043] Figure 2 An embodiment of an MR treatment system for treating a subject is illustrated schematically and exemplary.

[0044] Figure 3 A flowchart illustrating an embodiment of a motion determination method for determining the motion of an object is shown.

[0045] Figure 4 A flowchart illustrating an exemplary embodiment of an MR treatment method for a treatment subject is shown.

[0046] Figure 5 The diagram schematically and demonstratively illustrates organ deformation modeled as a change in variables.

[0047] Figure 6 The illustration schematically and demonstratively demonstrates the direct use of k-space data for motion determination.

[0048] Figure 7 The prior art motion determination process based on image registration is illustrated schematically and demonstratively.

[0049] Figure 8 The three-dimensional helical k-space trajectory is schematically and demonstratively illustrated, and

[0050] Figure 9 A steady-state MR sequence that can be used to acquire k-space data is illustrated schematically and demonstratively. Detailed Implementation

[0051] Figure 1An embodiment of a motion determination device for determining the motion of an object is illustrated schematically and exemplary. In this embodiment, the motion determination device 1 is an MR imaging system. The MR imaging system 1 includes an MR data acquisition device 2 for acquiring MR data, which is k-space data of the heart 6 of a person 4 lying on a support device 3 such as a patient examination table. Specifically, the MR data acquisition device 2 is adapted to acquire k-space data sufficient for reconstructing a three-dimensional static steady-state MR image of the heart 6. This reconstruction is performed by a static image generation unit 5 of the MR imaging system 1. In order to reconstruct the static steady-state MR image, which can also be considered a reference MR image, the k-space is preferably completely filled with k-space data, wherein this k-space data is then preferably used by the static image generation unit 5 to generate the reference image.

[0052] The MR data acquisition device 2 is further adapted to acquire k-space data at different acquisition times, wherein this k-space data is not used by the static image generation unit 5 to generate corresponding static MR images for the respective acquisition times. In fact, this k-space data acquired at different acquisition times, together with the static reference MR image generated by the static image generation unit 5, is provided to the motion determination unit 9 so that the motion determination unit 9 can determine the motion field describing the motion of the heart 6 based on the k-space data acquired at different times and the static reference MR image. The k-space data acquired at different times is also preferably steady-state data.

[0053] Steady-state magnetization preferably refers to the magnetization state that is repeatedly acquired after each repetition of radio frequency excitation. This state is therefore identical for each repetition. Steady-state k-space data is preferably data acquired during the readout interval when the magnetization is in a steady state. A steady-state MR image is preferably an image formed from the steady-state k-space data.

[0054] The k-space data not used to generate the static reference MR image (i.e., non-image MR data acquired at different acquisition times) does not completely fill the k-space. Preferably, at the corresponding acquisition time, the k-space data fills less than five percent of the k-space. Specifically, the k-space is formed by data point locations where data points (i.e., k-space data) can be acquired. The static reference MR image is preferably reconstructed based on k-space data for all data point locations (i.e., based on a fully filled k-space). The k-space data filling less than five percent of the k-space preferably corresponds to less than five percent of all data point locations in the k-space. In other words, the number of data point locations in the k-space (acquired by the k-space data at a specific acquisition time) is preferably less than five percent of the number of data point locations in the k-space (acquired by the k-space data for reconstructing the static reference MR image). In one embodiment, the k-space data forms a trajectory within the k-space with a spiral shape at the corresponding acquisition time.

[0055] The MR imaging system 1 further includes a motion model providing unit 7 and a non-image MR data function providing unit 8. The motion model providing unit 7 is used to provide a motion model for modeling the motion field, and the non-image MR data function providing unit 8 is used to provide a non-image MR data function describing the non-image MR data (i.e., k-space data) for different acquisition times based on an MR image like a static reference MR image and the provided motion model. The motion determination unit 9 is preferably configured to determine the motion field and thus the motion of the heart 6 by adjusting the provided motion model such that, given a static MR reference image generated by the static image generation unit 5, the non-image MR data function generates the provided k-space data for different acquisition times. Specifically, the non-image MR data function providing unit 8 is adapted to provide the non-image MR data function according to the formula (1) mentioned above.

[0056] Therefore, the motion determination unit 9 can be configured to adjust the motion model u j (r) (which can also be considered a transformation function) such that, given a static reference MR image (which has been reconstructed by the static image generation unit 5), k-space data acquired by the MR data acquisition device 2 at several acquisition times is generated by a non-image MR data function defined by formula (1). During this adjustment process, formula (1) is preferably approximated, wherein the motion model can be an affine motion model or another motion model. For adjustment, a gradient-based minimization algorithm (especially a Newtonian minimization algorithm) or another algorithm can be used.

[0057] The MR imaging system 1 also includes a dynamic MR image generation unit 10, used to generate static MR images based on static images generated by the static image generation unit 5 and based on a determined motion field (i.e., based on an adjusted motion model u). j(r)) is used to generate dynamic MR images of the heart 6. The generated dynamic MR images of the heart can be used to show the dynamic behavior of the heart wall, thereby revealing insights into stress and strain.

[0058] The MR imaging system 1 also includes an input unit 12 (such as a keyboard, computer mouse, touchpad, etc.) and an output unit 13 (such as a display). In addition, the imaging system 1 includes a controller 11 for controlling the different components of the MR imaging system 1.

[0059] Figure 2 An embodiment of an MR therapy system for treating a subject is illustrated schematically and exemplary. In this embodiment, subject 16 is the kidney of a person 4 lying on a support device 3. The MR therapy system 17 includes an MR data acquisition and treatment device 102, which is a combination of an MR data acquisition device 2 and a treatment device 4. The MR data acquisition device 2 is used to acquire MR data, such as k-space data, and the treatment device 4 is used to treat the kidney 16 by means of treatment energy 15 emitted by the treatment device 4. Similar to the above reference... Figure 1 The described MR imaging system 1 and MR therapy system 17 include a static image generation unit 5, a motion model providing unit 7, a non-image MR data function providing unit 8, a motion determination unit 9, and a dynamic MR image generation unit 10. The MR therapy system 17 also includes a controller 111 for controlling different components of the MR therapy system 17 (specifically, the MR data acquisition and treatment device 4) to treat the kidney 16 according to determined motion. Specifically, the treatment device 4 is controlled such that treatment energy 15 is always directed to the kidney 16 even if the kidney 16 moves. Therefore, the determined motion (specifically, a three-dimensional motion field of the organ and tumor) can be used to direct the treatment irradiation. In this embodiment, the treatment device 4 generates X-rays or high-energy electrons to treat the kidney's LINAC according to the determined motion. The MR therapy system 17 also includes an input unit 12 (such as a keyboard, mouse, touchpad, etc.) and an output unit 13 (such as a display).

[0060] In the following text, reference will be made to Figure 3 The flowchart shown illustrates an embodiment of a motion determination method for determining the motion of an object.

[0061] In step 201, an MR image of the object is provided. Therefore, for example, MR data acquisition device 2 or MR data acquisition and treatment device 102 acquires k-space data of the object at specific times, wherein this k-space data is used to generate a static image of the object. The provided MR image can also be a static MR image showing the object in a specific motion phase, wherein k-space data acquired at different acquisition times but in the same specific motion phase can be used to generate this static MR image. For this purpose, known gating techniques can be used. The provided MR image can be considered a reference MR image.

[0062] In step 202, non-image MR data of the object that has been acquired at different acquisition times are provided. Specifically, MR data acquisition device 2 or MR data acquisition and treatment device 102 acquires k-space data at different acquisition times. The k-space data acquired at different acquisition times is preferably insufficient to reconstruct an MR image for the corresponding acquisition time; that is, at the corresponding acquisition time, preferably only a few k-space data points forming a trajectory within the k-space are acquired, the trajectory being spiral-shaped or having another shape.

[0063] In step 203, the motion field describing the object's motion is determined based on the MR image provided in step 201 and the non-image MR data provided in step 202. Specifically, a motion model for modeling the object's motion field and a non-image MR data function describing the non-image MR data for different acquisition times based on the MR image and the motion model can be provided. The motion model is adjusted such that, given the MR image provided in step 201, the provided non-image MR data function generates the non-image MR data provided in step 202 for different acquisition times to determine the motion field and thus the object's motion.

[0064] In the following text, reference will be made to Figure 4 The flowchart shown illustrates an embodiment of an MR treatment method for treating a subject.

[0065] In step 301, a treatment plan is provided that defines how the object is treated using treatment energy. For example, the treatment plan can define which part of the object should be irradiated with which intensity of treatment radiation emitted by the treatment device 4 of the MR data acquisition and treatment equipment 102. In step 302, the movement of the object is determined, for example, according to the above reference... Figure 3The motion is determined by the described method. In step 303, the object is treated according to the treatment plan provided in step 301, taking into account the motion determined in step 302. Specifically, radiation or particles emitted by the treatment device 4 of the MR data acquisition and treatment device 102 are directed to the moving object according to the treatment plan provided in step 301. In step 304, it is determined whether the termination criterion is met, wherein if so, the MR treatment method ends in step 305. Otherwise, the MR treatment method continues in step 302. Thus, in one cycle, the motion of the object is determined, and the object is treated with the motion determined by consideration until the termination criterion is met. The termination criterion is, for example, whether a user, such as a physician, instructs the MR treatment method to stop via input unit 12, whether the treatment defined in the treatment plan has been fully performed, etc.

[0066] The following text will refer to Figure 5 Illustrated motion model u j It can also be considered a transformation function.

[0067] exist Figure 5 In this context, the organ-like object 26 is defined at three different times on the corresponding coordinate systems 400, 401, and 402. For example, it is possible to... Figure 5 As seen in the diagram, at time t1 (corresponding to coordinate system 401), object 26 has been moved, i.e., deformed in this example, and at time t2 (corresponding to coordinate system 402), object 26 has been moved further, i.e., further deformed. The deformation of object 26 and therefore its corresponding coordinate grid is achieved through the corresponding transformation u. 1 u 2 To describe, where these transformations form time-dependent transformation functions or adjusted motion models, which are generally expressed as u as explained above with reference to, for example, equation (1). j Due to the motion model u j It contains low-dimensional information, and very little data is sufficient for its reconstruction. Therefore, the acquisition time interval for collecting MR data (i.e., k-space data) at a specific acquisition time can be extremely short. Once the motion model u... j It has already been used, meaning that once the motion model is adjusted and the motion field is thus known, a dynamic 3D image immediately follows.

[0068] The motion model is preferably a low-dimensional model of the motion field and therefore the motion of the object, wherein the motion preferably also includes deformation of the object. The expression "low-dimensional" refers to the number of parameters in the motion model, which are tuned to adjust the motion model such that, given a provided MR image (i.e., given a provided static reference MR image), a non-image MR data function generates provided non-image MR data at different acquisition times. The number of parameters in the motion model is much smaller than the number of image elements (preferably voxels) in the reference MR image. In a preferred embodiment, the number of parameters in the model is less than five percent of the number of image elements in the reference image.

[0069] The term "static" refers to an MR image that does not show the movement of an object. This could be because, for example, the object did not actually move when the MR data was acquired to reconstruct a reference MR image, or because it shows the object in a single phase of motion if the motion is periodic, or because the MR data used for the reconstruction of the reference MR image was acquired at a single point in time.

[0070] Refer to the above Figure 1 and 2 The described MR imaging and MR therapy systems reconstruct motion models by directly fitting a motion model to non-image MR data, preferably time-domain data, which is also considered a transformation function. This will be referenced below. Figure 6 Let's illustrate this further.

[0071] K-space data 505 is acquired along a spiral trajectory 500 within an ultra-short acquisition time. It should be noted that... Figure 6 The s(k(t)) shown in the figure and the s mentioned in formula (1) j (k) represents the same parameter, i.e., k-space data at the corresponding acquisition time indicated by j. Since the acquisition along the k-space trajectory 500 is ultra-short, the corresponding acquisition time for performing the ultra-short k-space acquisition can be considered a time point. Alternatively, a specific time point within the ultra-short time period required to acquire k-space data along trajectory 500 can be considered the corresponding acquisition time. For example, the center of this ultra-short time period can be considered the corresponding acquisition time indicated by index j. At another acquisition time, further k-space data 507 is acquired along the k-space trajectory 501, wherein the k-space trajectory used at different acquisition times is preferably the same. The motion determination unit has already considered the reference MR image 504 by adjusting the motion model u. j After determining the motion field and therefore the motion of the object, Figure 6 The non-image MR data function generated by curves 506 and 508 is shown in the figure. Figure 6 The k-space data is measured by curves 505 and 507.

[0072] This is in Figure 7 The illustration contrasts with existing technology. In the prior art, several corresponding sets of k-space data 601 are acquired at different acquisition times. At each acquisition time, the k-space needs to be fully or almost fully filled, as indicated by several lines within rectangle 601, to allow for the reconstruction of static MR images 602. These static MR images are then registered, as indicated by reference numeral 600, wherein this registration produces a motion model u. j Therefore, at each acquisition time, a large amount of k-space data 601 needs to be acquired, resulting in a relatively low temporal resolution. Furthermore, the generated static MR images need to be registered to determine the motion model, which is time-consuming and introduces errors into the finally determined motion model. In contrast, the above reference... Figures 1 to 5 The described motion determination procedure does not require acquiring numerous k-space data to generate corresponding static MR images at each acquisition time. Only a single static reference image that can correspond to a specific motion phase of the object is needed. The resulting very high temporal resolution of motion determination allows, for example, monitoring cardiac dynamics or tracking the kidneys and / or pancreas during MR-LINAC radiotherapy. (Refer to the above...) Figures 1 to 5 The described motion determination process also allows for motion determination with high clinical-quality spatial resolution.

[0073] Equation (1) will be explained in more detail below. The MR phenomenon can be described by the Bloch equation:

[0074]

[0075] Where M(t,r)≡(M x (t,r),M y (t,r),M z (t,r)) T It is spin magnetization, M0(r) is the equilibrium value, proportional to the proton spin density ρ, T1(r) and T2(r) are tissue relaxation parameters, ΔB0(r) is the deviation from resonance, and G(t) ≡ (G x (t),G y (t),G z (t)) T The gradient field being applied is γ, where γ is the gyromagnetic ratio. and Where RF(t)∈C is the excitation radio frequency waveform, and It is a spatially varying emitted magnetic field. For the sake of simplicity in explanation, it is considered to be... However, in practice, The formula can be easily extended to this situation.

[0076] It is useful to scale the magnetization in formula (3) in the following way. Assume Then it can be easily shown that formula (3) can be expressed as:

[0077] in,

[0078] Therefore, it can be seen that M0 is eliminated from Bloch's formula for the scaling vector m. For ease of annotation, equation (4) is presented in a compact form:

[0079] Where m(0) = (0,0,1) and

[0080] Preferably, a steady-state MR sequence is applied to the object to acquire MR data for motion detection. The steady-state MR sequence preferably employs a short, single-shot, fully balanced readout gradient. The repetition time is determined by T. R The time for acquiring spiral k-space data at the corresponding acquisition time is given as T. A , among which, T A <<T R It is also possible to assume T A <<T1 and T A << T2, therefore the effects of lateral and longitudinal delays are negligible during readout. The signal at the j-th acquisition time is given as follows:

[0081]

[0082] Where, k≡(k x ,k y ,k z ) represents the gradient trajectory, i.e., the k-space trajectory, ρ j It is a self-selected density, and m j This is the lateral magnetization at the start of acquisition (see Equation (5)). For ease of annotation, s j The global constant of the proportionality between (k) and the integral on the right is ignored.

[0083] Preferably, it is assumed that the object deforms during the time between two steady-state acquisitions, i.e., there exists a (nonlinear) transformation u defined by r2 = u(r1), where r1 = (x1, y1, z1), and

[0084] r2=(x2,y2,z2)=(u x (x1,y1,z1),u y (x1,y1,z1),u z (x1,y1,z1))

[0085] Let represent the geometry before and after deformation, respectively, where ... A The time is approximately a few milliseconds, which makes it preferably assumed that there is no displacement during the acquisition period, and that the displacement only occurs during T. R The interval has a significant impact. The signal from the deformed object in the new acquisition will therefore be:

[0086]

[0087] The variable formula used for multidimensional integration has been modified, and J(u) is the Jacobian matrix of u with respect to x1, z1, and y1:

[0088]

[0089] The second form of formula (7) reveals important insights into the evolution of signals due to motion. First, displacement at T A The interval is negligible. Furthermore, through the magnetization component m... j+1 The spin represented by (u(r1)) undergoes the same T1, T2, and m. j The effect of the deviation from resonance (ΔB0) at (r1). Since a steady-state condition exists in this paradigm, the equilibrium for the spin at r1 is the same as the equilibrium for the spin that has now moved to r2 (after all, they are the same spin), therefore it can be set m. j+1 (u(r1))=m j (r1) and fill it into formula (7) to generate:

[0090]

[0091] Transmitting and receiving radio frequency (RF) fields can be spatially varied, which is the case in reality. If the RF field varies between locations, the corresponding spin dynamics will be different. However, it is preferable to assume that the spatial variation of these fields between adjacent locations r1 and r2 is negligible and therefore the corresponding spin dynamics are approximately equal. In reality, this is a reasonable assumption, given that the common MR imaging field strength can be 3 Tesla, 1.5 Tesla, or less.

[0092] As a next step, it is preferably assumed that the total number of spins of the infinitesimal volume element dr1, which is transformed into du(r1) = |J(u)|dr1, does not change. In other words, it is preferably assumed that the conservation of magnetization is maintained.

[0093] This leads to the following equation:

[0094] ρ j (r1)dr1=ρj+1 (u(r1))|J(u)|dr1 (10)

[0095] And thus obtain:

[0096]

[0097] More generally, it can be written as:

[0098]

[0099] Where m, without a subscript, indicates the steady state without motion (reference image), and u j It is a variation of the j-th acquisition. Formula (12) corresponds to formula (1).

[0100] Formulas (1) and (12) use the preferred steady-state reference MR image under static (non-motion) conditions to represent the j-th acquired signal s j (k) and displacement function u j (r) (i.e., motion model) is relevant. It does not require a deformed image at the acquisition point to reconstruct the displacement, which is of real interest during cinematic MRI or many other applications. This method has the advantage of directly aligning with the quantity of interest without requiring a full image acquisition step. Since u has relatively compact spatial and temporal frequency content, reconstruction can be efficiently performed in the Fourier domain of u or in another low-dimensional representation space.

[0101] If in one embodiment only rigid translation is assumed to be motion, this rigid translation can be transmitted through p j To describe, the generation of u j (r)=r+p j This reduces equation (12) to: using the Fourier transform shift theorem.

[0102]

[0103] It is the linear accumulation of the initial k-space data s(k).

[0104] In the following text, an exemplary embodiment of the reconstruction transformation u (i.e., the motion model is determined according to formula (12) and thus the motion is performed) will be described.

[0105] The static MR image (which in this embodiment may also be referred to as the reference MR image) can be represented as q(r)≡ρ(r)m(r), and has been provided by the MR information providing unit and is therefore known. At a specific time point, i.e., at the corresponding acquisition time, a very short 3D helical k-space trajectory acquisition is performed. However, non-helical trajectories can also be used. In this embodiment, the collected data is represented by d. The transformation u can be discretized and inverted using formula (12) to reconstruct it (i.e., by solving a nonlinear least squares problem):

[0106]

[0107] In the above formula, n is the spatial discretization subscript called the grid point location, and h is the k-space data point subscript. H and N represent the total number of data points and grid points, respectively. Generally, N is approximately (10^2)^2. 5 And H << N, and therefore the problem is ill-posed because the equation has far fewer unknowns than unknowns.

[0108] In one embodiment, an attempt is made to reduce the number of unknowns to less than H. Model reduction techniques can be applied to find a low-dimensional representation of u. One way to do this is, for example, to represent u(r) as... Spatial basis function expansion:

[0109]

[0110] Among them, u l Let a denote the spatial basis functions of order l, where L is the dimension of the reduced representation. a ≡ (a1, ..., a2) L () is a vector of expansion coefficients. The problem is then reconstructed and becomes:

[0111]

[0112] The problem defined by equation (16) can be solved using the standard minimization algorithm for nonlinear least squares. To effectively apply derivative-based methods (Newtonian type), the partial derivatives of the H component with respect to the L parameter can be used. They can be readily computed:

[0113]

[0114] For i = 1, K, L and h = 1, K, H, the problem defined by Equation (16) can be solved, for example, by using the built-in trust region reflection algorithm in Matlab.

[0115] In one embodiment, the transformation (i.e., the motion model) u is modeled as an affine transformation r. +≡u(r)=Ar+b, where matrix A can represent rotation and stretching / compression, specifically anisotropic stretching / compression, and vector b∈R 3 This indicates a spatial displacement relative to the origin.

[0116] In another embodiment, Equation (6) can be solved using a nonparametric model, so it is not necessary to explicitly express u(r) as a sum of basis functions as shown in Equation (15). Regularization can be applied starting from Equation (14) to obtain a good solution. While this allows for a good solution, the problem to be solved here is typically underdetermined, i.e., the number of unknowns exceeds the number of data points, where, for example, in a three-dimensional context, the number of unknowns is equal to three times the number of voxels, because the problem must be solved for three motion field components (i.e., for u in this example). x u y and u z The solution is then performed. The addition of the penalty term can be described by the following formula, where u is an unknown:

[0117]

[0118] In formula (18), R is the regularization function, and λ is a real parameter that weights the regularization term (i.e., the penalty term) with respect to the comparison objective. The real parameter is problem-dependent and can be determined in different ways. For example, by calibration or by solving the problem for a set of different λ values ​​(i.e., for a set of different parameters λ), and by determining the correct one as a tradeoff between the data discrepancies and the norm of the solution. The latter method is also known as the L-curve method. The regularization function can be, for example, Tikhonov regularization with a first-order spatial derivative:

[0119]

[0120] Tikhonov regularization with second-order spatial derivative:

[0121]

[0122] Total variation:

[0123] Or (21)

[0124] L1 regularization with compression sensing:

[0125] R(u)=||Ψu||1, (22)

[0126] Here, Ψ represents sparse transformation, such as wavelet transform.

[0127] exist Figure 8The diagram illustrates an exemplary k-space trajectory along which k-space data is acquired at a corresponding acquisition time. The k-space data is collected within a very short time, preferably less than one millisecond, at the corresponding acquisition time.

[0128] Figure 9 A steady-state MR sequence that can be used to acquire k-space data (i.e., non-image MR data) at different acquisition times is illustrated schematically and demonstratively. After each RF excitation 700, the gradient 701 (G) of the spiral gradient can be... x G y and G z ) in time interval T A This process is applied to signal acquisition during the time period T. R This was repeated, where T A <<T R For example, T A It is T R One-fifth. In an exemplary embodiment, T R It can be approximately 20ms, and T A It can be approximately 4ms. Because the time interval between different acquisition times is determined by T... R To limit, and because of T A <<T R The generation of k-space data at the corresponding acquisition time can be considered as acquisition at a single acquisition time point.

[0129] Although the steady-state sequence is balanced in the embodiments described above, it can also be unbalanced. For example, the steady-state sequence can be a perturbed steady-state sequence. The steady-state sequence used to acquire k-space data at several acquisition times can be, for example, a perturbed gradient echo (GRE), spin echo, or SSFP (specifically bSSFP) sequence. In one embodiment, a gradient echo steady-state sequence is used, as disclosed, for example, in Chapter 14 of "Handbook of MRI Pulse Sequences, 1st Edition" (Academic Press (2004)) by Matt Bernstein, Kevin King, Xiaohong Zhou, et al., which is incorporated herein by reference.

[0130] The k-space trajectory (which may also be referred to as the readout trajectory) used at the corresponding acquisition time is preferably very short, which means that the k-space data for the corresponding acquisition time is collected within a collection time preferably less than 10 ms, more preferably less than 4 ms, and even more preferably 1 ms. During this very short collection time, relaxation effects and organ motion can be ignored, i.e., the corresponding acquisition time for collecting k-space data can be considered a single corresponding time point. As explained above, the motion of the object (which preferably also includes deformation of the object) can be indicated by a motion model or transformation function u, which modifies the object by changing the grid points to new coordinates given by r2 = u(r1). The motion model or transformation function u can be determined, for example, by using formula (1) or the corresponding discretization formula as described above. Since it is not necessary to reconstruct, for example, deformed MR images at each acquisition time, the determination of motion by determining the motion model or transformation function u requires less MR data. For example, compared with known image-based motion determination methods, the above-referenced Figures 1 to 5 The described motion determination method can result in a reduction of approximately 100 to 1000 times in the required MR data. For example, a static reference image at a specific stage of the deformation cycle of an object is sufficient to derive the entire dynamics of the object. This static reference MR image can be acquired, for example, during a short breath-hold period, especially if the object is an organ in the abdomen or abdominal region, or using gated diastolic acquisition if the object is a heart. The nonlinear least squares problem obtained according to equations (1) and (12) can be solved, for example, by a Newtonian minimization algorithm, where the output of the algorithm is an adjusted motion model or transformation function u.

[0131] The motion determination process described above is preferably adapted to directly target, in the example described above, an automatically transforming motion model that can be nonlinear, without acquiring corresponding MR images for each acquisition time. The motion determination process can, for example, be adapted to determine motion at approximately 50 3D frames per second, where any periodic or non-periodic motion can be tracked. This motion tracking may not require any gating. However, if the motion to be determined is periodic, a reference image can represent a specific phase of the periodic motion and can have already been determined using gating techniques. Since motion determination is not based on image registration, there is no need for automatic comparison for each acquisition time, as the movement preferably involves a temporal signal. Furthermore, flexible design of trajectories in k-space is possible based on preferred temporal reconstruction.

[0132] Although the trajectory in the k-space used to acquire k-space data at the corresponding acquisition time is helical in the embodiments described above, the trajectory can also have another shape. For example, the trajectory can be Cartesian, echo-plane (EPI), or radial. While motion determination is suitable for determining, for example, the motion of the heart or pancreas in the embodiments described above, in other embodiments, motion determination can be adapted to determine the motion of other objects such as other organs or technical objects.

[0133] While some functions in the embodiments described above are used to describe motion models, in other embodiments, motion models can be represented in another way, particularly by parameterization. Furthermore, although specific non-image MR data functions have been described in the embodiments described above, in other embodiments, another non-image MR data function can be used to describe non-image MR data based on MR images and, based on motion models, for different acquisition times.

[0134] Those skilled in the art, through studying the accompanying drawings, the disclosure, and the claims, can understand and implement other variations of the disclosed embodiments when practicing the claimed invention.

[0135] In the claims, the word "comprising" does not exclude other elements or steps, and the words "a" or "an" do not exclude a plurality.

[0136] A single unit or device can perform the functions of several items recited in the claims. Although some measures are recited in different dependent claims, this does not mean that combinations of these measures cannot be used advantageously.

[0137] The definite operation of the motion of an object, which is performed by one or more units or devices, can be performed by any other number of units or devices. These operations and / or controls of the motion-determining device according to the motion-determining method and / or the control of the MR therapy system according to the MR therapy method can be implemented as computer program code modules and / or as dedicated hardware.

[0138] Computer programs can be stored / distributed on suitable media, such as optical storage media or solid-state media supplied together with or as part of other hardware, but can also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0139] No reference numerals in the claims should be construed as limiting the scope.

[0140] This invention relates to a motion determination device for determining the motion of an object. The motion determination device includes an MR information providing unit and a motion determination unit. The MR information providing unit provides MR images of the object and non-image MR data of the object, which has been acquired at different acquisition times. The motion determination unit describes the motion field of the object based on the provided non-image MR data acquired at the different acquisition times and the provided MR images. Since the non-image MR data, preferably k-space data, is directly used to determine the motion field, i.e., without the need for intermediate reconstruction of MR images based on the non-image MR data, the motion field can be determined with very high temporal resolution.

Claims

1. A motion determining device for determining the motion of an object, the motion determining device comprising: Magnetic resonance (MR) information providing unit (2, 5), which is used to provide the object (6); MR images of the object (6; 16) are used to provide non-image MR data of the object (6; 16), wherein the non-image MR data has been acquired at different acquisition times and is k-space data. The motion determination device is characterized in that it further includes a motion determination unit (9), which is used to determine the motion field describing the motion of the object (6; 16) based on the non-image MR data acquired at the different acquisition times and the provided MR images. The motion determination unit is adapted to directly use the non-image MR data to determine the motion field. The motion determining device (1) further includes: A motion model providing unit (7) is used to provide a motion model for modeling the motion field, and The non-image MR data function providing unit (8) is used to provide non-image MR data functions that describe non-image MR data based on MR images and according to the provided motion model for different acquisition times. The motion determination unit (9) is configured to determine the motion field by adjusting the motion model such that, given a provided MR image, the non-image MR data function generates provided non-image MR data acquired at the different acquisition times.

2. The motion determining device as described in claim 1, wherein, The motion determination device (1) further includes a dynamic MR image generation unit (10) for generating dynamic MR images of the object based on the provided MR images and the determined motion field, wherein the dynamic MR images of the object can be regarded as a sequence of different static MR images for different times, wherein the sequence of static MR images shows the motion of the object during the time period covered by the different times.

3. The motion determining device as described in claim 1, wherein, The MR information providing units (2, 5) are configured to provide a steady-state magnetized MR image as the MR image, and / or provide steady-state magnetized non-image MR data as the non-image MR data.

4. The motion determining device as described in claim 1, wherein, The MR information providing unit (2) is configured to provide k-space data that does not completely fill the k-space as the non-image MR data, such that the provided k-space data is undersampled compared to the k-space data already used to generate the provided MR image.

5. The motion determining device as described in claim 4, wherein, The MR information providing unit (2) is configured to provide the k-space data such that they fill less than five percent of the k-space.

6. The motion determining device as described in claim 5, wherein, The MR information providing unit is configured to provide the k-space data such that they form a spiral trajectory in the k-space.

7. The motion determining device as claimed in claim 1, wherein, The non-image MR data function providing unit (8) is configured to provide the non-image MR data function according to the following formula: ， in, Indicates the target index The non-image MR data at the indicated acquisition time, This indicates that the provided reference MR image is located at different spatial positions. MR image values ​​at that location, Let represent the gradient trajectory in the k-space, and This indicates that the indicator is passed. The motion model that indicates the acquisition time of the object defines the spatial position of a portion of the object, and the spatial position of the portion of the object is determined by a corresponding spatial position. To indicate, and R 3 Indicates spatial location The range in three-dimensional space.

8. An MR therapy system for disposing of an object as a living organism or a part of a living organism, said MR therapy system (17) comprising: The motion determining device for determining the motion of the object (16) as described in claim 1, Disposal device (14) for disposing of the object (16) according to the determined motion.

9. The MR therapy system as claimed in claim 8, wherein, The disposal device (14) is configured to emit disposal energy (15) in the direction of the object (16) by taking into account the determined motion.

10. A motion determination method for determining the motion of an object (6; 16), the motion determination method comprising: The object (6) is provided by the MR information providing units (2, 5); MR images of the object (6); 16) Non-image MR data, wherein the non-image MR data has been acquired at different acquisition times and is k-space data. The motion determination method is characterized in that it further includes a motion determination unit (9) determining a motion field describing the motion of the object (6; 16) based on non-image MR data acquired at the different acquisition times and based on the provided MR images, wherein the non-image MR data is directly used to determine the motion field. Provides a motion model for modeling the sports field, and Provides functions for describing non-image MR data based on MR images and, according to a provided motion model, for different acquisition times. The motion field is determined by adjusting the motion model such that, given a provided MR image, the non-image MR data function generates provided non-image MR data acquired at the different acquisition times.

11. A computer program product comprising computer-readable instructions, said computer-readable instructions, when executed by a processor, causing the processor to perform an MR treatment method for disposing of an object as a living organism or part of a living organism, said MR treatment method comprising: Determine the motion of the object (16) as described in claim 10. The object (16) is disposed of according to a determined motion by using a disposal device (14).

12. A computer-readable medium storing a computer program for controlling a motion determination device as claimed in claim 1, the computer program including program code modules that, when the computer program is run on a controller (11) controlling the motion determination device (1), the program code modules are configured to cause the motion determination device (1) to perform the motion determination method as claimed in claim 10.

Images